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Adaptive non-linear filter using a modular polynomial perceptron

IET SIGNAL PROCESSING 2010年第6期4卷 640-649页

作者： Zhao, H. Q. Zeng, X. P. Zhang, J. S. Liu, Y. G. Li, T. R. SW Jiaotong Univ Sch Elect Engn Chengdu 610031 Peoples R China SW Jiaotong Univ Sch Informat Sci & Technol Chengdu 610031 Peoples R China Zhejiang Univ Ningbo Inst Technol Ningbo 315100 Zhejiang Peoples R China

This study presents a joint adaptive non-linear filter with pipelined second-order polynomial perceptron (PSOVNN) to reduce the computational complexity and improve the non-linear processing capability of adaptive direct-form second-order Volterra (SOV) filter. The PSOVNN is a nesting modular structure comprising a number of modules that are interconnected in a chained form. Each module is implemented by a small-scale direct-form SOV neural network (SOVNN). These cascaded modules can perform a non-linear mapping from the input space to an intermediate space. In addition, the linear filter of the complete PSOVNN performs a linear mapping from the intermediate space to the output space. A modified real-time recurrent learning (RTRL) algorithm is developed, and its performance is evaluated by a series of simulation experiments. computer simulations indicate that the proposed non-linear filter exhibits better performance over the direct-form SOV filter with less computational complexity.

关键词： nonlinear filters adaptive nonlinear filter Filtering methods in signal processing polynomials Signal processing theory pipelined second-order polynomial perceptron computational complexity adaptive filters linear mapping algebra second-order Volterra filter SOV neural network real-time recurrent learning algorithm

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Smallest Reduction Matrix of Binary Quadratic Forms And Cryptographic applications

Smallest Reduction Matrix of Binary Quadratic Forms And Cryp...

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9th International Symposium on Algorithmic number theory

作者： Bernard, Aurore Gama, Nicolas XLIM Limoges France GREYC Ensicaen Caen France

ISBN: (纸本)9783642145179

We present a variant of the Lagrange-Gauss reduction of quadratic forms designed to minimize the norm of the reduction matrix within a quadratic complexity. The matrix computed by our algorithm on the input f has norm O(parallel to f parallel to(1/2) / Delta(1/4)(f)) which is the square root of the best previously known bounds using classical algorithms. This new bound allows us to fully prove the heuristic lattice based attack against NICE Cryptosystems, which consists in factoring a particular subclass of integers of the form pq(2). In the process, we set up a homogeneous variant of Boneh-Durfee-HowgraveGraham's algorithm which finds small rational roots of a polynomial modulo unknown divisors. Such algorithm can also be used to speed-up factorization of pq(r) for large r.

关键词： Matrix algebra

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Application of D-S Evidence theory to uncertainty of assessment result in E-government

Application of D-S Evidence theory to uncertainty of assessm...

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7th Web Information Systems and applications Conference, WISA 2010, 5th Workshop on Semantic Web and Ontology, SWON 2010, 4th Workshop on Electronic Government Technology and Application, EGTA 2010

作者： Xia, Bing Pan, Heng Zheng, Qiusheng Miao, Fengjun School of Computer Science Zhongyuan University of Technology Zhengzhou Key Lab of Computer Network Security Assessment Zhengzhou China

ISBN: (纸本)9780769541938

How to solve uncertainty of assessment result is an important issue in E-government. Current qualitative assessment are based on subjective qualitative evaluation and the rigid division of the quantitative data, however both methods are less objective ,precise and impartiality, as a result cause accuracy of assessment poorly. D-S Evidence theory is fit for processing the subjective judgment and synthesizing the uncertain knowledge. So, this theory is applied to the uncertainty of assessment results. Firstly used the classic 2/8 rule to build a dynamic contribution matrix. Then after weighted and normalized, we got a basic probability assignment MASS matrix. Final chosen one of the largest number of synthetic probability as assessment result. The algorithm has a strong versatility and an example is used to demonstrate its effectively in this text. © 2010 IEEE.

关键词： Matrix algebra

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A Classical Introduction to Cryptography: applications for Communications Security

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2010年

作者： Serge Vaudenay

ISBN: (纸本)9781441937971

A Classical Introduction to Cryptography: applicationsfor Communications Security introduces fundamentals of information and communication security by providing appropriate mathematical concepts to prove or break the security of cryptographic schemes. This advanced-level textbook covers conventional cryptographic primitives and cryptanalysis of these primitives; basic algebra and number theory for cryptologists; public key cryptography and cryptanalysis of these schemes; and other cryptographic protocols, e.g. secret sharing, zero-knowledge proofs and undeniable signature schemes. A Classical Introduction to Cryptography: applicationsfor Communications Securityis designed for upper-level undergraduate and graduate-level students in computer science. This book is also suitable for researchers and practitioners in industry. A separate exercise/solution booklet is available as well, please go to *** under author: Vaudenay for additional details on how to purchase this booklet.

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Dependent Randomized Rounding via Exchange Properties of Combinatorial Structures

Dependent Randomized Rounding via Exchange Properties of Com...

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IEEE 51st Annual Symposium on Foundations of computer Science (FOCS)

作者： Chekuri, Chandra Vondrak, Jan Zenklusen, Rico Univ Illinois Dept Comp Sci 1304 W Springfield Ave Urbana IL 61801 USA IBM Corp Almaden Res Ctr San Jose CA 95120 USA MIT Dept Math Cambridge MA 02139 USA

ISBN: (纸本)9780769542447

We consider the problem of randomly rounding a fractional solution x in an integer polytope P subset of [0;1](n) to a vertex X of P, so that E[X] = x. Our goal is to achieve concentration properties for linear and submodular functions of the rounded solution. Such dependent rounding techniques, with concentration bounds for linear functions, have been developed in the past for two polytopes: the assignment polytope (that is, bipartite matchings and b-matchings) [32], [19], [23], and more recently for the spanning tree polytope [2]. These schemes have led to a number of new algorithmic results. In this paper we describe a new swap rounding technique which can be applied in a variety of settings including matroids and matroid intersection, while providing Chernoff-type concentration bounds for linear and submodular functions of the rounded solution. In addition to existing techniques based on negative correlation, we use a martingale argument to obtain an exponential tail estimate for monotone submodular functions. The rounding scheme explicitly exploits exchange properties of the underlying combinatorial structures, and highlights these properties as the basis for concentration bounds. Matroids and matroid intersection provide a unifying framework for several known applications [19], [23], [7], [22], [2] as well as new ones, and their generality allows a richer set of constraints to be incorporated easily. We give some illustrative examples, with a more comprehensive discussion deferred to a later version of the paper.

关键词： Chernoff type concentration approximation theory bipartite matching combinatorial mathematics combinatorial structure dependent randomized rounding exchange property exponential tail estimate function approximation integer polytope linear function linear programming martingale argument matrix algebra matroid intersection monotone submodular function spanning tree polytope stochastic processes swap rounding technique

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Composition collisions and projective polynomials: statement of results 10

Composition collisions and projective polynomials: statement...

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Proceedings of the 2010 International Symposium on Symbolic and algebraic Computation

作者： Joachim von zur Gathen Mark Giesbrecht Konstantin Ziegler B-IT Universität Bonn Bonn Germany University of Waterloo Waterloo ON Canada

ISBN: (纸本)9781450301503

The functional decomposition of polynomials has been a topic of great interest and importance in pure and computer algebra and their applications. The structure of compositions of (suitably normalized) polynomials f = g o h in Fq[x] is well understood in many cases, but quite poorly when the degrees of both components are divisible by the characteristic p. This work investigates the decomposition of polynomials whose degree is a power of p. An (equal-degree) i-collision is a set of i distinct pairs (g, h) of polynomials, all with the same composition and deg g the same for all (g, h). Abhyankar (1997) introduced the projective polynomials xn+ ax + b, where n is of the form (rm -- 1)/(r -- 1) and r is a power of p. Our first tool is a bijective correspondence between i-collisions of certain additive trinomials, projective polynomials with i roots, and linear spaces with i Frobenius-invariant *** (2004b) has determined the possible number of roots of projective polynomials for m = 2, and how many polynomials there are with a prescribed number of roots. We generalize her first result to arbitrary m, and provide an alternative proof of her second result via elementary linear *** one of our additive trinomials is given, we can efficiently compute the number of its decompositions, and similarly the number of roots of a projective polynomial. The runtime of these algorithms depends polynomially on the sparse input size, and thus on the input degree only *** non-additive polynomials, we present certain decompositions and conjecture that these comprise all of the prescribed shape.

关键词： projective polynomials univariate polynomial decomposition linearized polynomials additive polynomials

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DNA Sequence Matching Using Boolean algebra

DNA Sequence Matching Using Boolean Algebra

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International Conference on Advances in computer Engineering (ACE)

作者： V. Anitha B. Poorna MCA Panimalar Engineering College Chennai India MCA Easwari Engineering College Chennai India

Alignment is the most basic component of biological sequence manipulation and has diverse applications in sequence assembly, sequence annotation, structural and functional predictions for genes and proteins, phylogeny and evolutionary analysis. Classical methods like Needleman Wunsch ( for global alignment) in 1970 and Smith-Waterman (for local alignment) in 1981 suffer from the drawback that it involves a large number of computational steps and has a statically allocate a large section of memory for computer implementation. This paper suggests an algorithm for global alignment between two DNA sequences and compares the performance of the algorithm with Needleman Wunsch. Complexity calculation shows that the proposed algorithm has a much less time complexity and requires very much less amount of memory storage than Needleman Wunsch algorithm.

关键词： DNA Sequences Boolean algebra Genomics Bioinformatics Evolution (biology) Biological information theory Educational institutions Genetics Periodic structures

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On the implementation of public keys algorithms based on algebraic graphs over finite commutative rings

On the implementation of public keys algorithms based on alg...

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International Multiconference on computer Science and Information Technology, IMCSIT

作者： Michał Klisowski Vasyl Ustimenko Institute of Mathematics Maria Curie Skĺodowska University Lublin Poland

We will consider balanced directed graphs, i.e., graphs of binary relations, for which the number of inputs and number of outputs are the same for each vertex. The commutative diagram is formed by two directed paths for which the same starting and ending points form the full list of common vertices. We refer to the length of the maximal path (the number of arrows) as the rank of the diagram. We will count a directed cycle of length m as a commutative diagram of rank m. We define the girth indicator gi, gi ≥ 2 of the directed graph as the minimal rank of its commutative diagram. We observe briefly the applications of finite automata related to balanced graphs of high girth in Cryptography. Finally, for each finite commutative ring K with more than two regular elements we consider the explicit construction of algebraic over K family of graphs of high girth and discuss the implementation of the public key algorithm based on finite automata corresponding to members of the family.

关键词： Color Modules (abstract algebra) Encryption Public key polynomials

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Exact Expressions for the Condition number Distribution of Complex Wishart Matrices

Exact Expressions for the Condition Number Distribution of C...

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IEEE International Conference on Communications (ICC)

作者： M. Matthaiou M. R. McKay P. J. Smith J. A. Nossek Institute of Circuit Theory and Signal Processing Technische Universität München Munich Germany Department of Electronic and Computer Engineering Hong Kong University of Science and Technology Hong Kong China Department of Electrical and Computer Engineering University of Canterbury Christchurch New Zealand

The standard condition number (SCN) is a fundamental metric in the context of multiple-input multiple-output communication systems, linear detection and classical linear algebra. Hence, in this paper we propose a novel generic framework for the SCN distribution of three different classes of Wishart matrices which leads to new results and insights. In particular, our analysis covers both central and non-central Wishart distributions of arbitrary dimension and therefore is applicable to uncorrelated/semi-correlated Rayleigh fading and Ricean fading scenarios. For the special case of dual semi-correlated central Wishart matrices, we derive exact and asymptotic polynomial expressions for the SCN distributions. All analytical results are validated via Monte-Carlo simulations with the attained accuracy being excellent in all cases. The impact of the model parameters on channel conditioning is also investigated in detail.

关键词： MIMO Covariance matrix Eigenvalues and eigenfunctions polynomials Context Rayleigh channels Probability density function Communications Society Circuit theory Signal Processing Society

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Efficiently decodable non-adaptive group testing

Efficiently decodable non-adaptive group testing

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21st Annual ACM-SIAM Symposium on Discrete Algorithms

作者： Indyk, Piotr Ngo, Hung Q. Rudra, Atri CSAIL MIT United States Department of Computer Science and Engineering University at Buffalo SUNY United States

ISBN: (纸本)9780898717013

We consider the following "efficiently decodable" non-adaptive group testing problem. There is an unknown string χ ∈ {0, 1} n with at most d ones in it. We are allowed to test any subset S ⊆ [n] of the indices. The answer to the test tells whether χi = 0 for all i ∈ S or not. The objective is to design as few tests as possible (say, t tests) such that χ can be identified as fast as possible (say, poly(t)-time). Efficiently decodable non-adaptive group testing has applications in many areas, including data stream algorithms and data forensics. A non-adaptive group testing strategy can be represented by a 1 x n matrix, which is the stacking of all the characteristic vectors of the tests. It is well-known that if this matrix is d-disjunct, then any test outcome corresponds uniquely to an unknown input string. Furthermore, we know how to construct d-disjunct matrices with t = O(d2 log n) efficiently. However, these matrices so far only allow for a "decoding" time of O(nt), which can be exponentially larger than poly(t) for relatively small values of d. This paper presents a randomness efficient construction of d-disjunct matrices with t = O(d2 log n) that can be decoded in time poly(d)·t log2 t + O(t2). To the best of our knowledge, this is the first result that achieves an efficient decoding time and matches the best known O(d2 log n) bound on the number of tests. We also derandomize the construction, which results in a polynomial time deterministic construction of such matrices when d = O(log n/ log log n). A crucial building block in our construction is the notion of (d, )-list disjunct matrices, which represent the more general "list group testing" problem whose goal is to output less than d + positions in χ, including all the (at most d) positions that have a one in them. List disjunct matrices turn out to be interesting objects in their own right and were also considered independently by [Cheraghchi, FCT 2009]. We present connections between list disjunct matrices

关键词： Matrix algebra

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