Related papers: Deterministic Dynamics and Chaos: Epistemology and…
From ancient philosophers to modern economists, biologists, and other researchers, there has been a continuous effort to unveil causal relations. The most formidable challenge lies in deducing the nature of the causal relationship: whether…
The concept of structural invariance previously introduced by the authors is used to argue that the connection between random matrix theory and quantum systems with a chaotic classical counterpart is in fact largely exact in the…
This paper provides an overview and critical analysis on the modeling and applications of the dynamics of human crowds, where social interactions can have an important influence on the behavioral dynamics of the crowd viewed as a living,…
Dynamics, the study of change, is normally the subject of mechanics. Whether the chosen mechanics is ``fundamental'' and deterministic or ``phenomenological'' and stochastic, all changes are described relative to an external time. Here we…
At its core, the physics paradigm adopts a reductionist approach, aiming to understand fundamental phenomena by decomposing them into simpler, elementary processes. While this strategy has been tremendously successful in physics, it has…
This paper formulates a new approach to the study of chaos in discrete dynamical systems based on the notions of inverse ill-posed problems, set-valued mappings, generalized and multivalued inverses, graphical convergence of a net of…
What is chaos? Despite several decades of research on this ubiquitous and fundamental phenomenon there is yet no agreed-upon answer to this question. Recently, it was realized that all stochastic and deterministic differential equations,…
This book chapter introduces to the concept of weak chaos, aspects of its ergodic theory description, and properties of the anomalous dynamics associated with it. In the first half of the chapter we study simple one-dimensional…
Is speculative mathematics dangerous? Recent interactions between physics and mathematics pose the question with some force: traditional mathematical norms discourage speculation, but it is the fabric of theoretical physics. In practice…
Mathematical oncology is an interdisciplinary research field where the mathematical sciences meet cancer research. Being situated at the intersection of these two fields makes mathematical oncology highly dynamic, as practicing researchers…
Questions concerning origin of mathematical knowledge and roles of language and intuition (imagery) in mathematical thoughts are long standing and widely debated. By introspection, mathematicians usually have some beliefs regarding these…
Physics is formulated in terms of timeless classical mathematics. A formulation on the basis of intuitionist mathematics, built on time-evolving processes, would offer a perspective that is closer to our experience of physical reality.
The paper analyzes dynamic epistemic logic from a topological perspective. The main contribution consists of a framework in which dynamic epistemic logic satisfies the requirements for being a topological dynamical system thus interfacing…
Chaos is omnipresent in nature, and its understanding provides enormous social and economic benefits. However, the unpredictability of chaotic systems is a textbook concept due to their sensitivity to initial conditions, aperiodic behavior,…
Several interdisciplinary areas have appeared at the interface between biological and physical sciences. In this work, we suggest a complex network-based methodology for analyzing the interrelationships between some of these…
Combinatorics is a powerful tool for dealing with relations among objectives mushroomed in the past century. However, an more important work for mathematician is to apply combinatorics to other mathematics and other sciences not merely to…
Dynamics, the physical change in time and a pillar of natural sciences, can be regarded as an emergent phenomenon when the system of interest is part of a larger, static one. This "relational approach to time", in which the system's…
Our aim is to detect mechanistic interaction between the effects of two causal factors on a binary response, as an aid to identifying situations where the effects are mediated by a common mechanism. We propose a formalization of mechanistic…
Discovery of causal relations is fundamental for understanding the dynamics of complex systems. While causal interactions are well defined for acyclic systems that can be separated into causally effective subsystems, a mathematical…
This work redefines the framework of chaos in dynamical systems by extending Devaney's definition to multiple mappings, emphasizing the pivotal role of nonlinearity. We propose a novel theorem demonstrating how nonlinear dynamics within a…