We gratefully acknowledge support from
the Simons Foundation
and member institutions

Mathematics

New submissions

[ total of 246 entries: 1-246 ]
[ showing up to 2000 entries per page: fewer | more ]

New submissions for Thu, 21 Sep 17

[1]  arXiv:1709.06559 [pdf, ps, other]
Title: Holomorphy of Osborn loops
Comments: 17 pages, 12 figures
Journal-ref: Analele Universitatii De Vest Din Timisoara, Seria Matematica-Informatica 53 (2015) 81-98
Subjects: Group Theory (math.GR)

Let $(L,\cdot)$ be any loop and let $A(L)$ be a group of automorphisms of $(L,\cdot)$ such that $\alpha$ and $\phi$ are elements of $A(L)$. It is shown that, for all $x,y,z\in L$, the $A(L)$-holomorph $(H,\circ)=H(L)$ of $(L,\cdot)$ is an Osborn loop if and only if $x\alpha (yz\cdot x\phi^{-1})= x\alpha (yx^\lambda\cdot x) \cdot zx\phi^{-1}$. Furthermore, it is shown that for all $x\in L$, $H(L)$ is an Osborn loop if and only if $(L,\cdot)$ is an Osborn loop, $(x\alpha\cdot x^{\rho})x=x\alpha$, $x(x^{\lambda}\cdot x\phi^{-1})=x\phi^{-1}$ and every pair of automorphisms in $A(L)$ is nuclear (i.e. $x\alpha\cdot x^{\rho},x^{\lambda}\cdot x\phi\in N(L,\cdot )$). It is shown that if $H(L)$ is an Osborn loop, then $A(L,\cdot)= \mathcal{P}(L,\cdot)\cap\Lambda(L,\cdot)\cap\Phi(L,\cdot)\cap\Psi(L,\cdot)$ and for any $\alpha\in A(L)$, $\alpha= L_{e\pi}=R^{-1}_{e\varrho}$ for some $\pi\in \Phi(L,\cdot)$ and some $\varrho\in \Psi(L,\cdot)$. Some commutative diagrams are deduced by considering isomorphisms among the various groups of regular bijections (whose intersection is $A(L)$) and the nucleus of $(L,\cdot)$.

[2]  arXiv:1709.06584 [pdf, ps, other]
Title: A Driven Tagged Particle in Asymmetric Simple Exclusion Processes
Authors: Zhe Wang
Comments: 27 pages, 9 figures
Subjects: Probability (math.PR)

We consider the asymmetric simple exclusion process with a driven tagged particle on Z which has a negative drift, and show that the tagged particle can have a positive speed when it jumps more slowly than the other particles. Coupling arguments are used.

[3]  arXiv:1709.06589 [pdf, ps, other]
Title: On the definition of Heisenberg category
Authors: Jonathan Brundan
Comments: 20 pages
Subjects: Representation Theory (math.RT)

We revisit the definition of the Heisenberg category of level k. In level -1, this category was introduced originally by Khovanov, but with some additional cyclicity relations which we show here are unnecessary. In other negative levels, the definition is due to Mackaay and Savage, also with some redundant relations, while the level zero case is the affine oriented Brauer category of Brundan, Comes, Nash and Reynolds. We also discuss cyclotomic quotients.

[4]  arXiv:1709.06590 [pdf, ps, other]
Title: Time-Optimal Collaborative Guidance using the Generalized Hopf Formula
Subjects: Optimization and Control (math.OC); Systems and Control (cs.SY)

Presented is a new method for calculating the time-optimal guidance control for a multiple vehicle pursuit-evasion system. A joint differential game of k pursuing vehicles relative to the evader is constructed, and a Hamilton-Jacobi-Isaacs (HJI) equation that describes the evolution of the value function is formulated. The value function is built such that the terminal cost is the squared distance from the boundary of the terminal surface. Additionally, all vehicles are assumed to have bounded controls. Typically, a joint state space constructed in this way would have too large a dimension to be solved with existing grid-based approaches. The value function is computed efficiently in high-dimensional space, without a discrete grid, using the generalized Hopf formula. The optimal time-to-reach is iteratively solved, and the optimal control is inferred from the gradient of the value function.

[5]  arXiv:1709.06591 [pdf, other]
Title: On Upper Approximations of Pareto Fronts
Comments: 31 pages, 9 figures, 33 references
Subjects: Optimization and Control (math.OC)

In one of our earlier works, we proposed to approximate Pareto fronts to multiobjective optimization problems by two-sided approximations, one from inside and another from outside of the feasible objective set, called, respectively, lower shell and upper shell. We worked there under the assumption that for a given problem an upper shell exists. As it is not always the case, in this paper we give some sufficient conditions for the existence of upper shells.
We also investigate how to constructively search infeasible sets to derive upper shells. We approach this issue by means of problem relaxations. We formally show that under certain conditions some subsets of lower shells to relaxed multiobjective optimization problems are upper shells in the respective unrelaxed problems.
Results presented are illustrated by a numerical example representing a~small but real mechanical problem. Practical implications of the results are discussed.

[6]  arXiv:1709.06592 [pdf, other]
Title: Finite element approximations of the nonhomogeneous fractional Dirichlet problem
Subjects: Numerical Analysis (math.NA)

We study finite element approximations of the nonhomogeneous Dirichlet problem for the fractional Laplacian. Our approach is based on weak imposition of the Dirichlet condition and incorporating a nonlocal analogous of the normal derivative as a Lagrange multiplier in the formulation of the problem. In order to obtain convergence orders for our scheme, regularity estimates are developed, both for the solution and its nonlocal derivative. The method we propose requires that, as meshes are refined, the discrete problems be solved in a family of domains of growing diameter.

[7]  arXiv:1709.06593 [pdf, other]
Title: Queuing with Heterogeneous Users: Block Probability and Sojourn times
Subjects: Probability (math.PR)

Communication networks need to support voice and data calls simultaneously. This results in a queueing system with heterogeneous agents. One class of agents demand immediate service, would leave the system if not provided. The second class of customers have longer job requirements and can wait for their turn. We discuss the achievable region of such a two class system, which is the region of all possible pairs of performance metrics. Blocking probability is the relevant performance for eager/impatient class while the expected sojourn time is appropriate for the second tolerant class. We obtain the achievable region, considering static policies that do not depend upon the state of the second class. We conjecture a pseudo conservation law, in a fluid limit for eager customers, which relates the blocking probability of eager customers with the expected sojourn time of the tolerant customers. Using this conjecture we obtain the static achievable region. We validate the pseudo conservation law using two example families of static schedulers, both of which achieve all the points on the achievable region. Along the way we obtain smooth control (sharing) of resources between voice and data calls.

[8]  arXiv:1709.06594 [pdf, ps, other]
Title: A Destroying Driven Tagged Particle in Symmetric Simple Exclusion Processes
Authors: Zhe Wang
Comments: 18 pages, 4 figures
Subjects: Probability (math.PR)

We consider the symmetric simple exclusion processes with a destroying tagged particle on Z. In this process, untagged particles disappear once they jump to the left of a tagged particle. We investigate the behavior of the displacement of the tagged particle and prove limit theorems. Martingale arguments and regenerative structures are used with two auxiliary processes.

[9]  arXiv:1709.06606 [pdf, other]
Title: Optimal projection of observations in a Bayesian setting
Subjects: Statistics Theory (math.ST); Numerical Analysis (math.NA); Probability (math.PR)

This work proposes optimal dimensionality reduction methods adapted to the Bayesian inference of a Gaussian linear model with additive noise in presence of overabundant data. Three different optimal projections of the observations are proposed based on information theory: the projection that minimizes the Kullback-Leibler divergence between the posterior distributions of the original and the projected models, the one that minimizes the expected Kullback-Leibler divergence between the same distributions, and the one that maximizes the mutual information between the parameter of interest and the projected observations. The first two optimization problems are formulated as the determination of an optimal subspace and therefore the solution is computed using Riemannian optimization algorithms on the Grassmann manifold. Regarding the maximization of the mutual information, it is shown that there exists an optimal subspace that minimizes the entropy of the posterior distribution of the reduced model; a basis of the subspace can be computed as the solution to a generalized eigenvalue problem; an a priori error estimate on the mutual information is available for this particular solution; and that the dimensionality of the subspace to exactly conserve the mutual information between the input and the output of the models is less than the number of parameters to be inferred. Numerical applications to linear and nonlinear models are used to assess the efficiency of the proposed approaches, and to highlight their advantages compared to standard approaches based on the principal component analysis of the observations.

[10]  arXiv:1709.06607 [pdf, ps, other]
Title: High-dimensional posterior consistency for hierarchical non-local priors in regression
Subjects: Statistics Theory (math.ST)

The choice of tuning parameter in Bayesian variable selection is a critical problem in modern statistics. Especially in the related work of nonlocal prior in regression setting, the scale parameter reflects the dispersion of the non-local prior density around zero, and implicitly determines the size of the regression coefficients that will be shrunk to zero. In this paper, we introduce a fully Bayesian approach with the pMOM nonlocal prior where we place an appropriate Inverse-Gamma prior on the tuning parameter to analyze a more robust model that is comparatively immune to misspecification of scale parameter. Under standard regularity assumptions, we extend the previous work where $p$ is bounded by the number of observations $n$ and establish strong model selection consistency when $p$ is allowed to increase at a polynomial rate with $n$. Through simulation studies, we demonstrate that our model selection procedure outperforms commonly used penalized likelihood methods in a range of simulation settings.

[11]  arXiv:1709.06608 [pdf, ps, other]
Title: Lectures on Clifford algebras
Authors: D. S. Shirokov
Comments: 44 pages
Subjects: Mathematical Physics (math-ph)

We discuss some well-known facts about Clifford algebras: matrix representations, Cartan's periodicity of 8, double coverings of orthogonal groups by spin groups, Dirac equation in different formalisms, spinors in $n$ dimensions, etc. We also present our point of view on some problems. Namely, we discuss the generalization of the Pauli theorem, the basic ideas of the method of averaging in Clifford algebras, the notion of quaternion type of Clifford algebra elements, the classification of Lie subalgebras of specific type in Clifford algebra, etc.

[12]  arXiv:1709.06610 [pdf, ps, other]
Title: Yaglom limits for R-transient chains with non-trivial Martin boundary
Subjects: Probability (math.PR)

We give conditions for the existence of a Yaglom limit for R-transient Markov chains with non-trivial rho-Martin entrance boundary (rho=1/R) and we characterize the rho-invariant limiting quasistationary distribution.

[13]  arXiv:1709.06612 [pdf, ps, other]
Title: Finite searches, Chowla's cosine problem, and large Newman polynomials
Authors: Idris Mercer
Subjects: Number Theory (math.NT)

A length $n$ cosine sum is an expression of the form $\cos a_1\theta + \cdots + \cos a_n\theta$ where $a_1 < \cdots < a_n$ are positive integers, and a length $n$ Newman polynomial is an expression of the form $z^{a_1} + \cdots + z^{a_n}$ where $a_1 < \cdots < a_n$ are nonnegative integers. We define $-\lambda(n)$ to be the largest minimum of a length $n$ cosine sum as $\{a_1,\ldots,a_n\}$ ranges over all sets of $n$ positive integers, and we define $\mu(n)$ to be the largest minimum modulus on the unit circle of a length $n$ Newman polynomial as $\{a_1,\ldots,a_n\}$ ranges over all sets of $n$ nonnegative integers. Since there are infinitely many possibilities for the $a_j$, it is not obvious how to compute $\lambda(n)$ or $\mu(n)$ for a given $n$ in finitely many steps. Campbell et al. found the value of $\mu(3)$ in 1983, and Goddard found the value of $\mu(4)$ in 1992. In this paper, we find the values of $\lambda(2)$ and $\lambda(3)$ and nontrivial bounds on $\mu(5)$. We also include further remarks on the seemingly difficult general task of reducing the computation of $\lambda(n)$ or $\mu(n)$ to a finite problem.

[14]  arXiv:1709.06616 [pdf, other]
Title: On Collaborative Compressive Sensing Systems: The Framework, Design and Algorithm
Subjects: Information Theory (cs.IT)

We propose a collaborative compressive sensing (CCS) framework consisting of a bank of $K$ compressive sensing (CS) systems that share the same sensing matrix but have different sparsifying dictionaries. This CCS system is guaranteed to yield better performance than each individual CS system in a statistical sense, while with the parallel computing strategy, it requires the same time as that needed for each individual CS system to conduct compression and signal recovery. We then provide an approach to designing optimal CCS systems by utilizing a measure that involves both the sensing matrix and dictionaries and hence allows us to simultaneously optimize the sensing matrix and all the $K$ dictionaries under the same scheme. An alternating minimization-based algorithm is derived for solving the corresponding optimal design problem. We provide a rigorous convergence analysis to show that the proposed algorithm is convergent. Experiments with real images are carried out and show that the proposed CCS system significantly improves on existing CS systems in terms of the signal recovery accuracy.

[15]  arXiv:1709.06618 [pdf, other]
Title: The dynamics of the free boundary in higher dimensions
Authors: Emanuel Indrei
Subjects: Analysis of PDEs (math.AP)

In this paper a classification is given of blow-up solutions at the intersection of the free and fixed boundary corresponding to obstacle problems generated by fully nonlinear uniformly elliptic operators. As a consequence, non-transversal intersection is shown to hold in any dimension. Several regularity results are also obtained.

[16]  arXiv:1709.06619 [pdf, other]
Title: On Sinc Quadrature Approximations of Fractional Powers of Regularly Accretive Operators
Comments: 3 figures
Subjects: Numerical Analysis (math.NA)

We consider the finite element approximation of fractional powers of regularly accretive operators via the Dunford-Taylor integral approach. We use a sinc quadrature scheme to approximate the Balakrishnan representation of the negative powers of the operator as well as its finite element approximation. We improve the exponentially convergent error estimates from [A. Bonito, J. E. Pasciak, IMA J. Numer. Anal. (2016) 00, 1-29] by reducing the regularity required on the data. Numerical experiments illustrating the new theory are provided.

[17]  arXiv:1709.06621 [pdf, ps, other]
Title: Localization in the Disordered Holstein model
Comments: 46 pages
Subjects: Mathematical Physics (math-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Spectral Theory (math.SP)

The Holstein model describes the motion of a tight-binding tracer particle interacting with a field of quantum harmonic oscillators. We consider this model with an on-site random potential. Provided the hopping amplitude for the particle is small, we prove localization for matrix elements of the resolvent, in particle position and in the field Fock space. These bounds imply a form of dynamical localization for the particle position that leaves open the possibility of resonant tunneling in Fock space between equivalent field configurations.

[18]  arXiv:1709.06623 [pdf, other]
Title: Secure Beamforming in Full-Duplex SWIPT Systems
Comments: submitted for journal publication
Subjects: Information Theory (cs.IT)

Physical layer security is a key issue in the full duplex (FD) communication systems due to the broadcast nature of wireless channels. In this paper, the joint design of information and artificial noise beamforming vectors is proposed for the FD simultaneous wireless information and power transferring (FD-SWIPT) systems. To guarantee high security and energy harvesting performance of the FD-SWIPT system, the proposed design is formulated as a sum information transmission rate (SITR) maximization problem under information-leakage and energy constraints. In addition, we consider the fairness issue between the uplink and downlink information transmission rates by formulating a \mbox{fairness-aware} SITR-maximization problem. Although the formulated \mbox{SITR-maximization} and \mbox{fairness-aware} \mbox{SITR-maximization} problems are non-convex, we solve them via semidefinite relaxation and one-dimensional search. The optimality of our proposed algorithms is theoretically proved, and the computation complexities are established. Moreover, we propose two suboptimal solutions to the formulated optimization problems. In terms of the SITR-maximization problem, numerical results show that the performance achieved by one of the two suboptimal algorithms is close to the performance of the optimal algorithm with increasing maximum transmission power of the FD-BST.

[19]  arXiv:1709.06624 [pdf, ps, other]
Title: On the multiplicity of isolated roots of sparse polynomial systems
Comments: 22 pages
Subjects: Algebraic Geometry (math.AG); Commutative Algebra (math.AC)

We give formulas for the multiplicity of any affine isolated zero of a generic polynomial system of $n$ equations in $n$ unknowns with prescribed sets of monomials. First, we consider sets of supports such that the origin is an isolated root of the corresponding generic system and prove formulas for its multiplicity. Then, we apply these formulas to solve the problem in the general case, by showing that the multiplicity of an arbitrary affine isolated zero of a generic system with given supports equals the multiplicity of the origin as a common zero of a generic system with an associated family of supports.
The formulas obtained are in the spirit of the classical Bernstein's theorem, in the sense that they depend on the combinatorial structure of the system, namely, geometric numerical invariants associated to the supports, such as mixed volumes of convex sets and, alternatively, mixed integrals of convex functions.

[20]  arXiv:1709.06625 [pdf, other]
Title: Dynamic Cross-Layer Beamforming in Hybrid Powered Communication Systems With Harvest-Use-Trade Strategy
Comments: accepted by IEEE Trans. Wireless Commun
Subjects: Information Theory (cs.IT)

The application of renewable energy is a promising solution to realize the Green Communications. However, if the cellular systems are solely powered by the renewable energy, the weather dependence of the renewable energy arrival makes the systems unstable. On the other hand, the proliferation of the smart grid facilitates the loads with two-way energy trading capability. Hence, a hybrid powered cellular system, which combines the smart grid with the base stations, can reduce the grid energy expenditure and improve the utilization efficiency of the renewable energy. In this paper, the long-term grid energy expenditure minimization problem is formulated as a stochastic optimization model. By leveraging the stochastic optimization theory, we reformulate the stochastic optimization problem as a \mbox{per-frame} grid energy plus weighted penalized packet rate minimization problem, which is NP-hard. As a result, two suboptimal algorithms, which jointly consider the effects of the channel quality and the packet reception failure, are proposed based on the successive approximation beamforming (SABF) technique and the \mbox{zero-forcing} beamforming (ZFBF) technique. The convergence properties of the proposed suboptimal algorithms are established, and the corresponding computational complexities are analyzed. Simulation results show that the proposed SABF algorithm outperforms the ZFBF algorithm in both grid energy expenditure and packet delay. By tuning a control parameter, the grid energy expenditure can be traded for the packet delay under the proposed stochastic optimization model.

[21]  arXiv:1709.06628 [pdf, ps, other]
Title: Homogeneous rank one perturbations and inverse square potentials
Authors: Jan Derezinski
Comments: 12 pages, 1 figure, talk given at the XXXVI Workshop on Geometric Methods in Physics in Bialowieza 2017
Subjects: Mathematical Physics (math-ph); Spectral Theory (math.SP)

Following [D,BDG,DR], I describe several exactly solvable families of closed operators. Some of these families are defined by the theory of singular rank one perturbations. The remaining families are Schrodinger operators with inverse square potentials and various boundary conditions. I describe a close relationship between these families. In all of them one can observe interesting renormalization group flows (action of the group of dilations).

[22]  arXiv:1709.06629 [pdf, ps, other]
Title: Composite quasianalytic functions
Comments: 13 pages
Subjects: Complex Variables (math.CV); Classical Analysis and ODEs (math.CA); Logic (math.LO)

We prove two main results on Denjoy-Carleman classes: (1) a composite function theorem which asserts that a function f(x) in a quasianalytic Denjoy-Carleman class Q, which is formally composite with a generically submersive mapping y=h(x) of class Q, at a single given point in the source (or in the target) of h, can be written locally as f(x) = g(h(x)), where g(y) belongs to a shifted Denjoy-Carleman class Q' ; (2) a statement on a similar loss of regularity for functions definable in the o-minimal structure given by expansion of the real field by restricted functions of quasianalytic class Q. Both results depend on an estimate for the regularity of an infinitely differentiable solution g of the equation f(x) = g(h(x)), with f and h as above. The composite function result depends also on a quasianalytic continuation theorem, which shows that the formal assumption at a given point in (1) propagates to a formal composition condition at every point in a neighbourhood.

[23]  arXiv:1709.06630 [pdf, other]
Title: On approximation of planar sets by polynomial Julia sets
Comments: 1 figure
Subjects: Complex Variables (math.CV)

We prove that a nonempty compact planar set $E$ can be approximated arbitrarily close by filled-in Julia sets of polynomials from above (with respect to inclusion) if and only if it is polynomially convex. The polynomials are obtained by a slight modification of fundamental Lagrange interpolation polynomials with nodes that guarantee good convergence properties. In particular we can use some pseudo Leja sequences, which are much easier to obtain than the extremal Fekete points or the classical Leja points. For some classes of sets we estimate the rate of approximation. We also discuss simultaneous approximation of a compact set $E$ by its polynomially convex supersets and of its boundary $\partial E$ by their boundaries.

[24]  arXiv:1709.06637 [pdf, ps, other]
Title: Structure of free semigroupoid algebras
Comments: 63 pages, 1 figure
Subjects: Operator Algebras (math.OA); Functional Analysis (math.FA)

A free semigroupoid algebra is the closure of the algebra generated by a TCK family of a graph in the weak operator topology. We obtain a structure theory for these algebras analogous to that of free semigroup algebra. We clarify the role of absolute continuity and wandering vectors. These results are applied to obtain a Lebesgue-von Neumann-Wold decomposition of TCK families, along with reflexivity, a Kaplansky density theorem and classification for free semigroupoid algebras. Several classes of examples are discussed and developed, including self-adjoint examples and a classification of atomic free semigroupoid algebras up to unitary equivalence.

[25]  arXiv:1709.06640 [pdf, other]
Title: Construction C*: an improved version of Construction C
Subjects: Information Theory (cs.IT)

Besides all the attention given to lattice contructions, it is common to find some very interesting nonlattice constellations, as Construction C, for example, which also has relevant applications in communication problems (multi-stage decoding, good quantization efficieny). In this work we present a generalization of Construction C, based on inter-level coding, which we call Construction C*. The generalized construction has better immunity to noise and also provides a simple way of describing the Leech lattice. We give necessary and sufficient condition under which Construction C* is a lattice constellation.

[26]  arXiv:1709.06651 [pdf, ps, other]
Title: On the Kottwitz conjecture for local Shimura varieties
Comments: Appendix by David Hansen
Subjects: Number Theory (math.NT)

Kottwitz's conjecture describes the contribution of a supercuspidal represention to the cohomology of a local Shimura variety in terms of the local Langlands correspondence. Using a Lefschetz-Verdier fixed-point formula, we prove a weakened generalized version of Kottwitz's conjecture. The weakening comes from ignoring the action of the Weil group and only considering the actions of the groups $G$ and $J_b$ up to non-elliptic representations. The generalization is that we allow arbitrary connected reductive groups $G$ and non-minuscule coweights $\mu$.

[27]  arXiv:1709.06659 [pdf, other]
Title: Benchmarking Numerical Methods for Lattice Equations with the Toda Lattice
Comments: 21 pages, 30 figures, data tables in the appendix
Subjects: Numerical Analysis (math.NA); Pattern Formation and Solitons (nlin.PS); Exactly Solvable and Integrable Systems (nlin.SI); Computational Physics (physics.comp-ph)

We compare performances of well-known numerical time-stepping methods that are widely used to compute solutions of the doubly-infinite Fermi-Pasta-Ulam-Tsingou (FPUT) lattice equations. The methods are benchmarked according to (1) their accuracy in capturing the soliton peaks and (2) in capturing highly-oscillatory parts of the solutions of the Toda lattice resulting from a variety of initial data. The numerical inverse scattering transform method is used to compute a reference solution with high accuracy. We find that benchmarking a numerical method on pure-soliton initial data can lead one to overestimate the accuracy of the method.

[28]  arXiv:1709.06665 [pdf, other]
Title: Inverse mean curvature evolution of entire graphs
Comments: 42 pages, 2 figures
Subjects: Differential Geometry (math.DG)

We study the evolution of strictly mean-convex entire graphs over $R^n$ by Inverse Mean Curvature flow. First we establish the global existence of starshaped entire graphs with superlinear growth at infinity. The main result in this work concerns the critical case of asymptotically conical entire convex graphs. In this case we show that there exists a time $ T < +\infty$, which depends on the growth at infinity of the initial data, such that the unique solution of the flow exists for all $t < T$. Moreover, as $t \to T$ the solution converges to a flat plane. Our techniques exploit the ultra-fast diffusion character of the fully-nonlinear flow, a property that implies that the asymptotic behavior at spatial infinity of our solution plays a crucial influence on the maximal time of existence, as such behavior propagates infinitely fast towards the interior.

[29]  arXiv:1709.06666 [pdf, other]
Title: Colored Khovanov-Rozansky homology for infinite braids
Comments: 29 pages, many figures
Subjects: Quantum Algebra (math.QA)

We show that the limiting unicolored $\mathfrak{sl}(N)$ Khovanov-Rozansky chain complex of any infinite positive braid categorifies a highest-weight projector. This result extends an earlier result of Cautis categorifying highest-weight projectors using the limiting complex of infinite torus braids. Additionally, we show that the results hold in the case of colored HOMFLY-PT Khovanov-Rozansky homology as well. An application of this result is given in finding a partial isomorphism between the HOMFLY-PT homology of any braid positive link and the stable HOMFLY-PT homology of the infinite torus knot as computed by Hogancamp.

[30]  arXiv:1709.06676 [pdf, other]
Title: Evolution of Interfaces for the Nonlinear Double Degenerate Parabolic Equation of Turbulent Filtration with Absorption
Comments: 29 pages, 12 fugures
Subjects: Analysis of PDEs (math.AP)

We prove the short-time asymptotic formula for the interfaces and local solutions near the interfaces for the nonlinear double degenerate reaction-diffusion equation of turbulent filtration with strong absorption \[ u_t=\Big(|(u^{m})_x|^{p-1}(u^{m})_x\Big)_x-bu^{\beta}, \, mp>1, \, \beta >0. \] Full classification is pursued in terms of the nonlinearity parameters $m, p,\beta$ and asymptotics of the initial function near its support. Numerical analysis using a weighted essentially nonoscillatory (WENO) scheme with interface capturing is implemented, and comparison of numerical and analytical results is presented.

[31]  arXiv:1709.06677 [pdf, ps, other]
Title: Balanced truncation for model order reduction of linear dynamical systems with quadratic outputs
Comments: 26 pages, 20 figures
Subjects: Numerical Analysis (math.NA)

We investigate model order reduction (MOR) for linear dynamical systems, where a quadratic output is defined as a quantity of interest. The system can be transformed into a linear dynamical system with many linear outputs. MOR is feasible by the method of balanced truncation, but suffers from the large number of outputs in approximate methods. To ameliorate this shortcoming we derive an equivalent quadratic-bilinear system with a single linear output and analyze the properties of this system. We examine MOR for this system via the technique of balanced truncation, which requires a stabilization of the system. Therein, the solution of two quadratic Lyapunov equations is traced back to the solution of just two linear Lyapunov equations. We present numerical results for several test examples comparing the two MOR approaches.

[32]  arXiv:1709.06679 [pdf, ps, other]
Title: Controllability and data-driven identification of bipartite consensus on nonlinear signed networks
Comments: To be presented at the 56th IEEE Conference on Decision and Control in Melbourne, Australia
Subjects: Optimization and Control (math.OC)

Nonlinear networked systems are of interest in several areas of research, such as multi-agent systems and social networks. In this paper, we examine the controllability of several classes of nonlinear networked dynamics on which the underlying graph admits negative weights. Such signed networks exhibit bipartite clustering when the underlying graph is structurally balanced. We show that structural balance is the key ingredient inducing uncontrollability when combined with a leader-node symmetry and a certain type of dynamical symmetry. We then examine the problem of extracting the bipartite structure of such graphs from data using Extended Dynamic Mode Decomposition to approximate the corresponding Koopman operator.

[33]  arXiv:1709.06682 [pdf, other]
Title: Random matrices: repulsion in spectrum
Authors: Hoi H. Nguyen
Comments: 26 pages
Subjects: Probability (math.PR)

We address repulsion property among the singular values of random iid matrices, as well as among the eigenvalues of random Wigner matrices. We show evidence of repulsion under arbitrary perturbation even in matrices of discrete entry distributions. In many cases our method yields nearly optimal bounds in long range repulsion.

[34]  arXiv:1709.06684 [pdf, ps, other]
Title: The Classification Problem for Simple Unital Finite Rank Dimension Groups
Authors: Paul Ellis
Comments: 32 pages. To be published in Israel Journal of Mathematics
Subjects: Logic (math.LO); Group Theory (math.GR)

The Borel complexity of the isomorphism problem for finite-rank unital simple dimension groups increases with rank. This implies that the isomorphism problems for the corresponding classes of Bratteli diagrams and LDA-groups also increase with rank.

[35]  arXiv:1709.06685 [pdf, other]
Title: Concentration of distances in Wigner matrices
Authors: Hoi H. Nguyen
Comments: 33 pages, 1 figure; to appear in Linear Algebra and its Applications
Subjects: Probability (math.PR)

It is well-known that distances in random iid matrices are highly concentrated around their mean. In this note we extend this concentration phenomenon to Wigner matrices. Exponential bounds for the lower tail are also included.

[36]  arXiv:1709.06688 [pdf, other]
Title: Property Testing in High Dimensional Ising models
Authors: Matey Neykov, Han Liu
Comments: 55 pages, 9 figures
Subjects: Statistics Theory (math.ST); Machine Learning (stat.ML)

This paper explores the information-theoretic limitations of graph property testing in zero-field Ising models. Instead of learning the entire graph structure, sometimes testing a basic graph property such as connectivity, cycle presence or maximum clique size is a more relevant and attainable objective. Since property testing is more fundamental than graph recovery, any necessary conditions for property testing imply corresponding conditions for graph recovery, while custom property tests can be statistically and/or computationally more efficient than graph recovery based algorithms. Understanding the statistical complexity of property testing requires the distinction of ferromagnetic (i.e., positive interactions only) and general Ising models. Using combinatorial constructs such as graph packing and strong monotonicity, we characterize how target properties affect the corresponding minimax upper and lower bounds within the realm of ferromagnets. On the other hand, by studying the detection of an antiferromagnetic (i.e., negative interactions only) Curie-Weiss model buried in Rademacher noise, we show that property testing is strictly more challenging over general Ising models. In terms of methodological development, we propose two types of correlation based tests: computationally efficient screening for ferromagnets, and score type tests for general models, including a fast cycle presence test. Our correlation screening tests match the information-theoretic bounds for property testing in ferromagnets.

[37]  arXiv:1709.06689 [pdf, ps, other]
Title: $n$-exangulated categories
Comments: 59 pages
Subjects: Category Theory (math.CT); Representation Theory (math.RT)

For each positive integer $n$ we introduce the notion of $n$-exangulated categories as higher dimensional analogues of extriangulated categories defined by Nakaoka-Palu. We characterize which $n$-exangulated categories are $n$-exact in the sense of Jasso and which are $(n+2)$-angulated in the sense of Geiss-Keller-Oppermann. For extriangulated categories with eough projectives and injectives we introduce the notion of $n$-cluster tilting subcategories and show that under certain conditions such $n$-cluster tilting subcategories are $n$-exangulated.

[38]  arXiv:1709.06691 [pdf, other]
Title: Presentations for cusped arithmetic hyperbolic lattices
Comments: 25 pages, 4 figures, 6 tables
Subjects: Group Theory (math.GR); Geometric Topology (math.GT)

We present a general method to compute a presentation for any cusped hyperbolic lattice $\Gamma$, applying a classical result of Macbeath to a suitable $\Gamma$-invariant horoball cover of the corresponding symmetric space. As applications we compute presentations for the Picard modular groups ${\rm PU}(2,1,\mathcal{O}_d)$ for $d=1,3,7$ and the quaternionic lattice ${\rm PU}(2,1,\mathcal{H})$ with entries in the Hurwitz integer ring $\mathcal{H}$.

[39]  arXiv:1709.06694 [pdf, other]
Title: Filtered subspace iteration for selfadjoint operators
Subjects: Numerical Analysis (math.NA)

We consider the problem of computing a cluster of eigenvalues (and its associated eigenspace) of a (possibly unbounded) selfadjoint operator in a Hilbert space. A rational function of the operator is constructed such that the eigenspace of interest is its dominant eigenspace, and a subspace iteration procedure is used to approximate this eigenspace. The computed space is then used to obtain approximations of the eigenvalues of interest. An eigenvalue and eigenspace convergence analysis that considers both iteration error and discretization error is provided. A realization of the proposed approach for a model second-order elliptic operator is based on a discontinuous Petrov-Galerkin discretization of the resolvent, and a variety of numerical experiments illustrate its performance.

[40]  arXiv:1709.06695 [pdf, ps, other]
Title: Effective dimension of weighted Sobolev spaces: non-periodic case
Authors: Art B. Owen
Subjects: Numerical Analysis (math.NA)

This paper considers two notions of effective dimension for quadrature in weighted Sobolev spaces. A space has effective dimension $s$ in the truncation sense if a ball in that space just large enough to contain a function of unit variance does not contain any functions with more than $\varepsilon$ variance attributable to ANOVA components of indices past $s$. A similar truncation sense notion replaces index $s$ by cardinality $s$. Some Poincar\'e type inequalities are used to bound variance components by multiples of the Sobolev space's squared norm. Some numerical results show that low effective dimension in the superposition sense holds for some spaces defined by product weights in which quadrature is strongly tractable. Surprisingly, even spaces where all subset weights are equal, regardless of their cardinality or included indices, have low superposition dimension in this sense. A previous paper by the author required the integrands to have periodic mixed partial derivatives. This paper removes that condition.

[41]  arXiv:1709.06696 [pdf, ps, other]
Title: Higher Distance Energies and Expanders with Structure
Subjects: Combinatorics (math.CO)

We adapt the idea of higher moment energies, originally used in Additive Combinatorics, so that it would apply to problems in Discrete Geometry. This new approach leads to a variety of new results, such as
(i) Improved bounds for the problem of distinct distances with local properties.
(ii) Improved bounds for problems involving expanding polynomials in ${\mathbb R}[x,y]$ (Elekes-Ronyai type bounds) when one or two of the sets have structure.
Higher moment energies seem to be related to additional problems in Discrete Geometry, to lead to new elegant theory, and to raise new questions.

[42]  arXiv:1709.06697 [pdf, ps, other]
Title: Genus fields of finite abelian extensions
Comments: 20 pages
Subjects: Number Theory (math.NT)

In this paper we find the genus field of a finite abelian extension of the global rational function field. We introduce the term conductor of constants for these extensions and determine it in terms of other invariants. We study the particular case of finite abelian $p$- extensions. Finally, we give an explicit description of the genus field of any finite abelian $p$--extension of a global rational function field.

[43]  arXiv:1709.06698 [pdf, ps, other]
Title: Blind Estimation of Sparse Broadband Massive MIMO Channels with Ideal and One-bit ADCs
Comments: Submitted to IEEE Transactions on Signal Processing
Subjects: Information Theory (cs.IT)

We study the maximum likelihood problem for the blind estimation of massive mmWave MIMO channels while taking into account their underlying sparse structure, the temporal shifts across antennas in the broadband regime, and ultimately one-bit quantization at the receiver. The sparsity in the angular domain is exploited as a key property to enable the unambiguous blind separation between user's channels. The main advantage of this approach is the fact that the overhead due to pilot sequences can be dramatically reduced especially when operating at low SNR per antenna. In addition, as sparsity is the only assumption made about the channel, the proposed method is robust with respect to the statistical properties of the channel and data and allows the channel estimation and the separation of interfering users from adjacent base stations to be performed in rapidly time-varying scenarios. For the case of one-bit receivers, a blind channel estimation is proposed that relies on the Expectation Maximization (EM) algorithm. Additionally, performance limits are derived based on the clairvoyant Cramer Rao lower bound. Simulation results demonstrate that this maximum likelihood formulation yields superior estimation accuracy in the narrowband as well as the wideband regime with reasonable computational complexity and limited model assumptions.

[44]  arXiv:1709.06705 [pdf, ps, other]
Title: Indecomposable exposed positive bi-linear maps between two by two matrices
Authors: Seung-Hyeok Kye
Subjects: Functional Analysis (math.FA)

Positive bi-linear maps between matrix algebras play important roles to detect tri-partite entanglement by the duality between bi-linear maps and tri-tensor products. We exhibit indecomposable positive bi-linear maps between $2\times 2$ matrices which generate extreme rays in the cone of all positive bi-linear maps. In fact, they are exposed, and so detect entanglement of positive partial transpose whose volume is nonzero.

[45]  arXiv:1709.06706 [pdf, ps, other]
Title: Reversible Joint Hilbert and Linear Canonical Transform Without Distortion
Comments: Accepted by IEEE Transactions on Signal Processing
Journal-ref: IEEE Transactions on Signal Processing, Volume 61, Issue 19, Oct.1, 2013
Subjects: Information Theory (cs.IT)

Generalized analytic signal associated with the linear canonical transform (LCT) was proposed recently by Fu and Li ["Generalized Analytic Signal Associated With Linear Canonical Transform," Opt. Commun., vol. 281, pp. 1468-1472, 2008]. However, most real signals, especially for baseband real signals, cannot be perfectly recovered from their generalized analytic signals. Therefore, in this paper, the conventional Hilbert transform (HT) and analytic signal associated with the LCT are concerned. To transform a real signal into the LCT of its HT, two integral transforms (i.e., the HT and LCT) are required. The goal of this paper is to simplify cascades of multiple integral transforms, which may be the HT, analytic signal, LCT or inverse LCT. The proposed transforms can reduce the complexity when realizing the relationships among the following six kinds of signals: a real signal, its HT and analytic signal, and the LCT of these three signals. Most importantly, all the proposed transforms are reversible and undistorted. Using the proposed transforms, several signal processing applications are discussed and show the advantages and flexibility over simply using the analytic signal or the LCT.

[46]  arXiv:1709.06707 [pdf, ps, other]
Title: Asymptotics of Chebyshev Polynomials, II. DCT Subsets of $\mathbb{R}$
Subjects: Classical Analysis and ODEs (math.CA)

We prove Szeg\H{o}-Widom asymptotics for the Chebyshev polynomials of a compact subset of $\mathbb{R}$ which is regular for potential theory and obeys the Parreau-Widom and DCT conditions.

[47]  arXiv:1709.06710 [pdf, ps, other]
Title: Noncommutative topology and Jordan operator algebras
Comments: 37 pages
Subjects: Operator Algebras (math.OA); Mathematical Physics (math-ph); Functional Analysis (math.FA)

Jordan operator algebras are norm-closed spaces of operators on a Hilbert space with $a^2 \in A$ for all $a \in A$. We study noncommutative topology, noncommutative peak sets and peak interpolation, and hereditary subalgebras of Jordan operator algebras. We show that Jordan operator algebras present perhaps the most general setting for a `full' noncommutative topology in the C*-algebraic sense of Akemann, L. G. Brown, Pedersen, etc, and as modified for not necessarily selfadjoint algebras by the authors with Read, Hay and other coauthors. Our breakthrough relies in part on establishing several strong variants of C*-algebraic results of Brown relating to hereditary subalgebras, proximinality, deeper facts about $L+L^*$ for a left ideal $L$ in a C*-algebra, noncommutative Urysohn lemmas, etc. We also prove several other approximation results in $C^*$-algebras and various subspaces of $C^*$-algebras, related to open and closed projections, and technical $C^*$-algebraic results of Brown.

[48]  arXiv:1709.06714 [pdf, ps, other]
Title: Superconducting phase in the BCS model with imaginary magnetic field. II. Multi-scale infrared analysis
Authors: Yohei Kashima
Comments: 148 pages
Subjects: Mathematical Physics (math-ph)

We analyze the reduced BCS model with an imaginary magnetic field in a large domain of the temperature and the imaginary magnetic field. The magnitude of the attractive reduced BCS interaction is fixed to be small but independent of the temperature and the imaginary magnetic field unless the temperature is high. We impose a series of conditions on the free dispersion relation. These conditions are typically satisfied by free electron models with degenerate Fermi surface. For example, our theory applies to the model with nearest-neighbor hopping on 3 or 4-dimensional (hyper-)cubic lattice having degenerate free Fermi surface or the model with nearest-neighbor hopping on the honeycomb lattice with zero chemical potential. We prove that a spontaneous U(1)-symmetry breaking (SSB) and an off-diagonal long range order (ODLRO) occur in many areas of the parameter space. The SSB and the ODLRO are proved to occur in low temperatures arbitrarily close to zero in particular. However, it turns out that the SSB and the ODLRO are not present in the zero-temperature limit. The proof is based on Grassmann Gaussian integral formulations and a multi-scale infrared analysis of the formulations. We keep using notations and lemmas of our previous work [Y. Kashima, submitted, arXiv:1609.06121] implementing the double-scale integration scheme. So the multi-scale analysis this paper presents is a continuation of the previous work.

[49]  arXiv:1709.06717 [pdf, ps, other]
Title: On the growth rate of periodic orbits for vector fields
Subjects: Dynamical Systems (math.DS)

We establish the relationship between the growth rate of periodic orbits and the topological entropy for $C^1$ generic vector fields: this extends a classical result of Katok for $C^{1+\alpha}(\alpha>0)$ surface diffeomorphisms to $C^1$ generic vector fields of any dimension. The main difficulty comes from the existence of singularities and the shear of the flow.

[50]  arXiv:1709.06730 [pdf, ps, other]
Title: Covering Numbers for Semicontinuous Functions
Subjects: Optimization and Control (math.OC)

Considering the metric space of extended real-valued lower semicontinuous functions under the epi-distance, the paper gives an upper bound on the covering numbers of bounded subsets of such functions. No assumptions about continuity, smoothness, variation, and even finiteness of the functions are needed. The bound is shown to be nearly sharp through the construction of a set of functions with covering numbers deviating from the upper bound only by a logarithmic factor. The analogy between lower and upper semicontinuous functions implies that identical covering numbers hold for bounded sets of the latter class of functions as well, but now under the hypo-distance metric.

[51]  arXiv:1709.06732 [pdf, ps, other]
Title: The Hermite-Joubert problem and a conjecture of Brassil-Reichstein
Authors: Khoa Dang Nguyen
Comments: 8 pages, comments are welcome
Subjects: Number Theory (math.NT)

We show that Hermite theorem fails for every integer $n$ of the form $3^{k_1}+3^{k_2}+3^{k_3}$ with integers $k_1>k_2>k_3\geq 0$. This confirms a conjecture of Brassil and Reichstein. We also obtain new results for the relative Hermite-Joubert problem over a finitely generated field of characteristic $0$.

[52]  arXiv:1709.06733 [pdf, ps, other]
Title: Locally compact groups whose ergodic or minimal actions are all free
Subjects: Group Theory (math.GR); Dynamical Systems (math.DS)

We construct locally compact groups with no non-trivial Invariant Random Subgroups and no non-trivial Uniformly Recurrent Subgroups.

[53]  arXiv:1709.06735 [pdf, ps, other]
Title: Some inequalities for $k$-colored partition functions
Comments: 10 pages, 1 table
Subjects: Combinatorics (math.CO)

Motivated by a partition inequality of Bessenrodt and Ono, we obtain analogous inequalities for $k$-colored partition functions $p_{-k}(n)$ for all $k\geq2$. This enables us to extend the $k$-colored partition function multiplicatively to a function on $k$-colored partitions, and characterize when it has a unique maximum. We conclude with one conjectural inequality that strengthens our results.

[54]  arXiv:1709.06736 [pdf, ps, other]
Title: The cohomology of abelian Hessenberg varieties and the Stanley-Stembridge conjecture
Comments: 38 pages
Subjects: Combinatorics (math.CO); Algebraic Geometry (math.AG); Representation Theory (math.RT)

We define a subclass of Hessenberg varieties called abelian Hessenberg varieties, inspired by the theory of abelian ideals in a Lie algebra developed by Kostant and Peterson. We prove that the cohomology of an abelian regular semisimple Hessenberg variety, with respect to the $\mathfrak{S}_n$-action defined by Tymoczko, is a non-negative combination of tabloid representations. Our result implies that the Stanley-Stembridge conjecture holds in the abelian case, and generalizes results obtained by Shareshian-Wachs and Teff. Our proof uses previous work of Stanley, Gasharov, Shareshian-Wachs, and Brosnan-Chow, as well as results of the second author on the geometry and combinatorics of Hessenberg varieties.

[55]  arXiv:1709.06748 [pdf, ps, other]
Title: Equilibrium fluctuations for the weakly asymmetric discrete Atlas model
Subjects: Probability (math.PR); Mathematical Physics (math-ph)

This contribution aims at presenting and generalizing a recent work of Hernandez, Jara and Valentim [DOI:10.1016/j.spa.2016.06.026]. We consider the weakly asymmetric version of the so-called discrete Atlas model, which has been introduced there. Precisely, we look at some equilibrium fluctuation field of a weakly asymmetric zero-range process which evolves on a discrete half-line, with a source of particles at the origin. We prove that its macroscopic evolution is governed by a stochastic heat equation with Neumann or Robin boundary conditions, depending on the range of the parameters of the model.

[56]  arXiv:1709.06756 [pdf, ps, other]
Title: The Fourth Characteristic of a Semimartingale
Comments: 20 pages
Subjects: Probability (math.PR)

We extend the class of semimartingales in a natural way. This allows us to incorporate processes having paths that leave the state space $R^d$. By carefully distinguishing between two killing states, we are able to introduce a fourth semimartingale characteristic which generalizes the fourth part of the L\'evy quadruple. Using the probabilistic symbol, we analyze the close relationship between the generators of certain Markov processes with killing and their (now four) semimartingale characteristics.

[57]  arXiv:1709.06760 [pdf, ps, other]
Title: Exponential concentration for zeroes of stationary Gaussian processes
Comments: 17 pages
Subjects: Probability (math.PR); Mathematical Physics (math-ph)

We show that for any centered stationary Gaussian process of integrable covariance, whose spectral measure has compact support, or finite exponential moments (and some additional regularity), the number of zeroes of the process in $[0,T]$ is within $\eta T$ of its mean value, up to an exponentially small in $T$ probability.

[58]  arXiv:1709.06763 [pdf, ps, other]
Title: Integrable deformations of the Bogoyavlenskij-Itoh Lotka-Volterra systems
Comments: 23 pages, 14 references
Subjects: Dynamical Systems (math.DS)

We construct a family of integrable deformations of the Bogoyavlenskij-Itoh systems and construct a Lax operator with spectral parameter for it. Our approach is based on the construction of a family of compatible Poisson structures for the undeformed system, whose Casimirs are shown to yield a generating function for the integrals in involution of the deformed systems. We show how these deformations are related to the Veselov-Shabat systems.

[59]  arXiv:1709.06765 [pdf, other]
Title: Numerical Solution of Monge-Kantorovich Equations via a dynamic formulation
Authors: Enrico Facca (1), Sara Daneri (2), Franco Cardin (1), Mario Putti (1) (Universita' degli Studi di Padova (1), Department Mathematik der Friedrich-Alexander-Universität Erlangen-Nürnberg (2))
Subjects: Numerical Analysis (math.NA)

We propose a biologically inspired dynamic model for the numerical solution of the $L^{1}$-PDE based optimal transportation model.

[60]  arXiv:1709.06769 [pdf, ps, other]
Title: Motivic and $p$-adic Localization Phenomena
Authors: Dimitri Wyss
Comments: Thesis
Subjects: Algebraic Geometry (math.AG)

In this thesis we compute motivic classes of hypertoric varieties, Nakajima quiver varieties and open de Rham spaces in a certain localization of the Grothendieck ring of varieties. Furthermore we study the $p$-adic pushforward of the Haar measure under a hypertoric moment map $\mu$. This leads to an explicit formula for the Igusa zeta function $I_\mu(s)$ of $\mu$, and in particular to a small set of candidate poles for $I_\mu(s)$. We also study various properties of the residue at the largest pole of $I_\mu(s)$. Finally, if $\mu$ is constructed out of a quiver $\Gamma$ we give a conjectural description of this residue in terms of indecomposable representations of $\Gamma$ over finite depth rings.
The connections between these different results is the method of proof. At the heart of each theorem lies a motivic or $p$-adic volume computation, which is only possible due to some surprising cancellations. These cancellations are reminiscent of a result in classical symplectic geometry by Duistermaat and Heckman on the localization of the Liouville measure, hence the title of the thesis.

[61]  arXiv:1709.06771 [pdf, ps, other]
Title: A Central Limit Theorem for Fleming-Viot Particle Systems with Hard Killing
Comments: 38 pages
Subjects: Probability (math.PR)

Fleming-Viot type particle systems represent a classical way to approximate the distribution of a Markov process with killing, given that it is still alive at a final deterministic time. In this context, each particle evolves independently according to the law of the underlying Markov process until its killing, and then branches instantaneously on another randomly chosen particle. While the consistency of this algorithm in the large population limit has been recently studied in several articles, our purpose here is to prove Central Limit Theorems under very general assumptions. For this, we only suppose that the particle system does not explode in finite time, and that the jump and killing times have atomless distributions. In particular, this includes the case of elliptic diffusions with hard killing.

[62]  arXiv:1709.06774 [pdf, ps, other]
Title: Information-Coupled Turbo Codes for LTE Systems
Comments: 13 pages, 12 figures
Subjects: Information Theory (cs.IT)

We propose a new class of information-coupled (IC) Turbo codes to improve the transport block (TB) error rate performance for long-term evolution (LTE) systems, while keeping the hybrid automatic repeat request protocol and the Turbo decoder for each code block (CB) unchanged. In the proposed codes, every two consecutive CBs in a TB are coupled together by sharing a few common information bits. We propose a feed-forward and feed-back decoding scheme and a windowed (WD) decoding scheme for decoding the whole TB by exploiting the coupled information between CBs. Both decoding schemes achieve a considerable signal-to-noise-ratio (SNR) gain compared to the LTE Turbo codes. We construct the extrinsic information transfer (EXIT) functions for the LTE Turbo codes and our proposed IC Turbo codes from the EXIT functions of underlying convolutional codes. An SNR gain upper bound of our proposed codes over the LTE Turbo codes is derived and calculated by the constructed EXIT charts. Numerical results show that the proposed codes achieve an SNR gain of 0.25 dB to 0.72 dB for various code parameters at a TB error rate level of $10^{-2}$, which complies with the derived SNR gain upper bound.

[63]  arXiv:1709.06777 [pdf, ps, other]
Title: Estimates near the origin for functional calculus on analytic semigroups
Comments: 17 pages, 1 figure
Subjects: Functional Analysis (math.FA); Complex Variables (math.CV)

This paper provides sharp lower estimates near the origin for the functional calculus $F(-uA)$ of a generator $A$ of an operator semigroup defined on a sector; here $F$ is given as the Fourier--Borel transform of an analytic functional. The results are linked to the existence of an identity element in the Banach algebra generated by the semigroup. Both the quasinilpotent and non-quasinilpotent cases are considered, and sharp results are proved extending many in the literature.

[64]  arXiv:1709.06784 [pdf, ps, other]
Title: On a system of $q$-partial differential equations with applications to $q$-series
Authors: Zhi-Guo Liu
Comments: 15 pages, accepted for the proceedings of the Alladi 60th birthday conference
Subjects: Complex Variables (math.CV)

Using the theory of functions of several variables and $q$-calculus, we prove an expansion theorem for the analytic function in several variables which satisfies a system of $q$-partial differential equations. Some curious applications of this expansion theorem to $q$-series are discussed. In particular, an extension of Andrews' transformation formula for the $q$-Lauricella function is given.

[65]  arXiv:1709.06785 [pdf, other]
Title: Stochastic Channel Modeling for Diffusive Mobile Molecular Communication Systems
Comments: 30 pages (single column), 2 tables, 13 figures. Submitted to IEEE Transactions on Communications (TCOM) on September 15, 2017. (Author's comment: Extended version of the conference paper arXiv:1704.06298)
Subjects: Information Theory (cs.IT); Emerging Technologies (cs.ET)

In this paper, we develop a mathematical framework for modeling time-variant stochastic channels in diffusive mobile molecular communication (MC) systems. In particular, we consider a diffusive mobile MC system consisting of a pair of transmitter and receiver nano-machines suspended in a fluid medium with a uniform bulk flow, where we model the mobility of the nano-machines by Brownian motion. The transmitter and receiver nano-machines exchange information via diffusive signaling molecules. Due to the random movements of the transmitter and receiver nano-machines, the statistics of the channel impulse response (CIR) change over time. In this paper, we introduce a statistical framework for characterization of the impulse response of time-variant MC channels. To this end, we derive closed-form expressions for the mean, the autocorrelation function, the cumulative distribution function (CDF), and the probability density function (PDF) of the time-variant CIR. Given the autocorrelation function, we define the coherence time of the time-variant MC channel as a metric for characterization of the variations of the impulse response. The derived CDF is employed for calculation of the outage probability of the system. We also show that under certain conditions, the PDF of the CIR can be accurately approximated by a Log-normal distribution. Given this approximation, we derive a simple model for outdated channel state information (CSI). Moreover, we derive an analytical expression for evaluation of the expected error probability of a simple detector for the considered MC system. In order to investigate the impact of CIR decorrelation over time, we compare the performances of a detector with perfect CSI knowledge and a detector with outdated CSI knowledge. The accuracy of the proposed analytical expressions is verified via particle-based simulation of the Brownian motion.

[66]  arXiv:1709.06787 [pdf, ps, other]
Title: Optimal interval length for the collocation of the Newton basis
Subjects: Numerical Analysis (math.NA)

It is known that the Lagrange interpolation problem at equidistant nodes is ill-conditioned. We explore the influence of the interval length in the computation of divided differences of the Newton interpolation formula. Condition numbers are computed for lower triangular matrices associated to the Newton interpolation formula at equidistant nodes. We consider the collocation matrices $L$ and $P_L$ of the monic Newton basis and a normalized Newton basis, so that $P_L$ is the lower triangular Pascal matrix. In contrast to $L$, $P_L$ does not depend on the interval length, and we show that the Skeel condition number of the $(n+1)\times (n+1)$ lower triangular Pascal matrix is $3^n$. The $\infty$-norm condition number of the collocation matrix $L$ of the monic Newton basis is computed in terms of the interval length. The minimum asymptotic growth rate is achieved for intervals of length 3.

[67]  arXiv:1709.06788 [pdf, ps, other]
Title: Seshadri constants on hyperelliptic surfaces
Comments: 14 pages, comments welcome
Subjects: Algebraic Geometry (math.AG)

We prove new results on single point Seshadri constants for ample line bundles on hyperelliptic surfaces. Given a hyperelliptic surface $X$ and an ample line bundle $L$ on $X$, we show that the least Seshadri constant $\varepsilon(L)$ of $L$ is a rational number when $X$ is not of type 6. We also prove new lower bounds for the Seshadri constant $\varepsilon(L,1)$ of $L$ at a very general point.

[68]  arXiv:1709.06789 [pdf, ps, other]
Title: New $ω$-Stable Planes
Authors: Gianluca Paolini
Subjects: Logic (math.LO)

We use (variations on) Mason's $\alpha$-function as a pre-dimension function to construct new examples of $\omega$-stable planes (i.e. simple rank $3$ matroids). Specifically, we construct infinitely many $\omega$-stable planes $P(n)$, for $n < \omega$, such that every finite plane is $\wedge$-embeddable into $P(n)$ for co-finitely many $n < \omega$. As a consequence, for co-finitely many $n < \omega$, the plane $P(n)$ is neither projective, nor affine, nor linear, nor algebraic.

[69]  arXiv:1709.06790 [pdf, ps, other]
Title: The uniform distribution of sequences generated by iterated polynomials
Authors: Emil Lerner
Subjects: Number Theory (math.NT); Cryptography and Security (cs.CR)

Assume that $m,s\in\mathbb N$, $m>1$, while $f$ is a polynomial with integer coefficients, $\text{deg}~f>1$, $f^{(i)}$ is the $i$th iteration of the polynomial $f$, $\kappa_n$ has a discrete uniform distribution on the set $\{0,1,\ldots,m^n - 1\}$. We are going to prove that with $n$ tending to infinity random vectors $\left(\frac{\kappa_n}{m^n},\frac{f(\kappa_n) \bmod m^n}{m^n},\ldots,\frac{f^{(s - 1)}(\kappa_n) \bmod m^n}{m^n}\right)$ weakly converge to a vector having a continuous uniform distribution in the $s$-dimensional unit cube. Analogous results were obtained earlier only for some classes of polynomials with $s\leqslant 3, \text{deg}~f = 2$.
The mentioned vectors represent sequential pseudorandom numbers produced by a polynomial congruential generator modulo $m^n$.

[70]  arXiv:1709.06791 [pdf, other]
Title: Propagation of a Three-dimensional Weak Shock Front Using Kinematical Conservation Laws
Subjects: Analysis of PDEs (math.AP)

In this paper we present a mathematical theory and a numerical method to study the propagation of a three-dimensional (3-D) weak shock front into a polytropic gas in a uniform state and at rest, though the method can be extended to shocks moving into nonuniform flows. The theory is based on the use of 3-D kinematical conservation laws (KCL), which govern the evolution of a surface in general and a shock front in particular. The 3-D KCL, derived purely on geometrical considerations, form an under-determined system of conservation laws. In the present paper the 3-D KCL system is closed by using two appropriately truncated transport equations from an infinite hierarchy of compatibility conditions along shock rays. The resulting governing equations of this KCL based 3-D shock ray theory, leads to a weakly hyperbolic system of eight conservation laws with three divergence-free constraints. The conservation laws are solved using a Godunov-type central finite volume scheme, with a constrained transport technique to enforce the constraints. The results of extensive numerical simulations reveal several physically realistic geometrical features of shock fronts and the complex structures of kink lines formed on them. A comparison of the results with those of a weakly nonlinear wavefront shows that a weak shock front and a weakly nonlinear wavefront are topologically same. The major important differences between the two are highlighted in the contexts of corrugational stability and converging shock fronts.

[71]  arXiv:1709.06794 [pdf, ps, other]
Title: Nodal solutions for the Robin $p$-Laplacian plus an indefinite potential and a general reaction term
Journal-ref: Commun. Pure Appl. Anal. 17:1 (2018), 231-241
Subjects: Analysis of PDEs (math.AP)

We consider a nonlinear Robin problem driven by the $p$-Laplacian plus an indefinite potential. The reaction term is of arbitrary growth and only conditions near zero are imposed. Using critical point theory together with suitable truncation and perturbation techniques and comparison principles, we show that the problem admits a sequence of distinct smooth nodal solutions converging to zero in $C^1(\overline{\Omega})$.

[72]  arXiv:1709.06798 [pdf, ps, other]
Title: Scalar conformal invariants of weight zero
Comments: This work was presented for the first time at the Spanish-Portuguese Relativity Meeting -- EREP 2017 held in M\'alaga (Spain), 12-15 September 2017. 7 pages, 1 table
Subjects: Differential Geometry (math.DG); General Relativity and Quantum Cosmology (gr-qc)

In the class of metrics of a generic conformal structure there exists a distinguishing metric. This was noticed by Albert Einstein in a lesser-known paper of 1921. There he also announced that it is possible to add an scalar equation to the field equations of General Relativity. We explore this suggestion from a geometrical point of view. Then, we obtain a family of scalar conformal invariants of weight 0 for generic pseudo-Riemannian conformal structures $[g]$ in more than three dimensions. In particular, we define the conformal scalar curvature of $[g]$ and calculate it for some well-known conformal spacetimes, comparing the results with the Ricci scalar and the Kretschmann scalar.

[73]  arXiv:1709.06802 [pdf, ps, other]
Title: Accessible Parts of Boundary for Simply Connected Domains
Comments: 11 pages
Subjects: Classical Analysis and ODEs (math.CA); Complex Variables (math.CV)

For a bounded simply connected domain $\Omega\subset\mathbb{R}^2$, any point $z\in\Omega$ and any $0<\alpha<1$, we give a lower bound for the $\alpha$-dimensional Hausdorff content of the set of points in the boundary of $\Omega$ which can be joined to $z$ by a John curve with John constant depending only on $\alpha$, in terms of the distance of $z$ to $\partial\Omega$. In fact this set in the boundary contains the intersection $\partial\Omega_z\cap\partial\Omega$ of the boundary of a John sub-domain $\Omega_z$ of $\Omega$, centered at $z$, with the boundary of $\Omega$. This may be understood as a quantitative version of a result of Makarov. This estimate is then applied to obtain the pointwise version of a weighted Hardy inequality.

[74]  arXiv:1709.06803 [pdf, ps, other]
Title: Some reductions of rank 2 and genera 2 and 3 Hitchin systems
Authors: Oleg K. Sheinman
Comments: 20 pages, LaTeX
Subjects: Mathematical Physics (math-ph)

Certain reductions of the rank 2, genera 2 and 3 Hitchin systems are considered, which are shown to give an integrable system of 2, resp. 3, interacting points on the line. It is shown that the reduced systems are particular cases of a certain universal integrable system related to the Lagrange interpolation polynomial. Admissibility of the reduction is proved using computer technique. The corresponding codes are given in the text.

[75]  arXiv:1709.06814 [pdf, ps, other]
Title: On $2$-chains inside thin subsets of $\mathbb{R}^d$ and product of distances
Authors: Bochen Liu
Subjects: Classical Analysis and ODEs (math.CA); Combinatorics (math.CO); Metric Geometry (math.MG)

We prove that if the Hausdorff dimension of $E\subset\mathbb{R}^d$, $d\geq 2$ is greater than $\frac{d}{2}+\frac{1}{3}$, the set of gaps of $2$-chains inside $E$, $$\Delta_2(E)=\{(|x-y|, |y-z|): x, y, z\in E \}\subset\mathbb{R}^2$$ has positive Lebesgue measure. It generalizes Wollf-Erdogan's result on distance set $$\Delta(E)= \{|x-y|: x, y\in E \}$$ and improves a result of Bennett, Iosevich and Taylor on finite chains.
We also consider the similarity class of $2$-chains, equivalently, $$S_2(E)=\left\{\frac{t_1}{t_2}:(t_1,t_2)\in\Delta_2(E)\right\}=\left\{\frac{|x-y|}{|y-z|}: x, y, z\in E \right\}\subset\mathbb{R},$$ and show that $|S_2(E)|>0$ whenever $\dim_{\mathcal{H}}(E)>\frac{d}{2}+\frac{1}{7}$. We also prove that when $\dim_{\mathcal{H}}(E)>\frac{d}{2}+\frac{1}{4k-1}$, the set of product of distances, $$(\Delta(E))^k=\left\{\prod_{j=1}^k t_j: t_j\in\Delta(E)\right\}= \left\{\prod_{j=1}^k |x^j-y^j|: x^j, y^j\in E\right\} $$ has positive Lebesgue measure, while whether $|\Delta(E)|>0$ is still unknown when $\dim_{\mathcal{H}}(E)\leq\frac{d}{2}+\frac{1}{3}$.

[76]  arXiv:1709.06817 [pdf, ps, other]
Title: Spectral Invariance of Pseudodifferential Boundary Value Problems on Manifolds with Conical Singularities
Subjects: Analysis of PDEs (math.AP); Operator Algebras (math.OA)

We prove the spectral invariance of the algebra of classical pseudodifferential boundary value problems on manifolds with conical singularities in the Lp-setting. As a consequence we also obtain the spectral invariance of the classical Boutet de Monvel algebra of zero order operators with parameters. In order to establish these results, we show the equivalence of Fredholm property and ellipticity for both cases.

[77]  arXiv:1709.06823 [pdf, ps, other]
Title: Initial-boundary value problem for distributed order time-fractional diffusion equations
Subjects: Analysis of PDEs (math.AP)

We examine initial-boundary value problems for diffusion equations with distributed order time-fractional derivatives. We prove existence and uniqueness results for the weak solution to these systems, together with its continuous dependency on initial value and source term. Moreover, under suitable assumption on the source term, we establish that the solution is analytic in time.

[78]  arXiv:1709.06826 [pdf, ps, other]
Title: On a ternary generalization of Jordan algebras
Comments: 17 pages
Subjects: Rings and Algebras (math.RA)

Based on the relation between the notions of Lie triple systems and Jordan algebras, we introduce the $n$-ary Jordan algebras,an $n$-ary generalization of Jordan algebras obtained via the generalization of the following property $\left[ R_{x},R_{y}\right] \in Der\left( \mathcal{A}\right)$, where $\mathcal{A}$ is an $n$-ary algebra. Next, we study a ternary example of these algebras. Finally, based on the construction of a family of ternary algebras defined by means of the Cayley-Dickson algebras, we present an example of a ternary $D_{x,y}$-derivation algebra ($n$-ary $D_{x,y}$-derivation algebras are the non-commutative version of $n$-ary Jordan algebras).

[79]  arXiv:1709.06827 [pdf, other]
Title: Miscorrection-free Decoding of Staircase Codes
Comments: 3 pages, 2 figures, author version of conference paper, European Conference on Optical Communciation (ECOC), Gothenburg, Sweden, 2017
Subjects: Information Theory (cs.IT)

We propose a novel decoding algorithm for staircase codes which reduces the effect of undetected component code miscorrections. The algorithm significantly improves performance, while retaining a low-complexity implementation suitable for high-speed optical transport networks.

[80]  arXiv:1709.06831 [pdf, ps, other]
Title: Differential transcendence & algebraicity criteria for the series counting weighted quadrant walks
Comments: 27 pages, 7 figures
Subjects: Combinatorics (math.CO)

We consider weighted small step walks in the positive quadrant, and provide algebraicity and differential transcendence results for the underlying generating functions: we prove that depending on the probabilities of allowed steps, certain of the generating series are algebraic over the field of rational functions, while some others do not satisfy any algebraic differential equation with rational functions coefficients. Our techniques involve differential Galois theory for difference equations as well as complex analysis (Weierstrass parameterization of elliptic curves). We also extend to the weighted case many key intermediate results, as a theorem of analytic continuation of the generating functions.

[81]  arXiv:1709.06832 [pdf, ps, other]
Title: Atomic Norm Denoising-Based Joint Channel Estimation and Faulty Antenna Detection for Massive MIMO
Comments: Accepted for publication in the IEEE Transactions on Vehicular Technology
Subjects: Information Theory (cs.IT)

We consider joint channel estimation and faulty antenna detection for massive multiple-input multiple-output (MIMO) systems operating in time-division duplexing (TDD) mode. For systems with faulty antennas, we show that the impact of faulty antennas on uplink (UL) data transmission does not vanish even with unlimited number of antennas. However, the signal detection performance can be improved with a priori knowledge on the indices of faulty antennas. This motivates us to propose the approach for simultaneous channel estimation and faulty antenna detection. By exploiting the fact that the degrees of freedom of the physical channel matrix are smaller than the number of free parameters, the channel estimation and faulty antenna detection can be formulated as an extended atomic norm denoising problem and solved efficiently via the alternating direction method of multipliers (ADMM). Furthermore, we improve the computational efficiency by proposing a fast algorithm and show that it is a good approximation of the corresponding extended atomic norm minimization method. Numerical simulations are provided to compare the performances of the proposed algorithms with several existing approaches and demonstrate the performance gains of detecting the indices of faulty antennas.

[82]  arXiv:1709.06834 [pdf, ps, other]
Title: Geodesics Currents and Counting Problems
Comments: 14 pages
Subjects: Geometric Topology (math.GT); Dynamical Systems (math.DS)

For every positive, continuous and homogeneous function $f$ on the space of currents on a closed surface $\Sigma$, and for every filling current $\alpha$, we compute as $L \to \infty$, the number of mapping classes $\phi$ so that $f(\phi(\alpha))\leq L$. As an application, we prove a lattice counting theorem for Teichm\"uller space equipped with the Thurston metric.

[83]  arXiv:1709.06838 [pdf, ps, other]
Title: Higher Order Concentration of Measure
Subjects: Probability (math.PR)

We study sharpened forms of the concentration of measure phenomenon typically centered at stochastic expansions of order $d-1$ for any $d \in \mathbb{N}$. The bounds are based on $d$-th order derivatives or difference operators. In particular, we consider deviations of functions of independent random variables and differentiable functions over probability measures satisfying a logarithmic Sobolev inequality, and functions on the unit sphere. Applications include concentration inequalities for $U$-statistics as well as for classes of symmetric functions via polynomial approximations on the sphere (Edgeworth-type expansions).

[84]  arXiv:1709.06839 [pdf, other]
Title: Products and coproducts in string topology
Subjects: Algebraic Topology (math.AT); Differential Geometry (math.DG); Geometric Topology (math.GT)

Let M be a closed Riemannian manifold. We extend the product of Goresky-Hingston, on the cohomology of the free loop space of $M$ relative to the constant loops, to a non-relative product. It is associative, graded commutative, and compatible with the length filtration on the loop space, like the original product. We prove the following new geometric property of the dual homology coproduct: the non-vanishing of the $k$--th iterate of the dual coproduct detects the presence of loops with $(k+1)$-fold self-intersections in the image of chain representatives of homology classes in the loop space. For spheres and projective spaces, we show that this is sharp, in the sense that the $k$--iterated coproduct vanishes precisely when a class has support in the loops with at most $k$--fold self-intersections. We study the interactions between this cohomology product and the more well-known Chas-Sullivan product, and show that both structures are preserved by degree 1 maps, proving in particular that the Goresky-Hingston product is homotopy invariant. We give explicit integral chain level constructions of these loop products and coproduct, including a new construction of the Chas-Sullivan product, which avoid the technicalities of infinite dimensional tubular neighborhoods or delicate intersections of chains in loop spaces.

[85]  arXiv:1709.06848 [pdf, ps, other]
Title: Berry-Esseen Bounds for typical weighted sums
Subjects: Probability (math.PR)

Under correlation-type conditions, we derive upper bounds of order $\frac{1}{\sqrt{n}}$ for the Kolmogorov distance between the distributions of weighted sums of dependent summands and the normal law.

[86]  arXiv:1709.06850 [pdf, ps, other]
Title: Higher dimensional foliated Mori theory
Authors: Calum Spicer
Subjects: Algebraic Geometry (math.AG); Dynamical Systems (math.DS)

We develop some basic results in a higher dimensional foliated Mori theory, and show how these results can be used to prove a structure theorem for the Kleiman-Mori cone of curves in terms of the numerical properties of $K_{\mathcal{F}}$ for rank 2 foliations on threefolds. We also make progress toward realizing a minimal model program for rank 2 foliations on threefolds.

[87]  arXiv:1709.06854 [pdf, ps, other]
Title: A note on the 4-girth-thickness of K_{n,n,n}
Authors: Xia Guo, Yan Yang
Subjects: Combinatorics (math.CO)

The $4$-girth-thickness $\theta(4,G)$ of a graph $G$ is the minimum number of planar subgraphs of girth at least four whose union is $G$. In this paper, we obtain that the 4-girth-thickness of complete tripartite graph $K_{n,n,n}$ is $\big\lceil\frac{n+1}{2}\big\rceil$ except for $\theta(4,K_{1,1,1})=2$. And we also show that the $4$-girth-thickness of the complete graph $K_{10}$ is three which disprove the conjecture $\theta(4,K_{10})=4$ posed by Rubio-Montiel (Ars Math Contemp 14(2) (2018) 319).

[88]  arXiv:1709.06856 [pdf, ps, other]
Title: On Energy Efficient Uplink Multi-User MIMO with Shared LNA Control
Subjects: Information Theory (cs.IT)

Implementation cost and power consumption are two important considerations in modern wireless communications, particularly in large-scale multi-antenna systems where the number of individual radio-frequency (RF) chains may be significantly larger than before. In this work, we propose to deploy a single low-noise amplifier (LNA) on the uplink multiple-input-multiple-output (MIMO) receiver to cover all antennas. This architecture, although favorable from the perspective of cost and power consumption, introduces challenges in the LNA gain control and user transmit power control. We formulate an energy efficiency maximization problem under practical system constraints, and prove that it is a constrained quasi-concave optimization problem. We then propose an efficient algorithm, Bisection -- Gradient Assisted Interior Point (B-GAIP), that solves this optimization problem. The optimality, convergence and complexity of B-GAIP are analyzed, and further corroborated via numerical simulations. In particular, the performance loss due to using a shared LNA as opposed to separate LNAs in each RF chain, when using B-GAIP to determine the LNA gain and user transmit power, is very small in both centralized and distributed MIMO systems.

[89]  arXiv:1709.06862 [pdf, ps, other]
Title: Completely separably MAD families and the modal logic of $βω$
Subjects: Logic (math.LO); General Topology (math.GN)

We show in ZFC that the existence of completely separable maximal almost disjoint families of subsets of $\omega$ implies that the modal logic S4.1.2 is complete with respect to the \v{C}ech-Stone compactification of the natural numbers, the space $\beta\omega$. In the same fashion we prove that the modal logic S4 is complete with respect to the space $\omega^*=\beta\omega\setminus\omega$. This improves the results of G. Bezhanishvili and J. Harding who prove these theorems under stronger assumptions ($\mathfrak{a}=\mathfrak{c}$). Our proof is also somewhat simpler.

[90]  arXiv:1709.06866 [pdf, other]
Title: On the postcritical set of a rational map
Subjects: Dynamical Systems (math.DS)

The postcritical set $P(f)$ of a rational map $f:\mathbb P^1\to \mathbb P^1$ is the smallest forward invariant subset of $\mathbb P^1$ that contains the critical values of $f$. In this paper we show that every finite set $X\subset \mathbb P^1(\overline{\mathbb Q})$ can be realized as the postcritical set of a rational map. We also show that every map $F:X\to X$ defined on a finite set $X\subset \mathbb P^1(\mathbb C)$ can be realized by a rational map $f:P(f)\to P(f)$, provided we allow small perturbations of the set $X$. The proofs involve Belyi's theorem and iteration on Teichm\"uller space.

[91]  arXiv:1709.06869 [pdf, other]
Title: Almost-Regular Dessins on a Sphere and Torus
Subjects: Geometric Topology (math.GT); Algebraic Geometry (math.AG); Group Theory (math.GR)

The Hurwitz problem asks which ramification data are realizable, that is appear as the ramification type of a covering. We use dessins d'enfant to show that families of genus 1 regular ramification data with small changes are realizable with the exception of four families which were recently shown to be nonrealizable. A similar description holds in the case of genus 0 ramification data.

[92]  arXiv:1709.06872 [pdf, ps, other]
Title: A note on perturbations of Fusion Frames
Authors: M. Ruiz, P. Calderón
Comments: 8 pages
Subjects: Functional Analysis (math.FA)

In this work, we consider some relationships between a closed range operator $T$ and a fusion frame $\mathcal{W}=(W_i,w_i)_{i\in I}$ for a Hilbert space $\mathcal{H}$ that provides that the sequence $(\overline{T(W_i)},v_i)_{i\in I}$ is a fusion frame sequence for $\mathcal{H}$, if we consider a suitable family of weights $\{v_i\}_{i\in I}$. This (sufficient) condition generalizes some previous work in the subject.

[93]  arXiv:1709.06878 [pdf, other]
Title: Mathematical properties of the Weertman equation
Authors: Marc Josien
Subjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph)

We derive here some mathematical properties of the Weertman equation and show it is the limit of an evolution equation. The Weertman equation is a semilinear integrodifferential equation involving a fractional Laplacian. In addition to this purely theoretical interest, the results proven here give a solid ground to a numerical approach that we have implemented (see https://arxiv.org/abs/1704.04489).

[94]  arXiv:1709.06879 [pdf, ps, other]
Title: Spaces with a $\mathbb{Q}$-diagonal
Authors: Ziqin Feng
Subjects: General Topology (math.GN)

A space $X$ has a $\mathbb{Q}$-diagonal if $X^2\setminus \Delta$ has a $\mathcal{K}(\mathbb{Q})$-directed compact cover. We show that any compact space with a $\mathbb{Q}$-diagonal is metrizable, hence any Tychonorff space with a $\mathbb{Q}$-diagonal is cosmic. These give a positive answer to Problem 4.2 and Problem 4.8 in \cite{COT11} raised by Cascales, Orihuela and Tkachuk.

[95]  arXiv:1709.06880 [pdf, other]
Title: Multiresolution Mode Decomposition for Adaptive Time Series Analysis
Authors: Haizhao Yang
Comments: arXiv admin note: text overlap with arXiv:1610.03819
Subjects: Numerical Analysis (math.NA)

This paper proposes the \emph{multiresolution mode decomposition} as a novel model for adaptive time series analysis. The main conceptual innovation is the introduction of the \emph{multiresolution intrinsic mode function} (MIMF) of the form \[ \sum_{n=-N/2}^{N/2-1} a_n\cos(2\pi n\phi(t))s_{cn}(2\pi N\phi(t))+\sum_{n=-N/2}^{N/2-1}b_n \sin(2\pi n\phi(t))s_{sn}(2\pi N\phi(t))\] to model nonlinear and non-stationary data with time-dependent amplitudes, frequencies, and waveforms. %The MIMF explains the intrinsic difficulty in concentrating time-frequency representation of nonlinear and non-stationary data and provides a new direction for mode decomposition. The multiresolution expansion coefficients $\{a_n\}$, $\{b_n\}$, and the shape function series $\{s_{cn}(t)\}$ and $\{s_{sn}(t)\}$ provide innovative features for adaptive time series analysis. For complex signals that are a superposition of several MIMFs with well-differentiated phase functions $\phi(t)$, a new recursive scheme based on Gauss-Seidel iteration and diffeomorphisms is proposed to identify these MIMFs, their multiresolution expansion coefficients, and shape function series. Numerical examples from synthetic data and natural phenomena are given to demonstrate the power of this new method.

[96]  arXiv:1709.06884 [pdf]
Title: Mathematical Knowledge and the Role of an Observer: Ontological and epistemological aspects
Authors: Mark Burgin
Subjects: History and Overview (math.HO)

As David Berlinski writes (1997), the existence and nature of mathematics is a more compelling and far deeper problem than any of the problems raised by mathematics itself. Here we analyze the essence of mathematics making the main emphasis on mathematics as an advanced system of knowledge. This knowledge consists of structures and represents structures, existence of which depends on observers in a nonstandard way. Structural nature of mathematics explains its reasonable effectiveness.

[97]  arXiv:1709.06886 [pdf, ps, other]
Title: On steady solutions to a model of chemically reacting heat conducting compressible mixture with slip boundary conditions
Comments: arXiv admin note: text overlap with arXiv:1612.05443
Subjects: Analysis of PDEs (math.AP)

We consider a model of chemically reacting heat conducting compressible mixture. We investigate the corresponding system of partial differential equations in the steady regime with slip boundary conditions for the velocity and, in dependence on the model parameters, we establish existence of either weak or variational entropy solutions. The results extend the range of parameters for which the existence of weak solutions is known in the case of homogeneous Dirichlet boundary conditions for the velocity.

[98]  arXiv:1709.06891 [pdf, ps, other]
Title: The diffusive limit of kinetic schemes based on S-matrices involving normal modes is Il'in's exponential-fitting
Authors: L Gosse (1), Nicolas Vauchelet (2) ((1) IAC, (2) LAGA)
Subjects: Analysis of PDEs (math.AP)

This paper is concerned with diffusive approximations of peculiar numerical schemes for several linear (or weakly nonlinear) kinetic models which are motivated by wide-range applications, including radiative transfer or neutron transport, run-and-tumble models of chemotaxis dynamics, and Vlasov-Fokker-Planck plasma modeling. The well-balanced method applied to such kinetic equations leads to time-marching schemes involving a "scattering S-matrix" , itself derived from a normal modes decomposition of the stationary solution. One common feature these models share is the type of diffusive approximation: their macroscopic densities solve drift-diffusion systems, for which a distinguished numerical scheme is Il'in/Scharfetter-Gummel's "exponential fitting" discretization. We prove that the well-balanced schemes relax, within a parabolic rescaling, towards the Il'in exponential-fitting discretization by means of an appropriate decomposition of the S-matrix. This is the so-called asymptotic preserving (or uniformly accurate) property.

[99]  arXiv:1709.06893 [pdf, ps, other]
Title: Explicit justification stit logic: a completeness result
Comments: 32 pages, 0 figures. arXiv admin note: substantial text overlap with arXiv:1707.03292
Subjects: Logic (math.LO)

We consider the explicit fragment of the basic justification stit logic introduced in earlier publications. We define a Hilbert-style axiomatic system for this logic and show that this system is strongly complete relative to the intended semantics.

[100]  arXiv:1709.06898 [pdf, ps, other]
Title: Forbidden Subgraphs for Chorded Pancyclicity
Comments: 14 pages, 14 figures
Journal-ref: Discrete Mathematics, Volume 340, Issue 12, December 2017, Pages 2878-2888
Subjects: Combinatorics (math.CO)

We call a graph $G$ pancyclic if it contains at least one cycle of every possible length $m$, for $3\le m\le |V(G)|$. In this paper, we define a new property called chorded pancyclicity. We explore forbidden subgraphs in claw-free graphs sufficient to imply that the graph contains at least one chorded cycle of every possible length $4, 5, \ldots, |V(G)|$. In particular, certain paths and triangles with pendant paths are forbidden.

[101]  arXiv:1709.06899 [pdf, ps, other]
Title: The random pinning model with correlated disorder given by a renewal set
Authors: Dimitris Cheliotis (1), Yuki Chino, Julien Poisat (2) ((1) University of Athens, (2) CEREMADE)
Subjects: Probability (math.PR)

We investigate the effect of correlated disorder on the localization transition undergone by a renewal sequence with loop exponent $\alpha>0$, when the correlated sequence is given by another independent renewal set with loop exponent $\hat \alpha >0$. Using the renewal structure of the disorder sequence, we compute the annealed critical point and exponent. Then, using a smoothing inequality for the quenched free energy and second moment estimates for the quenched partition function, combined with decoupling inequalities, we prove that in the case $\hat \alpha > 2$ (summable correlations), disorder is irrelevant if $\alpha<1/2$ and relevant if $\alpha >1/2$, which extends the Harris criterion for independent disorder. The case $\hat \alpha \in (1,2)$ (non-summable correlations) remains largely open, but we are able to prove that disorder is relevant for $\alpha > 1/\hat \alpha$, a condition that is expected to be non-optimal. Predictions on the criterion for disorder relevance in this case are discussed. Finally, the case $\hat\alpha \in (0,1)$ is somewhat special but treated for completeness: in this case, disorder has no effect on the quenched free energy, but the annealed model exhibits a phase transition.

[102]  arXiv:1709.06900 [pdf, ps, other]
Title: On the arithmetic of polynomials with coefficients in Mordell-Weil type groups
Subjects: Number Theory (math.NT)

In this paper we prove Hasse local-global principle for polynomials with coefficients in Mordell-Weil type groups over number fields like S-units, abelian varieties with trivial ring of endomorphisms and odd algebraic K-theory groups.

[103]  arXiv:1709.06906 [pdf, other]
Title: A symplectic perspective on constrained eigenvalue problems
Comments: 22 pages, 1 figures, comments welcome!
Subjects: Spectral Theory (math.SP); Analysis of PDEs (math.AP)

The Maslov index is a powerful tool for computing spectra of selfadjoint, elliptic boundary value problems. This is done by counting intersections of a fixed Lagrangian subspace, which designates the boundary condition, with the set of Cauchy data for the differential operator. We apply this methodology to constrained eigenvalue problems, in which the operator is restricted to a (not necessarily invariant) subspace. The Maslov index is defined and used to compute the Morse index of the constrained operator. We then prove a constrained Morse index theorem, which says that the Morse index of the constrained problem equals the number of constrained conjugate points, counted with multiplicity, and give an application to the nonlinear Schr\"odinger equation.

[104]  arXiv:1709.06913 [pdf, other]
Title: Poitou-Tate duality for arithmetic schemes
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG)

We give a generalization of Poitou-Tate duality to schemes of finite type over rings of integers of global fields.

[105]  arXiv:1709.06923 [pdf, ps, other]
Title: Ordered algebraic structures and classification of semifields
Authors: Guillaume Tahar
Comments: 4 pages
Subjects: Algebraic Geometry (math.AG); Rings and Algebras (math.RA)

Semifields are semirings in which every nonzero element has a multiplicative inverse. A rough classification uses the characteristic of the semifield, that is the isomorphism type of the semifield generated by the two neutral elements. For every characteristic, we provide a structure theorem that reduces the classification of semifields to the classification of better-known algebraic structures. Every semifield of characteristic $p$ is actually a field. There is an equivalence between semifields of characteristic one and lattice-ordered groups. Strict semifields of characteristic zero are quotients of cancellative semifields and there is an equivalence between concellative strict semifields and a particular class of partially ordered rings.

[106]  arXiv:1709.06924 [pdf, other]
Title: Fast Spherical Centroidal Voronoi Mesh Generation: A Lloyd-preconditioned LBFGS Method in Parallel
Subjects: Numerical Analysis (math.NA)

Centroidal Voronoi tessellations (CVT)-based mesh generation have been a very effective technique for creating high-quality Voronoi meshes and their dual Delaunay triangulations, which often play a crucial role in climate simulations using finite volume schemes. In the next generation of climate modeling, the spacing scales change dramatically across the whole sphere surface and also require ultra-high resolution, thus efficient spherical CVT (SCVT) meshing algorithms become highly desired. In this paper, we first propose a Lloyd-preconditioned Limited-memory BFGS method for constructing SCVTs, which is also applicable to computation of CVTs of general domains. This method is then parallelized based overlapping domain decomposition, enabling excellent scalability on distributed systems. Combination of these two approaches gives us a fast and effective SCVT mesh generation method, as demonstrated by various numerical tests. The experimental results show that our method could cost one order of magnitude smaller computational times, compared with some popular existing methods in generating large-scale highly variable multi-resolution meshes, while providing significantly improved mesh quality.

[107]  arXiv:1709.06925 [pdf, ps, other]
Title: On the Free Surface Motion of Highly Subsonic Heat-conducting Inviscid Flows
Authors: Tao Luo, Huihui Zeng
Subjects: Analysis of PDEs (math.AP)

For a free surface problem of a highly subsonic heat-conducting inviscid flow, motivated by a geometric approach developed by Christodoulou and Lindblad in the study of the free surface problem of incompressible inviscid flows, the a priori estimates of Sobolev norms in 2-D and 3-D are proved under the Taylor sign condition by identifying a suitable higher order energy functional. The estimates for some geometric quantities such as the second fundamental form and the injectivity radius of the normal exponential map of the free surface are also given. The novelty in our analysis includes dealing with the strong coupling of large variation of temperature, heat-conduction, compressibility of fluids and the evolution of free surface, loss of symmetries of equations, and loss of derivatives in closing the argument which is a key feature compared with Christodoulou and Lindblad's work. The motivation of this paper is to contribute to the program of understanding the role played by the heat-conductivity to free surface motions of inviscid compressible flows and the behavior of such motions when the Mach number is small.

[108]  arXiv:1709.06929 [pdf, ps, other]
Title: An automorphic approach to Darmon points
Subjects: Number Theory (math.NT)

We give archimedean and non-archimedean constructions of Darmon points on modular abelian varieties attached to automorphic forms over arbitrary number fields and possibly non-trivial central character. An effort is made to present a unifying point of view, emphasizing the automorphic nature of the construction.

[109]  arXiv:1709.06931 [pdf, ps, other]
Title: Plus and minus logarithms and Amice transform
Comments: 9 pages
Subjects: Number Theory (math.NT)

We give a new description of Pollack's plus and minus $p$-adic logarithms $\log_p^\pm$ in terms of distributions. In particular, if $\mu_\pm$ denote the pre-images of $\log_p^\pm$ under the Amice transform, we give explicit formulae for the values $\mu_\pm(a+p^n\mathbb{Z}_p)$ for all $a\in \mathbb{Z}_p$ and all integers $n\ge1$. Our formulae imply that the distribution $\mu_-$ agrees with a distribution studied by Koblitz in 1977. Furthermore, we show that a similar description exists for Loeffler's two-variable analogues of these plus and minus logarithms.

[110]  arXiv:1709.06932 [pdf, ps, other]
Title: Betti numbers of small covers and their two-fold coverings
Comments: 6 pages
Subjects: Algebraic Topology (math.AT)

We point out a gap in the proof of the Davis--Januszkiewicz theorem on cohomology of small covers of simple polytopes, and give a correction to this proof. We use this theorem to compute explicitly the Betti numbers for a wide class of two-fold coverings over small covers. We describe a series of examples in this class and explain why this class turns out to be special in the context of the general problem of computing the modulo two Betti numbers of two-fold coverings over small covers.

[111]  arXiv:1709.06945 [pdf, ps, other]
Title: Classifying approximable algebras
Authors: Catriona Maclean
Subjects: Algebraic Geometry (math.AG)

Approximable algebras were defined by Chen in his proof of the Fujita theorem in the arithmetic context. These were shown to not be necessarily subalgebras of section rings of big line bundles in a previous prepreint of the author. Here, we show that whilst approximable algebras are not necessarily subalgebras of section rings of big line bundles, they are necessarily subalgebras of section rings of infinite sums of Weil divisors.

[112]  arXiv:1709.06949 [pdf, ps, other]
Title: Symmetric critical knots for O'Hara's energies
Comments: 30 pages
Subjects: Classical Analysis and ODEs (math.CA); Differential Geometry (math.DG); Geometric Topology (math.GT)

We prove the existence of symmetric critical torus knots for O'Hara's knot energy family $E_\alpha$, $\alpha\in (2,3)$ using Palais' classic principle of symmetric criticality. It turns out that in every torus knot class there are at least two smooth $E_\alpha$-critical knots, which supports experimental observations using numerical gradient flows.

[113]  arXiv:1709.06951 [pdf, ps, other]
Title: NOMA Assisted Wireless Caching: Strategies and Performance Analysis
Subjects: Information Theory (cs.IT)

This paper investigates the coexistence of two important enabling techniques for future wireless networks, non-orthogonal multiple-access (NOMA) and wireless caching, and we show that the use of NOMA ensures that the two caching phases, content pushing and content delivery, can be more effectively carried out, compared to the conventional orthogonal multiple-access (OMA) based case. Two NOMA caching strategies are developed, namely the push-then-delivery strategy and the push-and-delivery strategy. In the push-then-delivery strategy, the NOMA principle is applied in the content pushing and content delivery phases, respectively. The presented analytical framework demonstrates that the push-then-delivery strategy not only significantly improves the cache hit probability, but also considerably reduces the delivery outage probability, compared to the OMA strategy. The push-and-delivery strategy is motivated by the fact that some users' requests cannot be accommodated locally and the base station has to serve them directly.The key idea of the push-and-delivery strategy is to merge the content pushing and delivery phases, i.e., the base station pushes new content to local servers while simultaneously serving the users. We show that this strategy can be straightforwardly extended to device-to-device caching, and corresponding analytical results are developed to illustrate the superiority of this caching strategy.

[114]  arXiv:1709.06958 [pdf, other]
Title: Stimulus sensitivity of a spiking neural network model
Authors: Julien Chevallier (LJK)
Subjects: Probability (math.PR); Neurons and Cognition (q-bio.NC)

Some recent papers relate the criticality of complex systems to their maximal capacity of information processing. In the present paper, we consider high dimensional point processes, known as age-dependent Hawkes processes, which have been used to model spiking neural networks. Using mean-field approximation, the response of the network to a stimulus is computed and we provide a notion of stimulus sensitivity. It appears that the maximal sensitivity is achieved in the sub-critical regime, yet almost critical for a range of biologically relevant parameters.

[115]  arXiv:1709.06960 [pdf, other]
Title: The Devil is in the Details: Spectrum and Eigenvalue Distribution of the Discrete Preisach Memory Model
Subjects: Mathematical Physics (math-ph)

We consider the adjacency matrix associated with a graph that describes transitions between $2^{N}$ states of the discrete Preisach memory model. This matrix can also be associated with the last-in-first-out inventory management rule. We present an explicit solution for the spectrum by showing that the characteristic polynomial is the product of Chebyshev polynomials. The eigenvalue distribution (density of states) is explicitly calculated and is shown to approach a scaled Devil's staircase. The eigenvectors of the adjacency matrix are also expressed analytically.

[116]  arXiv:1709.06961 [pdf, ps, other]
Title: Iterated Stochastic Integrals in Infinite Dimensions - Approximation and Error Estimates
Subjects: Probability (math.PR); Numerical Analysis (math.NA)

Higher order numerical schemes for stochastic partial differential equations that do not possess commutative noise require the simulation of iterated stochastic integrals. In this work, we extend the algorithms derived by Kloeden, Platen, and Wright (1992) and by Wiktorsson (2001) for the approximation of two-times iterated stochastic integrals involved in numerical schemes for finite dimensional stochastic ordinary differential equations to an infinite dimensional setting. These methods clear the way for new types of approximation schemes for SPDEs without commutative noise. Precisely, we analyze two algorithms to approximate two-times iterated integrals with respect to an infinite dimensional $Q$-Wiener process in case of a trace class operator $Q$ given the increments of the $Q$-Wiener process. Error estimates in the mean-square sense are derived and discussed for both methods. In contrast to the finite dimensional setting, which is contained as a special case, the optimal approximation algorithm cannot be uniquely determined but is dependent on the covariance operator $Q$. This difference arises as the stochastic process is of infinite dimension.

[117]  arXiv:1709.06962 [pdf, ps, other]
Title: Dyadic Steenrod algebra and its applications
Subjects: Algebraic Topology (math.AT)

First, by inspiration of the results of Wood \cite{differential,problems}, but with the methods of non-commutative geometry and different approach, we extend the coefficients of the Steenrod squaring operations from the filed $\mathbb{F}_2$ to the dyadic integers $\mathbb{Z}_2$ and call the resulted operations the dyadic Steenrod squares, denoted by $Jq^k$. The derivation-like operations $Jq^k$ generate a graded algebra, called the dyadic Steenrod algebra, denoted by $\mathcal{J}_2$ acting on the polynomials $\mathbb{Z}_2[\xi_1, \dots, \xi_n]$. Being $\mathcal{J}_2$ an Ore domain, enable us to localize $\mathcal{J}_2$ which leads to the appearance of the integration-like operations $Jq^{-k}$ satisfying the $Jq^{-k}Jq^k=1=Jq^kJq^{-k}$. These operations are enough to exhibit a kind of differential equation, the dyadic Steenrod ordinary differential equation. Then we prove that the completion of $\mathbb{Z}_2[\xi_1, \dots, \xi_n]$ in the linear transformation norm coincides with a certain Tate algebra. Therefore, the rigid analytic geometry is closely related to the dyadic Steenrod algebra. Finally, we define the Adem norm $\| \ \|_A$ in which the completion of $\mathbb{Z}_2[\xi_1, \dots, \xi_n]$ is $\mathbb{Z}_2\llbracket\xi_1,\dots,\xi_n\rrbracket$, the $n$-variable formal power series. We surprisingly prove that an element $f \in \mathbb{Z}_2\llbracket \xi_1,\dots,\xi_n\rrbracket$ is hit if and only if $\|f\|_A<1$. This suggests new techniques for the traditional Peterson hit problem in finding the bases for the cohit modules.

[118]  arXiv:1709.06966 [pdf, ps, other]
Title: Stochastic Burgers' Equation on the Real Line: Regularity and Moment Estimates
Comments: 29 pages
Subjects: Probability (math.PR)

In this project we investigate the stochastic Burgers' equation with multiplicative space-time white noise on an unbounded spatial domain. We give a random field solution to this equation by defining a process via a kind of Feynman-Kac representation which solves a stochastic partial differential equation such that its Hopf-Cole transformation solves Burgers' equation. Finally, we obtain H\"older regularity and moment estimates for the solution to Burgers' equation.

[119]  arXiv:1709.06969 [pdf, ps, other]
Title: Graded chain conditions and Leavitt path algebras of no-exit graphs
Authors: Lia Vas
Subjects: Rings and Algebras (math.RA)

We obtain a complete structural characterization of Cohn-Leavitt algebras over no-exit objects as graded involutive algebras. Corollaries of this result include graph-theoretic conditions characterizing when a Leavitt path algebra is a directed union of (graded) matricial algebras over the underlying field and over the algebra of Laurent polynomials and when the monoid of isomorphism classes of finitely generated projective modules is atomic and cancellative.
We introduce the non-unital generalizations of graded analogues of noetherian and artinian rings, graded locally noetherian and graded locally artinian rings, and characterize graded locally noetherian and graded locally artinian Leavitt path algebras without any restriction on the cardinality of the graph. As a consequence, we relax the assumptions of the Abrams-Aranda-Perera-Siles characterization of locally noetherian and locally artinian Leavitt path algebras.

[120]  arXiv:1709.06971 [pdf, ps, other]
Title: New Examples of Dimension Zero Categories
Authors: Andrew Gitlin
Subjects: Representation Theory (math.RT); Combinatorics (math.CO)

We say that a category $\mathscr{D}$ is dimension zero over a field $F$ provided that every finitely generated representation of $\mathscr{D}$ over $F$ is finite length. We show that $\textrm{Rel}(R)$, a category that arises naturally from a finite idempotent semiring $R$, is dimension zero over any infinite field. One special case of this result is that $\textrm{Rel}$, the category of finite sets with relations, is dimension zero over any infinite field.

[121]  arXiv:1709.06974 [pdf, other]
Title: Restrictions of Heterotic $G_2$ Structures and Instanton Connections
Comments: To appear in the proceedings for Nigel Hitchin's 70th birthday conference. 17 pages
Subjects: Differential Geometry (math.DG); High Energy Physics - Theory (hep-th)

This note revisits recent results regarding the geometry and moduli of solutions of the heterotic string on manifolds $Y$ with a $G_2$ structure. In particular, such heterotic $G_2$ systems can be rephrased in terms of a differential $\check {\cal D}$ acting on a complex $\check\Omega^*(Y , {\cal Q})$, where ${\cal Q}=T^*Y\oplus{\rm End}(TY)\oplus{\rm End}(V)$ and $\check {\cal D}$ is an appropriate projection of an exterior covariant derivative ${\cal D}$ which satisfies an instanton condition. The infinitesimal moduli are further parametrised by the first cohomology $H^1_{\check {\cal D}}(Y,{\cal Q})$. We proceed to restrict this system to manifolds $X$ with an $SU(3)$ structure corresponding to supersymmetric compactifications to four dimensional Minkowski space, often referred to as Strominger--Hull solutions. In doing so, we derive a new result: the Strominger-Hull system is equivalent to a particular holomorphic Yang-Mills covariant derivative on ${\cal Q}\vert_X=T^*X\oplus{\rm End}(TX)\oplus{\rm End}(V)$.

[122]  arXiv:1709.06979 [pdf, other]
Title: Characterization and enumeration of 3-regular permutation graphs
Comments: 12 pages, 12 figures
Subjects: Combinatorics (math.CO)

A permutation graph is a graph that can be derived from a permutation, where the vertices correspond to letters of the permutation, and the edges represent inversions. We provide a construction to show that there are infinitely many connected $r$-regular permutation graphs for $r \geq 3$. We prove that all $3$-regular permutation graphs arise from a similar construction. Finally, we enumerate all $3$-regular permutation graphs on $n$ vertices.

[123]  arXiv:1709.06980 [pdf, ps, other]
Title: Oscillating solutions for prescribed mean curvature equations: Euclidean and Lorentz-Minkowski cases
Authors: Alessio Pomponio
Comments: 10 pages
Subjects: Analysis of PDEs (math.AP)

This paper deals with the prescribed mean curvature equations both in the Euclidean case and in the Lorentz-Minkowski case in presence of a nonlinearity $g$ such that $g'(0)>0$. We show the existence of oscillating solutions, namely with an unbounded sequence of zeros, which decay to zero at infinity with their derivatives.

[124]  arXiv:1709.06981 [pdf, ps, other]
Title: Entropy Anomaly in Langevin-Kramers Dynamics with Matrix Drag and Diffusion
Authors: Jeremiah Birrell
Comments: 27 pages
Subjects: Mathematical Physics (math-ph)

We investigate entropy production in the small mass (or overdamped) limit of Langevin-Kramers dynamics. Our results apply to systems with magnetic field as well as matrix valued drag and diffusion coefficients that satisfy a version of the fluctuation dissipation relation with state dependent temperature. In particular, we generalize the anomalous entropy production results of [1].
As a part of this work, we develop a theory for homogenizing a class of integral processes involving the position and scaled velocity variables. This allows us to rigorously prove convergence of the entropy produced in the environment, including a bound on the convergence rate.

[125]  arXiv:1709.06982 [pdf, ps, other]
Title: On the number of generators of a separable algebra over a finite field
Comments: 12 pages
Subjects: Number Theory (math.NT); Rings and Algebras (math.RA)

Let $F$ be a field and let $E$ be an \'etale algebra over $F$, that is, a finite product of finite separable field extensions $E = F_1 \times \dots \times F_r$. The classical primitive element theorem asserts that if $r = 1$, then $E$ is generated by one element as an $F$-algebra. The same is true for any $r \geqslant 1$, provided that $F$ is infinite. However, if $F$ is a finite field and $r \geqslant 2$, the primitive element theorem fails in general. In this paper we give a formula for the minimal number of generators of $E$ when $F$ is finite. We also obtain upper and lower bounds on the number of generators of a (not necessarily commutative) separable algebra over a finite field.

[126]  arXiv:1709.06985 [pdf, other]
Title: Error-tolerant Multisecant Method for Nonlinearly Constrained Optimization
Subjects: Optimization and Control (math.OC)

We present a derivative-based algorithm for nonlinearly constrained optimization problems that is tolerant of inaccuracies in the data. The algorithm solves a semi-smooth set of nonlinear equations that are equivalent to the first-order optimality conditions, and it is matrix-free in the sense that it does not require the explicit Lagrangian Hessian or Jacobian of the constraints. The solution method is quasi-Newton, but rather than approximating only the Hessian or constraint Jacobian, the Jacobian of the entire nonlinear set of equations is approximated using a multisecant method. We show how preconditioning can be incorporated into the multisecant update in order to improve the performance of the method. For nonconvex problems, we propose a simple modification of the secant conditions to regularize the Hessian. Numerical experiments suggest that the algorithm is a promising alternative to conventional gradient-based algorithms, particularly when errors are present in the data.

[127]  arXiv:1709.06986 [pdf, ps, other]
Title: Equilibrium-Independent Dissipativity with Quadratic Supply Rates
Subjects: Optimization and Control (math.OC)

Equilibrium-independent dissipativity (EID) is a recently introduced system property which requires a system to be dissipative with respect to any forced equilibrium configuration. This paper is a detailed examination of EID with quadratic supply rates for a common class of nonlinear control-affine systems. First, we provide a characterization of such EID systems in the spirit of the Hill-Moylan nonlinear KYP lemma, where the usual stability condition is replaced by an incremental stability condition. Based on this characterization, we state results concerning internal stability, feedback stability, and absolute stability of EID systems. Finally, we study the discrete-time case, providing the relevant definitions and analogous KYP-type results. Results for both continuous-time and discrete-time systems are illustrated through examples on physical systems and convex optimization algorithms.

[128]  arXiv:1709.06989 [pdf, ps, other]
Title: Embedded eigenvalues of generalized Schrödinger operators
Comments: 18 pages; comments welcome
Subjects: Mathematical Physics (math-ph); Spectral Theory (math.SP)

We provide examples of operators $T(D)+V$ with decaying potentials that have embedded eigenvalues. The decay of the potential depends on the curvature of the Fermi surfaces of constant kinetic energy $T$. We make the connection to counterexamples in Fourier restriction theory.

Cross-lists for Thu, 21 Sep 17

[129]  arXiv:1709.03911 (cross-list from math-ph) [pdf, ps, other]
Title: An Evolution Equation Approach to the Klein-Gordon Operator on Curved Spacetime
Comments: 40 pages
Subjects: Mathematical Physics (math-ph); Analysis of PDEs (math.AP); Functional Analysis (math.FA)

We develop a theory of the Klein-Gordon equation on curved spacetimes. Our main tool is the method of (non-autonomous) evolution equations on Hilbert spaces. This approach allows us to treat low regularity of the metric, of the electromagnetic potential and of the scalar potential. Our main goal is a construction of various kinds of propagators needed in quantum field theory.

[130]  arXiv:1709.06588 (cross-list from stat.ME) [pdf, ps, other]
Title: Orthogonal Series Density Estimation for Complex Surveys
Comments: 16 pages, 1 figure
Subjects: Methodology (stat.ME); Statistics Theory (math.ST)

We propose an orthogonal series density estimator for complex surveys, where samples are neither independent nor identically distributed. The proposed estimator is proved to be design-unbiased and asymptotically design-consistent. The asymptotic normality is proved under both design and combined spaces. Two data driven estimators are proposed and studied via both simulations and a real data analysis.

[131]  arXiv:1709.06602 (cross-list from cond-mat.stat-mech) [pdf, other]
Title: The bilinear-biquadratic model on the complete graph
Subjects: Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph); Quantum Physics (quant-ph)

We study the spin-1 bilinear-biquadratic model on the complete graph of N sites, i.e., when each spin is interacting with every other spin with the same strength. Because of its complete permutation invariance, this Hamiltonian can be rewritten as the linear combination of the quadratic Casimir operators of su(3) and su(2). Using group representation theory, we explicitly diagonalize the Hamiltonian and map out the ground-state phase diagram of the model. Furthermore, the complete energy spectrum, with degeneracies, is obtained analytically for any number of sites.

[132]  arXiv:1709.06603 (cross-list from physics.soc-ph) [pdf, ps, other]
Title: On the Interplay between Behavioral Dynamics and Social Interactions in Human Crowds
Subjects: Physics and Society (physics.soc-ph); Dynamical Systems (math.DS)

This paper provides an overview and critical analysis on the modeling and applications of the dynamics of human crowds, where social interactions can have an important influence on the behavioral dynamics of the crowd viewed as a living, hence complex, system. The analysis looks at real physical situations where safety problems might arise in some specific circumstances. The approach is based on the methods of the kinetic theory of active particles. Computational applications enlighten the role of human behaviors.

[133]  arXiv:1709.06650 (cross-list from cs.DM) [pdf, ps, other]
Title: On Graphs and the Gotsman-Linial Conjecture for d = 2
Comments: 15 pages
Subjects: Discrete Mathematics (cs.DM); Combinatorics (math.CO)

We give an infinite class of counterexamples to the Gotsman-Linial conjecture when d = 2. On the other hand, we establish an asymptotic form of the conjecture for quadratic threshold functions whose non-zero quadratic terms define a graph with either low fractional chromatic number or few edges. Our techniques are elementary and our exposition is self-contained, if you're into that.

[134]  arXiv:1709.06653 (cross-list from cond-mat.stat-mech) [pdf, other]
Title: Unique Information via Dependency Constraints
Comments: 11 pages, 6 figures, 3 appendices; this http URL
Subjects: Statistical Mechanics (cond-mat.stat-mech); Information Theory (cs.IT); Learning (cs.LG); Statistics Theory (math.ST)

The partial information decomposition is perhaps the leading proposal for resolving shared information in a joint random variable into redundant, synergistic, and unique constituents. Unfortunately, the framework has been hindered by a lack of a generally agreed-upon, multivariate method of quantifying the constituents. Here, we take a step toward rectifying this by developing a decomposition based on a new method that quantifies unique information. The result is the first measure which satisfies the core axioms of the framework while also not treating identical but independent channels as redundant. This marks a key step forward in the practical application of the partial information decomposition.

[135]  arXiv:1709.06711 (cross-list from quant-ph) [pdf, ps, other]
Title: Classical states, quantum field measurement
Authors: Peter Morgan
Comments: 4 pages. For an alternative way to think about fermion fields. Comments very welcome
Subjects: Quantum Physics (quant-ph); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)

Manifestly Lorentz covariant representations of the algebras of the quantized electromagnetic field and of the observables of the quantized Dirac spinor field are constructed that act on Hilbert spaces that are generated using classical random fields acting on a vacuum state, allowing a comparatively classical interpretation of the states of the theory.

[136]  arXiv:1709.06712 (cross-list from gr-qc) [pdf, other]
Title: Dynamical deformation of 2+1 dimensional double torus universe
Authors: Masaru Siino
Comments: 19pages, 9 figures
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)

In (2+1)-dimensional pure gravity with cosmological constant, the dynamics of double torus universe with pinching parameter is investigated. Each mode of affine stretching deformation is illustrated in the context of horizontal foliation along the holomorphic quadratic differential. The formulation of the Einstein Hilbert action for the parameters of the affine stretching is developed. Then the dynamics along one holomorphic quadratic differential will be solved concretely.

[137]  arXiv:1709.06766 (cross-list from hep-th) [pdf, other]
Title: On actions for (entangling) surfaces and DCFTs
Comments: v1: 71pp, 1fig
Subjects: High Energy Physics - Theory (hep-th); Soft Condensed Matter (cond-mat.soft); General Relativity and Quantum Cosmology (gr-qc); Mathematical Physics (math-ph)

The dynamics of surfaces and interfaces describe many physical systems, including fluid membranes, entanglement entropy and the coupling of defects to quantum field theories. Based on the formulation of submanifold calculus developed by Carter, we introduce a new variational principle for (entangling) surfaces. This principle captures all diffeomorphism constraints on surface/interface actions and their associated spacetime stress tensor. The different couplings to the geometric tensors appearing in the surface action are interpreted in terms of linear response coefficients within elasticity theory. An example of a surface action with edges at the two-derivative level is studied, including both the parity-even and parity-odd sectors. Its conformally invariant counterpart restricts the type of conformal anomalies that can appear in two-dimensional submanifolds with boundaries. Analogously to hydrodynamics, it is shown that classification methods can be used to constrain the stress tensor of (entangling) surfaces at a given order in derivatives. This analysis reveals a purely geometric parity-odd contribution to the Young modulus of a thin elastic membrane. Extending this novel variational principle to BCFTs and DCFTs in curved spacetimes allows to obtain the Ward identities for diffeomorphism and Weyl transformations. In this context, we provide a formal derivation of the contact terms in the stress tensor and of the displacement operator for a broad class of actions.

[138]  arXiv:1709.06793 (cross-list from cs.NA) [pdf, other]
Title: A stencil scaling approach for accelerating matrix-free finite element implementations
Subjects: Numerical Analysis (cs.NA); Computational Engineering, Finance, and Science (cs.CE); Numerical Analysis (math.NA)

We present a novel approach to fast on-the-fly low order finite element assembly for scalar elliptic partial differential equations of Darcy type with variable coefficients optimized for matrix-free implementations. Our approach introduces a new operator that is obtained by appropriately scaling the reference stiffness matrix from the constant coefficient case. Assuming sufficient regularity, an a priori analysis shows that solutions obtained by this approach are unique and have asymptotically optimal order convergence in the $H^1$- and the $L^2$-norm on hierarchical hybrid grids. For the pre-asymptotic regime, we present a local modification that guarantees uniform ellipticity of the operator. Cost considerations show that our novel approach requires roughly one third of the floating-point operations compared to a classical finite element assembly scheme employing nodal integration. Our theoretical considerations are illustrated by numerical tests that confirm the expectations with respect to accuracy and run-time. A large scale application with more than a hundred billion ($1.6\cdot10^{11}$) degrees of freedom executed on 14,310 compute cores demonstrates the efficiency of the new scaling approach.

[139]  arXiv:1709.06809 (cross-list from cs.SY) [pdf, ps, other]
Title: Block-Diagonal Solutions to Lyapunov Inequalities and Generalisations of Diagonal Dominance
Comments: 6 pages, to appear in Proceedings of the Conference on Decision and Control 2017
Subjects: Systems and Control (cs.SY); Optimization and Control (math.OC)

Diagonally dominant matrices have many applications in systems and control theory. Linear dynamical systems with scaled diagonally dominant drift matrices, which include stable positive systems, allow for scalable stability analysis. For example, it is known that Lyapunov inequalities for this class of systems admit diagonal solutions. In this paper, we present an extension of scaled diagonally dominance to block partitioned matrices. We show that our definition describes matrices admitting block-diagonal solutions to Lyapunov inequalities and that these solutions can be computed using linear algebraic tools. We also show how in some cases the Lyapunov inequalities can be decoupled into a set of lower dimensional linear matrix inequalities, thus leading to improved scalability. We conclude by illustrating some advantages and limitations of our results with numerical examples.

[140]  arXiv:1709.06855 (cross-list from stat.ME) [pdf, ps, other]
Title: Specification tests in semiparametric transformation models
Subjects: Methodology (stat.ME); Statistics Theory (math.ST)

We consider semiparametric transformation models, where after pre-estimation of a parametric transformation of the response the data are modeled by means of nonparametric regression. We suggest subsequent procedures for testing lack-of-fit of the regression function and for significance of covariables, which -- in contrast to procedures from the literature -- are asymptotically not influenced by the pre-estimation of the transformation. The test statistics are asymptotically pivotal, have the same asymptotic distribution as in regression models without transformation, and standard wild bootstrap can be applied to the transformed data to conduct the tests.

[141]  arXiv:1709.06887 (cross-list from cs.SI) [pdf, other]
Title: A modularity based spectral method for simultaneous community and anti-community detection
Subjects: Social and Information Networks (cs.SI); Numerical Analysis (math.NA); Physics and Society (physics.soc-ph)

In a graph or complex network, communities and anti-communities are node sets whose modularity attains extremely large values, positive and negative, respectively. We consider the simultaneous detection of communities and anti-communities, by looking at spectral methods based on various matrix-based definitions of the modularity of a vertex set. Invariant subspaces associated to extreme eigenvalues of these matrices provide indications on the presence of both kinds of modular structure in the network. The localization of the relevant invariant subspaces can be estimated by looking at particular matrix angles based on Frobenius inner products.

[142]  arXiv:1709.06910 (cross-list from cs.GT) [pdf, other]
Title: Linear Quadratic Games with Costly Measurements
Comments: Accepted to IEEE Conference on Decision and Control (CDC) 2017
Subjects: Computer Science and Game Theory (cs.GT); Systems and Control (cs.SY); Optimization and Control (math.OC)

In this work we consider a stochastic linear quadratic two-player game. The state measurements are observed through a switched noiseless communication link. Each player incurs a finite cost every time the link is established to get measurements. Along with the usual control action, each player is equipped with a switching action to control the communication link. The measurements help to improve the estimate and hence reduce the quadratic cost but at the same time the cost is increased due to switching. We study the subgame perfect equilibrium control and switching strategies for the players. We show that the problem can be solved in a two-step process by solving two dynamic programming problems. The first step corresponds to solving a dynamic programming for the control strategy and the second step solves another dynamic programming for the switching strategy

[143]  arXiv:1709.06928 (cross-list from cs.NI) [pdf, other]
Title: Level-Triggered Harvest-then-Consume Protocol with Two Bits or Less Energy State Information
Subjects: Networking and Internet Architecture (cs.NI); Information Theory (cs.IT)

We propose a variation of harvest-then-consume protocol with low complexity where the harvest and consume phases change when the battery energy level reaches certain thresholds. The proposed protocol allows us to control the possible energy outage during consumption phase. Assuming that the battery is perfect and that the energy arrival is a renewal process, we analyze the duty cycle and the operating cycle speed of the protocol. The proposed protocol also allows for limited battery energy state information. The cases when the system has two-bits, one-bit, and zero-bit of battery energy state information are studied in detail. Numerical simulations verify the obtained formulas.

[144]  arXiv:1709.06964 (cross-list from gr-qc) [pdf, ps, other]
Title: Rotating and spatially twisting Locally Rotationally Symmetric Spacetimes in f(R)-Gravity: a No-Go theorem
Comments: 6 pages
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)

Recently, in a series of papers, we established the existence and found a general solution for the simultaneously rotating and twisting locally rotationally symmetric spacetimes in general relativity, which can model inhomogeneous and dynamic astrophysical bodies. However, these spacetimes necessarily require imperfect fluids with entropy flux. Therefore, in this paper, we investigate the existence of these spacetimes in generic f(R)-gravity models, where the entropy flux is generated purely by higher order curvature effects, while the standard matter still remains a perfect fluid. However, we transparently demonstrate here, that the symmetries of these spacetimes force the theory to be general relativity. This is a novel study that shows how the geometrical properties of a spacetime can be used to restrict the theories of gravity.

[145]  arXiv:1709.06973 (cross-list from physics.chem-ph) [pdf]
Title: Dynamics on the Double Morse Potential: A Paradigm for Roaming Reactions with no Saddle Points
Comments: 22 pages, 31 figures
Subjects: Chemical Physics (physics.chem-ph); Dynamical Systems (math.DS); Chaotic Dynamics (nlin.CD)

In this paper we analyze a two degree of freedom Hamiltonian system constructed from two planar Morse potentials. The resulting potential energy surface has two potential wells surrounded by an unbounded flat region containing no critical points. In addition, the model has an index one saddle between the potential wells. We study the dynamical mechanisms underlying transport between the two potential wells, with emphasis on the role of the flat region surrounding the wells. The model allows us to probe many of the features of the roaming mechanism whose reaction dynamics are of current interest in the chemistry community.

Replacements for Thu, 21 Sep 17

[146]  arXiv:0903.4952 (replaced) [pdf, ps, other]
Title: Concentration in Lotka-Volterra parabolic or integral equations: a general convergence result
Authors: Guy Barles (1), Sepideh Mirrahimi (2), Benoît Perthame (2) ((1) LMPT, (2) LJLL)
Journal-ref: Methods and Applications of Analysis, 2009, 16 (3), pp.321-340
Subjects: Analysis of PDEs (math.AP)
[147]  arXiv:1212.3604 (replaced) [pdf, other]
Title: Geometric study of Gardner equation
Subjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph); Differential Geometry (math.DG)
[148]  arXiv:1304.6053 (replaced) [pdf, ps, other]
Title: Introduction to high dimensional knots
Authors: Eiji Ogasa
Comments: 111 pages, many figures
Subjects: Geometric Topology (math.GT)
[149]  arXiv:1405.2752 (replaced) [pdf, ps, other]
Title: Tame Class Field Theory for Singular Varieties over Finite Fields
Comments: some typos corrected, to appear in Journal EMS
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG)
[150]  arXiv:1407.5025 (replaced) [pdf, ps, other]
Title: A cohomological interpretation of derivations on graded algebras
Comments: 19 pages
Subjects: Algebraic Geometry (math.AG)
[151]  arXiv:1502.03277 (replaced) [pdf, ps, other]
Title: Towards $A + B$ theory in conifold transitions for Calabi-Yau threefolds
Comments: 47 pages, references updated. To appear in J. Diff. Geometry
Subjects: Algebraic Geometry (math.AG)
[152]  arXiv:1506.06406 (replaced) [pdf, ps, other]
Title: Rational exponents in extremal graph theory
Comments: 11 pages
Subjects: Combinatorics (math.CO)
[153]  arXiv:1507.04536 (replaced) [pdf, other]
Title: A characterization of some families of Cohen--Macaulay, Gorenstein and/or Buchsbaum rings
Subjects: Commutative Algebra (math.AC)
[154]  arXiv:1507.05690 (replaced) [pdf, ps, other]
Title: A non-local Random Walk on the Hypercube
Authors: Evita Nestoridi
Comments: 17 pages, accepted for publication by the Applied Probability Trust in Advances in Applied Probability 49.4 (December 2017)
Subjects: Probability (math.PR); Combinatorics (math.CO)
[155]  arXiv:1507.06243 (replaced) [pdf, other]
Title: A Smooth Primal-Dual Optimization Framework for Nonsmooth Composite Convex Minimization
Comments: 35 pages, accepted for publication on SIAM J. Optimization. Tech. Report, Oct. 2015 (last update Sept. 2016)
Subjects: Optimization and Control (math.OC)
[156]  arXiv:1507.07132 (replaced) [pdf, ps, other]
Title: Inhomogeneous random graphs, isolated vertices, and Poisson approximation
Comments: 31 pages
Subjects: Probability (math.PR)
[157]  arXiv:1512.01457 (replaced) [pdf, ps, other]
Title: Beyond Abstract Elementary Classes: On The Model Theory of Geometric Lattices
Subjects: Logic (math.LO)
[158]  arXiv:1512.04296 (replaced) [pdf, ps, other]
Title: Expression asymptotique des valeurs propres d'une matrice de Toeplitz à symbole réel
Authors: Philippe Rambour
Comments: in French
Subjects: Functional Analysis (math.FA)
[159]  arXiv:1601.00581 (replaced) [pdf, ps, other]
Title: Triple crystal action in Fock spaces
Authors: Thomas Gerber
Comments: Version 2: Proof of Lemma 5.5 improved, Section 6 simplified and additional minor changes. Version 3: Section 4 rewritten (including simpler proof of Lemma 4.7 and Theorem 4.8), Theorem 6.26 replaced by Corollary 6.25, notation for "level-rank" dual objects modified, Section 7.1 slightly rewritten
Subjects: Representation Theory (math.RT); Combinatorics (math.CO)
[160]  arXiv:1602.01026 (replaced) [pdf, other]
Title: Resolution of the piecewise smooth visible-invisible two-fold singularity in $\mathbb{R}^3$ using regularization and blowup
Comments: The results are entirely unchanged, but the presentation is radically different. We now focus attention on the regularization function phi(s) = 2/pi arctan(s)
Subjects: Dynamical Systems (math.DS)
[161]  arXiv:1602.05082 (replaced) [pdf, ps, other]
Title: Homotopy linear algebra
Comments: 32 pages. This paper is one of six papers that formerly constituted the long manuscript arXiv:1404.3202. v2: slight notation changes and expository improvements. Final version, to appear in Proc Royal Soc. Edinburgh A
Subjects: Category Theory (math.CT); Algebraic Topology (math.AT)
[162]  arXiv:1603.01326 (replaced) [pdf, ps, other]
Title: A generalization of intertwining operators for vertex operator algebras
Authors: Kenichiro Tanabe
Comments: 33 pages, typos corrected
Journal-ref: J. Algebra 491 (2017), 372--401
Subjects: Quantum Algebra (math.QA)
[163]  arXiv:1603.07248 (replaced) [pdf, ps, other]
Title: Flat vector bundles and open coverings
Comments: 14 pages. Title changed. An error in the previous version was found. The current result counts the Euler number of a flat vector bundle in terms of vertices of transversal open coverings. The Chern conjecture remains open
Subjects: Differential Geometry (math.DG); Algebraic Topology (math.AT)
[164]  arXiv:1604.07151 (replaced) [pdf, ps, other]
Title: Achievable Moderate Deviations Asymptotics for Streaming Compression of Correlated Sources
Comments: 31 pages, 6 figures, under revision with IEEE Transactions on Information Theory; short version presented ISIT 2017
Subjects: Information Theory (cs.IT)
[165]  arXiv:1606.02343 (replaced) [pdf, ps, other]
Title: Geometric Analysis on the Diederich-Fornæss Index
Comments: Corrections on names of authors in references
Subjects: Complex Variables (math.CV); Differential Geometry (math.DG)
[166]  arXiv:1607.00370 (replaced) [pdf, ps, other]
Title: Parabolic subalgebras, parabolic buildings and parabolic projection
Comments: 26 pages, v2 minor clarifications
Subjects: Representation Theory (math.RT); Algebraic Geometry (math.AG); Differential Geometry (math.DG); Group Theory (math.GR)
[167]  arXiv:1607.03012 (replaced) [pdf, other]
Title: Motivic Realizations of Singularity Categories and Vanishing Cycles
Comments: Current version contains clarifications and corrections requested by referee. Submitted
Subjects: Algebraic Geometry (math.AG); K-Theory and Homology (math.KT)
[168]  arXiv:1607.06870 (replaced) [pdf, ps, other]
Title: The weighted Fourier inequality, polarity, and reverse Hölder inequality
Authors: Ryan Berndt
Comments: many improvement to previous versions
Subjects: Classical Analysis and ODEs (math.CA)
[169]  arXiv:1608.01630 (replaced) [pdf, ps, other]
Title: Sharp local boundedness and maximum principle in the infinitely degenerate regime via DeGiorgi iteration
Comments: 104 pages. A mistake in the proof of local boundedness fixed. All of the background material from arXiv:1506.09203v5 added and refined, making this paper a self-contained manuscript
Subjects: Classical Analysis and ODEs (math.CA)
[170]  arXiv:1608.03522 (replaced) [pdf, ps, other]
Title: On (a,b) Pairs in Random Fibonacci Sequences
Subjects: Number Theory (math.NT); Combinatorics (math.CO)
[171]  arXiv:1608.07149 (replaced) [pdf, ps, other]
Title: Time inhomogeneous Stochastic Differential Equations involving the local time of the unknown process, and associated parabolic operators
Authors: Pierre Etoré (1), Miguel Martinez (2) ((1) IPS, (2) LAMA)
Subjects: Probability (math.PR)
[172]  arXiv:1608.07165 (replaced) [pdf]
Title: Lots of Aperiodic Sets of Tiles
Subjects: Combinatorics (math.CO)
[173]  arXiv:1609.02413 (replaced) [pdf, ps, other]
Title: Macroscopic evolution of mechanical and thermal energy in a harmonic chain with random flip of velocities
Subjects: Probability (math.PR); Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph)
[174]  arXiv:1609.08040 (replaced) [pdf, other]
Title: Dimension reduction for the micromagnetic energy functional on curved thin films
Subjects: Analysis of PDEs (math.AP); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Materials Science (cond-mat.mtrl-sci); Mathematical Physics (math-ph)
[175]  arXiv:1610.06120 (replaced) [pdf, ps, other]
Title: Mean values of the Barnes double zeta-function
Authors: Takashi Miyagawa
Comments: 14 pages
Subjects: Number Theory (math.NT)
[176]  arXiv:1610.07546 (replaced) [pdf, ps, other]
Title: Cluster characters
Comments: 22 pages. v2: Added references, section 3.1.2, and minor corrections. v3: minor corrections
Subjects: Representation Theory (math.RT)
[177]  arXiv:1611.00515 (replaced) [pdf, ps, other]
Title: A Central Limit Theorem for Fleming-Viot Particle Systems with Soft Killing
Subjects: Probability (math.PR)
[178]  arXiv:1611.01051 (replaced) [pdf, other]
Title: Solving Reachability Problems by a Scalable Constrained Optimization Method
Subjects: Optimization and Control (math.OC)
[179]  arXiv:1611.01369 (replaced) [pdf, ps, other]
Title: Asymptotic Theory of a Bayesian Non-Marginal Multiple Testing Procedure and Comparison With Existing Methods
Comments: A significantly updated version
Subjects: Statistics Theory (math.ST)
[180]  arXiv:1611.06303 (replaced) [pdf, ps, other]
Title: Hilbert's Proof of His Irreducibility Theorem
Comments: 18 pages. Expanded article 3 to include reference to Gauss' polynomial lemma. Several additional changes to clarify key points in Hilbert's motivation for the formulation of his Cube Lemma. Many improvements. Accepted for publication in the American Mathematical Monthly
Subjects: History and Overview (math.HO)
[181]  arXiv:1611.06730 (replaced) [pdf, other]
Title: On the convergence of gradient-like flows with noisy gradient input
Comments: 36 pages, 5 figures; revised proof structure, added numerical case study in Section 5
Subjects: Optimization and Control (math.OC); Learning (cs.LG); Dynamical Systems (math.DS)
[182]  arXiv:1612.04533 (replaced) [pdf, ps, other]
Title: Some quasilinear elliptic equations involving multiple $p$-Laplacians
Comments: 18 pages, some minor revisions
Subjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph)
[183]  arXiv:1612.06332 (replaced) [pdf, other]
Title: On Dantzig figures from graded lexicographic orders
Comments: 27 pages, 3 figures
Subjects: Combinatorics (math.CO); Optimization and Control (math.OC)
[184]  arXiv:1612.07052 (replaced) [pdf, ps, other]
Title: An isoperimetric inequality in the plane with a log-convex density
Authors: I. McGillivray
Subjects: Differential Geometry (math.DG)
[185]  arXiv:1612.07647 (replaced) [pdf, ps, other]
Title: Stochastic invariance of closed sets for jump-diffusions with non-Lipschitz coefficients
Authors: Eduardo Abi Jaber (CEREMADE)
Subjects: Probability (math.PR)
[186]  arXiv:1612.07717 (replaced) [pdf, ps, other]
Title: Multilevel Monte Carlo and Improved Timestepping Methods in Atmospheric Dispersion Modelling
Comments: 30 pages, 13 figures, 3 tables, revised version, submitted to Journal of Computational Physics
Subjects: Numerical Analysis (math.NA); Atmospheric and Oceanic Physics (physics.ao-ph); Fluid Dynamics (physics.flu-dyn)
[187]  arXiv:1612.09400 (replaced) [pdf, ps, other]
Title: Inhomogeneous supersymmetric bilinear forms
Comments: 13 pages
Subjects: Representation Theory (math.RT)
[188]  arXiv:1612.09500 (replaced) [pdf]
Title: Paving the Way to Smart Micro Energy Internet: Concepts, Design Principles, and Engineering Practices
Comments: 11 pages, 12 figures, journal
Subjects: Optimization and Control (math.OC); Networking and Internet Architecture (cs.NI)
[189]  arXiv:1701.00293 (replaced) [pdf, ps, other]
Title: The Diederich-Fornæss index I: for domains of non-trivial index
Authors: Bingyuan Liu
Comments: Corrections on names of authors in references
Subjects: Complex Variables (math.CV); Differential Geometry (math.DG)
[190]  arXiv:1701.02689 (replaced) [pdf, ps, other]
Title: Scattering above energy norm of a focusing size-dependent log energy-supercritical Schrodinger equation with radial data below ground state
Authors: Tristan Roy
Comments: 18 pages. Update
Subjects: Analysis of PDEs (math.AP)
[191]  arXiv:1701.04963 (replaced) [pdf, ps, other]
Title: On the Existence of Tableaux with Given Modular Major Index
Comments: Incorporated referee comments
Subjects: Combinatorics (math.CO)
[192]  arXiv:1701.07418 (replaced) [pdf, ps, other]
Title: The Diederich--Fornæss index II: for domains of trivial index
Authors: Bingyuan Liu
Comments: Correction on names of authors in the references
Subjects: Complex Variables (math.CV); Differential Geometry (math.DG)
[193]  arXiv:1701.08952 (replaced) [pdf, other]
Title: Characterizations of input-to-state stability for infinite-dimensional systems
Subjects: Optimization and Control (math.OC); Analysis of PDEs (math.AP); Dynamical Systems (math.DS)
[194]  arXiv:1702.02984 (replaced) [pdf, other]
Title: Graded multiplications on iterated bar constructions
Authors: Bruno Stonek
Comments: Revised version. To appear in Contemporary Mathematics
Subjects: Algebraic Topology (math.AT); Category Theory (math.CT)
[195]  arXiv:1702.04228 (replaced) [pdf, ps, other]
Title: Quenched equals annealed at leading order in the colored SYK model
Authors: Razvan Gurau
Comments: final version
Subjects: High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)
[196]  arXiv:1702.04305 (replaced) [pdf, ps, other]
Title: Azumaya loci and discriminant ideals of PI algebras
Comments: Submitted version, main result strengthened by removing hypotheses on field characteristic; typos removed and references updated
Subjects: Rings and Algebras (math.RA); Representation Theory (math.RT)
[197]  arXiv:1702.05845 (replaced) [pdf, other]
Title: Intertwining operators among twisted modules associated to not-necessarily-commuting automorphisms
Authors: Yi-Zhi Huang
Comments: 33 pages. Final version to appear in Journal of Algebra
Subjects: Quantum Algebra (math.QA); High Energy Physics - Theory (hep-th)
[198]  arXiv:1702.07211 (replaced) [pdf, ps, other]
Title: A minimax and asymptotically optimal algorithm for stochastic bandits
Authors: Pierre Ménard (1), Aurélien Garivier (1) ((1) IMT)
Journal-ref: Algorithmic Learning Theory, Springer, 2017, 2017 Algorithmic Learning Theory Conference 76
Subjects: Machine Learning (stat.ML); Learning (cs.LG); Statistics Theory (math.ST)
[199]  arXiv:1702.07937 (replaced) [pdf, ps, other]
Title: Reconstruction and stability in Gel'fand's inverse interior spectral problem
Subjects: Analysis of PDEs (math.AP); Differential Geometry (math.DG)
[200]  arXiv:1702.08446 (replaced) [pdf, ps, other]
Title: Monte Carlo on manifolds: sampling densities and integrating functions
Comments: New version. 32 pages, 11 figures
Subjects: Numerical Analysis (math.NA); Statistical Mechanics (cond-mat.stat-mech); Computation (stat.CO)
[201]  arXiv:1703.00774 (replaced) [pdf, ps, other]
Title: Continuity of weak solutions to rough infinitely degenerate equations
Comments: 11 pages. Proof of Theorem 2 (continuity of week solutions) is fixed. The result is no longer Holder continuity, and the range of geometries is now much smaller
Subjects: Analysis of PDEs (math.AP)
[202]  arXiv:1703.01483 (replaced) [pdf, ps, other]
Title: Theta Graph Designs
Comments: 88 pages (including 74-page Appendix). Abridged version in Journal of Algorithms and Computation, volume 49
Subjects: Combinatorics (math.CO)
[203]  arXiv:1703.01995 (replaced) [pdf, ps, other]
Title: Transseries as germs of surreal functions
Comments: 45 pages; minor corrections; numbering changes in Sections 4 and 5
Subjects: Logic (math.LO)
[204]  arXiv:1703.04109 (replaced) [pdf, ps, other]
Title: Hyperbolic quasiperiodic solutions of U-monotone systems on Riemannian manifolds
Authors: Igor Parasyuk
Comments: 22 pages
Subjects: Dynamical Systems (math.DS)
[205]  arXiv:1703.07512 (replaced) [pdf, ps, other]
Title: Eilenberg-MacLane mapping algebras and higher distributivity up to homotopy
Comments: v2: Shortened the exposition and restructured it slightly
Subjects: Algebraic Topology (math.AT)
[206]  arXiv:1704.01828 (replaced) [pdf, ps, other]
Title: Kinematic Basis of Emergent Energetic Descriptions of General Stochastic Dynamics
Authors: Hong Qian
Comments: 5 pages
Subjects: General Physics (physics.gen-ph); Mathematical Physics (math-ph)
[207]  arXiv:1704.06781 (replaced) [pdf, other]
Title: Homotopy Type Theory in Lean
Comments: 17 pages, accepted for ITP 2017
Subjects: Logic in Computer Science (cs.LO); Logic (math.LO)
[208]  arXiv:1704.07149 (replaced) [pdf, other]
Title: Axiomatizing Epistemic Logic of Friendship via Tree Sequent Calculus
Authors: Katsuhiko Sano
Comments: 15 pages, 1 figure
Subjects: Logic in Computer Science (cs.LO); Logic (math.LO)
[209]  arXiv:1704.07259 (replaced) [pdf, other]
Title: A finite state projection algorithm for the stationary solution of the chemical master equation
Comments: 8 figures
Subjects: Quantitative Methods (q-bio.QM); Probability (math.PR)
[210]  arXiv:1704.08081 (replaced) [pdf, other]
Title: Asymptotics for periodic systems
Comments: 18 pages, 2 figures
Subjects: Functional Analysis (math.FA); Analysis of PDEs (math.AP)
[211]  arXiv:1704.08173 (replaced) [pdf, ps, other]
Title: Scalar products of Bethe vectors in the models with $\mathfrak{gl}(m|n)$ symmetry
Comments: LATEX, 33 pages, no figures, typos are corrected
Journal-ref: Nucl. Phys. B, 923 (2017) 277-311
Subjects: Mathematical Physics (math-ph)
[212]  arXiv:1704.08396 (replaced) [pdf, ps, other]
Title: Strong density of definable types and closed ordered differential fields
Comments: There was a mistake page 3, spotted by Anand Pillay, on the canonical base of a type. (It did not affect the results of the paper.)
Subjects: Logic (math.LO)
[213]  arXiv:1705.00245 (replaced) [pdf, ps, other]
Title: Jordan operator algebras
Comments: 35 pages. To appear. Some of this material was described in an OTOA2016 Conference workshop lecture in ISIBANG Bangalore, December 2016. We thank the organizers of that conference for the invitation and support
Subjects: Operator Algebras (math.OA); Mathematical Physics (math-ph); Functional Analysis (math.FA)
[214]  arXiv:1705.02582 (replaced) [pdf, ps, other]
Title: Group Metrics for Graph Products of Cyclic Groups
Subjects: Logic (math.LO)
[215]  arXiv:1705.03861 (replaced) [pdf, ps, other]
Title: Instability of pulses in gradient reaction-diffusion systems: A symplectic approach
Comments: 19 pages, 1 figure. To appear in Philos. Trans. Roy. Soc. A
Subjects: Dynamical Systems (math.DS); Mathematical Physics (math-ph); Classical Analysis and ODEs (math.CA)
[216]  arXiv:1705.08540 (replaced) [pdf, ps, other]
Title: Critical two-point function for long-range $O(n)$ models below the upper critical dimension
Comments: 32 pages
Subjects: Mathematical Physics (math-ph); Probability (math.PR)
[217]  arXiv:1705.09917 (replaced) [pdf, ps, other]
Title: From a cotangent sum to a generalized totient function
Subjects: Classical Analysis and ODEs (math.CA)
[218]  arXiv:1706.07142 (replaced) [src]
Title: Proof of a conjecture of Abdollahi-Akbari-Maimani concerning the non-commutative graph of finite groups
Comments: The main result is false. It is an error
Subjects: Group Theory (math.GR)
[219]  arXiv:1706.08421 (replaced) [pdf, ps, other]
Title: Ergodic aspects of some Ornstein-Uhlenbeck type processes related to Lévy processes
Authors: Jean Bertoin
Comments: This new version gives credits to earlier works in the literature that I first missed
Subjects: Probability (math.PR)
[220]  arXiv:1706.09941 (replaced) [pdf, other]
Title: Quantum transfer-matrices for the sausage model
Comments: 88 pages, 10 figures, v2: misprints corrected, some comments added
Subjects: High Energy Physics - Theory (hep-th); Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph)
[221]  arXiv:1706.10034 (replaced) [pdf, other]
Title: Asymptotic behaviour methods for the Heat Equation. Convergence to the Gaussian
Comments: Corrected and extended version, 37 pages, 71 references
Subjects: Analysis of PDEs (math.AP)
[222]  arXiv:1707.01289 (replaced) [pdf, other]
Title: Topological $K$-theory with coefficients and the $e$-invariant
Authors: Yi-Sheng Wang
Comments: 63 pages, 10 Figures, v2: corrected typos
Subjects: K-Theory and Homology (math.KT); Geometric Topology (math.GT)
[223]  arXiv:1707.01437 (replaced) [pdf, ps, other]
Title: Loops in SL(2,C) and Factorization
Comments: 21 pages; some minor corrections and examples have been added. arXiv admin note: text overlap with arXiv:0903.4983
Subjects: Functional Analysis (math.FA)
[224]  arXiv:1707.02888 (replaced) [pdf, ps, other]
Title: Cas d'existence de solutions d'EDP
Authors: Samy Skander Bahoura (IHP)
Subjects: Analysis of PDEs (math.AP)
[225]  arXiv:1707.03201 (replaced) [pdf, other]
Title: Functional approach to the error control in adaptive IgA schemes for elliptic boundary value problems
Comments: 34 pages, 18 figures, 31 tables
Subjects: Numerical Analysis (cs.NA); Numerical Analysis (math.NA)
[226]  arXiv:1707.05186 (replaced) [pdf, ps, other]
Title: Computing the number of induced copies of a fixed graph in a bounded degree graph
Comments: In this version we have improved the running time from $O(c^m\cdot n^2)$ to $O(c^m\cdot n)$. To incorporate this, we had to apply some minor changes, mostly in Section 2, leaving the overall approach essentially unaffected. 10 pages
Subjects: Data Structures and Algorithms (cs.DS); Discrete Mathematics (cs.DM); Combinatorics (math.CO)
[227]  arXiv:1707.06517 (replaced) [pdf, ps, other]
Title: Densities For The Repeating Decimals Problems
Authors: N. A. Carella
Comments: Eleven Pages. Keywords: Repeated Decimal; Primitive root; Distribution of Prime. arXiv admin note: substantial text overlap with arXiv:1701.03188, arXiv:1609.01147
Subjects: Number Theory (math.NT)
[228]  arXiv:1707.07664 (replaced) [pdf, ps, other]
Title: Equality of the Jellium and Uniform Electron Gas next-order asymptotic terms for Riesz potentials
Comments: 41 pages
Subjects: Mathematical Physics (math-ph); Analysis of PDEs (math.AP); Probability (math.PR)
[229]  arXiv:1707.09628 (replaced) [pdf, other]
Title: A shape theorem for the scaling limit of the IPDSAW at criticality
Comments: 39 pages, 1 figure
Subjects: Probability (math.PR)
[230]  arXiv:1708.01575 (replaced) [pdf, other]
Title: Poincaré index and the volume functional of unit vector fields on punctured spheres
Comments: Revised version. 15 pages, 2 figures
Subjects: Differential Geometry (math.DG)
[231]  arXiv:1708.06514 (replaced) [src]
Title: Fixed point results for a generalized class of simulation functions with applications
Comments: Now, all authors are not interesting to make this paper available online
Subjects: Functional Analysis (math.FA)
[232]  arXiv:1708.06942 (replaced) [pdf, other]
Title: Hyperbolic Covariant Coherent Structures in two dimensional flows
Subjects: Chaotic Dynamics (nlin.CD); Mathematical Physics (math-ph); Atmospheric and Oceanic Physics (physics.ao-ph); Fluid Dynamics (physics.flu-dyn)
[233]  arXiv:1708.09305 (replaced) [pdf, ps, other]
Title: A Pseudo Knockoff Filter for Correlated Features
Comments: 25 pages, 7 figures; updates: provided a proof on the equivalence of (15) and (16) on page 5 below (16), provided more detail in deriving (36) on page 11, provided a sharper mean-variance estimate in Section 4.3 on pages 18-19, and included the proof of the revised Lemma 4.2 in the Appendix
Subjects: Methodology (stat.ME); Statistics Theory (math.ST)
[234]  arXiv:1709.00633 (replaced) [pdf, ps, other]
Title: Openness of the Anosov families
Subjects: Dynamical Systems (math.DS)
[235]  arXiv:1709.00636 (replaced) [pdf, ps, other]
Title: Local Stable and Unstable Manifolds for Anosov Families
Subjects: Dynamical Systems (math.DS)
[236]  arXiv:1709.00735 (replaced) [pdf, ps, other]
Title: Quantum Path Computing: A Quantum Computing Architecture with Feynman's Path Integrals, Wave-Particle Duality and Entangled Histories
Authors: Burhan Gulbahar
Comments: 37 single column pages, 7 figures (19 subfigures), 4 tables. The revised version has significant differences compared with v1 to further clarify the contributions compared with the state of the art. The title, abstract, introduction, conclusion and some sections have been revised. A new section is included discussing entangled histories. Typing errors are also corrected
Subjects: Quantum Physics (quant-ph); Computational Complexity (cs.CC); Information Theory (cs.IT); Mathematical Physics (math-ph)
[237]  arXiv:1709.01333 (replaced) [pdf, ps, other]
Title: On Jensen-type inequalities for unbounded radial scattering solutions of a loglog energy-supercritical Schrodinger equation
Authors: Tristan Roy
Comments: 32 pages. Update. arXiv admin note: text overlap with arXiv:0911.0127
Subjects: Analysis of PDEs (math.AP)
[238]  arXiv:1709.01475 (replaced) [pdf, other]
Title: Multiscale Finite Element Modeling of Nonlinear Magnetoquasistatic Problems Using Magnetic Induction Conforming Formulations
Comments: Paper accepted for publication in the SIAM MMS journal
Subjects: Numerical Analysis (math.NA)
[239]  arXiv:1709.01983 (replaced) [pdf, ps, other]
Title: The Cauchy problem for two dimensional generalized Kadomtsev-Petviashvili-I equation in anisotropic Sobolev spaces
Comments: 57 pages
Subjects: Analysis of PDEs (math.AP)
[240]  arXiv:1709.02229 (replaced) [pdf, ps, other]
Title: Riordan arrays and generalized Euler polynomials
Authors: E. Burlachenko
Comments: Corrected typos
Subjects: Number Theory (math.NT)
[241]  arXiv:1709.03173 (replaced) [src]
Title: Symbolic computation of Lyapunov coefficients in a planar Bautin bifurcation
Comments: 15 pages, 22 code charts, Several Compiling Problems, Major algorithm errors
Subjects: Dynamical Systems (math.DS)
[242]  arXiv:1709.03911 (replaced) [pdf, ps, other]
Title: An Evolution Equation Approach to the Klein-Gordon Operator on Curved Spacetime
Comments: 40 pages
Subjects: Mathematical Physics (math-ph); Analysis of PDEs (math.AP); Functional Analysis (math.FA)
[243]  arXiv:1709.04620 (replaced) [pdf, ps, other]
Title: Random matrix approach for primal-dual portfolio optimization problems
Comments: 24 pages, 4 figures
Subjects: Portfolio Management (q-fin.PM); Disordered Systems and Neural Networks (cond-mat.dis-nn); Computational Engineering, Finance, and Science (cs.CE); Learning (cs.LG); Optimization and Control (math.OC)
[244]  arXiv:1709.05049 (replaced) [pdf, ps, other]
Title: From support $τ$-tilting posets to algebras
Authors: Ryoichi Kase
Comments: 42 pages (v2) typo corrected
Subjects: Representation Theory (math.RT); Rings and Algebras (math.RA)
[245]  arXiv:1709.05270 (replaced) [pdf, ps, other]
Title: Triviality of the ground-state metastate in long-range Ising spin glasses in one dimension
Authors: N. Read
Comments: 18 pages. v2: subsection on bond-diluted models added, few extra references. 19 pages
Subjects: Statistical Mechanics (cond-mat.stat-mech); Disordered Systems and Neural Networks (cond-mat.dis-nn); Mathematical Physics (math-ph)
[246]  arXiv:1709.06452 (replaced) [src]
Title: On Björner and Lovász's conjecture
Comments: There is an error in one of my results
Subjects: Combinatorics (math.CO)
[ total of 246 entries: 1-246 ]
[ showing up to 2000 entries per page: fewer | more ]

Disable MathJax (What is MathJax?)