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Cells forming various epithelial tissues have a strikingly universal distribution for the number of their edges. It is generally assumed that this topological feature is predefined by the statistics of individual cell divisions in growing…
Panic may spread over a crowd in a similar fashion as contagious diseases do in social groups. People no exposed to a panic source may express fear, alerting others of imminent danger. This social mechanism initiates an evacuation process,…
The reasons of the crisis in the contemporary (Riemannian) geometry are discussed. The conventional method of the generalized geometries construction, based on a use of the topology, leads to a overdetermination of the Riemannian geometry.…
The effect of topology on the collapse transition and instantaneous shape of an energy polydisperse polymer (a model heteropolymer) is studied by means of computer simulations. In particular, we consider three different chain topology,…
Diffusion in a linear potential in the presence of position-dependent killing is used to mimic a default process. Different assumptions regarding transport coefficients, initial conditions, and elasticity of the killing measure lead to…
This work concerns a structural topology optimisation problem for 4D printing based on the phase field approach. The concept of 4D printing as a targeted evolution of 3D printed structures can be realised in a two-step process. One first…
Several natural and artificial structures and systems are somehow optimized for performing specific functionalities. The structure and topology of cities is no exception, as it is critically important to ensure effective access to the…
In most OTC markets, a small number of market makers provide liquidity to other market participants. More precisely, for a list of assets, they set prices at which they agree to buy and sell. Market makers face therefore an interesting…
Mandatory emission trading schemes are being established around the world. Participants of such market schemes are always exposed to risks. This leads to the creation of an accompanying market for emission-linked derivatives. To evaluate…
An extensive statistical survey of universal approximators shows that as the dimension of a typical dissipative dynamical system is increased, the number of positive Lyapunov exponents increases monotonically and the number of parameter…
The first (Russian) edition of the book was among the first monographs on econophysics. The book gives an explanation of several intriguing phenomena, providing new insights and answers to some deeply vexing questions. Why the economic…
The question of whether biological populations survive or are eventually driven to extinction has long been examined using mathematical models. In this work we study population survival or extinction using a stochastic, discrete…
Multiple species in the ecosystem are believed to compete cyclically for survival and thus maintain balance in nature. Stochasticity has also an inevitable role in this dynamics. Considering these attributes of nature, the stochastic…
The paper surveys topological problems relevant to the motion planning problem of robotics and includes some new results and constructions. First we analyse the notion of topological complexity of configuration spaces which is responsible…
Epidemiological processes are studied within a recently proposed hierarchical network model using the susceptible-infected-refractory dynamics of an epidemic. Within the network model, a population may be characterized by $H$ independent…
We consider stochastic growth models for populations organized in colonies and subject to uniform catastrophes. To assess population viability, we analyze scenarios in which individuals adopt dispersion strategies after catastrophic events.…
The behavior of pedestrians shows certain regularities, which can be described by quantitative (partly stochastic) models. The models are based on the behavior of individual pedestrians, which depends on the pedestrian intentions and on the…
Routing choices of walking pedestrians in geometrically complex environments are regulated by the interplay of a multitude of factors such as local crowding, (estimated) time to destination, (perceived) comfort. As individual choices…
An individual-based model of stochastic branching is proposed and studied, in which point particles drift in $\bar{\mathds{R}}_{+}:=[0,+\infty)$ towards the origin (edge) with unit speed, where each of them splits into two particles that…
Elucidating emergent regularities in intriguing crowd dynamics is a fundamental scientific problem arising in multiple fields. In this work, based on the social force model, we simulate the typical scenario of collective escape towards a…