one of the models that can be used to study the relationship between boolean random sets and explanatory variables is growth regression model which is defined by generalization of boolean model and permitting its grains distribution to be dependent on the values of explanatory variables. this model can be used in the study of behavior of boolean random sets when their coverage regions variation...

Let A = {a1, . . . , an} be a set and F = {F1, . . . , Fm} a family of subsets of A. A subset H ⊆ A has the hitting set property, or is a hitting set, iff H ∩ Fi 6= ∅ for 1 ≤ i ≤ m (i.e., H “hits” each set Fi). If we are given a cost function c : A → N, the cost of H is ∑ a∈H c(a). A hitting set is of minimum cost if its cost is minimal among all hitting sets. The problem of finding a minimum-c...

The paper considers a particular family of set–valued stochastic processes modeling birth–and–growth processes. The proposed setting allows us to investigate the nucleation and the growth processes. A decomposition theorem is established to characterize the nucleation and the growth. As a consequence, different consistent set–valued estimators are studied for growth process. Moreover, the nucle...

The paper considers a particular family of fuzzy monotone set–valued stochastic processes. The proposed setting allows us to investigate suitable α-level sets of such processes, modeling birth–and–growth processes. A decomposition theorem is established to characterize the nucleation and the growth. As a consequence, different consistent set–valued estimators are studied for growth process. Mor...

Given a dynamical system and a subset A of its phase space, we consider those orbits which, on average, spend as long as possible in A. This largest possible average is the maximum hitting frequency. We study the variation of the (orbits of) maximum hitting frequency as a function of A. Mathematics Subject Classification: 37A, 37B20

We obtain sufficient conditions for the finiteness of the moments of the single-server queue busy period in discrete and continuous time. In the cases of power and exponential moments, the conditions found coincide with the known necessary ones. 1. Introduction and notation. Consider a sequence t n n of random vectors with nonnegative coordinates which are i.i.d. in n, but any dependence betwee...

Introduction. The Weighted Minimum Hitting Set Problem (WMHSP) and the standard Minimum Hitting Set Problem (MHSP), are combinatorial problems of great interest for many applications. Although, these problems lend themselves quite naturally to an evolutionary approach. To our knowledge, there are no significant results of evolutionary algorithms applied to either the WMHSP or the MHSP, except f...

When does a small drift increase the hitting probability of a boundary point / the expected hitting time of the boundary, compared to the driftless case? We analyze this for diffusion processes on [0,1] by expanding the Green function. In this way, in the appropriate diffusion approximation setting, we rederive and extend the one-third rule of evolutionary game theory (Nowak et al., 2004) and e...

This work proposes an adaptive trajectory planning approach for a single quad-rotor unmanned aerial vehicle (UAV). The objective is to drive the system from an initial position to a final one without hitting actuator constraints while minimizing the total time of the mission. The approach employs differential flatness to represent the control inputs to be applied in function of the desired traj...