In this paper, we present and analyse two Hopfield-like nonlinear networks, in continuous-time and discrete-time respectively. The proposed network is based on an autonomous linear system with a symmetric weight matrix, which is designed to be unstable, and a nonlinear function stabilizing the whole network thanks to a manipulated state variable called“ultimate SIR”. This variable is observed t...

The symmetric interior penalty discontinuous Galerkin finite element method is presented for the numerical discretization of the second-order wave equation. The resulting stiffness matrix is symmetric positive definite and the mass matrix is essentially diagonal; hence, the method is inherently parallel and leads to fully explicit time integration when coupled with an explicit timestepping sche...

A generating function of the number of homomorphisms from the fundamental group of a compact oriented or non-orientable surface without boundary into a finite group is obtained in terms of an integral over a real group algebra. We calculate the number of homomorphisms using the decomposition of the group algebra into irreducible factors. This gives a new proof of the classical formulas of Frobe...

Suppose that X has a k -variate spherically symmetric distribution with mean vector θ and identity covariance matrix. We present two spherical confidence sets for θ, both centred at a positive part Stein estimator T C S .X/. In the first, we obtain the radius by approximating the upper α-point of the sampling distribution of kT C S .X/ θk2 by the first two non-zero terms of its Taylor series ab...

The eigenvalues of the elliptic N-body Ruijsenaars operator are obtained by a dynamical version of the algebraic nested Bethe ansatz method. The result is derived by using the construction given in [1], where the Ruijsenaars operator was obtained as the transfer matrix associated to the symmetric power of the vector representation of the elliptic quantum group Eτ,γ(glN ).

Let P be an r×smatrix of Laurent polynomials with symmetry such that P(z)P∗(z) = Ir for all z ∈ C\{0} and the symmetry of P is compatible. The matrix extension problem with symmetry is to find an s × s square matrix Pe of Laurent polynomials with symmetry such that [Ir,0]Pe = P (that is, the submatrix of the first r rows of Pe is the given matrix P), Pe is paraunitary satisfying Pe(z)Pe(z) = Is...

We study the spectrum of certain two-particle operators in supergravity regime D1-D5 system, focussing on four-point correlators tensor multiplets $AdS_3\times S^3$ at tree level. In Mellin space, these are nicely determined by a single amplitude, which makes manifest large $p$ limit, connection with flat space S-matrix, and six dimensional conformal symmetry. compute $(1,1)\times \overline{(1,...

This memo specifies how to incorporate International Data Encryption Algorithm (IDEA) into CMS or S/MIME as an additional strong algorithm for symmetric encryption. For organizations who make use of IDEA for data security purposes it is of high interest that IDEA is also available in S/MIME. The intention of this memo is to provide the OIDs and algorithms required that IDEA can be included in S...

This talk will focus on preconditioning techniques for solving sequences of symmetric indefinite systems Aixi = bi, where the matrices Ai are supposed to slightly change. This case often arises in Computational Science and Engineering, for example when a Newton-type method is used to solve a nonlinear problem. With this aim in mind, we study the case of a sequence with a given matrix A ∈ Rn×n a...

We present an efficient and robust method for the calculation of all S matrix elements (elastic, inelastic, and reactive) over an arbitrary energy range from a single real-symmetric Lanczos recursion. Our new method transforms the fundamental equations associated with Light's artificial boundary inhomogeneity approach from the primary representation (original grid or basis representation of the...