Erdős and Rényi proposed in 1960 a probabilistic model for sums of s integral sth powers. Their model leads almost surely to a positive density for sums of s pseudo sth powers, which does not reflect the case of sums of two squares. We refine their model by adding arithmetical considerations and show that our model is in accordance with a zero density for sums of two pseudo-squares and a positi...

The present study deals with word frequencies distributions and their relation to probabilistic Information Retrieval (IR) models. We examine the burstiness phenomenon (a rich get richer phenomenon) of word frequencies in textual collections. We propose to model this phenomenon as a property of probability distributions and we show that the Beta Negative Binomial distribution is a good statisti...

We introduce pseudo-deterministic interactive proofs (psdAM): interactive proof systems for search problems where the verifier is guaranteed with high probability to output the same output on different executions. As in the case with classical interactive proofs, the verifier is a probabilistic polynomial time algorithm interacting with an untrusted powerful prover. We view pseudo-deterministic...

In this paper we study the kaleidoscopic pseudo-randomness of finite Euclidean graphs using probabilistic methods. Roughly speaking, we show that sufficiently large subsets of d-dimensional vector spaces over finite fields contain every possible finite configurations.

Several formal models combine probabilistic and nondeterministic features. To allow their probabilistic simulation and statistical model checking by means of pseudo-random number sampling, all sources of nondeterminism must first be quantified. However, current tools offer limited flexibility for the user to define how the nondeterminism should be quantified. In this paper, we propose an expres...

There is given an overview on the results related to the generalization of the decision theory to non probabilistic uncertainty based on the characterization of the families of operations involved in generalized mixtures. It turns out that this is based on a previous result on the characterization of the pair of continuous t-norm T and t-conorm S such that the former is conditionally distributi...

Failure of the quay walls due to earthquakes results in severe economic loss. Because of hazards threatening such inexpensive nodes of national and international transportation networks, seismic design of quay walls is still an evolving topic in marine structural engineering. This study investigates the sensitivity of the gravity-type quay wall stability respect to uncertain soil and seismic pr...

Abstract In this paper, we develop a way to extract information about random walk associated with typical Thurston’s construction. We first observe that construction entails free group of rank 2. also present proof the spectral theorem for walks have finite 2nd moment respect Teichmüller metric. Its general case was remarked by Dahmani and Horbez. Finally, under hypothesis not involving conditi...

The problem of finding the consensus (most probable string) for a distribution generated by a weighted finite automaton or a probabilistic grammar is related to a number of important questions: computing the distance between two distributions or finding the best translation (the most probable one) given a probabilistic finite state transducer. The problem is undecidable with general weights and...