Discrete hotelling pure location games: potentials and equilibria

We study two-player one-dimensional discrete Hotelling pure location games assuming that demand f(d) as a function of distance d is constant or strictly decreasing. We show that this game admits a best-response potential. This result holds in particular for f(d) = wd with 0 < w ≤ 1. For this case special attention will be given to the structure of the equilibrium set and a conjecture about the increasingness of best-response correspondences will be made.

THERMODYNAMIC PROPERTIES OF SILVER-CONTAINING COMPOUNDS OF THE Ag–Fe–Sn–S SYSTEM OBTAINED BY LOW-TEMPERATURE SOLID-STATE SYNTHESIS

The existence of the AgFeS2 and Ag2FeS2 compounds in the equilibrium concentration space of the Ag–Fe–S system was established by the EMF method. Investigations were performed in the electrochemical cells (ECCs) of the type (−) С | Ag | SЕ | R(Ag+) | PЕ | С (+), where C is the inert electrode (graphite), Ag is the negative (left) electrode, SE is the solid electrolyte, PE is the positive (right) electrode, R(Ag+) is the region of Ag+ diffusion into PE. Ag2GeS3 glass was used as the solid-state electrolyte with purely Ag+ ionic conductivity. The SnS2–FeS2–Ag2FeS2 (A) phase region of the Ag–Fe–Sn–S system is formed with the participation of three-component compounds. The cross-sections AgFeS2–Ag2FeSnS4, AgFeS2–Ag2FeSn3S8, and AgFeS2–SnS2 carry out the division of (A). Spatial position of the two-phases FeS2–AgFeS2, AgFeS2–Ag2FeS2 and three-phases AgFeS2–Ag2FeSn3S8–SnS2, AgFeS2–Ag2FeSnS4–Ag2FeSn3S8 regions of (A) regarding the point of silver was used to write the equations of the overall potential-forming reactions. Reactions were realized in the positive electrodes of ECCs. PE at the stage of the cell preparation is a well-mixed composition of finely ground (particle size ~5 μm) of the compounds Ag2S, FeS, FeS2 and Ag2S, FeS, FeS2, SnS2 in two- and three-phases regions of (A), respectively. The ratios of compounds in PE of ECCs were determined from the equations of the overall potential-forming reactions in respective phase regions. The decomposition of the metastable set of binary compounds and the synthesis of the equilibrium set of phases were carried out in the nanoscale region of the PE of ECC in contact with SE, i.e. in the R(Ag+) region. The Ag+ ions displaced from the left electrode to the right one for thermodynamic reasons act as nucleation centers for the equilibrium compounds. The process of forming the equilibrium set of phases in the R(Ag+) region for the particle size of the metastable phase mixture ~5 μm and Т=580 K took less than 72 h. The linear dependencies of EMF vs T of ECCs with PE of two- and three-phases regions were established in the ranges of (455–519) K and (450–514) K, respectively. Based on these dependencies, the standard thermodynamic quantities of the AgFeS2, Ag2FeS2, Ag2FeSnS4, and Ag2FeSn3S8 compounds were experimentally determined for the first time. The reliability of the established equilibrium sets of phases that provide the potential-forming reactions in ECCs was confirmed by the coincidence of the calculated and literature values of the Gibbs energy of the Ag2FeSnS4 and Ag2FeSn3S8 compounds.

Computing and optimizing over all fixed-points of discrete systems on large networks

Equilibria, or fixed points, play an important role in dynamical systems across various domains, yet finding them can be computationally challenging. Here, we show how to efficiently compute all equilibrium points of discrete-valued, discrete-time systems on sparse networks. Using graph partitioning, we recursively decompose the original problem into a set of smaller, simpler problems that are easy to compute, and whose solutions combine to yield the full equilibrium set. This makes it possible to find the fixed points of systems on arbitrarily large networks meeting certain criteria. This approach can also be used without computing the full equilibrium set, which may grow very large in some cases. For example, one can use this method to check the existence and total number of equilibria, or to find equilibria that are optimal with respect to a given cost function. We demonstrate the potential capabilities of this approach with examples in two scientific domains: computing the number of fixed points in brain networks and finding the minimal energy conformations of lattice-based protein folding models.

Computing and Optimizing Over All Fixed-Points of Discrete Systems on Large Networks

Equilibria, or fixed points, play an important role in dynamical systems across various domains, yet finding them can be computationally challenging. Here, we show how to efficiently compute all equilibrium points of discrete-valued, discrete-time systems on sparse networks. Using graph partitioning, we recursively decompose the original problem into a set of smaller, simpler problems that are easy to compute, and whose solutions combine to yield the full equilibrium set. This makes it possible to find the fixed points of systems on arbitrarily large networks meeting certain criteria. This approach can also be used without computing the full equilibrium set, which may grow very large in some cases. For example, one can use this method to check the existence and total number of equilibria, or to find equilibria that are optimal with respect to a given cost function. We demonstrate the potential capabilities of this approach with examples in two scientific domains: computing the number of fixed points in brain networks and finding the minimal energy conformations of lattice-based protein folding models.

Chaos in a Meminductor-Based Circuit

A smooth curve model of meminductor and its equivalent circuit have been designed, on the condition that the meminductor is commonly unavailable. The equivalent circuit can be used for breadboard experiments for various application circuit designs of meminductor. Based on the meminductor, a new chaotic oscillator is proposed. The dynamical behaviors of the oscillator are investigated, including equilibrium set, Lyapunov exponent spectrum, bifurcations and dynamical map of the system. Particularly, the amplitude controlling is analyzed and coexisting attractors are found for conditions of different parameters. Furthermore, the experimental results are given to confirm the correction of the proposed meminductor model and the meminductor-based oscillator.

NASH EQUILIBRIA IN 2 × 2 × 2 TRIMATRIX GAMES WITH IDENTICAL ANONYMOUS BEST-REPLIES

This paper introduces the class of 2 × 2 × 2 trimatrix games with identical anonymous best-replies. For this class a complete classification on the basis of the Nash equilibrium set is provided.