The notion of a probabilistic metric  space  corresponds to thesituations when we do not know exactly the  distance.  Probabilistic Metric space was  introduced by Karl Menger. Alsina, Schweizer and Sklar gave a general definition of  probabilistic normed space based on the definition of Menger [1]. In this note we study the PN spaces which are  topological vector spaces and the open mapping an...

We survey various notions of probabilistic automata and probabilistic bisimulation, accumulating in an expressiveness hierarchy of probabilistic system types. The aim of this paper is twofold: On the one hand it provides an overview of existing types of probabilistic systems and, on the other hand, it explains the relationship between these models. We overview probabilistic systems with discret...

Evolutionary innovation must occur in the context of some genomic background, which limits available evolutionary paths. For example, protein evolution by sequence substitution is constrained by epistasis between residues. In prokaryotes, evolutionary innovation frequently happens by macrogenomic events such as horizontal gene transfer (HGT). Previous work has suggested that HGT can be influenc...

A wide range of niching techniques have been investigated in evolutionary and genetic algorithms. In this article, we focus on niching using crowding techniques in the context of what we call local tournament algorithms. In addition to deterministic and probabilistic crowding, the family of local tournament algorithms includes the Metropolis algorithm, simulated annealing, restricted tournament...

We consider the problem of automatically verifying that a parameterized family of probabilistic concurrent systems terminates with probability one for all instances against adversarial schedulers. A parameterized family defines an infinite-state system: for each number n, the family consists of an instance with n finite-state processes. In contrast to safety, the parameterized verification of l...

We consider the problem of automatically verifying that a parameterized family of probabilistic concurrent systems terminates with probability one for all instances against adversarial schedulers. A parameterized family defines an infinite-state system: for each number n, the family consists of an instance with n finite-state processes. In contrast to safety, the parameterized verification of l...

Recently there have been advances in strati ed sampling techniques that attempt to enforce equal distributions not only across the design variables, but also onto the design space itself. This requires a numerically intensive optimization routine. Until now, no optimization strategy was able to distribute sample points evenly in the design space, but Evolutionary Algorithms (EA) act as an enabl...

If intelligent design (ID) is to compete with evolutionary theory (ET), it must meet the modified falsifiability challenge, that is, make some deductive or probabilistic observational assertions. It must also meet the modified translatability challenge, which it fails if ET makes all the observational assertions of ID, while ID does not make all the observational assertions of ET. I discuss fou...

The paper is focused on evolutionary synthesis of analog circuit realization of cube root function using proposed Graph Hybrid Estimation of Distribution Algorithm. The problem of cube root function circuit realization was adopted to demonstrate synthesis capability of the proposed method. Individuals of the population of the proposed method which represent promising topologies are encoded usin...

Protein can be represented by amino acid interaction network. This network is a graph whose vertices are the proteins amino acids and whose edges are the interactions between them. This interaction network is the first step of proteins three-dimensional structure prediction. In this paper we present a multi-objective evolutionary algorithm for interaction prediction and ant colony probabilistic...