Evolutionary Game Dynamics for Two Interacting Populations under Environmental Feedback

We study the evolutionary dynamics of games under environmental feedback using replicator equations for two interacting populations. One key feature is to consider jointly the co-evolution of the dynamic payoff matrices and the state of the environment: the payoff matrix varies with the changing environment and at the same time, the state of the environment is affected indirectly by the changing payoff matrix through the evolving population profiles. For such co-evolutionary dynamics, we investigate whether convergence will take place, and if so, how. In particular, we identify the scenarios where oscillation offers the best predictions of long-run behavior by using reversible system theory. The obtained results are useful to describe the evolution of multi-community societies in which individuals' payoffs and societal feedback interact.Comment: 7 pages, submitted to a conferenc

Impactless biped walking on a slope

AbstractWalking without impacts has been considered in dynamics as a motion/force control problem. In order to avoid impacts, an approach for both the specified motion of the biped and its ground reaction forces was presented yielding a combined motion and force control problem. As an application, a walker on a horizontal plane has been considered. In this paper, it is shown how the control of the ground reaction forces and the energy consumption depend on the gradient of a slope. The biped dynamics and the constraints within the biped system and on the ground are discussed. A motion control synthesis is developed using the inverse dynamics principle proven to be most efficient for human walking research, too. The impactless walking with controlled legs is illustrated by a seven-link biped. The “flying” biped has nine degrees of freedom, with six control inputs. During locomotion, the standing leg has three scleronomic constraints, and the trunk has three rheonomic constraints. However, there are three rheonomic constraints for the prescribed leg motion or three scleronomic constraints for reaction forces of the trailing leg, respectively. The nominal control action for impactless walking can be precomputed and stored. The model proposed allows the investigation of several problems: uphill and downhill walking, optimization of step length, stiction of the feet on the slope and many more. All these findings are also of interest in biomechanics

Astrocytes as a mechanism for meta-plasticity and contextually-guided network function

Astrocytes are a ubiquitous and enigmatic type of non-neuronal cell and are found in the brain of all vertebrates. While traditionally viewed as being supportive of neurons, it is increasingly recognized that astrocytes may play a more direct and active role in brain function and neural computation. On account of their sensitivity to a host of physiological covariates and ability to modulate neuronal activity and connectivity on slower time scales, astrocytes may be particularly well poised to modulate the dynamics of neural circuits in functionally salient ways. In the current paper, we seek to capture these features via actionable abstractions within computational models of neuron-astrocyte interaction. Specifically, we engage how nested feedback loops of neuron-astrocyte interaction, acting over separated time-scales may endow astrocytes with the capability to enable learning in context-dependent settings, where fluctuations in task parameters may occur much more slowly than within-task requirements. We pose a general model of neuron-synapse-astrocyte interaction and use formal analysis to characterize how astrocytic modulation may constitute a form of meta-plasticity, altering the ways in which synapses and neurons adapt as a function of time. We then embed this model in a bandit-based reinforcement learning task environment, and show how the presence of time-scale separated astrocytic modulation enables learning over multiple fluctuating contexts. Indeed, these networks learn far more reliably versus dynamically homogeneous networks and conventional non-network-based bandit algorithms. Our results indicate how the presence of neuron-astrocyte interaction in the brain may benefit learning over different time-scales and the conveyance of task-relevant contextual information onto circuit dynamics.Comment: 42 pages, 14 figure

Evolutionary dynamics of two communities under environmental feedback:Special Issue on Control and Network Theory for Biological Systems

In this paper, we study the evolutionary dynamics of two different types of communities in an evolving environment. We model the dynamics using an evolutionary differential game consisting of two sub-games: 1) a game between two different communities and 2) a game between communities and the environment. Our interest is to clarify when the two communities and environment can coexist dynamically under the feedback from the changing environment. Mathematically speaking, we show that for specific game payoffs, the corresponding three dimensional replicator dynamics induced by the evolutionary game have an infinite number of periodic orbits

Copper-based charge transfer multiferroics with a d9d^9 configuration

Multiferroics are materials with a coexistence of magnetic and ferroelectric order allowing the manipulation of magnetism by applications of an electric field through magnetoelectric coupling effects. Here we propose an idea to design a class of multiferroics with a $d^9$ configuration using the magnetic order in copper-oxygen layers appearing in copper oxide high-temperature superconductors by inducing ferroelectricity. Copper-based charge transfer multiferroics SnCuO2 and PbCuO2 having the inversion symmetry breaking $P4mm$ polar space group are predicted to be such materials. The active inner s electrons in Sn and Pb hybridize with O $2p$ states leading the buckling in copper-oxygen layers and thus induces ferroelectricity, which is known as the lone pair mechanism. As a result of the $d^9$ configuration, SnCuO2 and PbCuO2 are charge transfer insulators with the antiferromagnetic ground state of the moment on Cu retaining some strongly correlated physical properties of parent compounds of copper oxide high-temperature superconductors. Our work reveals the possibility of designing multiferroics based on copper oxide high-temperature superconductors.Comment: 18 pages, 5 figures, 1 tabl

Elemental topological ferroelectrics and polar metals of few-layer materials

Ferroelectricity can exist in elemental phases as a result of charge transfers between atoms occupying inequivalent Wyckoff positions. We investigate the emergence of ferroelectricity in two-dimensional elemental materials with buckled honeycomb lattices. Various multi-bilayer structures hosting ferroelectricity are designed by stacking-engineering. Ferroelectric materials candidates formed by group IV and V elements are predicted theoretically. Ultrathin Bi films show layer-stacking-dependent physical properties of ferroelectricity, topology, and metallicity. The two-bilayer Bi film with a polar stacking sequence is found to be an elemental topological ferroelectric material. Three and four bilayers Bi films with polar structures are ferroelectric-like elemental polar metals with topological nontrivial edge states. For Ge and Sn, trivial elemental polar metals are predicted. Our work reveals the possibility of design two-dimensional elemental topological ferroelectrics and polar metals by stacking-engineering.Comment: 18 pages, 6 figure