Consider non-negative lattice paths ending at their maximum height, which will be called admissible paths. We show that the probability for a lattice path to be admissible is related to the Chebyshev polynomials of the first or second kind, depending on whether the lattice path is defined with a reflective barrier or not. Parameters like the number of admissible paths with given length or the e...

When designing Networked Control Systems (NCS), the maximum allowable transmission interval (MATI) is an important quantity, as it provides admissible time between two instants. An efficient procedure to compute a bound on MATI such that stability can be guaranteed for general nonlinear NCS emulation of continuous-time controller. In this paper, we present simple but modification well-establish...

We propose a method for upper bounding the general adversary bound for certain boolean functions. Due to the the tightness of query complexity and the general adversary bound [5], this gives an upper bound on the quantum query complexity of those functions. We give an example where this upper bound is smaller than the query complexity of any known quantum algorithm.

We investigate the maximum number of simple cycles and the maximum number of Hamiltonian cycles in a planar graph G with n vertices. Using the transfer matrix method we construct a family of graphs which have at least 2.4262 simple cycles and at least 2.0845 Hamilton cycles. Based on counting arguments for perfect matchings we prove that 2.3404 is an upper bound for the number of Hamiltonian cy...

This paper deals with the NP-hard graph problem that consists on determining the maximum cardinality subset of vertices inducing a k-regular subgraph. For any graph G, this maximum will be denoted by αk(G). From a well known Motzkin-Straus result, it is deduced a relationship between αk(G) and the independence number α(G). Next, it is proved that the upper bounds υk(G) introduced in Cardoso, Ka...

State-of-the-art branch-and-bound algorithms for the maximum clique problem (Maxclique) frequently use an upper bound based on a partition P of a graph into independent sets for a maximum clique of the graph, which cannot be very tight for imperfect graphs. In this paper we propose a new encoding from Maxclique into MaxSAT and use MaxSAT technology to improve the upper bound based on the partit...

We consider the numerical stability of discretisation schemes for continuous-time state estimation filters. The dynamical systems we consider model the indirect observation of a continuous-time Markov chain. Two candidate observation models are studied. These models are (a) the observation of the state through a Brownian motion, and (b) the observation of the state through a Poisson process. It...

This paper presents a method for evaluating an upper bound of simultaneous switching gates in combinational circuits. In this method, the original circuit is partitioned into subcircuits, and the upper bound is approximately computed as the sum of maximum switching gates for all subcircuits. In order to increase the accuracy, we adopted an evaluation function that takes account of both the inte...

We give a new upper bound on the maximum size Aq(n, d) of a code of word length n and minimum Hamming distance at least d over the alphabet of q ≥ 3 letters. By blockdiagonalizing the Terwilliger algebra of the nonbinary Hamming scheme, the bound can be calculated in time polynomial in n using semidefinite programming. For q = 3, 4, 5 this gives several improved upper bounds for concrete values...

The two-party key agreement problem via public discussion, known as the source model problem, is considered. Assuming an erasure model for Eve’s side information, the maximum erasure probability for which the secret-key capacity is zero is studied. Our first main contribution is to give a lower and an upper bound on this maximum erasure probability. The lower and upper bounds are shown to match...