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Is Lipschitz Continuity Preserved under Sampled-Data Discretization?Dec 27 2016Usually, given a continuous-time nonlinear model, a closed form solution for an exact discretization can not be found explicitly, originating the need of approximating discrete-time models. This note studies the preservation of the Lipschitz continuity ... More

Static Output Feedback Control for Nonlinear Systems subject to Parametric and Nonlinear UncertaintiesJun 25 2016This work addresses the design of static output feedback control of discrete-time nonlinear systems satisfying a local Lipschitz continuity condition with time-varying uncertainties. The controller has also a guaranteed disturbance attenuation level (Hinfty ... More

Analysis of a Legendre spectral element method (LSEM) for the two-dimensional system of a nonlinear stochastic advection-reaction-diffusion modelsApr 12 2019In this work, we develop a Legendre spectral element method (LSEM) for solving the stochastic nonlinear system of advection-reaction-diffusion models. The used basis functions are based on a class of Legendre functions such that their mass and diffuse ... More

On the stability of generalized mixed type quadratic and quartic functional equation in quasi-Banach spacesDec 30 2008In this paper, we establish the general solution of the functional equation $$f(nx+y)+f(nx-y)=n^2f(x+y)+n^2f(x-y)+2(f(nx)-n^2f(x))-2(n^2-1)f(y)\eqno {0 cm}$$for fixed integers $n$ with $n\neq0,\pm1$ and investigate the generalized Hyers-Ulam-Rassias stability ... More

Deep Learning-Based Classification Of the Defective Pistachios Via Deep Autoencoder Neural NetworksJun 10 2019Pistachio nut is mainly consumed as raw, salted or roasted because of its high nutritional properties and favorable taste. Pistachio nuts with shell and kernel defects, besides not being acceptable for a consumer, are also prone to insects damage, mold ... More

Liouville theorems for stable solutions of symmetric systems on Riemannian manifoldsJun 05 2015We examine stable solutions of the following symmetric system on a complete, connected, smooth Riemannian manifold $\mathbb{M}$ without boundary, \begin{equation*} -\Delta_g u_i = H_i(u) \end{equation*} where $\Delta_g$ stands for the Laplace-Beltrami ... More

Stable solutions of symmetric systems on Riemannian manifoldsJun 05 2015Nov 01 2016We examine stable solutions of the following symmetric system on a complete, connected, smooth Riemannian manifold $\mathbb{M}$ without boundary, \begin{equation*} -\Delta_g u_i = H_i(u_1,\cdots,u_m) \ \ \text{on} \ \ \mathbb{M}, \end{equation*} when ... More

Solutions of multi-component fractional symmetric systemsJun 04 2015Nov 03 2016We study the following elliptic system concerning the fractional Laplacian operator $$(- \Delta)^ {s_i} u_i = H_i ( u_1,\cdots,u_m) \ \ \text{in}\ \ \mathbb{R}^n,$$ when $0<s_i<1$, $u_i: \mathbb R^n\to R$ and $H_i$ belongs to $C^{1,\gamma}(\mathbb{R}^m)$ ... More

Entire solutions of quasilinear symmetric systemsJun 08 2015Oct 31 2015We study the following quasilinear elliptic system for all $i=1,\cdots,m$ \begin{equation*} \label{} -div(\Phi'(|\nabla u_i|^2) \nabla u_i) = H_i(u) \quad \text{in} \ \ \mathbb{R}^n \end{equation*} where $u=(u_i)_{i=1}^m: \mathbb R^n\to \mathbb R^m$ and ... More

Rigidity results for stable solutions of symmetric systemsOct 07 2014We study stable solutions of the following nonlinear system $$ -\Delta u = H(u) \quad \text{in} \ \ \Omega$$ where $u:\mathbb R^n\to \mathbb R^m$, $H:\mathbb R^m\to \mathbb R^m$ and $\Omega$ is a domain in $\mathbb R^n$. We introduce the novel notion ... More

Stable solutions of symmetric systems involving hypoelliptic operatorsMar 06 2018Please see the article for the abstract.

Effect of weights on stable solutions of a quasilinear elliptic equationSep 23 2011May 24 2013In this note, we study Liouville theorems for the stable and finite Morse index weak solutions of the quasilinear elliptic equation $-\Delta_p u= f(x) F(u) $ in $\mathbb{R}^n$ where $p\ge 2$, $0\le f\in C(\mathbb{R}^n)$ and $F\in C^1(\mathbb{R})$. We ... More

Liouville type theorems for stable solutions of certain elliptic systemsSep 23 2011Nov 22 2011We establish Liouville type theorems for elliptic systems with various classes of non-linearities on $\mathbb{R}^N$. We show among other things, that a system has no semi-stable solution in any dimension, whenever the infimum of the derivatives of the ... More

Composition operators acting on weighted Hilbert spaces of analytic functionsJun 05 2013Aug 06 2013In this paper, we consider composition operators on weighted Hilbert spaces of analytic functions and observe that a formula for the essential norm, give a Hilbert-Schmidt characterization and characterize the membership in Schatten-class for these operators. ... More

Ultra High Energy Cosmic RaysNov 11 2011Ultra high energy particles arrive at Earth constantly. They provide a beam at energies higher than any man-made accelerator, but at a very low rate. Two large experiments, the Pierre Auger Observatory and the Telescope Array experiment, have been taking ... More

The Hybrid Activities of the Pierre Auger ObservatoryAug 30 2006The Pierre Auger Observatory detects ultra-high energy cosmic rays by implementing two complementary air-shower techniques. The combination of a large ground array and fluorescence detectors, known as the hybrid concept, means that a rich variety of measurements ... More

De Giorgi type results for equations with nonlocal lower-order termsMay 30 2019It is known that the De Giorgi's conjecture does not hold in two dimensions for semilinear elliptic equations with a nonzero drift, in general, $$ \Delta u+ q\cdot \nabla u+f(u)=0 \ \ \text{in } \ \ \mathbb R^2, $$ when $q=(0,-c)$ for $c\neq 0$. This ... More

Liouville theorems for the polyharmonic Henon-Lane-Emden systemAug 01 2013We study Liouville theorems for the following polyharmonic H\'{e}non-Lane-Emden system \begin{eqnarray*} \left\{\begin{array}{lcl} (-\Delta)^m u&=& |x|^{a}v^p \ \ \text{in}\ \ \mathbb{R}^n,\\ (-\Delta)^m v&=& |x|^{b}u^q \ \ \text{in}\ \ \mathbb{R}^n, ... More

Super Star Products and Quantum SuperalgebrasOct 29 2000We prove that the super star product on a Poisson Lie supergroup leads to the structure of quantum superalgebra (triangular Hopf superalgebra) on the super quantized enveloping algebra of the Lie superalgebra of the Lie supergroup and that equivalents ... More

On the quantum super Virasoro algebraOct 21 2000The quantum super-algebra structure on the deformed super Virasoro algebra is investigated. More specifically we established the possibility of defining a non trivial Hopf super-algebra on both one and two-parameters deformed super Virasoro algebras.

Linear and Nonlinear Identification of Dryer System Using Artificial Intelligence and Neural NetworksNov 16 2018Feb 08 2019As you read these words you are using a complex biological neural network. You have a highly interconnected set of some neurons to facilitate your reading, breathing, motion and thinking. Each of your biological neurons, a rich assembly of tissue and ... More

Regularity of extremal solutions of nonlocal elliptic systemsFeb 12 2019We examine regularity of the extremal solution of nonlinear nonlocal eigenvalue problems with an integro-differential operator, including the fractional Laplacian, of the form of $$ \mathcal L(u (x))= \lim_{\epsilon\to 0} \int_{\mathbb R^n\setminus B_\epsilon(x) ... More

Stability Control of Walking Biped Robots based on Total MomentumMay 05 2019Principle Equation of Motion (for walkers) is derived that later results in introducing two piecewise-continuous dynamical systems namely Simplified Walking Model (SWM) and Complete Walking Model (CWM) which both describe the behavior of walker with emphasis ... More

Modelling and Analysing Behaviours and Emotions via Complex User InteractionsFeb 20 2019Over the past 15 years, the volume, richness and quality of data collected from the combined social networking platforms has increased beyond all expectation, providing researchers from a variety of disciplines to use it in their research. Perhaps more ... More

Magneto-photonic phenomena at terahertz frequenciesApr 14 2014Magneto-terahertz phenomena are the main focus of the thesis. This work started as supporting research for the science of an X-ray laser (SwissFEL). X-ray lasers have recently drawn great attention as an unprecedented tool for scientific research on the ... More

Artificial neural network approach for condition-based maintenanceNov 03 2015In this research, computerized maintenance management will be investigated. The rise of maintenance cost forced the research community to look for more effective ways to schedule maintenance operations. Using computerized models to come up with optimal ... More

Comments on "Achievable Rates in Cognitive Radio Channels"Sep 21 2015In a premier paper on the information-theoretic analysis of a two-user cognitive interference channel(CIC), Devroye et al. presented an achievable rate region for the two-user discrete memoryless CIC. The coding scheme proposed by Devroye et al. is correct ... More

Higher-dimensional solutions for a nonuniformly elliptic equationNov 24 2013We prove $m$-dimensional symmetry results, that we call $m$-Liouville theorems, for stable and monotone solutions of the following nonuniformly elliptic equation \begin{eqnarray*}\label{mainequ} - div(\gamma(\mathbf x') \nabla u(\mathbf x)) =\lambda (\mathbf ... More

On The Dunkl Intertwining OpereatorMay 08 2016May 11 2016Dunkl operators are differential-difference operators parametrized by a finite reflection group and a weight function. The commutative algebra generated by these operators generalizes the algebra of standard differential operators and intertwines with ... More

Some abstract Wegner estimates with applicationsDec 09 2012Jul 18 2013We prove some abstract Wegner bounds for random self-adjoint operators. Applications include elementary proofs of Wegner estimates for discrete and continuous Anderson Hamiltonians with possibly sparse potentials, as well as Wegner bounds for quantum ... More

Adaptive Model Predictive Control of a Batch Solution Polymerization Process using Trajectory LinearizationOct 12 2015A sequential trajectory linearized adaptive model based predictive controller is designed using the DMC algorithm to control the temperature of a batch MMA polymerization process. Using the mechanistic model of the polymerization, a parametric transfer ... More

Uncertainty Quantification in Molecular Signals using Polynomial Chaos ExpansionJan 30 2019Molecular signals are abundant in engineering and biological contexts, and undergo stochastic propagation in fluid dynamic channels. The received signal is sensitive to a variety of input and channel parameter variations. Currently we do not understand ... More

Generalized Nonlinear Robust Energy-to-Peak Filtering for Differential Algebraic SystemsFeb 25 2014The problem of robust nonlinear energy-to-peak filtering for nonlinear descriptor systems with model uncertainties is addressed. The system is assumed to have nonlinearities both in the state and output equations as well as norm-bounded time-varying uncertainties ... More

A Generalized Robust Filtering Framework for Nonlinear Differential-Algebraic SystemsFeb 22 2014A generalized dynamical robust nonlinear filtering framework is established for a class of Lipschitz differential algebraic systems, in which the nonlinearities appear both in the state and measured output equations. The system is assumed to be affected ... More

Computer Algebra Methods in Control SystemsDec 26 2017Dec 29 2017As dynamic and control systems become more complex, relying purely on numerical computations for systems analysis and design might become extremely expensive or totally infeasible. Computer algebra can act as an enabler for analysis and design of such ... More

A Multi Objective Reliable Location-Inventory Capacitated Disruption Facility Problem with Penalty Cost Solve with Efficient Meta Historic AlgorithmsNov 26 2017Logistics network is expected that opened facilities work continuously for a long time horizon without any failure, but in real world problems, facilities may face disruptions. This paper studies a reliable joint inventory location problem to optimize ... More

Supervised learning based on temporal coding in spiking neural networksJun 27 2016Gradient descent training techniques are remarkably successful in training analog-valued artificial neural networks (ANNs). Such training techniques, however, do not transfer easily to spiking networks due to the spike generation hard non-linearity and ... More

Supervised learning based on temporal coding in spiking neural networksJun 27 2016Aug 16 2017Gradient descent training techniques are remarkably successful in training analog-valued artificial neural networks (ANNs). Such training techniques, however, do not transfer easily to spiking networks due to the spike generation hard non-linearity and ... More

One-dimensional symmetry for integral systems in two dimensionsJun 10 2015The purpose of this brief paper is to prove De Giorgi type results for stable solutions of the following nonlocal system of integral equations in two dimensions $$ L(u_i) = H_i(u) \quad \text{in} \ \ \mathbb R^2 , $$ where $u=(u_i)_{i=1}^m$ for $u_i: ... More

Analytical expression for variance of homogeneous-position quantum walk with decoherent positionMay 29 2017Sep 19 2017We have derived an analytical expression for variance of homogeneous-position decoherent quantum walk (HPDQW) with general form of noise on its position, and have shown that, while the quadratic ($t^2$) term of variance never changes by position decoherency, ... More

Anderson Localization for a Multi-Particle Quantum GraphJan 30 2012Jul 18 2013We study a multi-particle quantum graph with random potential. Taking the approach of multiscale analysis we prove exponential and strong dynamical localization of any order in the Hilbert-Schmidt norm near the spectral edge. Apart from the results on ... More

Fractional spin through quantum strange superalgebra $\tilde{P}_{Q}(n)$Feb 24 2015Mar 01 2015The purposes of this paper is to investigate the properties of the quantum extended strange superalgebra $\tilde{P}_{Q}(n)$ when his deformation parameter $Q$ goes to a root of unity.

Coherence Pursuit: Fast, Simple, and Robust Principal Component AnalysisSep 15 2016This paper presents a remarkably simple, yet powerful, algorithm for robust Principal Component Analysis (PCA). In the proposed approach, an outlier is set apart from an inlier by comparing their coherence with the rest of the data points. As inliers ... More

A Subspace Learning Approach to High-Dimensional Matrix Decomposition with Efficient Information SamplingFeb 01 2015Feb 13 2016This paper is concerned with the problem of low-rank plus sparse matrix decomposition for big data. Conventional algorithms for matrix decomposition use the entire data to extract the low-rank and sparse components, and are based on optimization problems ... More

Parameter Efficient Training of Deep Convolutional Neural Networks by Dynamic Sparse ReparameterizationFeb 15 2019Deep neural networks are typically highly over-parameterized with pruning techniques able to remove a significant fraction of network parameters with little loss in accuracy. Recently, techniques based on dynamic re-allocation of non-zero parameters have ... More

Learning to Rank from Samples of Variable QualityJun 21 2018Training deep neural networks requires many training samples, but in practice, training labels are expensive to obtain and may be of varying quality, as some may be from trusted expert labelers while others might be from heuristics or other sources of ... More

Data Dropout in Arbitrary Basis for Deep Network RegularizationDec 04 2017Dec 05 2017An important problem in training deep networks with high capacity is to ensure that the trained network works well when presented with new inputs outside the training dataset. Dropout is an effective regularization technique to boost the network generalization ... More

Quantum Ergodicity on Graphs : from Spectral to Spatial DelocalizationApr 10 2017Mar 05 2019We prove a quantum-ergodicity theorem on large graphs, for eigenfunctions of Schr\"odinger operators in a very general setting. We consider a sequence of finite graphs endowed with discrete Schr\"odinger operators, assumed to have a local weak limit. ... More

Distribution of global defensive $k$-alliances over some graph productsDec 07 2018If $G=(V_G, E_G)$ is a graph, then $S\subseteq V_G$ is a global defensive $k$-alliance in $G$ if (i) each vertex not in $S$ has a neighbor in $S$ and (ii) each vertex of $S$ has at least $k$ more neighbors inside $S$ than outside of it. The global defensive ... More

On stable entire solutions of semi-linear elliptic equations with weightsAug 15 2011We are interested in the existence versus non-existence of non-trivial stable sub- and super-solutions of {equation} \label{pop} -div(\omega_1 \nabla u) = \omega_2 f(u) \qquad \text{in}\ \ \IR^N, {equation} with positive smooth weights $ \omega_1(x),\omega_2(x)$. ... More

Interpretability of Multivariate Brain Maps in Brain Decoding: Definition and QuantificationMar 29 2016Brain decoding is a popular multivariate approach for hypothesis testing in neuroimaging. It is well known that the brain maps derived from weights of linear classifiers are hard to interpret because of high correlations between predictors, low signal ... More

Stochastic Interpretation of Quasi-periodic Event-based SystemsDec 09 2015Many networks used in machine learning and as models of biological neural networks make use of stochastic neurons or neuron-like units. We show that stochastic artificial neurons can be realized on silicon chips by exploiting the quasi-periodic behavior ... More

Partial isometries and the conjecture of C. K. Fong and S. K. TsuiNov 29 2015We investigate some bounded linear operators T on a Hilbert space which satisfy the condition |T | less or equal to |ReT |. We describe the maximum invariant subspace for a contraction T on which T is a partial isometry to obtain that, in certain cases, ... More

Randomized Robust Subspace Recovery for High Dimensional Data MatricesMay 21 2015Apr 08 2016This paper explores and analyzes two randomized designs for robust Principal Component Analysis (PCA) employing low-dimensional data sketching. In one design, a data sketch is constructed using random column sampling followed by low dimensional embedding, ... More

Contact equivalence problem for KDV-type equationsAug 25 2014Dec 15 2014The Cartan's method of equivalence and moving coframe method has been applied to solve the local equivalence problem for KDV-type equations under the action of a pseudo-group of contact transformations. The structure equations, the sets of differential ... More

On the Hénon-Lane-Emden conjectureJul 28 2011Sep 27 2012We consider Liouville-type theorems for the following H\'{e}non-Lane-Emden system \hfill -\Delta u&=& |x|^{a}v^p \text{in} \mathbb{R}^N, \hfill -\Delta v&=& |x|^{b}u^q \text{in} \mathbb{R}^N, when $pq>1$, $p,q,a,b\ge0$. The main conjecture states that ... More

Comparison of the nonrelativistic limit of Amelino-Camelia and MS Doubly Special RelativityApr 17 2011Apr 19 2011This paper is devoted to the study of the nonrelativitic limit of Amelino-Camelia Doubly Special Relativity, and the corresponding modified Klein-Gordon and Dirac equations. We show that these equations reduce to the Schrodinger equations for the particle ... More

Optimization of Clustering for Clustering-based Image DenoisingJun 12 2013Oct 28 2013In this paper, the problem of de-noising of an image contaminated with additive white Gaussian noise (AWGN) is studied. This subject has been continued to be an open problem in signal processing for more than 50 years. In the present paper, we suggest ... More

Improving Waiting Time of Tasks Scheduled Under Preemptive Round Robin Using Changeable Time QuantumMar 28 2010Minimizing waiting time for tasks waiting in the queue for execution is one of the important scheduling cri-teria which took a wide area in scheduling preemptive tasks. In this paper we present Changeable Time Quan-tum (CTQ) approach combined with the ... More

Sketch-based Randomized Algorithms for Dynamic Graph RegressionMay 28 2019Jun 04 2019A well-known problem in data science and machine learning is {\em linear regression}, which is recently extended to dynamic graphs. Existing exact algorithms for updating the solution of dynamic graph regression problem require at least a linear time ... More

Morse inequalities for manifolds with boundaryJul 31 2008Oct 06 2008The aim of this paper is to provide a proof for a version of Morse inequality for manifolds with boundary. Our main results are certainly known to the experts on Morse theory, nevertheless it seems necessary to write down a complete proof for it. Our ... More

On the $FRS$-generic family of space cuspsDec 23 2017We consider in this paper the $FRS$-deformations of a family of space curves with codimension $\leq 3$. Some geometric aspects of a space curve such as flattenings, vertices and twistings points has been studied.

Möbius Quantum WalkJun 15 2017Nov 12 2017By adding an extra Hilbert space to Hadamard Quantum Walk on Cycles (QWC), we presented a new type of QWCs called M\"obius Quantum Walk (MQW). The new space configuration enables the particle to rotate around the axis of movement. We defined factor $\alpha$ ... More

Coherence Pursuit: Fast, Simple, and Robust Principal Component AnalysisSep 15 2016Jul 13 2017This paper presents a remarkably simple, yet powerful, algorithm termed Coherence Pursuit (CoP) to robust Principal Component Analysis (PCA). As inliers lie in a low dimensional subspace and are mostly correlated, an inlier is likely to have strong mutual ... More

Poisson kernel expansions for Schrödinger operators on treesOct 19 2016Aug 25 2017We study Schr\"odinger operators on trees and construct associated Poisson kernels, in analogy to the laplacian on the unit disc. We show that in the absolutely continuous spectrum, the generalized eigenfunctions of the operator are generated by the Poisson ... More

Local metric dimension of graphs: generalized hierarchical products and some applicationsFeb 25 2019Let $G$ be a graph and $S\subseteq V(G)$. If every two adjacent vertices of $G$ have different metric $S$-representations, then $S$ is a local metric generator for $G$. A local metric generator of smallest order is a local metric basis for $G$, its order ... More

Parameter Efficient Training of Deep Convolutional Neural Networks by Dynamic Sparse ReparameterizationFeb 15 2019Mar 19 2019Deep neural networks are typically highly over-parameterized with pruning techniques able to remove a significant fraction of network parameters with little loss in accuracy. Recently, techniques based on dynamic re-allocation of non-zero parameters have ... More

Relevant perturbation of entanglement entropy of singular surfacesFeb 13 2019Feb 25 2019We study the entanglement entropy of theories that are derived from relevant perturbation of given CFTs for regions with a singular boundary by using the AdS/CFT correspondence. In the smooth case, it is well known that a relevant deformation of the boundary ... More

Modeling Impact of Human Errors on the Data Unavailability and Data Loss of Storage SystemsMay 26 2018Jun 10 2018Data storage systems and their availability play a crucial role in contemporary datacenters. Despite using mechanisms such as automatic fail-over in datacenters, the role of human agents and consequently their destructive errors is inevitable. Due to ... More

Spatial Random Sampling: A Structure-Preserving Data Sketching ToolMay 09 2017Jul 12 2017Random column sampling is not guaranteed to yield data sketches that preserve the underlying structures of the data and may not sample sufficiently from less-populated data clusters. Also, adaptive sampling can often provide accurate low rank approximations, ... More

Quantum ergodicity for the Anderson model on regular graphsApr 10 2017Oct 13 2017We prove a result of delocalization for the Anderson model on the regular tree (Bethe lattice). When the disorder is weak, it is known that large parts of the spectrum are a.s. purely absolutely continuous, and that the dynamical transport is ballistic. ... More

Thermal vacancies in close-packing solidsNov 20 2013Based on Stillinger's version of cell cluster theory, we derive an expression for the equilibrium concentration of thermal monovacancies in solids which allows for a transparent interpretation of the vacancy volume and the energetic/entropic part in the ... More

De Giorgi type results for elliptic systemsMar 27 2012Apr 23 2012We consider the following elliptic system \Delta u =\nabla H (u) \ \ \text{in}\ \ \mathbf{R}^N, where $u:\mathbf{R}^N\to \mathbf{R}^m$ and $H\in C^2(\mathbf{R}^m)$, and prove, under various conditions on the nonlinearity $H$ that, at least in low dimensions, ... More

Extending Weakly-Sticky Datalog+/-: Query-Answering Tractability and OptimizationsJul 10 2016Weakly-sticky (WS) Datalog+/- is an expressive member of the family of Datalog+/- programs that is based on the syntactic notions of stickiness and weak-acyclicity. Query answering over the WS programs has been investigated, but there is still much work ... More

Tractable Query Answering and Optimization for Extensions of Weakly-Sticky Datalog+-Apr 13 2015We consider a semantic class, weakly-chase-sticky (WChS), and a syntactic subclass, jointly-weakly-sticky (JWS), of Datalog+- programs. Both extend that of weakly-sticky (WS) programs, which appear in our applications to data quality. For WChS programs ... More

The Ontological Multidimensional Data ModelMar 10 2017May 04 2017In this extended abstract we describe, mainly by examples, the main elements of the Ontological Multidimensional Data Model, which considerably extends a relational reconstruction of the multidimensional data model proposed by Hurtado and Mendelzon by ... More

Analysis of Aperture Evolution in a Rock Joint Using a Complex Network ApproachNov 24 2008In this study, we develop a complex network approach on a rough fracture, where evolution of elementary aperture during translational shear is characterized. In this manner, based on some hidden metric spaces (similarity measurements) between apertures ... More

An Iterative Regularized Incremental Projected Subgradient Method for a Class of Bilevel Optimization ProblemsSep 26 2018We study a class of bilevel convex optimization problems where the goal is to find the minimizer of an objective function in the upper level, among the set of all optimal solutions of an optimization problem in the lower level. A wide range of problems ... More

Parameter Efficient Training of Deep Convolutional Neural Networks by Dynamic Sparse ReparameterizationFeb 15 2019May 13 2019Modern deep neural networks are typically highly overparameterized. Pruning techniques are able to remove a significant fraction of network parameters with little loss in accuracy. Recently, techniques based on dynamic reallocation of non-zero parameters ... More

Generalized inverses and the maximal radius of regularity of a Fredholm operatorDec 19 1996Operators possessing analytic generalized inverses satisfying the resolvent identity are studied. Several characterizations and necessary conditions are obtained. The maximal radius of regularity for a Fredholm operator T is computed in terms of the spectral ... More

Innovation Pursuit: A New Approach to Subspace ClusteringDec 02 2015In subspace clustering, a group of data points belonging to a union of subspaces are assigned membership to their respective subspaces. This paper presents a new approach dubbed Innovation Pursuit (iPursuit) to the problem of subspace clustering using ... More

On supercritical coupled elliptic systems with power nonlinearitiesSep 27 2015Consider the following coupled elliptic system of equations $$ (-\Delta)^s u_i = |u|^{p-1} u_i \quad \text{in} \ \ \mathbb{R}^n $$ where $0<s\le 2$, $p>1$, $m\ge1$, $u=(u_i)_{i=1}^m$ and $u_i: \mathbb{R}^n \to \mathbb{R}$. The qualitative behaviour of ... More

Subspace Clustering via Optimal Direction SearchJun 12 2017Nov 26 2017This letter presents a new spectral-clustering-based approach to the subspace clustering problem. Underpinning the proposed method is a convex program for optimal direction search, which for each data point d finds an optimal direction in the span of ... More

Tannakian formalism for fiber functors over tensor categoriesSep 10 2016In this paper we generalize Tannakian formalism to fiber functors over general tensor categories. We will show that (under some technical conditions) if the fiber functor has a section, then the source category is equivalent to the category of comodules ... More

Capacity Enlargement Of The PVD Steganography Method Using The GLM TechniqueJan 03 2016In most steganographic methods, increasing in the capacity leads to decrease in the quality of the stego-image, so in this paper, we propose to combine two existing techniques, Pixel value differencing and Gray Level Modification, to come up with a hybrid ... More

High Dimensional Low Rank plus Sparse Matrix DecompositionFeb 01 2015Mar 16 2017This paper is concerned with the problem of low rank plus sparse matrix decomposition for big data. Conventional algorithms for matrix decomposition use the entire data to extract the low-rank and sparse components, and are based on optimization problems ... More

On finite Morse index solutions of higher order fractional Lane-Emden equationsOct 20 2014Oct 30 2015We classify finite Morse index solutions of the fractional Lane-Emden equation $(-\Delta)^{s} u=|u|^{p-1} u \ \ \ \mathbb{R}^n $ for $1<s<2$. For the local case, $s=1$ and $s=2$ this classification was done by Farina in [10] and Davila, Dupaigne, Wang ... More

Uniqueness of solutions for a nonlocal elliptic eigenvalue problemSep 23 2011Sep 11 2012We examine equations of the form {eqnarray*} \{{array}{lcl} \hfill \HA u &=& \lambda g(x) f(u) \qquad \text{in}\ \Omega \hfill u&=& 0 \qquad \qquad \qquad \text{on}\ \pOm, {array}. {eqnarray*} where $ \lambda >0$ is a parameter and $ \Omega$ is a smooth ... More

Adaptive Resource Management for Multimedia Applications in Femtocellular and Macrocellular NetworksDec 14 2014The increasing demands of various high data rate wireless applications have been seen in the recent years and it will continue in the future. To fulfill these demands, the limited existing wireless resources should be utilized properly or new wireless ... More

A higher index theorem for foliated manifolds with boundaryJan 17 2007Dec 16 2009Following Gorokhovsky and Lott and using an extension of the b-pseudodifferential calculus of Melrose, we give a formula for the Chern character of the Dirac index class of a longitudinal Dirac type operators on a foliated manifold with boundary. For ... More

Symmetry properties for solutions of nonlocal equations involving nonlinear operatorsJul 17 2018We pursue the study of one-dimensional symmetry of solutions to nonlinear equations involving nonlocal operators. We consider a vast class of nonlinear operators and in a particular case it covers the fractional $p-$Laplacian operator. Just like the classical ... More

Finite unitary ring with minimal non-nilpotent group of unitsDec 11 2018Let $R$ be a finite unitary ring such that $R=R_0[R^*]$ where $R_0$ is the prime ring and $R^*$ is not a nilpotent group. We show that if all proper subgroups of $R^*$ are nilpotent groups, then the cardinal of $R$ is a power of prime number 2. In addition, ... More

Existence, positivity and stability for a nonlinear model of cellular proliferationApr 16 2009In this paper, we investigate a system of two nonlinear partial differential equations, arising from a model of cellular proliferation which describes the production of blood cells in the bone marrow. Due to cellular replication, the two partial differential ... More

Global stability of a partial differential equation with distributed delay due to cellular replicationApr 16 2009In this paper, we investigate a nonlinear partial differential equation, arising from a model of cellular proliferation. This model describes the production of blood cells in the bone marrow. It is represented by a partial differential equation with a ... More

Poisson kernel expansions for Schr{ö}dinger operators on treesOct 19 2016We study Schr{\"o}dinger operators on trees and construct associated Poisson kernels, in analogy to the laplacian on the unit disc. We show that in the absolutely continuous spectrum, the generalized eigenfunctions of the operator are generated by the ... More

Relevant perturbation of entanglement entropy of singular surfacesFeb 13 2019We study the entanglement entropy of theories that are derived from relevant perturbation of given CFTs for regions with a singular boundary by using the AdS/CFT correspondence. In the smooth case, it is well known that a relevant deformation of the boundary ... More

Efficient Algorithms for Approximate Triangle CountingApr 23 2013Counting the number of triangles in a graph has many important applications in network analysis. Several frequently computed metrics like the clustering coefficient and the transitivity ratio need to count the number of triangles in the network. Furthermore, ... More

Entanglement entropy of singular surfaces under relevant deformations in holographySep 24 2017Jan 16 2018In the vacuum state of a CFT, the entanglement entropy of singular surfaces contains a logarithmic universal term which is only due to the singularity of the entangling surface. We consider the relevant perturbation of a three dimensional CFT for singular ... More

ex uno pluria: The Service-Infrastructure Cycle, Ossification, and the Fragmentation of the InternetDec 12 2017In this article I will first argue that a Service-Infrastructure Cycle is fundamental to networking evolution. Networks are built to accommodate certain services at an expected scale. New applications and/or a significant increase in scale require a rethinking ... More

A learning framework for winner-take-all networks with stochastic synapsesAug 14 2017Feb 05 2018Many recent generative models make use of neural networks to transform the probability distribution of a simple low-dimensional noise process into the complex distribution of the data. This raises the question of whether biological networks operate along ... More