In this paper, a novel deinterlacing algorithm is proposed. The proposed algorithm approximates the distribution of the luminance into a polynomial function. Instead of using one polynomial function for all pixels, different polynomial functions are used for the uniform, texture, and directional edge regions. The function coefficients for each region are computed by matrix multiplications. Expe...

This paper presents a combinatorial polynomial-time algorithm for minimizing submod-ular set functions. The algorithm employs a scaling scheme that uses a ow in the complete directed graph on the underlying set with each arc capacity equal to the scaled parameter. The resulting algorithm runs in time bounded by a polynomial in the size of the underlying set and the largest length of the functio...

We assume the existence of a function f that is computable in polynomial time but cannot be inverted by a randomized average-case polynomial algorithm. The cryptographic setting is, however, different: even for a weak one-way function, a successful adversary should fail on a polynomial fraction of inputs. Nevertheless, we show how to construct an infinitely-often one-way function based on f . §

In this paper, we consider approximation algorithms for optimizing a generic multivariate polynomial function in discrete (typically binary) variables. Such models have natural applications in graph theory, neural networks, error-correcting codes, among many others. In particular, we focus on three types of optimization models: (1) maximizing a homogeneous polynomial function in binary variable...

design of crystal-like lattices can be achieved by using some net operations. hypothetical networks, thus obtained, can be characterized in their topology by various counting polynomials and topological indices derived from them. the networks herein presented are related to the dyck graph and described in terms of omega polynomial and piv polynomials.

We consider the asymptotics of the second-order correlation function of the characteristic polynomial of a random matrix. We show that the known result for a random matrix from the Gaussian Unitary Ensemble essentially continues to hold for a general Hermitian Wigner matrix. Our proofs rely on an explicit formula for the exponential generating function of the second-order correlation function o...

Recently, Stanley [21] has defined a symmetric function generalization of the chromatic polynomial of a graph. Independently, Chung and Graham [4] have defined a digraph polynomial called the cover polynomial which is closely related to the chromatic polynomial of a graph (in fact, as we shall see, the cover polynomial of a certain digraph associated to a poset P coincides with the chromatic po...

A function from the group GL(2, R) to itself is called polynomial if it can be written as some product of constant functions, the identity function, and the function that maps every element to its inverse. We give a necessary topological condition for a function to be polynomial. As a consequence we prove that transposition is not polynomial. Mathematics Subject Classification 2000. 08A40 (20G20)