Modern Personal Digital Assistant (PDA) architectures often utilize a wholesale data transfer protocol known as “slow sync” for synchronizing PDAs with Personal Computers (PCs). This approach is markedly inefficient with respect to bandwidth usage and latency, since the PDA and PC typically share many common records. We propose, analyze, and implement a novel PDA synchronization scheme (CPIsync...

We study the order in Grammatical Inference algorithms, and its influence on the polynomial (with respect to the data) identification of languages. This work is motivated by recent results on the polynomial convergence of data-driven grammatical inference algorithms. In this paper, we prove a sufficient condition that assures the existence of a characteristic sample whose size is polynomial wit...

We present the first fully dynamic algorithm for computing the characteristic polynomial of a matrix. In the generic symmetric case our algorithm supports rank-one updates in O(n log n) randomized time and queries in constant time, whereas in the general case the algorithm works in O(nk log n) randomized time, where k is the number of invariant factors of the matrix. The algorithm is based on t...

A characteristic polynomial was recently de!ned for greedoids, generalizing the notion for matroids. When chordal graphs are viewed as antimatroids by shelling of simplicial vertices, the greedoid characteristic polynomial gives additional information about those graphs. In particular, the characteristic polynomial for a chordal graph is an alternating clique generating function and is expressi...

A characteristic pair is a pair (G, C) of polynomial sets in which G is a reduced lexicographic Gröbner basis, C is the minimal triangular set contained in G, and C is normal. In this paper, we show that any finite polynomial set P can be decomposed algorithmically into finitely many characteristic pairs with associated zero relations, which provide representations for the zero set of P in term...

In a signed graph G, a negative clique is a complete subgraph having negative edges only. In this article, we give characteristic polynomial expressions, and eigenvalues of some signed graphs having negative cliques. This includes signed cycle graph, signed path graph, a complete graph with disjoint negative cliques, and star block graph with negative cliques.

Generalizing a result of Yoshinaga in dimension 3, we show that a central hyperplane arrangement in 4-space is free exactly if its restriction with multiplicities to a fixed hyperplane of the arrangement is free and its reduced characteristic polynomial equals the characteristic polynomial of this restriction. We show that the same statement holds true in any dimension when imposing certain tam...

The concept of average degree-eccentricity matrix ADE(G) of a connected graph $G$ is introduced. Some coefficients of the characteristic polynomial of ADE(G) are obtained, as well as a bound for the eigenvalues of ADE(G). We also introduce the average degree-eccentricity graph energy and establish bounds for it.

Multiple orthogonal polynomials (MOP) are a non-definite version of matrix orthogonal polynomials. They are described by a Riemann-Hilbert matrix Y consisting of four blocks Y1,1, Y1,2, Y2,1 and Y2,2. In this paper, we show that detY1,1 (detY2,2) equals the average characteristic polynomial (average inverse characteristic polynomial, respectively) over the probabilistic ensemble that is associa...

Abstract. We investigate the moments of the derivative, on the unit circle, of characteristic polynomials of random unitary matrices and use this to formulate a conjecture for the moments of the derivative of the Riemann ζ function on the critical line. We do the same for the analogue of Hardy’s Z-function, the characteristic polynomial multiplied by a suitable factor to make it real on the uni...