Bruce M. Boghosian
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View article: A Dynamical Equation for the Lorenz Curve: Dynamics of incomplete moments of probability distributions arising from Fokker-Planck equations
A Dynamical Equation for the Lorenz Curve: Dynamics of incomplete moments of probability distributions arising from Fokker-Planck equations Open
Fokker-Planck equations (forward Kolmogorov equations) evolve probability densities in time from an initial condition. For distributions over the real line, these evolution equations can sometimes be transformed into dynamics over the inco…
View article: The Statistics of q-Statistics
The Statistics of q-Statistics Open
Almost two decades ago, Ernesto P. Borges and Bruce M. Boghosian embarked on the intricate task of composing a manuscript to honor the profound contributions of Constantino Tsallis to the realm of statistical physics, coupled with a concis…
View article: The Statistics of q-Statistics
The Statistics of q-Statistics Open
Almost two decades ago, Ernesto P. Borges and Bruce M. Boghosian embarked on the intricate task of composing a manuscript to honor the profound contributions of Constantino Tsallis to the realm of statistical physics, coupled with a concis…
View article: Numerical approximations of a lattice Boltzmann scheme with a family of partial differential equations
Numerical approximations of a lattice Boltzmann scheme with a family of partial differential equations Open
In this contribution, we address the numerical solutions of high-order asymptotic equivalent partial differential equations with the results of a lattice Boltzmann scheme for an inhomogeneous advection problem in one spatial dimension. We …
View article: ODE Models of Wealth Concentration and Taxation
ODE Models of Wealth Concentration and Taxation Open
We refer to an individual holding a non-negligible fraction of the country’s total wealth as an oligarch. We explain how a model due to Boghosian et al. can be used to explore the effects of taxation on the emergence of oligarchs. The mode…
View article: Bounding the approach to oligarchy in a variant of the yard-sale model
Bounding the approach to oligarchy in a variant of the yard-sale model Open
We present analytical results for the Gini coefficient of economic inequality under the dynamics of a modified Yard-Sale Model of kinetic asset exchange. A variant of the Yard-Sale Model is introduced by modifying the underlying binary tra…
View article: ODE models of wealth concentration and taxation
ODE models of wealth concentration and taxation Open
We refer to an individual holding a non-negligible fraction of the country's total wealth as an oligarch. We explain how a model due to Boghosian et al. can be used to explore the effects of taxation on the emergence of oligarchs. The mode…
View article: A blue sky bifurcation in the dynamics of political candidates
A blue sky bifurcation in the dynamics of political candidates Open
Political candidates often shift their positions opportunistically in hopes of capturing more votes. When there are only two candidates, the best strategy for each of them is often to move towards the other. This eventually results in two …
View article: A Geospatial Bounded Confidence Model Including Mega-Influencers with an Application to Covid-19 Vaccine Hesitancy
A Geospatial Bounded Confidence Model Including Mega-Influencers with an Application to Covid-19 Vaccine Hesitancy Open
We introduce a geospatial bounded confidence model with mega-influencers, inspired by Hegselmann and Krause (2002).The inclusion of geography gives rise to large-scale geospatial patterns evolving out of random initial data; that is, spati…
View article: A particle method for continuous Hegselmann-Krause opinion dynamics
A particle method for continuous Hegselmann-Krause opinion dynamics Open
We derive a differential-integral equation akin to the Hegselmann-Krause model of opinion dynamics, and propose a particle method for solving the equation. Numerical experiments demonstrate second-order convergence of the method in a weak …
View article: A geospatial bounded confidence model including mega-influencers with an application to Covid-19 vaccine hesitancy
A geospatial bounded confidence model including mega-influencers with an application to Covid-19 vaccine hesitancy Open
We introduce a geospatial bounded confidence model with mega-influencers, inspired by Hegselmann and Krause. The inclusion of geography gives rise to large-scale geospatial patterns evolving out of random initial data; that is, spatial clu…
View article: A generalization of the standard map and its statistical characterization
A generalization of the standard map and its statistical characterization Open
From the statistical mechanical point of view, area-preserving maps have great potential and importance. These maps exhibit chaotic and regular behavior separately or together in the available phase space as the control parameter changes. …
View article: Covid-19 vaccine hesitancy and mega-influencers
Covid-19 vaccine hesitancy and mega-influencers Open
Covid-19 vaccines are widely available in the United States, yet our Covid-19 vaccination rates have remained far below 100%. Not only that, but CDC data shows that even in places where vaccine acceptance was proportionally high at the out…
View article: Simulation of a generalized asset exchange model with economic growth and wealth distribution
Simulation of a generalized asset exchange model with economic growth and wealth distribution Open
The agent-based yard-sale model of wealth inequality is generalized to incorporate exponential economic growth and its distribution. The distribution of economic growth is nonuniform and is determined by the wealth of each agent and a para…
View article: The Nonuniversality of Wealth Distribution Tails Near Wealth Condensation Criticality
The Nonuniversality of Wealth Distribution Tails Near Wealth Condensation Criticality Open
In this work, we modify the affine wealth model of wealth distributions to examine the effects of nonconstant redistribution on the very wealthy. Previous studies of this model, restricted to flat redistribution schemes, have demonstrated …
View article: Unexpected convergence of lattice Boltzmann schemes
Unexpected convergence of lattice Boltzmann schemes Open
In this work, we study numerically the convergence of the scalar D2Q9 lattice Boltzmann scheme with multiple relaxation times when the time step is proportional to the space step and tends to zero. We do this by a combination of theory and…
View article: A New Pathology in the Simulation of Chaotic Dynamical Systems on Digital Computers
A New Pathology in the Simulation of Chaotic Dynamical Systems on Digital Computers Open
Systematic distortions are uncovered in the statistical properties of chaotic dynamical systems when represented and simulated on digital computers using standard IEEE floating‐point numbers. This is done by studying a model chaotic dynami…
View article: Curious Convergence Properties of Lattice Boltzmann Schemes for Diffusion with Acoustic Scaling
Curious Convergence Properties of Lattice Boltzmann Schemes for Diffusion with Acoustic Scaling Open
We consider the D1Q3 lattice Boltzmann scheme with an acoustic scale for the simulation of diffusive processes. When the mesh is refined while holding the diffusivity constant, we first obtain asymptotic convergence. When the mesh size ten…
View article: Efficient lattice Boltzmann models for the Kuramoto-Sivashinsky equation
Efficient lattice Boltzmann models for the Kuramoto-Sivashinsky equation Open
In this work, we improve the accuracy and stability of the lattice Boltzmann model for the Kuramoto-Sivashinsky equation proposed in \cite{2017_Otomo}. This improvement is achieved by controlling the relaxation time, modifying the equilibr…
View article: The Growth of Oligarchy in a Yard-Sale Model of Asset Exchange: A Logistic Equation for Wealth Condensation
The Growth of Oligarchy in a Yard-Sale Model of Asset Exchange: A Logistic Equation for Wealth Condensation Open
The addition of wealth-attained advantage (WAA) to the Yard-Sale Model (YSM) of asset exchange has been demonstrated to induce wealth condensation. In a model of WAA for which the bias is a continuous function of the wealth difference of t…
View article: Describing Realistic Wealth Distributions with the Extended Yard-Sale Model of Asset Exchange
Describing Realistic Wealth Distributions with the Extended Yard-Sale Model of Asset Exchange Open
The Extended Yard-Sale Model of asset exchange is an agent-based economic model with binary transactions, and simple models of redistribution and Wealth-Attained Advantage. As recently shown, the model exhibits a second-order phase transit…
View article: The Affine Wealth Model: An agent-based model of asset exchange that\n allows for negative-wealth agents and its empirical validation
The Affine Wealth Model: An agent-based model of asset exchange that\n allows for negative-wealth agents and its empirical validation Open
We present a stochastic, agent-based, binary-transaction Asset-Exchange Model\n(AEM) for wealth distribution that allows for agents with negative wealth. This\nmodel retains certain features of prior AEMs such as redistribution and\nwealth…
View article: The Growth of Oligarchy in a Yard-Sale Model of Asset Exchange - A Logistic Equation for Wealth Condensation
The Growth of Oligarchy in a Yard-Sale Model of Asset Exchange - A Logistic Equation for Wealth Condensation Open
The addition of wealth-attained advantage (WAA) to the Yard-Sale Model (YSM)\nof asset exchange has been demonstrated to induce wealth condensation. In a\nmodel of WAA for which the bias is a continuous function of the wealth\ndifference o…