We study a model describing the spread of a globalized culture in a population of individuals localized at the nodes of a social network. The influence of this globalized culture, assumed to be foreign to the local culture, is measured by a probability to convince each individual to adopt its cultural traits. This probability depends upon the degree s—a real between 0 and 1—of “wise” skepticism...

In this paper n is a natural number. One can prove the following propositions: (1) For every non empty subset X of E2 T and for every compact subset Y of E2 T such that X ⊆ Y holds N-boundX ¬ N-boundY. (2) For every non empty subset X of E2 T and for every compact subset Y of E2 T such that X ⊆ Y holds E-boundX ¬ E-boundY. (3) For every non empty subset X of E2 T and for every compact subset Y ...

We consider the occupancy problem where balls are thrown independently at infinitely many boxes with fixed positive frequencies. It is well known that the random number of boxes occupied by the first n balls is asymptotically normal if its variance Vn tends to infinity. In this work, we mainly focus on the opposite case where Vn is bounded, and derive a simple necessary and sufficient condition...

where ρ is the correlation between x1 and x2. For each random number we sample ρ from the uniform distribution (0, 0.5). We set this correlation range because we want to illustrate the performance of the indirect mapping in a setting of low correlation between the two data types. In order to represent noisy data types we added independent standard Gaussian noise to both x1 and x2. We treat x1 a...

In this paper we describe a random walk clustering technique to address the Website Boundary Detection (WBD) problem. The technique is fully described and compared with alternative (breadth and depth first) approaches. The reported evaluation demonstrates that the random walk technique produces comparable or better results than those produced by these alternative techniques, while at the same t...

This paper discusses basic security aspects of distributed random number generation in potentially hostile environments. The goal is to outline and discuss a distributed approach, which comes to question in the case of attacker being able to target one or several mobile devices. We define communication paths and attacker models instead of providing technical details of local generation. This pa...

We prove that the solution of the Kac analogue of Boltzmann’s equation can be viewed as a probability distribution of a sum of a random number of random variables. This fact allows us to study convergence to equilibrium by means of a few classical statements pertaining to the central limit theorem. In particular, a new proof of the convergence to the Maxwellian distribution is provided, with a ...

The goal of the paper is to study asymptotic behavior of the number of lost messages. Long messages are assumed to be divided into a random number of packets which are transmitted independently of one another. An error in transmission of a packet results in the loss of the entire message. Messages arrive to the M/GI/1 finite buffer model and can be lost in two cases as either at least one of it...