Latest in math.sp

total 5610took 0.11s
On the absolutely continuous spectrum of generalized indefinite stringsFeb 21 2019We investigate absolutely continuous spectrum of generalized indefinite strings. By following an approach of Deift and Killip, we establish stability of the absolutely continuous spectra of two model examples of generalized indefinite strings under rather ... More
Geometric wave propagator on Riemannian manifoldsFeb 19 2019We study the propagator of the wave equation on a closed Riemannian manifold $M$. We propose a geometric approach to the construction of the propagator as a single oscillatory integral global both in space and in time with a distinguished complex-valued ... More
On simultaneous approximation of several eigenvalues of a semi-definite self-adjoint linear operator in a Hilbert spaceFeb 18 2019A lower semi-definite self-adjoint linear operator in a Hilbert space is taken whose discrete spectrum is not empty and comprises at least several eigenvalues $\lambda_{min}=\lambda_1\leqslant\ldots\leqslant\lambda_m<\sigma_{ess}$. The problem of approximation ... More
A Cheeger inequality for graphs based on a reflection principleFeb 18 2019Given a graph with a designated set of boundary vertices, we define a new notion of a Neumann Laplace operator on a graph using a reflection principle. We show that the first eigenvalue of this Neumann graph Laplacian satisfies a Cheeger inequality.
Convergence of expansions for eigenfunctions and asymptotics of the spectral data of the Sturm-Liouville problemFeb 18 2019Uniform convergence of the expansion of an absolutely continuous function for eigenfunctions of the Sturm-Liouville problem $-y" + q \left( x \right) y = \mu y,$ $y \left(0\right)=0,$ $y\left( \pi \right)\cos \beta + y'\left( \pi \right)\sin \beta = 0,$ ... More
DeepMIMO: A Generic Deep Learning Dataset for Millimeter Wave and Massive MIMO ApplicationsFeb 18 2019Machine learning tools are finding interesting applications in millimeter wave (mmWave) and massive MIMO systems. This is mainly thanks to their powerful capabilities in learning unknown models and tackling hard optimization problems. To advance the machine ... More
Distributed Learning for Channel Allocation Over a Shared SpectrumFeb 17 2019Channel allocation is the task of assigning channels to users such that some objective (e.g., sum-rate) is maximized. In centralized networks such as cellular networks, this task is carried by the base station which gathers the channel state information ... More
Distributed Learning for Channel Allocation Over a Shared SpectrumFeb 17 2019Feb 19 2019Channel allocation is the task of assigning channels to users such that some objective (e.g., sum-rate) is maximized. In centralized networks such as cellular networks, this task is carried by the base station which gathers the channel state information ... More
Functions of noncommuting operators under perturbation of class $\boldsymbol{S}_p$Feb 17 2019In this article we prove that for $p>2$, there exist pairs of self-adjoint operators $(A_1,B_1)$ and $(A_2,B_2)$ and a function $f$ on the real line in the homogeneous Besov class $B_{\infty,1}^1({\Bbb R}^2)$ such that the differences $A_2-A_1$ and $B_2-B_1$ ... More
Repartition of the quasi-stationary distribution and first exit point density for a double-well potentialFeb 17 2019Let $f: \mathbb R^{d} \to \mathbb R$ be a smooth function and $(X_t)_{t\ge 0}$ be the stochastic process solution to the overdamped Langevin dynamics $$d X_t = -\nabla f(X_t) d t + \sqrt{h} \ d B_t.$$ Let $\Omega\subset \mathbb R^d$ be a smooth bounded ... More
Spatial Channel Covariance Estimation for Hybrid Architectures Based on Tensor DecompositionsFeb 17 2019Spatial channel covariance information can replace full instantaneous channel state information for the analog precoder design in hybrid analog/digital architectures. Obtaining spatial channel covariance estimation, however, is challenging in the hybrid ... More
Finite-gap CMV matrices: Periodic coordinates and a Magic FormulaFeb 15 2019We prove a bijective unitary correspondence between 1) the isospectral torus of almost-periodic, absolutely continuous CMV matrices having fixed finite-gap spectrum and 2) special periodic block-CMV matrices satisfying a Magic Formula. This latter class ... More
Steklov Eigenvalue Problem on Subgraphs of Integer LatticesFeb 15 2019We study the eigenvalues of the Dirichlet-to-Neumann operator on a finite subgraph of the integer lattice Zn. We estimate the first n+1 eigenvalues using the number of vertices of the subgraph. As a corollary, we prove that the first non-trivial eigenvalue ... More
On nodal and generalized singular structures of Laplacian eigenfunctions and applicationsFeb 15 2019In this paper, we present some novel and intriguing findings on the geometric structures of Laplacian eigenfunctions and their deep relationship to the quantitative behaviours of the eigenfunctions. We consider the nodal lines and also introduce the notion ... More
Discrete eigenvalues of the spin-boson Hamiltonian with two photons: on a conjecture of Minlos and SpohnFeb 14 2019Under minimal regularity conditions on the photon dispersion and the coupling function, we prove that the spin-boson model with two massless photons in $\mathbb{R}^d$ can not have more than two bound state energies for any coupling strength. This solves ... More
Shrinking scale equidistribution for monochromatic random waves on compact manifoldsFeb 14 2019We prove equidistribution at shrinking scales for the monochromatic ensemble on a compact Riemannian manifold of any dimension. This ensemble on an arbitrary manifold takes a slowly growing spectral window in order to synthesize a random function. With ... More
Generalized subdifferentials of spectral functions over Euclidean Jordan algebrasFeb 14 2019This paper is devoted to the study of generalized subdifferentials of spectral functions over Euclidean Jordan algebras. Spectral functions appear often in optimization problems field playing the role of "regularizer", "barrier", "penalty function" and ... More
Positive Lyapunov Exponents and a Large Deviation Theorem for Continuum Anderson Models, BrieflyFeb 12 2019In this short note, we prove positivity of the Lyapunov exponent for 1D continuum Anderson models by leveraging some classical tools from inverse spectral theory. The argument is much simpler than the existing proof due to Damanik--Sims--Stolz, and it ... More
Spectral analysis of the Laplacian acting on discrete cusps and funnelsFeb 12 2019We study the Laplacian acting on a discret cusp and a discret funnel. We perturb the metric in a long-range way. Then, we establish a Limiting Absorption Principle away the possible embedded eigenvalues. The approach is based on a positive commutator ... More
An Extension of The First Eigen-type Ambarzumyan theoremFeb 11 2019An extension of the first eigenvalue-type Ambarzumyan's theorem are provided for the arbitrary self-adjoint Sturm-Liouville differential operators. The result makes a contribution to the P\"oschel-Trubowitz inverse spectral theory as well.
Massive MIMO is a Reality - What is Next? Five Promising Research Directions for Antenna ArraysFeb 11 2019Massive MIMO (multiple-input multiple-output) is no longer a "wild" or "promising" concept for future cellular networks - in 2018 it became a reality. Base stations (BSs) with 64 fully digital transceiver chains were commercially deployed in several countries, ... More
Weighted prime geodesic theoremsFeb 11 2019Prime geodesic theorems for weighted infinite graphs and weighted building quotients are given. The growth rates are expressed in terms of the spectral data of suitable translation operators inspired by a paper of Bass.
Cell-free Massive MIMO for UAV CommunicationsFeb 10 2019We study support for unmanned aerial vehicle (UAV) communications through a cell-free massive MIMO architecture. Under the general assumption that the propagation channel between the mobile stations, either UAVs or ground users, and the access points ... More
On the Yang-Yau inequality for the first Laplace eigenvalueFeb 09 2019In a seminal paper published in 1980, P. C. Yang and S.-T. Yau proved an inequality bounding the first eigenvalue of the Laplacian on an orientable Riemannian surface in terms of its genus $\gamma$ and the area. The equality in Yang-Yau's estimate is ... More
Optimal Bit Allocation Variable-Resolution ADC for Massive MIMOFeb 09 2019In this paper, we derive an optimal ADC bit-allocation (BA) condition for a Single-User (SU) Millimeter wave (mmWave) Massive Multiple-Input Multiple-Output (Ma-MIMO) receiver equipped with variable-resolution ADCs under power constraint with the following ... More
Green function and self-adjoint Laplacians on polyhedral surfacesFeb 08 2019Using Roelcke formula for the Green function, we explicitly construct a basis in the kernel of the adjoint Laplacian on a compact polyhedral surface $X$ and compute the $S$-matrix of $X$ at the zero value of the spectral parameter. We apply these results ... More
Spectral geometry in a rotating frame: properties of the ground stateFeb 08 2019We investigate spectral properties of the operator describing a quantum particle confined to a planar domain $\Omega$ rotating around a fixed point with an angular velocity $\omega$ and demonstrate several properties of its principal eigenvalue $\lambda_1^\omega$. ... More
On Convergence of Spectral Expansions of Dirac Operators with Regular Boundary ConditionsFeb 08 2019Spectral problem for the Dirac operator with regular but not strongly regular boundary conditions and complex-valued potential summable over a finite interval is considered. The purpose of this paper is to find conditions under which the root function ... More
Spectra of eccentricity matrices of graphsFeb 07 2019The eccentricity matrix of a connected graph $G$ is obtained from the distance matrix of $G$ by retaining the largest distances in each row and each column, and setting the remaining entries as $0$. In this article, a conjecture about the least eigenvalue ... More
Spectral Analysis of Iterated Rank-One PerturbationsFeb 07 2019The authors study the spectral theory of self-adjoint operators that are subject to certain types of perturbations. An iterative introduction of infinitely many randomly coupled rank-one perturbations is one of our settings. Spectral theoretic tools are ... More
Stationary phase type estimates for low symbol regularityFeb 06 2019The well-known stationary phase formula gives us a way to precisely compute oscillating integrals so long as the symbol is regular enough (in comparison to the large parameter controlling the oscillation). However in a number of applications we find ourselves ... More
Asymptotics of orthogonal polynomials with slowly oscillating recurrence coefficientsFeb 06 2019We study solutions of three-term recurrence relations whose $N$-step transfer matrices belong to the uniform Stolz class. In particular, we derive the first order of their uniform asymptotics. For orthonormal polynomials we show more. Namely, we find ... More
On the Limiting Absorption Principle for Schr{ö}dinger operators on waveguidesFeb 06 2019We prove a Limiting Absorption Principle for Schr{\"o}dinger operators in tubes about infinite curves embedded in the Euclidian space with different types of boundary conditions. The argument is based on the Mourre theory with conjugate operators different ... More
Wireless Networks Design in the Era of Deep Learning: Model-Based, AI-Based, or Both?Feb 05 2019This work deals with the use of emerging deep learning techniques in future wireless communication networks. It will be shown that data-driven approaches should not replace, but rather complement traditional design techniques based on mathematical models. ... More
MIMO Capacity with Average Total and Per-Antenna Power ConstraintsFeb 05 2019MIMO capacity with a joint total and per-antenna average power constraint is considered in this work. The problem arises when, besides having a limited available power at the transmitter, also the individual antennas cannot radiate power beyond the limits ... More
Magneto-Inductive Powering and Uplink of In-Body Microsensors: Feasibility and High-Density EffectsFeb 05 2019This paper studies magnetic induction for wireless powering and the data uplink of microsensors, in particular for future medical in-body applications. We consider an external massive coil array as power source (1 W) and data sink. For sensor devices ... More
Spectral flow of Dirac operators with magnetic cable knotFeb 04 2019We study the spectral flow of Dirac operators with magnetic links on $\mathbb{S}^3$. These are generalisations of Aharonov-Bohm solenoids where the magnetic fields contain finitely many field lines coinciding with the components of a link, the flux of ... More
Finite term relations for the exponential orthogonal polynomialsFeb 03 2019The exponential orthogonal polynomials encode via the theory of hyponormal operators a shade function $g$ supported by a bounded planar shape. We prove under natural regularity assumptions that these complex polynomials satisfy a three term relation if ... More
State Estimation over Worst-Case Erasure and Symmetric Channels with MemoryFeb 02 2019Worst-case models of erasure and symmetric channels are investigated, in which the number of channel errors occurring in each sliding window of a given length is bounded. Upper and lower bounds on their zero-error capacities are derived, with the lower ... More
On the spectra of three Steklov eigenvalue problems on warped product manifoldsFeb 02 2019Let $M^n=[0,R)\times \mathbb{S}^{n-1}$ be an $n$-dimensional ($n\geq 2$) smooth Riemannian manifold equipped with the warped product metric $g=dr^2+h^2(r)g_{\mathbb{S}^{n-1}}$ and diffeomorphic to a Euclidean ball. Assume that $M$ has strictly convex ... More
Low rank perturbation of regular matrix pencils with symmetry structuresFeb 01 2019The generic change of the Weierstrass Canonical Form of regular complex structured matrix pencils under generic structure-preserving additive low-rank perturbations is studied. Several different symmetry structures are considered and it is shown that ... More
Trigonometric series and self-similar setsFeb 01 2019Feb 06 2019Let $F$ be a self-similar set on $\mathbb{R}$ associated to contractions $f_j(x) = r_j x + b_j$, $j \in \mathcal{A}$, for some finite $\mathcal{A}$, such that $F$ is not a singleton. We prove that if $\log r_i / \log r_j$ is irrational for some $i \neq ... More
Bethe-Sommerfeld conjecture in semiclassical settingsFeb 01 2019Under certain assumptions (including $d\ge 2)$ we prove that the spectrum of a scalar operator in $\mathscr{L}^2(\mathbb{R}^d)$ \begin{equation*} A_\varepsilon (x,hD)= A^0(hD) + \varepsilon B(x,hD), \end{equation*} covers interval $(\tau-\epsilon,\tau+\epsilon)$, ... More
Spectral analysis of the spin-boson Hamiltonian with two bosons for arbitrary coupling and bounded dispersion relationJan 31 2019We study the spectrum of the spin-boson Hamiltonian with two bosons for arbitrary coupling $\alpha>0$ in the case when the dispersion relation of the free field is a bounded function. We derive an explicit description of the essential spectrum which consists ... More
On Dirac operators in $\mathbb{R}^3$ with electrostatic and Lorentz scalar $δ$-shell interactionsJan 31 2019In this article Dirac operators $A_{\eta, \tau}$ coupled with combinations of electrostatic and Lorentz scalar $\delta$-shell interactions of constant strength $\eta$ and $\tau$, respectively, supported on compact surfaces $\Sigma \subset \mathbb{R}^3$ ... More
A Level Set Approach to Online Sensing and Trajectory Optimization with Time DelaysJan 30 2019Presented is a method to compute certain classes of Hamilton-Jacobi equations that result from optimal control and trajectory generation problems with time delays. Many robotic control and trajectory problems have limited information of the operating ... More
Recovering the characteristic functions of the Sturm-Liouville differential operators with singular potentials on star-type graph with cycleJan 30 2019We consider Sturm-Liouville operators with singular potentials from the class on star-type graph with cycle, which consist the edges with commensurable lengths. Asymptotic representation for eigenvalues for such operators is obtained. Recovering of the ... More
Inverse spectral theory for perturbed torusJan 30 2019We consider an inverse problem for Laplacians on rotationally symmetric manifolds, which are finite for the transversal direction and periodic with respect to the axis of the manifold, i.e., Laplacians on tori. We construct an infinite dimensional analytic ... More
Geometric structure of graph Laplacian embeddingsJan 30 2019We analyze the spectral clustering procedure for identifying coarse structure in a data set $x_1, \dots, x_n$, and in particular study the geometry of graph Laplacian embeddings which form the basis for spectral clustering algorithms. More precisely, ... More
Support Recovery in the Phase Retrieval Model: Information-Theoretic Fundamental LimitsJan 30 2019The support recovery problem consists of determining a sparse subset of variables that is relevant in generating a set of observations. In this paper, we study the support recovery problem in the phase retrieval model consisting of noisy phaseless measurements, ... More
On non-uniqueness for the anisotropic Calder{ó}n problem with partial dataJan 29 2019We show that there is non-uniqueness for the Calder{\'o}n problem with partial data for Riemannian metrics with H{\"o}lder continuous coefficients in dimension greater or equal than three. We provide simple counterexamples in the case of cylindrical Riemannian ... More
Two-term spectral asymptotics for the Dirichlet Laplacian in a Lipschitz domainJan 28 2019We prove a two-term Weyl-type asymptotic formula for sums of eigenvalues of the Dirichlet Laplacian in a bounded open set with Lipschitz boundary. Moreover, in the case of a convex domain we obtain a universal bound which correctly reproduces the first ... More
Detection of a Signal in Colored Noise: A Random Matrix Theory Based AnalysisJan 28 2019This paper investigates the classical statistical signal processing problem of detecting a signal in the presence of colored noise with an unknown covariance matrix. In particular, we consider a scenario where m-dimensional p possible signal-plus-noise ... More
On a trace formula for functions of noncommuting operatorsJan 28 2019The main result of the paper is that the Lifshits--Krein trace formula cannot be generalized to the case of functions of noncommuting self-adjoint operators. To prove this, we show that for pairs $(A_1,B_1)$ and $(A_2,B_2)$ of bounded self-adjoint operators ... More
On the Friedlander-Nadirashvili invariants of surfacesJan 27 2019Let $M$ be a closed smooth manifold. In 1999, L. Friedlander and N. Nadirashvili introduced a new differential invariant $I_1(M)$ using the first normalized nonzero eigenvalue of the Lalpace-Beltrami operator $\Delta_g$ of a Riemannian metric $g$. They ... More
Toeplitz band matrices with small random perturbationsJan 25 2019We study the spectra of $N\times N$ Toeplitz band matrices perturbed by small complex Gaussian random matrices, in the regime $N\gg 1$. We prove a probabilistic Weyl law, which provides an precise asymptotic formula for the number of eigenvalues in certain ... More
Using Erasure Feedback for Online Timely Updating with an Energy Harvesting SensorJan 24 2019A real-time status updating system is considered, in which an energy harvesting sensor is acquiring measurements regarding some physical phenomenon and sending them to a destination through an erasure channel. The setting is online, in which energy arrives ... More
IR-truncated $\mathcal{PT}-$symmetric $ix^3$ model and its asymptotic spectral scaling graphJan 24 2019The $\mathcal{PT}-$symmetric quantum mechanical $V=ix^3$ model over the real line, $x\in\mathbb{R}$, is infrared (IR) truncated and considered as Sturm-Liouville problem over a finite interval $x\in\left[-L,L\right]\subset\mathbb{R}$. Via WKB and Stokes ... More
Intersymbol and Intercarrier Interference in OFDM Transmissions through Highly Dispersive ChannelsJan 23 2019This work quantifies, for the first time, intersymbol and intercarrier interferences induced by very dispersive channels in OFDM systems. The resulting achievable data rate for \wam{suboptimal} OFDM transmissions is derived based on the computation of ... More
A Gelfand-Levitan trace formula for generic quantum graphsJan 23 2019We formulate and prove a Gelfand-Levitan trace formula for general quantum graphs with arbitrary edge lengths and coupling conditions which cover all self-adjoint operators on quantum graphs, except for a set of measure zero. The formula is reminiscent ... More
On integrals over a convex set of the Wigner distributionJan 22 2019We provide an example of a normalized $L^{2}(\mathbb R)$ function $u$ such that its Wigner distribution $\mathcal W(u,u)$ has an integral $>1$ on the square $[0,a]\times[0,a]$ for a suitable choice of $a$. This provides a negative answer to a question ... More
Schrödinger operators with Coulomb-like and $δ'$-like potentialsJan 22 2019We study the convergence of Schr\"odinger operators $$ H_\varepsilon= -\frac{d^2}{dx^2}+Q_\varepsilon(x)+\varepsilon^{-2}U(\varepsilon^{-1}x) +\varepsilon^{-1}V(\varepsilon^{-1}x) $$ as $\varepsilon\to 0$, where $Q_\varepsilon$ is a regularization of ... More
WKB eigenmode construction for analytic Toeplitz operatorsJan 22 2019We provide almost eigenfunctions for Toeplitz operators with real-analytic symbols, at the bottom of non-degenerate wells. These almost eigenfunctions follow the WKB ansatz; the error is O(exp(--cN)), where c > 0 and N $\rightarrow$ +$\infty$ is the inverse ... More
Maximum Principles for Matrix-Valued Analytic FunctionsJan 22 2019To what extent is the maximum modulus principle for scalar-valued analytic functions valid for matrix-valued analytic functions? In response, we discuss some maximum norm principles for such functions that do not appear to be widely known, deduce maximum ... More
Stability of the Malvinas CurrentJan 21 2019Deterministic and probabilistic tools from nonlinear dynamics are used to assess enduring near-surface Lagrangian aspects of the Malvinas Current. The deterministic tools are applied on a multi-year record of velocities derived from satellite altimetry ... More
Nonlinear Spectral Decompositions by Gradient Flows of One-Homogeneous FunctionalsJan 21 2019The aim of this paper is to establish a theory of nonlinear spectral decompositions in an infinite dimensional setting by considering the eigenvalue problem related to an absolutely one-homogeneous functional in a Hilbert space. This approach is motivated ... More
Rate Balancing in Full-Duplex MIMO Two-Way Relay NetworksJan 21 2019Jan 28 2019Maximizing the minimum rate for a full-duplex multiple-input multiple-output (MIMO) wireless network encompassing two sources and a two-way (TW) relay operating in a two hop manner is investigated. To improve the overall performance, using a zero-forcing ... More
Holographic Phase Retrieval and Optimal Reference DesignJan 19 2019A general mathematical framework and recovery algorithm is presented for the holographic phase retrieval problem. In this problem, which arises in holographic coherent diffraction imaging, a "reference" portion of the signal to be recovered via phase ... More
Interface Asymptotics of Eigenspace Wigner distributions for the Harmonic OscillatorJan 18 2019Feb 03 2019Eigenspaces of the quantum isotropic Harmonic Oscillator $\hat{H}_{\hbar} : = - \frac{\hbar^2}{2} \Delta + \frac{||x||^2}{2}$ on $\mathbb{R}^d$ have extremally high multiplicites and the eigenspace projections $\Pi_{\hbar, E_N(\hbar)} $ have special asymptotic ... More
Two new topological indices based on graph adjacency matrix eigenvalues and eigenvectorsJan 18 2019The Estrada topological index EE, based on the eigenvalues of the adjacency matrix, is degenerate for cospectral graphs. By additionally considering the eigenvectors, two new topological indices are devised (RV_a and RV_b), which have reduced degeneracy ... More
Eigenvalues of the Kohn Laplacian and deformations of pseudohermitian structures on compact embedded strictly pseudoconvex CR manifoldsJan 17 2019We study the eigenvalues of the Kohn Laplacian on a closed embedded strictly pseudoconvex CR manifold as functionals on the set of positive oriented contact forms $\mathcal{P}_+$. We show that the functionals are continuous with respect to a natural topology ... More
Schatten class conditions for functions of Schrödinger operatorsJan 17 2019We consider the difference $f(H_1)-f(H_0)$, where $H_0=-\Delta$ and $H_1=-\Delta+V$ are the free and the perturbed Schr\"odinger operators in $L^2(\mathbb R^d)$, and $V$ is a real-valued short range potential. We give a sharp sufficient condition for ... More
Trace formula for the magnetic LaplacianJan 17 2019The Guillemin-Uribe trace formula is a semiclassical version of the Selberg trace formula and more general Duistermaat-Guillemin formula for elliptic operators on compact manifolds, which reflects the dynamics of magnetic geodesic flows in terms of eigenvalues ... More
Quantum Graphs on Radially Symmetric AntitreesJan 16 2019We investigate spectral properties of Kirchhoff Laplacians on radially symmetric antitrees. This class of metric graphs enjoys a rich group of symmetries, which enables us to obtain a decomposition of the corresponding Laplacian into the orthogonal sum ... More
Gap Localization of TE-Modes by arbitrarily weak defects - multiband caseJan 16 2019This paper considers the propagation of TE-modes in photonic crystal waveguides. The waveguide is created by introducing a linear defect into a periodic background medium. Both the periodic background problem and the perturbed problem are modelled by ... More
Lieb-Thirring inequalities for wave functions vanishing on the diagonal setJan 15 2019We propose a general strategy to derive Lieb-Thirring inequalities for scale-covariant quantum many-body systems. As an application, we obtain a generalization of the Lieb-Thirring inequality to wave functions vanishing on the diagonal set of the configuration ... More
Kato smoothness and functions of perturbed self-adjoint operatorsJan 15 2019We consider the difference $f(H_1)-f(H_0)$ for self-adjoint operators $H_0$ and $H_1$ acting in a Hilbert space. We establish a new class of estimates for the operator norm and the Schatten class norms of this difference. Our estimates utilise ideas of ... More
Spectral properties of Landau Hamiltonians with non-local potentialsJan 14 2019We consider the Landau Hamiltonian $H_0$, self-adjoint in $L^2({\mathbb R}^2)$, whose spectrum consists of an arithmetic progression of infinitely degenerate positive eigenvalues $\Lambda_q$, $q \in {\mathbb Z}_+$. We perturb $H_0$ by a non-local potential ... More
Predicting the Mumble of Wireless Channel with Sequence-to-Sequence ModelsJan 14 2019Accurate prediction of fading channel in future is essential to realize adaptive transmission and other methods that can save power and provide gains. In practice, wireless channel model can be regarded as a new language model, and the time-varying channel ... More
Universal Continuous Calculus for Su*-AlgebrasJan 13 2019Universal continuous calculi are defined and it is shown that for every finite tuple of pairwise commuting Hermitian elements of a Su*-algebra (an ordered *-algebra that is symmetric, i.e. "strictly" positive elements are invertible, and uniformly complete), ... More
Mitigating Jamming Attacks Using Energy HarvestingJan 11 2019The use of energy harvesting as a counter-jamming measure is investigated on the premise that part of the harmful interference can be harvested to increase the transmit power. We formulate the strategic interaction between a pair of legitimate nodes and ... More
Dynamic Mobility-Aware Interference Avoidance for Aerial Base Stations in Cognitive Radio NetworksJan 09 2019Jan 18 2019Aerial base station (ABS) is a promising solution for public safety as it can be deployed in coexistence with cellular networks to form a temporary communication network. However, the interference from the primary cellular network may severely degrade ... More
On spectra of hyperbolic surfaces without thin handlesJan 05 2019We obtain a sharp lower estimate on eigenvalues of Laplace--Beltrami operator on a hyperbolic surface with injectivity radius bounded from the below.
Instability of unidirectional flows for the 2D $α$-Euler equationsJan 05 2019Jan 21 2019We study stability of unidirectional flows for the linearized 2D $\alpha$-Euler equations on the torus. The unidirectional flows are steady states whose vorticity is given by Fourier modes corresponding to a vector $\mathbf p \in \mathbb Z^{2}$. We linearize ... More
An estimate of Green's function of the problem of bounded solutions in the case of a triangular coefficientJan 03 2019An estimate of Green's function of the bounded solutions problem for the ordinary differential equation $x'(t)-Bx(t)=f(t)$ is proposed. It is assumed that the matrix coefficient $B$ is triangular. This estimate is a generalization of the estimate of the ... More
On the Decomposition of the Laplacian on Metric GraphsJan 02 2019We study the Laplacian on family preserving metric graphs. These are graphs that have a certain symmetry that, as we show, allows for a decomposition into a direct sum of one-dimensional operators whose properties are explicitly related to the structure ... More
Haplotype Assembly Using Manifold Optimization and Error Correction MechanismJan 01 2019Recent matrix completion based methods have not been able to properly model the Haplotype Assembly Problem (HAP) for noisy observations. To cope with such a case, in this letter we propose a new Minimum Error Correction (MEC) based matrix completion optimization ... More
Quantum time delay for unitary operators: general theoryDec 27 2018We present a suitable framework for the definition of quantum time delay in terms of sojourn times for unitary operators in a two-Hilbert spaces setting. We prove that this time delay defined in terms of sojourn times (time-dependent definition) exists ... More
Study of Robust Diffusion Recursive Least Squares Algorithms with Side Information for Networked AgentsDec 24 2018This work develops a robust diffusion recursive least squares algorithm to mitigate the performance degradation often experienced in networks of agents in the presence of impulsive noise. This algorithm minimizes an exponentially weighted least-squares ... More
Design of generalized fractional order gradient descent methodDec 24 2018This paper focuses on the convergence problem of the emerging fractional order gradient descent method, and proposes three solutions to overcome the problem. In fact, the general fractional gradient method cannot converge to the real extreme point of ... More
Geometrical representation of real and reactive powers of load demand by orbit diagrams in the Mandelbrot setDec 24 2018This paper presents the geometrical representation of the load demand by using orbits diagrams in the Mandelbrot set, to identify changing behaviors during a day period of the real and reactive powers. To perform this, different power combinations were ... More
Fractal representation of the power daily demand based on topological properties of Julia setsDec 24 2018In a power system, the load demand considers two components such as the real power (P) because of resistive elements, and the reactive power (Q) because inductive or capacitive elements. This paper presents a graphical representation of the electric power ... More
A game theory approach to the existence and uniqueness of nonlinear Perron-Frobenius eigenvectorsDec 24 2018We establish a generalized Perron-Frobenius theorem, based on a combinatorial criterion which entails the existence of an eigenvector for any nonlinear order-preserving and positively homogeneous map $f$ acting on the open orthant $\mathbb{R}_{\scriptscriptstyle ... More
Topological properties of fractal Julia sets related to the signs and magnitudes of the real and reactive powersDec 23 2018In AC electrical systems, the power depends on the real power (P) due to resistive elements and the reactive power (Q) due to the inductive and capacitive elements, which are commonly studied by using phasor and scalar methods. Thus, this paper focuses ... More
The Landau Hamiltonian with $δ$-potentials supported on curvesDec 21 2018The spectral properties of the singularly perturbed self-adjoint Landau Hamiltonian $A_\alpha =(i \nabla + A)^2 + \alpha\delta$ in $L^2(R^2)$ with a $\delta$-potential supported on a finite $C^{1,1}$-smooth curve $\Sigma$ are studied. Here $A = \frac{1}{2} ... More
Scaling Limits of Jacobi Matrices and the Christoffel-Darboux KernelDec 18 2018We study scaling limits of deterministic Jacobi matrices at a fixed point, $x_0$, and their connection to the scaling limits of the Christoffel-Darboux kernel at that point. We show that in the case that the orthogonal polynomials are bounded at $x_0$, ... More
Stability in the inverse Steklov problem on warped product Riemannian manifoldsDec 18 2018In this paper, we study the amount of information contained in the Steklov spectrum of some compact manifolds with connected boundary equipped with a warped product metric. Examples of such manifolds can be thought of as deformed balls in R^d. We first ... More
LORA: Learning to Optimize for Resource Allocation in Wireless Networks with Few Training SamplesDec 18 2018Effective resource allocation plays a pivotal role for performance optimization in wireless networks. Unfortunately, typical resource allocation problems are mixed-integer nonlinear programming (MINLP) problems, which are NP-hard in general. Machine learning-based ... More
A Noncoherent Space-Time Code from Quantum Error CorrectionDec 18 2018Jan 29 2019In this work, we develop a space-time block code for noncoherent communication using techniques from the field of quantum error correction. We decompose the multiple-input multiple-output (MIMO) channel into operators from quantum mechanics, and design ... More
A pair of commuting hypergeometric operators on the complex plane and bispectralityDec 17 2018We consider the standard hypergeometric differential operator $D$ regarded as an operator on the complex plane $C$ and the complex conjugate operator $\overline D$. These operators formally commute and are formally adjoint one to another with respect ... More