In this paper, we give a probabilistic counterpart of  Mazur-Ulam theorem  in probabilistic normed groups. We show, under some conditions, that every surjective isometry between two probabilistic normed groups is a homomorphism.

Probabilistic model building Genetic Algorithm (PMBGA) is a novel concept in the field of evolutionary computation which is motivated by an idea of building a probabilistic model of the population to preserve important building blocks in subsequent generation. Growing number of research is being carried out in this field and different variant of PMBGA s has been purposed. Aim of this paper is t...

In this paper, we formalize the Menger probabilistic normed space as a category in which its objects are the Menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. Then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. So, we can easily apply the results of topological vector spaces...

In recent years, the study of the phase transition behavior and typical-case complexity of search and optimization problems have become an active research topic, drawing attention from researchers from computer science, mathematics, and statistical physics. The probabilistic method that has been developed since 1960s plays an important role in this development. We give a brief introduction to t...

Universally conserved positions in ribosomal proteins have significant biases in amino acid usage, likely indicating the expansion of the genetic code at the time leading up to the most recent common ancestor(s) (MRCA). Here, we apply this principle to the evolutionary history of the ribosome before the MRCA. It has been proposed that the experimentally determined order of assembly for ribosoma...

Temporal Text Mining (TTM) is concerned with discovering temporal patterns in text information collected over time. Since most text information bears some time stamps, TTM has many applications in multiple domains, such as summarizing events in news articles and revealing research trends in scientific literature. In this paper, we study a particular TTM task – discovering and summarizing the ev...

Understanding the functioning of extinct ecosystems is a complicated knot ecological, evolutionary, and preservational strands that must be untangled. For instance, anatomical behavioral differences can profoundly alter fossilization pathways. This particularly true in exceptionally preserved soft-bodied biotas record earliest phases animal evolution during Cambrian Explosion Ordovician Radiati...

New contributions toward generalizing evolutionary models expand greatly our ability to analyze complex evolutionary characters and advance phylogeny reconstruction. In this article, we extend the binary stochastic Dollo model to allow for multi-state characters. In doing so, we align previously incompatible Wagner and Dollo parsimony principles under a common probabilistic framework by embeddi...

in this paper, we formalize the menger probabilistic normed space as a category in which its objects are the menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. so, we can easily apply the results of topological vector spaces...