Latest in math.sp

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Inverse resonance scattering for on rotationally symmetric manifoldsApr 18 2019We discuss inverse resonance scattering for the Laplacian on a rotationally symmetric manifold $M = (0,\infty) \times Y$ whose rotation radius is constant outside some compact interval. The Laplacian on $M$ is unitarily equivalent to a direct sum of one-dimensional ... More
Local semicircle law under fourth moment conditionApr 18 2019We consider a random symmetric matrix ${\bf X} = [X_{jk}]_{j,k=1}^n$ with upper triangular entries being independent random variables with mean zero and unit variance. Assuming that $\max_{jk} {\mathbb E} |X_{jk}|^{4+\delta} < \infty, \delta > 0$, it ... More
Bounds on eigenvalues of perturbed Lamé operators with complex potentialsApr 17 2019Several recent papers have focused their attention in proving the correct analogue to the Lieb-Thirring inequalities for non self-adjoint operators and in finding bounds on the distribution of their eigenvalues in the complex plane. This paper provides ... More
Non-Stochastic Hypothesis Testing with Application to Privacy Against Hypothesis-Testing AdversaryApr 16 2019In this paper, we consider privacy against hypothesis testing adversaries within a non-stochastic framework. We develop a theory of non-stochastic hypothesis testing by borrowing the notion of uncertain variables from non-stochastic information theory. ... More
Outage-Optimized Deployment of UAVsApr 15 2019We consider multiple unmanned aerial vehicles (UAVs) serving a density of ground terminals (GTs) as mobile base stations. The objective is to minimize the outage probability of GT-to-UAV transmissions. In this context, the optimal placement of UAVs under ... More
A boundary integral equation approach to computing eigenvalues of the Stokes operatorApr 15 2019The eigenvalues and eigenfunctions of the Stokes operator have been the subject of intense analytical investigation and have applications in the study and simulation of the Navier-Stokes equations. As the Stokes operator is a fourth-order operator, computing ... More
Generalized eigenfunctions and eigenvalues: a unifying framework for Shnol-type theoremsApr 15 2019Let $H$ be a generalized Schr\"odinger operator on a domain of a non-compact connected Riemannian manifold, and a generalized eigenfunction $u$ for $H$: that is, $u$ satisfies the equation $Hu=\lambda u$ in the weak sense but is not necessarily in $L^2$. ... More
Cramer-Rao Bound for Estimation After Model Selection and its Application to Sparse Vector EstimationApr 15 2019In many practical parameter estimation problems, such as coefficient estimation of polynomial regression and direction-of-arrival (DOA) estimation, model selection is performed prior to estimation. In these cases, it is assumed that the true measurement ... More
Large Intelligent Surface-Based Index Modulation: A New Beyond MIMO Paradigm for 6GApr 14 2019Transmission through large intelligent surfaces (LIS), which modify the phases of incident waves in a deliberate manner to enhance the signal quality at the receiver, has been recently put forward as a promising candidate for future wireless communication ... More
Spectra of comb graphs with tailsApr 14 2019Given two graphs, a backbone and a finger, a comb product is a new graph obtained by grafting a copy of the finger into each vertex of the backbone. We study the comb graphs in the case when both components are the paths of order $n$ and $k$, respectively, ... More
TDMR Detection System with Local Area Influence Probabilistic a Priori DetectorApr 13 2019We propose a three-track detection system for two dimensional magnetic recording (TDMR) in which a local area influence probabilistic (LAIP) detector works with a trellis-based Bahl-Cocke-Jelinek-Raviv (BCJR) detector to remove intersymbol interference ... More
Design of optimized backstepping controller for the synchronization of chaotic Colpitts oscillator using shark smell algorithmApr 13 2019In this paper, an adaptive backstepping controller has been tuned to synchronize two chaotic Colpitts oscillators in a master slave configuration. The parameters of the controller are determined using shark smell optimization (SSO) algorithm. Numerical ... More
Joint Scheduling and Power Control for V2V Broadcast Communication with Adjacent Channel InterferenceApr 13 2019This paper investigates how to mitigate the impact of adjacent channel interference (ACI) in vehicular broadcast communication, using scheduling and power control. Our objective is to maximize the number of connected vehicles. First, we formulate the ... More
On the Displacement of Eigenvalues when Removing a Twin VertexApr 11 2019Twin vertices of a graph have the same common neighbours. If they are adjacent, then they are called duplicates and contribute the eigenvalue zero to the adjacency matrix. Otherwise they are termed co-duplicates, when they contribute $-1$ as an eigenvalue ... More
The Asymptotic Behaviour of the Sum of Negative Eigenvalues of a Self-Adjoint Operator Given in Semi-AxisApr 11 2019In this work, we find the asymptotic formulas for the sum of the negative eigenvalues smaller than $-\varepsilon$ $(\varepsilon >0)$ of a self-adjoint operator $L$ which is defined by the following differential expression $$\ell(y)=-(p(x)y'(x))'-Q(x)y(x)$$ ... More
On Model Coding for Distributed Inference and Transmission in Mobile Edge Computing SystemsApr 11 2019Consider a mobile edge computing system in which users wish to obtain the result of a linear inference operation on locally measured input data. Unlike the offloaded input data, the model weight matrix is distributed across wireless Edge Nodes (ENs). ... More
Essential self-adjointness of perturbed quadharmonic operators on Riemannian manifolds with an application to the separation problemApr 11 2019We consider perturbed quadharmonic operators, $\Delta^4 + V$, acting on sections of a Hermitian vector bundle over a complete Riemannian manifold, with the potential $V$ satisfying a bound from below by a non-positive function depending on the distance ... More
Adaptive Virtual Waveform Design for Millimeter-Wave Joint Communication-RadarApr 11 2019Joint communication and radar (JCR) waveforms with fully digital baseband generation and processing can now be realized at the millimeter-wave (mmWave) band. Prior work has proposed a mmWave wireless local area network (WLAN)-based JCR that exploits the ... More
Cell Discovery in Millimeter Wave Systems: Physical Layer ImplementationsApr 10 2019Cell discovery is the procedure in which an user equipment (UE) in a cellular network finds a suitable base station (BS) and its physical layer cell identity, in order to establish a link-layer connection. When beamforming with antenna arrays is done ... More
Generic Variance Bounds on Estimation and Prediction Errors in Time Series Analysis: An Entropy PerspectiveApr 09 2019In this paper, we obtain generic bounds on the variances of estimation and prediction errors in time series analysis via an information-theoretic approach. It is seen in general that the error bounds are determined by the conditional entropy of the data ... More
Generic Variance Bounds on Estimation and Prediction Errors in Time Series Analysis: An Entropy PerspectiveApr 09 2019Apr 15 2019In this paper, we obtain generic bounds on the variances of estimation and prediction errors in time series analysis via an information-theoretic approach. It is seen in general that the error bounds are determined by the conditional entropy of the data ... More
Accelerated Nuclear Magnetic Resonance Spectroscopy with Deep LearningApr 09 2019Nuclear magnetic resonance (NMR) spectroscopy serves as an indispensable tool in chemistry and biology but often suffers from long experimental time. We present a proof-of-concept of harnessing deep learning and neural network for high-quality, reliable, ... More
Generalized Drazin-meromorphic invertible operators and generalized Kato-meromorphic decompositionApr 09 2019A bounded linear operator $T$ on a Banach space $X$ is said to be generalized Drazin-meromorphic invertible if there exists a bounded linear operator $S$ acting on $X$ such that $TS=ST$, $STS=S$, $ TST-T$ is meromorphic. We shall say that $T$ admits a ... More
Convergence of Message-Passing for Distributed Convex Optimisation with Scaled Diagonal DominanceApr 09 2019This paper studies the convergence properties the well-known message-passing algorithm for convex optimisation. Under the assumption of pairwise separability and scaled diagonal dominance, asymptotic convergence is established and a simple bound for the ... More
Harnessing Sparsity over the Continuum: Atomic Norm Minimization for Super ResolutionApr 08 2019Convex optimization recently emerges as a compelling framework for performing super resolution, garnering significant attention from multiple communities spanning signal processing, applied mathematics, and optimization. This article offers a friendly ... More
Scattering theory for repulsive Schrödinger operators and applications to limit circle problemApr 08 2019Apr 09 2019In this note, we study existence of the outgoing/incoming resolvents of repulsive Schr\"odinger operators which may not be essentially self-adjoint on the Schwartz space. Moreover, we recover the classical result: The repulsive Schro\"odinger operators ... More
Scattering theory for repulsive Schroöinger operators and applications to limit circle problemApr 08 2019In this note, we study existence of the outgoing/incoming resolvents of repulsive Schr\"odinger operators which may not be essentially self-adjoint on the Schwartz space. Moreover, we recover the classical result: The repulsive Schro\"odinger operators ... More
Scaling up MIMO radar for target detectionApr 08 2019This work focuses on target detection in a colocated MIMO radar system. Instead of exploiting the classical temporal domain, we propose to explore the spatial dimension (i.e., number of antennas $M$) to derive asymptotic results for the detector. Specifically, ... More
On the spectra of $g$-circulant matrices and applicationsApr 08 2019A g-circulant matrix of order n is defined as a matrix of order n where each row is a right cyclic shift in g-places to the preceding row. Using number theory, certain nonnegative g-circulant real matrices are constructed. In particular, it is shown that ... More
Improved eigenvalue bounds for Schrödinger operators with slowly decaying potentialsApr 08 2019We extend a result of Davies and Nath on the location of eigenvalues of Schr\"odinger operators with slowly decaying complex-valued potentials to higher dimensions. In this context, we also discuss various examples related to the Laptev--Safronov conjecture. ... More
Spectral and scattering theory of one-dimensional coupled photonic crystalsApr 08 2019Apr 09 2019We study the spectral and scattering theory of light transmission in a system consisting of two asymptotically periodic waveguides, also known as one-dimensional photonic crystals, coupled by a junction. Using analyticity techniques and commutator methods ... More
Spectral and scattering theory of one-dimensional coupled photonic crystalsApr 08 2019We study the spectral and scattering theory of light transmission in a system consisting of two asymptotically periodic waveguides, also known as one-dimensional photonic crystals, coupled by a junction. Using analyticity techniques and commutator methods ... More
Spatial Beam Tracking and Data Detection for an FSO Link to a UAV in the Presence of Hovering FluctuationsApr 07 2019Recent advances in small-scale unmanned aerial vehicles (UAVs) have opened up new horizons for establishing UAV-based free-space optical (FSO) links. However, FSO technology requires precise beam alignment while random fluctuations of hovering UAVs can ... More
Canonical systems with discrete spectrumApr 07 2019We study spectral properties of two-dimensional canonical systems $y'(t)=zJH(t)y(t)$, $t\in[a,b)$, where the Hamiltonian $H$ is locally integrable on $[a,b)$, positive semidefinite, and Weyl's limit point case takes place at $b$. We answer the following ... More
A Bayesian Theory of Change Detection in Statistically Periodic Random ProcessesApr 06 2019A new class of stochastic processes called independent and periodically identically distributed (i.p.i.d.) processes is defined to capture periodically varying statistical behavior. A novel Bayesian theory is developed for detecting a change in the distribution ... More
Towards Massive MIMO 2.0: Understanding spatial correlation, interference suppression, and pilot contaminationApr 06 2019Since the seminal paper by Marzetta from 2010, Massive MIMO has changed from being a theoretical concept with an infinite number of antennas to a practical technology. The key concepts are adopted in 5G and base stations (BSs) with $M=64$ full-digital ... More
The Derivation of Failure Event Correlation Based on Shadowing Cross-CorrelationApr 05 2019In this document we derive the mapping between the failure event correlation and shadowing cross-correlation in dual connectivity architectures. In this case, we assume that a single UE is connected to two gNBs (next generation NodeB).
Self-adjointness of perturbed bi-Laplacians on infinite graphsApr 03 2019We give a sufficient condition for the essential self-adjointness of a perturbation of the square of the magnetic Laplacian on an infinite weighted graph. The main result is applicable to graphs whose degree function is not necessarily bounded. The result ... More
Recent results on the spectra of lens spacesApr 01 2019In this paper we report on recent results by several authors, on the spectral theory of lens spaces and orbifolds and similar locally symmetric spaces of rank one. Most of these results are related to those obtained by the authors in [IMRN (2016), 1054--1089], ... More
Exploring the Trade-Off between Privacy and Coordination in Millimeter Wave Spectrum SharingApr 01 2019The synergetic gains of spectrum sharing and millimeter wave communication networks have recently attracted attention, owing to the interference canceling benefits of highly-directional beamforming in such systems. In principle, fine-tuned coordinated ... More
Balanced frames: a useful tool in signal processing with good propertiesApr 01 2019So far there has not been paid attention in the literature to frames that are balanced, i.e. those frames which sum is zero. In this paper we study balanced frames, and in particular balanced unit norm tight frames in finite dimensional Hilbert spaces. ... More
Balanced frames: a useful tool in signal processing with good propertiesApr 01 2019Apr 12 2019So far there has not been paid attention in the literature to frames that are balanced, i.e. those frames which sum is zero. In this paper we consider balanced frames, and in particular balanced unit norm tight frames in finite dimensional Hilbert spaces. ... More
On the circle, $GMC^γ= CβE_\infty$ for $γ= \sqrt{\frac{2}β}, $ $( γ\leq 1 )$Apr 01 2019We identify an equality between two objects arising from different contexts of mathematical physics: Kahane's Gaussian Multiplicative Chaos ($GMC^\gamma$) on the circle, and the Circular Beta Ensemble $(C\beta E)$ from Random Matrix Theory. This is obtained ... More
Limiting absorption principle on Lp-spaces and scattering theoryMar 31 2019In this paper, we study the mapping property form Lp to Lq of the resolvent of the Fourier multiplier operators and scattering theory of generalized Schr\"odinger operators. Though the first half of the subject is studied in [4], we extend their result ... More
The Broken Ray Transform: Additional Properties and New Inversion FormulaMar 31 2019The significance of the broken ray transform (BRT) is due to its occurrence in a number of modalities spanning optical, x-ray, and nuclear imaging. Decomposing the BRT as a combination of cone beam transforms clarifies the extent of data required for ... More
Coordinated Beam Selection in Millimeter Wave Multi-User MIMO Using Out-of-Band InformationMar 29 2019Using out-of-band (OOB) side-information has recently been shown to accelerate beam selection in single-user millimeter wave (mmWave) massive MIMO communications. In this paper, we propose a novel OOB-aided beam selection framework for a mmWave uplink ... More
Robust Data Detection for MIMO Systems with One-Bit ADCs: A Reinforcement Learning ApproachMar 29 2019The use of one-bit analog-to-digital converters (ADCs) at a receiver is a power-efficient solution for future wireless systems operating with a large signal bandwidth and/or a massive number of receive radio frequency chains. This solution, however, induces ... More
Interface Asymptotics of Wigner-Weyl Distributions for the Harmonic OscillatorMar 29 2019We prove several types of scaling results for Wigner distributions of spectral projections of the isotropic Harmonic oscillator on $\mathbb R^d$. In prior work, we studied Wigner distributions $W_{\hbar, E_N(\hbar)}(x, \xi)$ of individual eigenspace projections. ... More
Above the Nyquist Rate, Modulo Folding Does Not HurtMar 28 2019We consider the problem of recovering a continuous-time bandlimited signal from the discrete-time signal obtained from sampling it every $T_s$ seconds and reducing the result modulo $\Delta$, for some $\Delta>0$. For $\Delta=\infty$ the celebrated Shannon-Nyquist ... More
Information Theoretic Feature Transformation Learning for Brain InterfacesMar 28 2019Objective: A variety of pattern analysis techniques for model training in brain interfaces exploit neural feature dimensionality reduction based on feature ranking and selection heuristics. In the light of broad evidence demonstrating the potential sub-optimality ... More
Information Theoretic Feature Transformation Learning for Brain InterfacesMar 28 2019Apr 05 2019Objective: A variety of pattern analysis techniques for model training in brain interfaces exploit neural feature dimensionality reduction based on feature ranking and selection heuristics. In the light of broad evidence demonstrating the potential sub-optimality ... More
On the continuity of the integrated density of states in the disorderMar 28 2019Recently, Hislop and Marx studied the dependence of the integrated density of states on the underlying probability distribution for a class of discrete random Schr\"odinger operators, and established a quantitative form of continuity in weak* topology. ... More
Progressive intrinsic ultracontractivity and heat kernel estimates for non-local Schrödinger operatorsMar 28 2019We study the long-time asymptotic behaviour of semigroups generated by non-local Schr\"odinger operators of the form $H = -L+V$; the free operator $L$ is the generator of a symmetric L\'evy process in $\mathbb R^d$, $d > 1$ (with non-degenerate jump measure) ... More
Inertial Sensor Aided mmWave Beam Tracking to Support Cooperative Autonomous DrivingMar 28 2019This paper presents an inertial sensor aided technique for beam alignment and tracking in massive multiple-input multiple-output (MIMO) vehicle-to-vehicle (V2V) communications based on millimeter waves (mmWave). Since directional communications in vehicular ... More
Asymptotics and estimates of the discrete spectrum of the Schrodinger operator on a discrete periodic graphMar 28 2019The periodic Schrodinger operator $ H $ on a discrete periodic graph is considered. We estimate the discrete spectrum of the perturbed operator $ H _ {-} (t) = H-tV $, $ t> 0 $, where the potential $ V \ ge 0 $ is decreasing and $t>0$ is the coupling ... More
The spectral density of Hankel operators with piecewise continuous symbolsMar 27 2019In 1966, H. Widom proved an asymptotic formula for the distribution of eigenvalues of the $N\times N$ truncated Hilbert matrix for large values of $N$. In this paper, we extend this formula to Hankel matrices with symbols in the class of piece-wise continuous ... More
Global eigenvalue distribution of matrices defined by the skew-shiftMar 27 2019We consider large Hermitian matrices whose entries are defined by evaluating the exponential function along orbits of the skew-shift $\binom{j}{2} \omega+jy+x \mod 1$ for irrational $\omega$. We prove that the eigenvalue distribution of these matrices ... More
Energy-Efficient Power Control in Cell-Free and User-Centric Massive MIMO at Millimeter WaveMar 27 2019In a cell-free massive MIMO architecture a very large number of distributed access points simultaneously and jointly serves a much smaller number of mobile stations; a variant of the cell-free technique is the user-centric approach, wherein each access ... More
Digital Signal Processing Techniques for High-Speed Optical Communications LinksMar 27 2019The main topic of this thesis is the application of advanced Digital Signal Processing (DSP) techniques to high data-rate optical links. This thesis is divided in two parts: Direct-Detection systems, and Coherent systems. In the first part, it is proposed ... More
Differential Geometric Foundations for Power Flow ComputationsMar 26 2019This paper aims to systematically and comprehensively initiate a foundation for using concepts from computational differential geometry as instruments for power flow computing and research. At this point we focus our discussion on the static case, with ... More
On a continuum limit of discrete Schrödinger operators on square latticeMar 26 2019The norm resolvent convergence of discrete Schr\"odinger operators to a continuum Schr\"odinger operator in the continuum limit is proved under relatively weak assumptions. This result implies, in particular, the convergence of the spectrum with respect ... More
Making Cell-Free Massive MIMO Competitive With MMSE Processing and Centralized ImplementationMar 25 2019Cell-free Massive MIMO is considered as a promising technology for satisfying the increasing number of users and high rate expectations in beyond-5G networks. The key idea is to let many distributed access points (APs) communicate with all users in the ... More
Eigenvalue and Resonance Asymptotics in perturbed periodically twisted tubes: Twisting versus BendingMar 25 2019We consider the Dirichlet Laplacian in a three-dimensional waveguide that is a small deformation of a periodically twisted tube. The deformation is given by a bending and an additional twisting of the tube, both parametrized by a coupling constant $\delta$. ... More
Courant-sharp Robin eigenvalues for the square -- the case with small Robin parameter--Mar 25 2019This article is the continuation of our first work on the determination of the cases where there is equality in Courant's Nodal Domain theorem in the case of a Robin boundary condition (with Robin parameter $h$). For the square, our first paper focused ... More
Asymptotics of eigenvalues of large symmetric Toeplitz matrices with smooth simple-loop symbolsMar 25 2019This paper is devoted to the asymptotic behavior of all eigenvalues of Symmetric (in general non Hermitian) Toeplitz matrices with moderately smooth symbols which trace out a simple loop on the complex plane line as the dimension of the matrices increases ... More
Hamiltonian Realization of spectraMar 25 2019A $2n\times 2n$ real matrix $A$ is said to be a Hamiltonian matrix if $A^{T}J+JA=0$, where $J=\left( \begin{array}{cc} 0 & I_{n} \\ -I_{n} & 0\\ \end{array} \right)$. Hamiltonian matrices appear in many areas of applications, such as linear control theory, ... More
Transfer matrices for discrete Hermitian operators and absolutely continuous spectrumMar 25 2019We introduce a transfer matrix method for the spectral analysis of discrete Hermitian operators with locally finite hopping. Such operators can be associated with a locally finite graph structure and the method works in principle on any such graph. The ... More
Blow-up profile of neutron stars in the Hartree-Fock-Bogoliubov theoryMar 24 2019We consider the gravitational collapse for neutron stars in the Hartree-Fock-Bogoliubov theory. We prove that when the number particle becomes large and the gravitational constant is small such that the attractive interaction strength approaches the Chandrasekhar ... More
Billiard flow and eigenfunction concentration on polyhedronsMar 23 2019We study dynamical properties of the billiard flow on $3$ dimensional convex polyhedrons away from "pockets" and establish a finite tube condition for rational polyhedrons that extends well-known results in dimension $2$. Furthermore, we establish a new ... More
Connections between spectral properties of asymptotic mappings and solutions to wireless network problemsMar 23 2019Apr 10 2019In this study we establish connections between asymptotic functions and properties of solutions to important problems in wireless networks. We start by introducing a class of self-mappings (called asymptotic mappings) constructed with asymptotic functions, ... More
Connections between spectral properties of asymptotic mappings and solutions to wireless network problemsMar 23 2019In this study we establish connections between asymptotic functions and properties of solutions to important problems in wireless networks. We start by introducing a class of self-mappings (called asymptotic mappings) constructed with asymptotic functions, ... More
Super-Resolution DOA Estimation for Arbitrary Array Geometries Using a Single Noisy SnapshotMar 22 2019We address the problem of search-free DOA estimation from a single noisy snapshot for sensor arrays of arbitrary geometry, by extending a method of gridless super-resolution beamforming to arbitrary arrays with noisy measurements. The primal atomic norm ... More
Learning Mixtures of Separable Dictionaries for Tensor Data: Analysis and AlgorithmsMar 22 2019This work addresses the problem of learning sparse representations of tensor data using structured dictionary learning. It proposes learning a mixture of separable dictionaries to better capture the structure of tensor data by generalizing the separable ... More
Controllability-Gramian Submatrices for a Network Consensus ModelMar 21 2019Principal submatrices of the controllability Gramian and their inverses are examined, for a network-consensus model with inputs at a subset of network nodes. Specifically, several properties of the Gramian submatrices and their inverses -- including dominant ... More
Cognitive Wireless Power Transfer in the Presence of Reactive Primary Communication UserMar 21 2019This paper studies a cognitive or secondary multi-antenna wireless power transfer (WPT) system over a multi-carrier channel, which shares the same spectrum with a primary wireless information transfer (WIT) system that employs adaptive water-filling power ... More
Effective upper bound of analytic torsion under Arakelov metricMar 20 2019Mar 26 2019Given a choice of metric on the Riemann surface, the regularized determinant of Laplacian (analytic torsion) is defined via the complex power of elliptic operators: $$ \det(\Delta)=\exp(-\zeta'(0)) $$ In this paper we gave an asymptotic effective estimate ... More
Effective upper bound of analytic torsion under Arakelov metricMar 20 2019Given a choice of metric on the Riemann surface, the regularized determinant of Laplacian (analytic torsion) is defined via the complex power of elliptic operators: $$ \det(\Delta)=\exp(-\zeta'(0)) $$ In this paper we gave an asymptotic effective estimate ... More
Noisy Accelerated Power Method for Eigenproblems with ApplicationsMar 20 2019This paper introduces an efficient algorithm for finding the dominant generalized eigenvectors of a pair of symmetric matrices. Combining tools from approximation theory and convex optimization, we develop a simple scalable algorithm with strong theoretical ... More
Spectral enclosures for non-self-adjoint discrete Schrödinger operatorsMar 20 2019We study location of eigenvalues of one-dimensional discrete Schr\"odinger operators with complex $\ell^{p}$-potentials for $1\leq p\leq \infty$. In the case of $\ell^{1}$-potentials, the derived bounds are sharp and apply also to embedded eigenvalues. ... More
Periodic Dirac operator on the half-lineMar 20 2019We consider the Dirac operator with a periodic potential on the half-line with the Dirichlet boundary condition at zero. Its spectrum consists of an absolutely continuous part plus at most one eigenvalue in each open gap. The Dirac resolvent admits a ... More
Eigenfunction concentration via geodesic beamsMar 20 2019In this article we develop new techniques for studying concentration of Laplace eigenfunctions $\phi_\lambda$ as their frequency, $\lambda$, grows. The method consists of controlling $\phi_\lambda(x)$ by decomposing $\phi_\lambda$ into a superposition ... More
On the $j$-th Eigenvalue of Sturm-Liouville Problem and the Maslov IndexMar 19 2019In the previous papers \cite{HLWZ,KWZ}, the jump phenomena of the $j$-th eigenvalue were completely characterized for Sturm-Liouville problems. In this paper, we show that the jump number of these eigenvalue branches is exactly the Maslov index for the ... More
High-Dimensional Bernoulli Autoregressive Process with Long-Range DependenceMar 19 2019We consider the problem of estimating the parameters of a multivariate Bernoulli process with auto-regressive feedback in the high-dimensional setting where the number of samples available is much less than the number of parameters. This problem arises ... More
Laplacian eigenvalues of the zero divisor graph of the ring $\mathbb{Z}_{n}$Mar 19 2019We study the Laplacian eigenvalues of the zero divisor graph $\Gamma\left(\mathbb{Z}_{n}\right)$ of the ring $\mathbb{Z}_{n}$ and prove that $\Gamma\left(\mathbb{Z}_{p^t}\right)$ is Laplacian integral for every prime $p$ and positive integer $t\geq 2$. ... More
On the Second-order Frechet Derivatives of Eigenvalues of Sturm-Liouville Problems in PotentialsMar 19 2019The works of V. A. Vinokurov have shown that eigenvalues and normalized eigenfunctions of Sturm-Liouville problems are analytic in potentials, considered as mappings from the Lebesgue space to the space of real numbers and the Banach space of continuous ... More
Periodic spectrum of $n$-cubic quantun graphsMar 18 2019Apr 04 2019We study the spectrum of some periodic differential operators, in particular the periodic Schr\"{o}dinger operator acting on infinite $n$-cubic graphs. Using Floquet-Bloch theory, we derive and analyze on the dispersion relations of the periodic quantum ... More
Periodic spectrum of $n$-cubic quantun graphsMar 18 2019We study the spectrum of some periodic differential operators, in particular the periodic Schr\"{o}dinger operator acting on infinite $n$-cubic graphs. Using Floquet-Bloch theory, we derive and analyze on the dispersion relations of the periodic quantum ... More
Dispersion relations of periodic quantum graphs associated with Archimedean tilings (II)Mar 18 2019We continue the work of a previous paper \cite{LJL} to derive the dispersion relations of the periodic quantum graphs associated with the remaining 5 of the 11 Archimedean tilings, namely the truncated hexagonal tiling $(3,12^2)$, rhombi-trihexagonal ... More
Dispersion relations of periodic quantum graphs associated with Archimedean tilings (II)Mar 18 2019Apr 04 2019We continue the work of a previous paper \cite{LJL} to derive the dispersion relations of the periodic quantum graphs associated with the remaining 5 of the 11 Archimedean tilings, namely the truncated hexagonal tiling $(3,12^2)$, rhombi-trihexagonal ... More
Linearly Constrained Smoothing Group Sparsity Solvers in Off-grid ModelMar 17 2019In compressed sensing, the sensing matrix is assumed perfectly known. However, there exists perturbation in the sensing matrix in reality due to sensor offsets or noise disturbance. Directions-of-arrival (DoA) estimation with off-grid effect satisfies ... More
Joint Block Low Rank and Sparse Matrix Recovery in Array Self-Calibration Off-Grid DoA EstimationMar 17 2019This letter addresses the estimation of directions-of-arrival (DoA) by a sensor array using a sparse model in the presence of array calibration errors and off-grid directions. The received signal utilizes previously used models for unknown errors in calibration ... More
Convergence rate for eigenvalues of the elastic Neumann--Poincaré operator on smooth and real analytic boundaries in two dimensionsMar 17 2019The elastic Neumann--Poincar\'e operator is a boundary integral operator associated with the Lam\'e system of linear elasticity. It is known that if the boundary of a planar domain is smooth enough, it has eigenvalues converging to two different points ... More
A Universality Law For Sign Correlations of Eigenfunctions of Differential OperatorsMar 15 2019We establish a universality law for sequences of functions $\{w_n\}_{n \in \mathbb{N}}$ satisfying a form of WKB approximation on compact intervals. This includes eigenfunctions of generic Schr\"odinger operators, as well as Laguerre and Chebyshev polynomials. ... More
A central limit theorem for integrals of random wavesMar 15 2019We derive a central limit theorem for the mean-square of random waves in the high-frequency limit over shrinking sets. Our proof applies to any compact Riemannian manifold of arbitrary dimension, thanks to the universality of the local Weyl law. The key ... More
QoS Aware Power Allocation and User Selection in Massive MIMO Underlay Cognitive Radio NetworksMar 15 2019We address the problem of power allocation and secondary user (SU) selection in the downlink from a secondary base station (SBS) equipped with a large number of antennas in an underlay cognitive radio network. A new optimization framework is proposed ... More
Power Control and Frequency Band Selection Policies for Underlay MIMO Cognitive RadioMar 15 2019We study power control and frequency band selection policies for multi-band underlay MIMO cognitive radio with the objective of maximizing the rate of a secondary user (SU) link while limiting the interference leakage towards primary users (PUs) below ... More
Analytic torsion and Reidemeister torsion of hyperbolic manifolds with cuspsMar 14 2019On an odd-dimensional oriented hyperbolic manifold of finite volume with strongly acyclic coefficient systems, we derive a formula relating analytic torsion with the Reidemeister torsion of the Borel-Serre compactification of the manifold. In a companion ... More
On the multiplicity of the second eigenvalue of the Laplacian in non simply connected domains--with some numerics--Mar 14 2019We revisit an interesting example proposed by Maria Hoffmann-Ostenhof, the second author and Nikolai Nadirashvili of a bounded domain in R2 for which the second eigenvalue of the Dirichlet Laplacian has multiplicity three. We also analyze carefully the ... More
Rate Statistics in Cellular Downlink: PHY Rateless vs Adaptive Modulation and CodingMar 14 2019In this letter, we focus on rateless coded adaptive transmission in a cellular downlink. Based on a stochastic geometry model for the locations of BSs, we evaluate the meta-distribution of rate, i.e., the distribution of rate conditioned on the point ... More
Large-Scale Beamforming for Massive MIMO via Randomized SketchingMar 14 2019Massive MIMO system yields significant improvements in spectral and energy efficiency for future wireless communication systems. The regularized zero-forcing (RZF) beamforming is able to provide good performance with the capability of achieving numerical ... More