A randomized method aimed at evaluation of probabilistic bounds for function values is considered. Stochastic intervals tightly covering ranges of function values with probability close to one are modelled by a randomized method inspired by interval arithmetic. Statistical properties of the modelled intervals are investigated experimentally. The experimental results are discussed with respect t...

The paper considers a generalization of Peano arithmetic, Hilbert arithmetic as the basis world in Pythagorean manner. unifies foundations mathematics (Peano and set theory), physics (quantum mechanics information), philosophical transcendentalism (Husserl’s phenomenology) into formal theory mathematical structure literally following Husserl’s tracе “philosophy rigorous science”. In pathway to ...

We study a stochastic matrix model to understand the mechanics of risk spreading (or bet hedging) by dispersion. Up to now, this model has been mostly dealt with numerically, except for the well-mixed case. Here, we present an analytical result that shows that optimal dispersion leads to Zipf's law. Moreover, we found that the arithmetic ensemble average of the total growth rate converges to th...

This paper introduces the algorithmic design and implementation of Tulip, an open-source interior-point solver for linear optimization. It implements a regularized homogeneous algorithm with multiple centrality corrections, therefore handles unbounded infeasible problems. The is written in Julia, thus allowing flexible efficient implementation: Tulip's framework fully disentangled from algebra ...

Fuzzy control is one of the most important parts of fuzzy theory for which several approaches exist. Mamdani uses $alpha$-cuts and builds the union of the membership functions which is called the aggregated consequence function. The resulting function is the starting point of the defuzzification process. In this article, we define a more natural way to calculate the aggregated consequence funct...

The aim of this paper is to present a new method and the tool validate numerical results Volterra integral equation with discontinuous kernels in linear non-linear forms obtained from Adomian decomposition method. Because disadvantages traditional absolute error show accuracy mathematical methods which based on floating point arithmetic, we apply stochastic arithmetic condition study efficiency...

Frequency histograms are ubiquitous, being practically used in any field of science. In this paper, we present a partial order for frequency and, to our knowledge, no kind has been yet defined. This is based on the stochastic discrete probability distributions and it invariance properties that make unique. First, model histogram as sequence bins associated with (or relative frequency) distribut...

Unweighted Pair Group Method with Arithmetic Mean (UPGMA) is one of the most popular distance-based methods to reconstruct an equidistant phylogenetic tree from a distance matrix computed alignment sequences. Since we use trees as gene for phylogenomic analyses under multi-species coalescent model and since input each in genome estimated via maximum likelihood estimators, it important conduct r...