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Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…
Interconnected dynamic systems are a pervasive component of our modern infrastructures. The complexity of such systems can be staggering, which motivates simplified representations for their manipulation and analysis. This work introduces…
In this note, we survey some elementary theorems and proofs concerning dynamical matrices theory. Some mathematical concepts and results involved in quantum information theory are reviewed. A little new result on the matrix representation…
We seek random versions of some classical theorems on complex approximation by polynomials and rational functions, as well as investigate properties of random compact sets in connection to complex approximation.
The aim of this work is an analytic investigation of differential equations producing mirror maps as well as giving new examples of mirror maps; one of these examples is related to (rational approximations to) $\zeta(4)$. We also indicate…
The content of this contribution is based on the course on numerical analysis techniques for non-linear dynamics. After introducing basic concepts as the visual analysis of trajectories in phase space and the importance of the nature of…
Fluctuations in the return time statistics of a dynamical system can be described by a new spectrum of dimensions. Comparison with the usual multifractal analysis of measures is presented, and difference between the two corresponding sets…
In economic theory, an agent chooses from available alternatives -- modeled as a set. In decisions in the field or in the lab, however, agents do not have access to the set of alternatives at once. Instead, alternatives are represented by…
The multi-layered nature of societal developments poses a challenge in the teaching and learning of history of mathematics. As an attempt to tackle this challenge we experimented with the use of Knowledge-Maps. The focus of our interest…
This paper is concerned with configurations of points in a plane lattice which determine angles that are rational multiples of $\pi$. We shall study how many such angles may appear in a given lattice and in which positions, allowing the…
The focus of this paper is to propose a driver model that incorporates human reasoning levels as actions during interactions with other drivers. Different from earlier work using game theoretical human reasoning levels, we propose a dynamic…
Argumentation is a process of evaluating and comparing a set of arguments. A way to compare them consists in using a ranking-based semantics which rank-order arguments from the most to the least acceptable ones. Recently, a number of such…
While compactness is an essential assumption for many results in dynamical systems theory, for many applications the state space is only locally compact. Here we provide a general theory for compactifying such systems, i.e. embedding them…
These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.
Multiple testing problems arise naturally in scientific studies because of the need to capture or convey more information with more variables. The literature is enormous, but the emphasis is primarily methodological, providing numerous…
The gap in statistics between multi-variate and time-series analysis can be bridged by using entropy statistics and recent developments in multi-dimensional scaling. For explaining the evolution of the sciences as non-linear dynamics, the…
Random walks on graphs are widely used in all sciences to describe a great variety of phenomena where dynamical random processes are affected by topology. In recent years, relevant mathematical results have been obtained in this field, and…
In this paper, we propose a fresh perspective on argumentation semantics, to view them as a relational database. It offers encapsulation of the underlying argumentation graph, and allows us to understand argumentation semantics under a…
We report on progress in the qualitative study of rational points on rationally connected varieties over number fields, also examining integral points, zero-cycles, and non-rationally connected varieties. One of the main objectives is to…
We study dynamical systems arising from word maps on simple groups. We develop a geometric method based on the classical trace map for investigating periodic points of such systems. These results lead to a new approach to the search of…