We show that the class of strongly connected graphical models with treewidth at most k can be properly efficiently PAC-learnt with respect to the Kullback-Leibler Divergence. Previous approaches to this problem, such as those of Chow ([1]), and Hoffgen ([7]) have shown that this class is PAClearnable by reducing it to a combinatorial optimization problem. However, for k > 1, this problem is NPc...

Inspired by the study of community structure in connection networks, we introduce the graph polynomial Q (G;x, y), the bivariate generating function which counts the number of connected components in induced subgraphs. We give a recursive definition of Q (G; x, y) using vertex deletion, vertex contraction and deletion of a vertex together with its neighborhood and prove a universality property....

Let G be a simple graph. We assign a polynomial C(G; x) to G, called the clique polynomial, where the coefficient of Xi, i > 0, is the number of cliques of G with i vertices, and the constant term is 1. Fisher and Solow (1990), proved that this polynomial always has a real root. We prove this result by a simple and elementary method, which also implies the following results. If (G is the greate...

In this work we propose a novel ap roach for demodulating Continuous Phase Modulation CPM) signals based Q on the modeling of the instantaneous phase as a piecewise polynomial-phase function. The polynomial modeling can be a good approximation for currently used modulations or it can be-exact if the shaping pulse is chosen to be a oiecewise polvnomial function. The crucial step in the demodulat...

We show that the class of strongly connected graphical models with tree-width at most k can be properly efficiently PAC-learnt with respect to the Kullback-Leibler Divergence. Previous approaches to this problem, such as those of Chow ([1]), and Hoffgen ([7]) have shown that this class is PAC-learnable (though not necessarily efficiently unless k = 1) by reducing to a NP-complete combinatorial ...

1. Abelian functions by Poincaré. 1-1. If the variable x and a general solution y of a linear differential equation with polynomial coefficients are algebraically dependent, the periods of abelian integrals of the first kind associated with the curve f(x, y) = 0 satisfy certain relations. In his earliest works on abelian functions Poincaré examined such relations in some special cases. He also ...

A set of multivariate polynomials, over a field of zero or large characteristic, can be tested for algebraic independence by the well-known Jacobian criterion. For fields of other characteristic p > 0, no analogous characterization is known. In this paper we give the first such criterion. Essentially, it boils down to a non-degeneracy condition on a lift of the Jacobian polynomial over (an unra...

A quantum superintegrable system is an integrable n-dimensional Hamiltonian system with potential: H = ∆n + V that admits 2n − 1 algebraically independent partial differential operators commuting with the Hamiltonian, the maximum number possible. The system is of order ` if the maximum order of the symmetry operators, other than H, is `. Typically, the algebra generated by the symmetry operator...