arXiv subjects

Minggang Wang

Publications and source records attributed to Minggang Wang.

5 recordsLinked to original sources

arXiv2026

Algebraic Degree of Network Games: Balanced Factors and Strategy Scaling

The algebraic degree of a network game is the generic number of isolated complex-torus solutions of its polynomial indifference system. We recast the classical semi-mixed coefficient formula as an edge-marked player-level polynomial whose monomials are balanced directed multigraphs with prescribed in- and out-degrees. This representation separates the intrinsic counting problem from strategy-label refinements: exact evaluation remains $\#\mathrm P$-complete, but for a fixed number of players it is polynomial in the numerical strategy dimensions, while nonvanishing is decided by a capacitated flow test. It also characterizes inclusion-minimal positive-degree supports as integral transportation forests and yields a sharp $2N-1$-arc positive core. Exact-support coefficients form connected transportation fibers and give a nonnegative support calculus. Under proportional strategy growth $m\mathbf k$, a lattice local limit theorem expresses the first-order degree asymptotic through the capacity and maximum-entropy flow of the essential support. All counts are generic and complex; reality and simplex feasibility remain payoff-dependent.

math.AG↗

arXiv2026

Tropical Degenerations of Network Games:Valuation Classes and Equilibrium Coalescence

A valuation-theoretic framework is developed for studying tropical degenerations of multilinear network games. Equilibrium conditions are modeled by an ideal over the Puiseux field, and valuation classes and cluster multiplicities are used to describe the organization of Puiseux equilibrium branches under degeneration. For valuation vectors lying in the relative interiors of generator-wise maximal tropical cells, multilinearity is shown to force a binomial reduction of the generator-wise initial system. The resulting binomial systems are governed by exponent-difference graphs, strongly connected component decompositions, and lattice indices computed via Smith normal form. In particular, unimodular diagonal blocks yield initial-coefficient rigidity, whereas non-unimodular blocks give rise to torsion-type leading-coefficient multiplicities. The generic binomial theory is complemented by a collision-normalized cross-prism family. In this family, 2^L Puiseux equilibrium branches share the same valuation vector and the same leading-coefficient vector. The corresponding limiting initial fiber is supported at a single torus point, but this point is nonreduced with scheme-theoretic length 2^L. Thus valuation coalescence is realized as an intrinsic scheme-theoretic collision rather than merely as a loss of higher-order terms. These local degeneration invariants are then related to the algebraic-degree theory of network games, showing how global equilibrium counts can be refined by valuation classes, binomial initial systems, Smith lattice data, and nonreduced collision fibers.

math.AG↗

arXiv2019

Three-state Majority-Vote Model on Barabási-Albert and Cubic Networks and the Unitary Relation for Critical Exponents

We investigate the three-state majority-vote model with noise on scale-free and regular networks. In this model, an individual selects an opinion equal to the opinion of the majority of its neighbors with probability $1 - q$ and opposite to it with probability $q$. The parameter $q$ is called the noise parameter of the model. We build a network of interactions where $z$ neighbors are selected by each added site in the system, yielding a preferential attachment network with degree distribution $k^{-λ}$, where $λ\sim 3$. In this work, $z$ is called growth parameter. Using finite-size scaling analysis, we show that the critical exponents associated with the magnetization and magnetic susceptibility add up to unity when a volumetric scaling is used, regardless of the dimension of the network of interactions. Using Monte Carlo simulations, we calculate the critical noise parameter $q_c$ as a function of $z$ for the scale-free networks and obtain the phase diagram of the model. We find that the critical noise is an increasing function of the growth parameter $z$, and we define and verify numerically the unitary relation $\upsilon$ for the critical exponents by calculating $β/\barν$, $γ/\barν$ and $1/\barν$ for several values of the network parameter $z$. We also obtain the critical noise and the critical exponents for the two and three-state majority-vote model on cubic lattices networks where we illustrate the application of the unitary relation with a volumetric scaling.

cond-mat.stat-mech↗

arXiv2018

Inferring dissipation from the violation of Fluctuation-Dissipation Theorem

The Harada-Sasa equality elegantly connects the energy dissipation rate of a moving object with its measurable violation of the Fluctuation-Dissipation Theorem (FDT). Although proven for Langevin processes, its validity remains unclear for discrete Markov systems whose forward and backward transition rates respond asymmetrically to external perturbation. A typical example is a motor protein called kinesin. Here we show generally that the FDT violation persists surprisingly in the high-frequency limit due to the asymmetry, resulting in a divergent FDT violation integral and thus a complete breakdown of the Harada-Sasa equality. A renormalized FDT violation integral still well predicts the dissipation rate when each discrete transition produces a small entropy in the environment. Our study also suggests a new way to infer this perturbation asymmetry based on the measurable high-frequency-limit FDT violation.

cond-mat.stat-mech↗

arXiv2017

Exact results of the limited penetrable horizontal visibility graph associated to random time series and its application

The limited penetrable horizontal visibility algorithm is a new time analysis tool and is a further development of the horizontal visibility algorithm. We present some exact results on the topological properties of the limited penetrable horizontal visibility graph associated with random series. We show that the random series maps on a limited penetrable horizontal visibility graph with exponential degree distribution $P(k)\sim exp[-λ(k-2ρ-2)], λ= ln[(2ρ+3)/(2ρ+2)],ρ=0,1,2,...,k=2ρ+2,2ρ+3,...$, independent of the probability distribution from which the series was generated. We deduce the exact expressions of the mean degree and the clustering coefficient and demonstrate the long distance visibility property. Numerical simulations confirm the accuracy of our theoretical results. We then examine several deterministic chaotic series (a logistic map, the H$\acute{e}$non map, the Lorentz system, and an energy price chaotic system) and a real crude oil price series to test our results. The empirical results show that the limited penetrable horizontal visibility algorithm is direct, has a low computational cost when discriminating chaos from uncorrelated randomness, and is able to measure the global evolution characteristics of the real time series.

stat.ME↗