A symmetric matroid is a matroid deened on the edge-set of some countably innnite complete graph K in a way that ranks of nite sub-graphs of K are invariant under isomorphism. Thus a symmetric ma-troid M induces on any nite graph G a uniquely determined matroid M(G). We study connectivity properties of circuits and generalized trees of symmetric matroids. We give several characterizations of a ...

We propose a new family of symmetric unimodal distributions on the circle which contains the uniform, von Mises, cardioid and wrapped Cauchy distributions, amongst others, as special cases. The basic form of the densities of this family is very simple, although its normalisation constant involves an associated Legendre function. The family of distributions can also be derived by conditioning an...

Spherically symmetric random walks in arbitrary dimension D can be described in terms of Gegenbauer (ultraspherical) polynomials. For example, Legendre polynomials can be used to represent the special case of two-dimensional spherically symmetric random walks. In general, there is a connection between orthogonal polynomials and semibounded one-dimensional random walks; such a random walk can be...

We introduce eigenfunctions of the Reed-Muller transform. Eigenfunctions are functions whose canonical sumof-products expression and PPRM (positive polarity ReedMuller expression) are isomorphic. In the case of symmetric functions, the eigenfunction can be viewed as a function whose reduced truth vector is identical to the reduced ReedMuller spectrum. We show that the number of symmetric (ordin...

We have found a formalism that lets us present generalizations of several stability theorems (see Chua & Roska, 1990; Chua & Wu, 1992; Gilli, 1993; Forti, 2002] on Multi-Layer Cellular Neural/Nonlinear Networks (MLCNN) formerly claimed for Single-Layer Cellular Neural/Nonlinear Networks (CNN). The theorems were selected with special regard to usefulness in engineering applications. Hence, in co...

This paper following a geometric approach proves new, and reproves old, vanishing and nonvanishing results on the space of twisted symmetric differentials, H(X, SΩX⊗ OX(k)) with k ≤ m, on subvarieties X ⊂ P . The case of k = m is special and the nonvanishing results are related to the space of quadrics containing X and lead to interesting geometrical objects associated to X, as for example the ...

Entropy and other fundamental quantities of information theory are customarily expressed and manipulated as functions of probabilities. Here we study the entropy H and subentropy Q as functions of the elementary symmetric polynomials in the probabilities, and reveal a series of remarkable properties. Derivatives of all orders are shown to satisfy a complete monotonicity property. H and Q themse...

In this paper, the different operator forms of classical Yang-Baxter equation are given in the tensor expression through a unified algebraic method. It is closely related to left-symmetric algebras which play an important role in many fields in mathematics and mathematical physics. By studying the relations between left-symmetric algebras and classical Yang-Baxter equation, we can construct lef...

In the theory of symmetric Jack polynomials the coefficients in the expansion of the pth elementary symmetric function ep(z) times a Jack polynomial expressed as a series in Jack polynomials are known explicitly. Here analogues of this result for the non-symmetric Jack polynomials Eη(z) are explored. Necessary conditions for non-zero coefficients in the expansion of ep(z)Eη(z) as a series in no...

In the paper we derive and discuss a wide class of algorithms for 3D Super-symmetric nonnegative Tensor Factorization (SNTF) or nonnegative symmetric PARAFAC, and as a special case: Symmetric Nonnegative Matrix Factorization (SNMF) that have many potential applications, including multi-way clustering, feature extraction, multisensory or multi-dimensional data analysis, and nonnegative neural sp...