Towards a mathematical theory of behavioral human crowds

The first part of our paper presents a general survey on the modeling, analytic problems, and applications of the dynamics of human crowds, where the specific features of living systems are taken into account in the modeling approach. This critical analysis leads to the second part which is devoted to research perspectives on modeling, analytic problems, multiscale topics which are followed by hints towards possible achievements. Perspectives include the modeling of social dynamics, multiscale problems and a detailed study of the link between crowds and swarms modeling.

RESEARCH OF OPERATION TECHNOLOGY OF HEAVY LOADS PROCESSING POINTS

Target. The transportation of oversized and heavy cargo is considered one of the most important transport services that bring the greatest profit. This requires powerful equipment and highly qualified specialists. The modern system of organizing transportation provides for the acceptance and delivery of small shipments of heavy cargo yards, during which each shipment can be reloaded several times at the cargo sites. Despite the relatively average transportation distances within Ukraine, the number of processing can reach 3 times, and the time spent at such sites is several days. Therefore, an increase in the delivery time for heavy small consignments arises due to their long stay at the cargo yards. Improvement of the technology of cargo yards and their technical equipment is of paramount importance for improving the organization of transportation of heavy cargo by small consignments. Methods. Comprehensive analysis of technical equipment and technology of work of points for processing heavy cargo on railway transport, statistical analysis, mathematical theory of inventory management, methods of correlation analysis. Results. The analysis of the technology and technical equipment of heavy cargo handling points is carried out, recommendations for their improvement are given. The nature of the arrival of vehicles on the cargo front has been studied, the mode of using loading and unloading machines has been studied, and a method for optimizing the technical equipment of the cargo front has been provided. The method for determining the optimal capacity of sites for heavy cargo has been improved. Practical significance. The studies carried out have shown that there are reserves for improving the transportation of goods by heavy small shipments through the development and application of optimal technology. The main direction in reducing the idle time of wagons is to optimize the processes of handling heavy cargo: increasing the capacity of technical equipment, improving the system of operational planning and management of the operation of points for processing heavy cargo. The application of the methodology makes it possible to evaluate various options for technical equipment at reduced costs, to calculate the optimal capacity of processing points for local and transit heavy cargo using the mathematical theory of inventory management and methods of correlation analysis. The task of drawing up an optimal operational plan for sorting heavy cargo is reduced to a linear programming transport problem and is solved with the help of computer technology.

Plankton growth dynamic driven by plankton body size in deterministic and stochastic environments

In this paper, we establish a new phytoplankton-zooplankton model by considering the effects of plankton body size and stochastic environmental fluctuations. Mathematical theory work mainly gives the existence of boundary and positive equilibria, and shows their local as well as global stability in the deterministic model. Additionally, we explore the dynamics of V-geometric ergodicity, stochastic ultimate boundedness, stochastic permanence, persistence in the mean, stochastic extinction and the existence of a unique ergodic stationary distribution in the corresponding stochastic version. Numerical simulation work mainly reveals that plankton body size can generate great influences on the interactions between phytoplankton and zooplankton, which in turn proves the effectiveness of mathematical theory analysis. It is worth emphasizing that for the small value of phytoplankton cell size, the increase of zooplankton body size can not change the phytoplankton density or zooplankton density; for the middle value of phytoplankton cell size, the increase of zooplankton body size can decrease zooplankton density or phytoplankton density; for the large value of phytoplankton body size, the increase of zooplankton body size can increase zooplankton density but decrease phytoplankton density. Besides, it should be noted that the increase of zooplankton body size can not affect the effect of random environmental disturbance, while the increase of phytoplankton cell size can weaken its effect. There results may enrich the dynamics of phytoplankton-zooplankton models.

Knowledge capitalization in mechatronic collaborative design

In mechatronic collaborative design, there is a synergic integration of several expert domains, where heterogeneous knowledge needs to be shared. To address this challenge, ontology-based approaches are proposed as a solution to overtake this heterogeneity. However, dynamic exchange between design teams is overlooked. Consequently, parametric-based approaches are developed to use constraints and parameters consistently during collaborative design. The most valuable knowledge that needs to be capitalized, which we call crucial knowledge, is identified with informal solutions. Thus, a formal identification and extraction is required. In this paper, we propose a new methodology to formalize the interconnection between stakeholders and facilitate the extraction and capitalization of crucial knowledge during the collaboration, based on the mathematical theory ‘Category Theory’ (CT). Firstly, we present an overview of most used methods for crucial knowledge identification in the context of collaborative design as well as a brief review of CT basic concepts. Secondly, we propose a methodology to formally extract crucial knowledge based on some fundamental concepts of category theory. Finally, a case study is considered to validate the proposed methodology.

Non-Mathematical Musings on Information Theory and Networked Musical Practice

Claude Shannon’s 1948 paper ‘A Mathematical Theory of Communication’ provided the essential foundation for the digital/information revolution that enables these very pixels to glow in meaningful patterns and permeates nearly every aspect of modern life. Information Theory, born fully grown from this paper, has been applied and mis-applied to a multitude of disciplines in the last 70-odd years, from quantum physics to psychology. Shannon himself famously decried those jumping on the ‘scientific bandwagon’ of Information Theory without sufficient mathematical rigour. Nevertheless, having a brief personal connection to Dr Shannon (and being extremely grateful for it), I will take the liberty of colouring some of my experience with computer network music with less-than-rigorous insights gained from his work.

Individual consumer surplus in the Edgeworth Box

Subject. The consumer surplus conception is an important part of the modern microeconomic theory at the introductory and intermediate levels. Consumer surplus measures the change in the consumer’s real welfare. The article addresses the peculiarities of generation and the main property of the generalized individual consumer surplus, using the Edgeworth Box case. Objectives. The purpose is to find the main property of individual consumer surplus in the Edgeworth Box economy. Methods. The study draws on methods of logical and mathematical analysis. The generalized consumer surplus is correctly constructed, using the mathematical theory of curve integrals of the second type (the theory of line integrals in the Western mathematics). Results. The generalized individual consumer surplus is defined through the respective curve integral along some admissible trajectory in the simple exchange economy (Edgeworth Box). The paper also introduces the notion of the marginal individual consumer surplus, and demonstrates that consumer surplus is a correct individual welfare measure in the Edgeworth Box, and that consumer surplus is zero along any given indifference curve. I consider the numerical example of individual surplus calculation and presentation in the Edgeworth Box. Conclusions. The generalized individual consumer surplus is a correct measure of consumer’s utility change along monotone (weakly monotone) trajectories in the Edgeworth Box. Geometrically, the consumer surplus is presented as an area limited by the reservation price curve from the top and by the reallocation line (curve) from the bottom.

The evolution of color naming reflects pressure for efficiency: Evidence from the recent past

It has been proposed that semantic systems evolve under pressure for efficiency. This hypothesis has so far been supported largely indirectly, by synchronic cross-language comparison, rather than directly by diachronic data. Here, we directly test this hypothesis in the domain of color naming, by analyzing recent diachronic data from Nafaanra, a language of Ghana and Côte d'Ivoire, and comparing it with quantitative predictions derived from the mathematical theory of efficient data compression. We show that color naming in Nafaanra has changed over the past four decades while remaining near-optimally efficient, and that this outcome would be unlikely under a random drift process that maintains structured color categories without pressure for efficiency. To our knowledge, this finding provides the first direct evidence that color naming evolves under pressure for efficiency, supporting the hypothesis that efficiency shapes the evolution of the lexicon.

Complex Spacetimes and the Newman-Janis Trick

<p>In this thesis, we explore the subject of complex spacetimes, in which the mathematical theory of complex manifolds gets modified for application to General Relativity. We will also explore the mysterious Newman-Janis trick, which is an elementary and quite short method to obtain the Kerr black hole from the Schwarzschild black hole through the use of complex variables. This exposition will cover variations of the Newman-Janis trick, partial explanations, as well as original contributions.</p>

Complex Spacetimes and the Newman-Janis Trick

<p>In this thesis, we explore the subject of complex spacetimes, in which the mathematical theory of complex manifolds gets modified for application to General Relativity. We will also explore the mysterious Newman-Janis trick, which is an elementary and quite short method to obtain the Kerr black hole from the Schwarzschild black hole through the use of complex variables. This exposition will cover variations of the Newman-Janis trick, partial explanations, as well as original contributions.</p>

A Medida de Informação de Shannon: Entropia

Logo após Claude E. Shannon, em 1948, ter publicado o artigo A Mathematical Theory of Communication, diversas áreas se valeram de seus escritos, principalmente por ele ter desenvolvido uma fórmula para “medir informação” em seu modelo matemático de comunicação, denominando-a entropia. Shannon optou pela justificativa operacional da existência de sua fórmula de entropia. Por conseguinte, houve uma expansão das áreas de investigações matemáticas sobre as possíveis caracterizações de medidas de informação. Neste texto o objetivo é focar nas estruturas matemáticas que fundamentam o conceito de medidas de informação. Estima-se com isso, no sentido didático, que haja esclarecimentos com relação às múltiplas leituras do conceito de entropia.