Evolutionary Constraints on Connectivity Patterns in the Mammalian Suprachiasmatic Nucleus

The mammalian suprachiasmatic nucleus (SCN) comprises about 20,000 interconnected oscillatory neurons that create and maintain a robust circadian signal which matches to external light cues. Here, we use an evolutionary game theoretic framework to explore how evolutionary constraints can influence the synchronization of the system under various assumptions on the connection topology, contributing to the understanding of the structure of interneuron connectivity. Our basic model represents the SCN as a network of agents each with two properties—a phase and a flag that determines if it communicates with its neighbors or not. Communication comes at a cost to the agent, but synchronization of phases with its neighbors bears a benefit. Earlier work shows that when we have “all-to-all” connectivity, where every agent potentially communicates with every other agent, there is often a simple trade-off that leads to complete communication and synchronization of the system: the benefit must be greater than twice the cost. This trade-off for all-to-all connectivity gives us a baseline to compare to when looking at other topologies. Using simulations, we compare three plausible topologies to the all-to-all case, finding that convergence to synchronous dynamics occurs in all considered topologies under similar benefit and cost trade-offs. Consequently, sparser, less biologically costly topologies are reasonable evolutionary outcomes for organisms that develop a synchronizable oscillatory network. Our simulations also shed light on constraints imposed by the time scale on which we observe the SCN to arise in mammals. We find two conditions that allow for a synchronizable system to arise in relatively few generations. First, the benefits of connectivity must outweigh the cost of facilitating the connectivity in the network. Second, the game at the core of the model needs to be more cooperative than antagonistic games such as the Prisoner’s Dilemma. These results again imply that evolutionary pressure may have driven the system towards sparser topologies, as they are less costly to create and maintain. Last, our simulations indicate that models based on the mutualism game fare the best in uptake of communication and synchronization compared to more antagonistic games such as the Prisoner’s Dilemma.

FUZZY MODELS OF ANTAGONISTIC GAMES

The article is a continuation of a series of works on modeling situations in competitive markets at both micro and macro levels and the development of approaches to finding solutions to the obtained models. The paper proposes a method for solving a certain class of game-theoretic models under conditions of uncertainty. It is substantiated that a significant part of the problems of economic competition can be reduced to a finite matrix game of two players with zero sum, the matrix of winnings of the first player which has a specific form. Given the high degree of uncertainty in modern domestic markets and the need to simplify the current situation in its modeling due to the impossibility of including in the developed model of all real multifaceted relationships, the article considers antagonistic games with fuzzy parameters. It is proposed to look for the solution of the considered class of finite matrix games by reducing them to two dual optimization problems of linear programming with flexible limit constraints. The case is considered when the coefficients in the system of constraints of these models of linear programming are approximated by piecewise-linear membership functions, because they do not raise the question of linearity of the studied models. Using certain linear transformations, the optimization models of linear programming obtained in this work are reduced to models of a special kind, the method of solving which has been developed by other scientists. The essence of this method is that according to the Bellman-Zadeh approach, the resulting fuzzy model is reduced to the decision problem described by the multi-purpose optimization model, the solution of which includes only those alternatives, in such problems are called Pareto effective. Using this method, the fuzzy model obtained in the work is reduced to a "clear" problem of linear programming, some parameters of which are rationally determined by the person making managerial decisions, based on certain limitations obtained by solving two "clear" optimization models with known coefficients. By finding the solution to these dual problems and calculating the mixed strategies of the two players, the person making management decisions will be able to make the right choice among a set of alternative solutions.

Game theory and its economic applications

The manual describes the main sections of game theory, the basic concepts of the theory of economic risks and the conceptual framework for modeling the process of making managerial decisions in the economy based on the combined application of statistical and antagonistic games. Antagonistic games (AG) are the finite games of two persons with zero sum, i.e. matrix games, with classical antagonistic games called AG, given by completely known matrices, and neoclassical antagonistic games – AG, given by partially known matrices. The manual is intended primarily for masters who study in the direction of training "business information". However, it will be useful for students and postgraduates studying in large groups of areas of training "Economics and Management", "Mathematics and Mechanics", "Management in Technical Systems", as well as scientific and pedagogical workers specializing in the field of the theory of games, risk managers , managers and economists-practitioners.