We consider an important class of dynamic singleinput single-output nonlinear systems where the system model is polynomial in observations but linear in parameters. The investigation is done in the errors-in-variables framework, i.e. both input and output are observed with noise. Assuming white Gaussian measurement noise that is characterized by a magnitude and a covariance structure, we propos...

We give a bijection between partially directed paths in the symmetric wedge y = ±x and matchings, which sends north steps to nestings. This gives a bijective proof of a result of Prellberg et al. that was first discovered through the corresponding generating functions: the number of partially directed paths starting at the origin confined to the symmetric wedge y = ±x with k north steps is equa...

In this paper, we study the distribution of the number of consecutive pattern matches of the five up-down permutations of length four, 1324, 2314, 2413, 1432, and 3412, in the set of up-down permutations. We show that for any such τ , the generating function for the distribution of the number of consecutive pattern matches of τ in the set of up-down permutations can be expressed in terms of wha...

For a graph G let L(G) and l(G) denote the size of the largest and smallest maximum matching of a graph obtained from G by removing a maximum matching of G. We show that L(G) ≤ 2l(G), and L(G) ≤ 3 2 l(G) provided that G contains a perfect matching. We also characterize the class of graphs for with L(G) = 2l(G). Our characterization implies the existence of a polynomial algorithm for testing the...

Let [Formula: see text] be an instance of the stable marriage problem in which every vertex ranks its neighbors a strict order preference. A matching is popular if does not lose head-to-head election against any matching. Popular matchings generalize matchings. Unfortunately, when there are edge costs, to find or even approximate up factor minimum cost NP-hard. min-cost Our goal efficiently com...

Given an undirected graph G = (V,E) and a delta-matroid (V,F), the delta-matroid matching problem is to find a maximum cardinality matching M such that the set of the end vertices of M belongs to F . This problem is a natural generalization of the matroid matching problem to delta-matroids, and thus it cannot be solved in polynomial time in general. This paper introduces a class of the delta-ma...

For an arbitrary tree we investigate the problems of constructing a maximum matching which minimizes or maximizes the cardinality of a maximum matching of the graph obtained from original one by its removal and present corresponding polynomial algorithms.

Suppose we have a well-solved optimization problem, such as minimum spanning tree, maximum cut in planar graphs, minimum weight perfect matching, or maximum weight independent set in a bipartite graph. How hard is it to determine whether there exists a solution with a given weight ? Papadimitriou and Yannakakis showed in [PAPADIMITRIOU 82] that these so-called exact versions of the above optimi...