In this paper a correspondence is derived between regularization operators used in regularization networks and support vector kernels. We prove that the Green's Functions associated with regularization operators are suitable support vector kernels with equivalent regularization properties. Moreover, the paper provides an analysis of currently used support vector kernels in the view of regulariz...

In this paper we consider the problem of characterizing whether a symmetric polynomial matrix is positive definite on a semi-algebraic set. Based on suitable sum-of-squares representations we can construct LMI relaxation for this decision problem. As key novel technical contributions it is possible to prove that these relaxations are exact. Our proof is based on a sum-of-squares representation ...

In recent years, finding new satisfiability algorithms for various circuit classes has been a very active line of research. Despite considerable progress, we are still far away from a definite answer on which circuit classes allow fast satisfiability algorithms. This survey takes a (far from exhaustive) look at some recent satisfiability algorithms for a range of circuit classes and highlights ...

be a positive definite quadratic form with determinant D R and integer coefficients a ;Call it an even form if all a ; ; are even ., an odd form if at least one a ;; is odd . Then Í,, is called non-decomposable, if it cannot be expressed as a sum of two non-negative quadratic forms with integer coefficients . Mordell 1 ) proved that f, can always be decomposed into a sum of five squares of line...

Employing the concept of termination of sequence of SDS sets to describe the positive semidefinite property of a form, we establish a necessary and sufficient condition for deciding whether a given form on Rn+ is positive semi-definite or not, and show that, for a form which is (strictly) positive definite on Rn+, the corresponding sequence of SDS sets is positively terminating. The above resul...

literal: Let p be a proposition. Then p and -p are literals. clause: A clause is a disjunction of literals. Horn Clause: A Horn Clause is a clause in which there is at most one positive literal. definite clause: A definite clause is a Hom Clause in which there is exactly one positive literal. A definite clause such as can also be written as We call pi the head of the clause, and the conjunction...

Many studies in natural language processing are concerned with how to generate definite descriptions that evoke a discourse entity already introduced in the context. A solution to this problem has been initially proposed by Dale (1989) in terms of distinguishing descriptions and distinguishable entities. In this paper, we give a formal definition of the terms “distinguishable entity” in non tri...

In this note, a simple theorem on proportionality of indefinite real quadratic forms is proved, and is used to clarify the proof of the invariance of the interval in special relativity from Einstein’s postulate on the universality of the speed of light; students are often rightfully confused by the incomplete or incorrect proofs given in many texts. The result is illuminated and generalized usi...

Let f ∈ C(M,R) be a functional defined on a Hilbert manifold M. It is well known that if f is a Morse functional (i.e. every critical point of f is nondegenerate) and f satisfies the so called Palais–Smale condition, the Morse relations hold. More precisely, let x ∈ M be a critical point of f , and m(x, f) denote the Morse index at x (i.e. the maximal dimension of the subspaces of TxM where the...

The preconditioned conjugate gradient (CG) is often applied in image reconstruction as a regularizing method. When the blurring matrix has Toeplitz structure, the modified circulant preconditioner and the inverse Toeplitz preconditioner have been shown to be effective. We introduce here a preconditioner for symmetric positive definite Toeplitz matrices based on a trigonometric polynomial fit wh...