Limit cycles analysis and control of evolutionary game dynamics with environmental feedback

Recently, an evolutionary game dynamics model taking into account the environmental feedback has been proposed to describe the co-evolution of strategic actions of a population of individuals and the state of the surrounding environment; correspondingly a range of interesting dynamic behaviors have been reported. In this paper, we provide new theoretical insight into such behaviors and discuss control options. Instead of the standard replicator dynamics, we use a more realistic and comprehensive model of replicator–mutator dynamics, to describe the strategic evolution of the population. After integrating the environment feedback, we study the effect of mutations on the resulting closed-loop system dynamics. We prove the conditions for two types of bifurcations, Hopf bifurcation and Heteroclinic bifurcation, both of which result in stable limit cycles. These limit cycles have not been identified in existing works, and we further prove that such limit cycles are in fact persistent in a large parameter space and are almost globally stable. In the end, an intuitive control policy based on incentives is applied, and the effectiveness of this control policy is examined by analysis and simulations

Limit Cycles in Replicator-Mutator Dynamics with Game-Environment Feedback

This paper considers the coevolutionary game and environment dynamics under mutations of strategies. Individuals’ game play affects the dynamics of changing environments while the environment in turn affects the decision-making dynamics of individuals through modulating game payoffs. For some such closed-loop systems, we prove that limit cycles will never appear; however, in sharp contrast, after allowing mutations of strategies in these systems, the resulting replicator-mutator dynamics under environmental feedback may well exhibit Hopf bifurcation and limit cycles. We prove conditions for the Hopf bifurcation and thus the existence of stable limit cycles, and also illustrate these results using simulations. For the coevolutionary game and environment system, these stable limit cycles correspond to sustained oscillations of population’s decisions and richness of the environmental resource

Theory for charge and orbital density-wave states in manganite La0.5_{0.5}Sr1.5_{1.5}MnO4_4

We investigate the high temperature phase of layered manganites, and demonstrate that the charge-orbital phase transition without magnetic order in La$_{0.5}$Sr$_{1.5}$MnO$_4$ can be understood in terms of the density wave instability. The orbital ordering is found to be induced by the nesting between segments of Fermi surface with different orbital characters. The simultaneous charge and orbital orderings are elaborated with a mean field theory. The ordered orbitals are shown to be $d_{x^2-y^2} \pm d_{3z^2-r^2}$.Comment: published versio

The Analysis of the Properties of Bus Network Topology in Beijing Basing on Complex Networks

The transport network structure plays a crucial role in transport dynamics. To better understand the property of the bus network in big city and reasonably configure the bus lines and transfers, this paper seeks to take the bus network of Beijing as an example and mainly use space L and space P to analyze the network topology properties. The approach is applied to all the bus lines in Beijing which includes 722 lines and 5421 bus station. In the first phase of the approach, space L is used. The results show that the bus network of Beijing is a scale-free network and the degree of more than 99 percent of nodes is lower than 10. The results also show that the network is an assortative network with 46 communities. In a second phase, space P is used to analyze the property of transfer. The results show that the average transfer time of Beijing bus network which is 1.88 and 99.8 percent of arbitrary two pair nodes is reachable within 4 transfers

LMSFC: A Novel Multidimensional Index based on Learned Monotonic Space Filling Curves

The recently proposed learned indexes have attracted much attention as they can adapt to the actual data and query distributions to attain better search efficiency. Based on this technique, several existing works build up indexes for multi-dimensional data and achieve improved query performance. A common paradigm of these works is to (i) map multi-dimensional data points to a one-dimensional space using a fixed space-filling curve (SFC) or its variant and (ii) then apply the learned indexing techniques. We notice that the first step typically uses a fixed SFC method, such as row-major order and z-order. It definitely limits the potential of learned multi-dimensional indexes to adapt variable data distributions via different query workloads. In this paper, we propose a novel idea of learning a space-filling curve that is carefully designed and actively optimized for efficient query processing. We also identify innovative offline and online optimization opportunities common to SFC-based learned indexes and offer optimal and/or heuristic solutions. Experimental results demonstrate that our proposed method, LMSFC, outperforms state-of-the-art non-learned or learned methods across three commonly used real-world datasets and diverse experimental settings.Comment: Extended Version. Accepted by VLDB 202

Relightable 3D Gaussian: Real-time Point Cloud Relighting with BRDF Decomposition and Ray Tracing

We present a novel differentiable point-based rendering framework for material and lighting decomposition from multi-view images, enabling editing, ray-tracing, and real-time relighting of the 3D point cloud. Specifically, a 3D scene is represented as a set of relightable 3D Gaussian points, where each point is additionally associated with a normal direction, BRDF parameters, and incident lights from different directions. To achieve robust lighting estimation, we further divide incident lights of each point into global and local components, as well as view-dependent visibilities. The 3D scene is optimized through the 3D Gaussian Splatting technique while BRDF and lighting are decomposed by physically-based differentiable rendering. Moreover, we introduce an innovative point-based ray-tracing approach based on the bounding volume hierarchy for efficient visibility baking, enabling real-time rendering and relighting of 3D Gaussian points with accurate shadow effects. Extensive experiments demonstrate improved BRDF estimation and novel view rendering results compared to state-of-the-art material estimation approaches. Our framework showcases the potential to revolutionize the mesh-based graphics pipeline with a relightable, traceable, and editable rendering pipeline solely based on point cloud. Project page:https://nju-3dv.github.io/projects/Relightable3DGaussian/