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Grassmann integral representation for spanning hyperforests
 Journal of Physics A: Mathematical and Theoretical
, 2007
"... Given a hypergraph G, we introduce a Grassmann algebra over the vertex set, and show that a class of Grassmann integrals permits an expansion in terms of spanning hyperforests. Special cases provide the generating functions for rooted and unrooted spanning (hyper)forests and spanning (hyper)trees. A ..."
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Given a hypergraph G, we introduce a Grassmann algebra over the vertex set, and show that a class of Grassmann integrals permits an expansion in terms of spanning hyperforests. Special cases provide the generating functions for rooted and unrooted spanning (hyper)forests and spanning (hyper)trees. All these results are generalizations of Kirchhoff’s matrixtree theorem. Furthermore, we show that the class of integrals describing unrooted spanning (hyper)forests is induced by a theory with an underlying OSP(12) supersymmetry.
The Construction Of rRegular Wavelets For Arbitrary Dilations
 J. Fourier Anal. Appl
"... . Given any dilation matrix with integer entries and a natural number r we construct an associated rregular multiresolution analysis with rregular wavelet basis. We also prove that regular wavelets have vanishing moments. 1. Introduction The main aim of this note is the construction of rregular ..."
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. Given any dilation matrix with integer entries and a natural number r we construct an associated rregular multiresolution analysis with rregular wavelet basis. We also prove that regular wavelets have vanishing moments. 1. Introduction The main aim of this note is the construction of rregular wavelet family with an associated rregular multiresolution analysis for an arbitrary dilation matrix A preserving some lattice . Strichartz [Sr] achieved this goal for a wide class of dilations having a Haar type wavelet basis, or equivalently a selfane tiling, see [GM]. Theorem 1.1 (Strichartz). Assume the existence of a selfane tiling. For every r there exists an rregular multiresolution analysis and an associated wavelet basis. We extend this result by removing the assumption of the existence of a selfane tiling. This assumption is highly non trivial and it was studied by many authors, see [CHR], [GH], [LW1]{[LW6], [KSW] and [SW]. Using methods of algebraic number theory classes of...
On matrices with common invariant cones with applications in neural and gene networks. Linear Algebra and its Applications
"... Motivated by a differential continuoustime switching model for gene and neural networks, we investigate matrix theoretic problems regarding the relative location and topology of the dominant eigenvectors of words constructed multiplicatively from two matrices A and B. These problems are naturally a ..."
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Motivated by a differential continuoustime switching model for gene and neural networks, we investigate matrix theoretic problems regarding the relative location and topology of the dominant eigenvectors of words constructed multiplicatively from two matrices A and B. These problems are naturally associated with the existence of common invariant subspaces and common invariant proper cones of A and B. The commuting case and the two dimensional case are rich and considered analytically. We also analyze and recast the problem of the existence of a common invariant polyhedral cone in a multilinear framework, as well as present necessary conditions for the existence of low dimensional common invariant cones.
Multilinear Algebra and Chess Endgames
 of No Chance: Combinatorial Games at MRSI
, 1996
"... Abstract. This article has three chief aims: (1) To show the wide utility of multilinear algebraic formalism for highperformance computing. (2) To describe an application of this formalism in the analysis of chess endgames, and results obtained thereby that would have been impossible to compute usi ..."
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Abstract. This article has three chief aims: (1) To show the wide utility of multilinear algebraic formalism for highperformance computing. (2) To describe an application of this formalism in the analysis of chess endgames, and results obtained thereby that would have been impossible to compute using earlier techniques, including a win requiring a record 243 moves. (3) To contribute to the study of the history of chess endgames, by focusing on the work of Friedrich Amelung (in particular his apparently lost analysis of certain sixpiece endgames) and that of Theodor Molien, one of the founders of modern group representation theory and the first person to have systematically numerically analyzed a pawnless endgame. 1.
Linear Operators Preserving Decomposable Numerical Radii on Orthonormal Tensors
, 1988
"... Let 1 m n, and let : H ! C be a degree 1 character on a subgroup H of the symmetric group of degree m. The generalized matrix function on an m \Theta m matrix B = (b ij ) associated with is defined by d (B) = P oe2H (oe) Q m j=1 b j;oe(j) ; and the decomposable numerical radius of an n \Thet ..."
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Let 1 m n, and let : H ! C be a degree 1 character on a subgroup H of the symmetric group of degree m. The generalized matrix function on an m \Theta m matrix B = (b ij ) associated with is defined by d (B) = P oe2H (oe) Q m j=1 b j;oe(j) ; and the decomposable numerical radius of an n \Theta n matrix A on orthonormal tensors associated with is defined by r ? (A) = maxfjd (X AX)j : X is an n \Theta m matrix such that X X = I mg: We study those linear operators L on n \Theta n complex matrices that satisfy r ? (L(A)) = r ? (A) for all A 2 M n . In particular, it is shown that if 1 m ! n, such an operator must be of the form A 7! U AU or A 7! U A t U for some unitary matrix U and some 2 C with jj = 1.
Universal similarity factorization equalities over real Clifford algebras
 Adv. Appl. Clifford algebras
"... Abstract. A variety of universal similarity factorization equalities over real Clifford algebras Rp,q are established. On the basis of these equalities, real, complex and quaternion matrix representations of elements in Rp,q can be explicitly determined. Key words: Clifford algebras; similarity fact ..."
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Abstract. A variety of universal similarity factorization equalities over real Clifford algebras Rp,q are established. On the basis of these equalities, real, complex and quaternion matrix representations of elements in Rp,q can be explicitly determined. Key words: Clifford algebras; similarity factorization equalities; matrix representations. AMS subject classifications: 15A66, 15A23. 1.
Hodge duality and the Evans function
 Phys. Lett. A
, 1999
"... Two generalisations of the Evans function, for the analysis of the linearisation about solitary waves, are shown to be equivalent. The generalisation introduced by Alexander, Gardner and Jones (1990) is based on exterior algebra and the generalisation introduced by Swinton (1992) is based on a matri ..."
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Two generalisations of the Evans function, for the analysis of the linearisation about solitary waves, are shown to be equivalent. The generalisation introduced by Alexander, Gardner and Jones (1990) is based on exterior algebra and the generalisation introduced by Swinton (1992) is based on a matrix formulation and adjoint systems. In regions of the complex plane where both formulations are defined, the equivalence is geometric: we show that the formulations are dual and the duality can be made explicit using Hodge duality and the Hodge star operator. Swinton's formulation excludes potential branch points at which the Alexander, Gardner and Jones formulation is welldefined. Therefore we consider the implications of equivalence on the analytic continuation of the two formulations.
A robust numerical method to study oscillatory instability of gap solitary waves
 SIAM J. APPL. DYN. SYS
, 2005
"... ..."
Delay effects on static output feedback stabilization
 Proc. 39th IEEE Conf. Dec. Contr
, 2000
"... This paper addresses conditions for characterizing static output feedback controllers including delays for some proper transfer functions. The interest of such study is in controlling systems which can not be stabilized by the classical, nondelayed static output feedback, and its difficulty lies in ..."
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This paper addresses conditions for characterizing static output feedback controllers including delays for some proper transfer functions. The interest of such study is in controlling systems which can not be stabilized by the classical, nondelayed static output feedback, and its difficulty lies in computing delay intervals guaranteeing closedloop stability, since for the same matrix gain, stability “switches ” may occur. The proposed approach is based on the computation of generalized eigenvalues of some appropriate matrix pencils. Illustrative examples are also presented. 1
The Matrix Dynamic Programming Property And Its Implications
, 1997
"... . The dynamic programming (DP) technique rests on a very simple idea, the principle of optimality due to Bellman. This principle is instrumental in solving numerous problems of optimal control. The control law minimizes a cost functional and is determined by using the optimality principl ..."
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.<F4.039e+05> The dynamic programming (DP) technique rests on a very simple idea, the principle of optimality due to Bellman. This principle is instrumental in solving numerous problems of optimal control. The control law minimizes a cost functional and is determined by using the optimality principle. However, applicability of the optimality principle requires that the cost functional satisfies the property called "matrix dynamic programming (MDP) property." A simple definition of this property will be provided and functionals having it will be considered.<F4.601e+05> Key words.<F4.039e+05> dynamic programming, determinants, monotonicity, target tracking<F4.601e+05> AMS subject classifications.<F4.039e+05> 49L20, 15A15, 15A45, 15A69<F4.601e+05> PII.<F4.039e+05> S0895479895288334<F5.406e+05> 1. Introduction.<F4.753e+05> The DP technique rests on a very simple idea, the principle of optimality due to Bellman [1]. This principle simply asserts that if<F4.491e+05> #<F4.162e+05> #<F4.753e+...