Hyperbolic tilings and formal language theory

In this paper, we try to give the appropriate class of languages to which belong various objects associated with tessellations in the hyperbolic plane.Comment: In Proceedings MCU 2013, arXiv:1309.104

Continuum and discrete approach in modeling biofilm development and structure: a review

The scientific community has recognized that almost 99% of the microbial life on earth is represented by biofilms. Considering the impacts of their sessile lifestyle on both natural and human activities, extensive experimental activity has been carried out to understand how biofilms grow and interact with the environment. Many mathematical models have also been developed to simulate and elucidate the main processes characterizing the biofilm growth. Two main mathematical approaches for biomass representation can be distinguished: continuum and discrete. This review is aimed at exploring the main characteristics of each approach. Continuum models can simulate the biofilm processes in a quantitative and deterministic way. However, they require a multidimensional formulation to take into account the biofilm spatial heterogeneity, which makes the models quite complicated, requiring significant computational effort. Discrete models are more recent and can represent the typical multidimensional structural heterogeneity of biofilm reflecting the experimental expectations, but they generate computational results including elements of randomness and introduce stochastic effects into the solutions

A glimpse into Thurston's work

We present an overview of some significant results of Thurston and their impact on mathematics. The final version of this paper will appear as Chapter 1 of the book "In the tradition of Thurston: Geometry and topology", edited by K. Ohshika and A. Papadopoulos (Springer, 2020)

The computer-aided design of nano-scaled digital circuits

The use of CMOS-based transistors to implement digital logic is the prevalent means of modern computation. It is, however, not the only means. Advances in nano-science and engineering demonstrate that nano-scale integrated circuits are in fact a viable technology for computation. The dominant means for information propagation in these devices is quantum tunneling - a phenomenon that is not wholly compatible with current design techniques. This paper is an explanation of one process used to both design and simulate digital logic circuits utilizing the topology of the hypercube. The aim of the paper is to demonstrate the ease of designing and implementing a streamlined design environment and to demonstrate the utility that such an environment affords the designer. The hypercube topology is used as the dominant example for constructing 3D circuits. In this topology, each device is required to operate as a doubly gated switch and computation is performed utilizing a concept similar to pass-gate technology. The paper details the software required to generate the logic circuit and the means of simulation. Each device of the structure is modeled using a non-linear state-space representation. The paper concludes with two examples of implementable technologies: single-electron transistors (wrap-gate structures with quantum dots), and endohederal fullerenes acting as gate switches

Complexity, Emergent Systems and Complex Biological Systems:\ud Complex Systems Theory and Biodynamics. [Edited book by I.C. Baianu, with listed contributors (2011)]

An overview is presented of System dynamics, the study of the behaviour of complex systems, Dynamical system in mathematics Dynamic programming in computer science and control theory, Complex systems biology, Neurodynamics and Psychodynamics.\u