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International Workshop on Compressed Sensing theory and its applications to Radar, Sonar and Remote Sensing (CoSeRa)

作者： Nithin Sugavanam Siddharth Baskar Emre Ertin Department of Electrical and Computer Engineering The Ohio State University Columbus

ISBN: (纸本)9781509029211

We present a compressive radar design that combines multitone linear frequency modulated (LFM) waveforms on transmit with classical stretch processor and sub-Nyquist sampling on receive. The proposed compressive illumination scheme has much fewer random elements compared to previously proposed compressive radar designs based on stochastic waveforms, resulting in reduced storage and complexity for implementation. We present bounds on the operator norm and mutual coherence of the sensing matrix of the proposed scheme and show that for sufficiently large number of modulating tones, high resolution range recovery is guaranteed for a sparse scene using sampling rates that scale linearly with the scene sparsity. Simulation results are presented to study recovery performance as a function of system parameters for targets both on and off the grid. In addition, we present experimental results using a high speed digital waveform generator and a custom designed analog stretch processor.

关键词： radar imaging compressed sensing FM radar image resolution image sampling matrix algebra frequency modulated radars image samples Radar imaging matrix algebra image resolution Compressed sensing system parameter High resolution radar waveform generators

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An explicit version of the Chebyshev-Markov-Stieltjes inequalities and its applications

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JOURNAL OF INEQUALITIES AND applications 2015年第1期2015卷 1-16页

作者： Huerlimann, Werner 1.Feldstrasse 145 Zürich CH-8004 Switzerland

Given is the Borel probability space on the set of real numbers. The algebraic-analytical structure of the set of all finite atomic random variables on it with a given even number of moments is determined. It is used to derive an explicit version of the Chebyshev-Markov-Stieltjes inequalities suitable for computation. These inequalities are based on the theory of orthogonal polynomials, linear algebra, and the polynomial majorant/minorant method. The result is used to derive generalized Laguerre-Samuelson bounds for finite real sequences and generalized Chebyshev-Markov value-at-risk bounds. A financial market case study illustrates how the upper value-at-risk bounds work in the real world.

关键词： Hamburger moment problem algebraic moment problem orthogonal polynomials Laplace formula Christoffel-Darboux kernel Laguerre-Samuelson bound value-at-risk

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Polynomial-time algorithms for quadratic isomorphism of polynomials: The regular case

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JOURNAL OF COMPLEXITY 2015年第4期31卷 590-616页

作者： Berthomieu, Jeremy Faugere, Jean-Charles Perret, Ludovic Univ Paris 06 Sorbonne Univ Equipe PoLSvs LIP6 F-75005 Paris France CNRS LIP6 UMR 7606 F-75005 Paris France INRIA Equipe PoLSYs Ctr Paris Rocquencourt F-75005 Paris France

Let f = (f1,...,f(m)) and g = (g(1),...,gm) be two sets of in >= 1 nonlinear polynomials in K[x(1),...,x(n)] (K being a field). We consider the computational problem of finding - if any - an invertible transformation on the variables mapping f to g. The corresponding equivalence problem is known as Isomorphism of polynomials with one Secret (IP1S) and is a fundamental problem in multivariate cryptography. Amongst its applications, we can cite Graph Isomorphism (GI) which reduces to equivalence of cubic polynomials with respect to an invertible linear change of variables, according to Agrawal and Saxena. The main result is a randomized polynomialtime algorithm for solving IP1S for quadratic instances a particular case of importance in cryptography. To this end, we show that IP1S for quadratic polynomials can be reduced to a variant of the classical module isomorphism problem in representation theory. We show that we can essentially linearize the problem by reducing quadratic-IP1S to test the orthogonal simultaneous similarity of symmetric matrices;this latter problem was shown by Chistov, Ivanyos and Karpinski (ISSAC 1997) to be equivalent to finding an invertible matrix in the linear space K-nxn of n x n matrices over K and to compute the square root in a certain representation in a matrix algebra. While computing square roots of matrices can be done efficiently using numerical methods, it seems difficult to control the bit complexity of such methods. However, we present exact and polynomial-time algorithms for computing a representation of the square root of a matrix in K-nxn, for various fields (including finite fields), as a product of two matrices. Each coefficient of these matrices lies in an extension field of K of polynomial degree. We then consider #IP1S, the counting version of IP1S for quadratic instances. In particular, we provide a (complete) characterization of the automorphism group of homogeneous quadratic polynomials. Finally, we also consider the mo

关键词： Quadratic forms computer algebra Polynomial isomorphism Multivariate cryptography Module isomorphism

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On a Criterion for Simultaneous Block-Diagonalization of Normal Matrices

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OPEN SYSTEMS & INFORMATION DYNAMICS 2016年第1期23卷 1650003-1650003页

作者： Pastuszak, G. Kamizawa, T. Jamiolkowski, A. Nicolaus Copernicus Univ Fac Math & Comp Sci Torun Poland Nicolaus Copernicus Univ Fac Phys Astron & Informat Torun Poland

Assume that A(1), ..., A(s) are complex normal n x n matrices, p is a natural number and S-2p is the standard polynomial in 2 p non-commutative variables. It follows from classical results of S. Amitsur, J. Levitzki and H. Shapiro that A(1),...,A(s) can be simultaneously block-diagonalized by a unitary matrix with blocks of sizes not greater than p if and only if the algebra generated by A(1),...,A(s) satisfies the polynomial identity S-2p - 0. We call this theorem the ALS-criterion for simultaneous block-diagonalization of normal matrices. In this paper, we present some application of the ALS-criterion in quantum theory. Namely, we give another proof of the renowned Morris-Shore transformation. Moreover, we discuss computable versions of the ALS-criterion. These versions allow one to verify the condition S-2p = 0 in a finite number of steps. Such an approach is more useful in practical applications than the original one.

关键词： Block-diagonalization quasi-diagonalization computable criteria stardard polynomials Morris-Shore transformation

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Tropical effective primary and dual Nullstellensätz 32

Tropical effective primary and dual Nullstellensätz

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32nd International Symposium on Theoretical Aspects of computer Science, STACS 2015

作者： Grigoriev, Dima Podolskii, Vladimir V. CNRS Mathématiques Université de Lille France Steklov Mathematical Institute Moscow Russia National Research University Higher School of Economics Moscow Russia

ISBN: (纸本)9783939897781

Tropical algebra is an emerging field with a number of applications in various areas of mathematics. In many of these applications appeal to tropical polynomials allows to study properties of mathematical objects such as algebraic varieties and algebraic curves from the computational point of view. This makes it important to study both mathematical and computational aspects of tropical polynomials. In this paper we prove tropical Nullstellensatz and moreover we show effective formulation of this theorem. Nullstellensatz is a next natural step in building algebraic theory of tropical polynomials and effective version is relevant for computational aspects of this field. © 2015 LIPICS.

关键词： polynomials

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Matrix polynomials with specified eigenvalues

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LINEAR algebra AND ITS applications 2015年 466卷 457-482页

作者： Karow, Michael Mengi, Emre TU Berlin Dept Math D-10623 Berlin Germany Koc Univ Dept Math TR-34450 Istanbul Turkey

This work concerns the distance in the 2-norm from a given matrix polynomial to a nearest polynomial with a specified number of its eigenvalues at specified locations in the complex plane. Initially, we consider perturbations of the constant coefficient matrix only. A singular value optimization characterization is derived for the associated distance. We also consider the distance in the general setting, when all of the coefficient matrices are perturbed. In this general setting, we obtain a lower bound in terms of another singular value optimization problem. The singular value optimization problems derived facilitate the numerical computation of the distances. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Matrix polynomial Linearization Singular values Sylvester equation Eigenvalue perturbation theory

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17th International Workshop on computer algebra in Scientific Computing, CASC 2015

17th International Workshop on Computer Algebra in Scientifi...

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17th International Workshop on computer algebra in Scientific Computing, CASC 2015

ISBN: (纸本)9783319240206

The proceedings contain 35 papers. The special focus in this conference is on computer algebra in Scientific Computing. The topics include: Hypergeometric solutions of first-order linear difference systems with rational-function coefficients;janet bases and resolutions in CoCoALib;regular chains under linear changes of coordinates and applications;a standard basis free algorithm for computing the tangent cones of a space curve;research on the stability of relative equilibria of oblate axisymmetric gyrostat by means of symbolic-numerical modelling;a new approach for computing regular solutions of linear difference systems;solving polynomial systems in the cloud with polynomial homotopy continuation;finding first integrals using normal forms modulo differential regular chains;simplification of cylindrical algebraic formulas;intuition, perturbation theory and algorithmic algebra;polynomial complexity recognizing a tropical linear variety;computing highest-order divisors for a class of quasi-linear partial differential equations;symbolic-numeric solution of boundary-value problems for the schrodinger equation using the finite element method;application of computer algebra methods to investigation of influence of constant torque on stationary motions of satellite;bounds for the condition number of polynomials systems with integer coefficients;on invariant manifolds and their stability in the problem of motion of a rigid body under the influence of two force fields;homotopy analysis method for stochastic differential equations with maxima;on the topology and visualization of plane algebraic curves;piecewise-quadratics and reparameterizations for interpolating reduced data and parametric solvable polynomial rings and applications.

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An optimized and scalable eigensolver for sequences of eigenvalue problems

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CONCURRENCY AND COMPUTATION-PRACTICE & EXPERIENCE 2015年第4期27卷 905-922页

作者： Berljafa, Mario Wortmann, Daniel Di Napoli, Edoardo Univ Manchester Sch Math Manchester M13 9PL Lancs England Forschungszentrum Julich Peter Grunberg Inst D-52425 Julich Germany JARA D-52425 Julich Germany Forschungszentrum Julich Inst Adv Simulat Julich Supercomp Ctr D-52425 Julich Germany

In many scientific applications, the solution of nonlinear differential equations are obtained through the setup and solution of a number of successive eigenproblems. These eigenproblems can be regarded as a sequence whenever the solution of one problem fosters the initialization of the next. In addition, in some eigenproblem sequences, there is a connection between the solutions of adjacent eigenproblems. Whenever it is possible to unravel the existence of such a connection, the eigenproblem sequence is said to be correlated. When facing with a sequence of correlated eigenproblems, the current strategy amounts to solving each eigenproblem in isolation. We propose an alternative approach that exploits such correlation through the use of an eigensolver based on subspace iteration and accelerated with Chebyshev polynomials (Chebyshev filtered subspace iteration (ChFSI)). The resulting eigensolver is optimized by minimizing the number of matrix-vector multiplications and parallelized using the Elemental library framework. Numerical results show that ChFSI achieves excellent scalability and is competitive with current dense linear algebra parallel eigensolvers. Copyright (c) 2014 John Wiley & Sons, Ltd.

关键词： Chebyshev polynomials subspace iteration eigenproblem sequence density functional theory Elemental

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Anomaly-free policy composition in software-defined networks

Anomaly-free policy composition in software-defined networks

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IFIP Networking Conference

作者： Mohsen Rezvani Aleksandar Ignjatovic Maurice Pagnucco Sanjay Jha School of Computer Science and Engineering UNSW Australia

Software Defined Networking (SDN) provides considerable simplification of design and deployment of various network applications for large networks. Each application has its own view of network policy and sends its policy to a network hypervisor in which a composed policy is generated from the application policies and deployed into the data plane. A significant challenge for the hypervisor is to detect and resolve both intra and inter policy anomalies during the policy composition. However, current SDN compilers do not consider the policy anomalies well and generate large number of unnecessary rules for the data plane. This leads to a considerable inefficiency in both policy composition and policy deployment. In this paper, we propose a novel framework for policy composition in a SDN hypervisor which takes into account both inter and intra policy anomalies. Moreover, we augment the framework with an efficient insertion transformation mechanism which allows the applications to issue rule insertion and priority change updates. Our evaluation shows that our method is several orders of magnitude more efficient than the state of the art in both policy composition and compiling the rule insertion updates.

关键词： Virtual machine monitors Electronics packaging Protocols Complexity theory algebra Data structures

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theory of 2-rotation symmetric cubic Boolean functions

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DESIGNS CODES AND CRYPTOGRAPHY 2015年第1期76卷 113-133页

作者： Cusick, Thomas W. Johns, Bryan SUNY Buffalo Buffalo NY 14260 USA

A Boolean function in variables is -rotation symmetric if it is invariant under even powers of the cyclic permutation of the variables, but not under the first power (ordinary rotation symmetry);for brevity, we call such a function a -function. A -function is said to be monomial rotation symmetric (MRS) if it is generated by applying powers of to a single monomial. This paper develops the theory of cubic MRS -functions in variables generated by a monomial with and and not both odd (notation );it turns out that such functions with and both odd are essentially the same as ordinary cubic MRS functions in only variables. A complete description of affine equivalence for these cubic MRS -functions is given, including a simple necessary and sufficient condition for two such functions to be affine equivalent. It is proved that affine equivalence for these functions is the same as affine equivalence under permutations which preserve -rotation symmetry. This is the first time that all affine equivalence classes have been explicitly determined for any large general family of Boolean functions with degree 2. An exact count of the equivalence classes is given and their number is proved to be very small, in fact for any It is proved that the sequence of Hamming weights satisfies a linear recursion with integer coefficients. A similar result for ordinary cubic MRS functions was proved recently (papers by Bileschi, Cusick and Padgett, and by Brown and Cusick), but this paper uses a new method for the -functions proof. Unlike the ordinary MRS function case, both the orders of the recursions for the -functions and the precise values of the roots of the corresponding recursion polynomials can be given explicitly. Finally, a precise value for the weights of the -functions is proved, using a 2011 formula of Cusick and Padgett. These weights are connected to powers of members of the well known Lucas sequence, and so the weights can be found without computing initial values for the recurs

关键词： Boolean function Rotation symmetric Affine equivalence Hamming weight Recursion Cryptography

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