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This work presents a tensorial approach to constructing data-driven reduced-order models corresponding to semi-discrete partial differential equations with canonical Hamiltonian structure. By expressing parameter-varying operators with…

Numerical Analysis · Mathematics 2025-05-14 Arjun Vijaywargiya , Shane A. McQuarrie , Anthony Gruber

The complex unit appearing in the equations of quantum mechanics is generalised to a quaternionic structure on spacetime, leading to the consideration of complex quantum mechanical particles whose dynamical behaviour is governed by…

High Energy Physics - Theory · Physics 2007-05-23 S. P. Brumby , G. C. Joshi

Engines are open systems that can generate work cyclically, at the expense of an external disequilibrium. They are ubiquitous in nature and technology, but the course of mathematical physics over the last 300 years has tended to make their…

Statistical Mechanics · Physics 2021-09-01 Robert Alicki , David Gelbwaser-Klimovsky , Alejandro Jenkins

This paper focuses on a model for opinion dynamics, where the influence weights of agents evolve in time. We formulate a control problem of consensus type, in which the objective is to drive all agents to a final target point under suitable…

Analysis of PDEs · Mathematics 2020-11-10 Nastassia Duteil , Benedetto Piccoli

We investigate a one-dimenisonal Hamiltonian system that describes a system of particles interacting through short-range repulsive potentials. Depending on the particle mean energy, $\epsilon$, the system demonstrates a spectrum of kinetic…

Statistical Mechanics · Physics 2009-11-10 S. Denisov , A. Filippov , J. Klafter , M. Urbakh

Mass Media outlets have occupied the central role of the political scenario, and are persuasive in the process of opinion formation of the citizens. In particular, the study of the relationship between Mass Media and behaviour of citizens…

Physics and Society · Physics 2019-10-02 Federico Albanese , Claudio J. Tessone , Viktoriya Semeshenko , Pablo Balenzuela

Group behavior has received much attention as a test case of self-organization. There has been much written in recent years to investigate interactions within groups of agents. These agents can be animals moving in an interactive way, such…

Physics and Society · Physics 2011-03-14 Max D. Steel

Modelling efforts in opinion dynamics have to a large extent ignored that opinion exchange between individuals can also have an effect on how willing they are to express their opinion publicly. Here, we introduce a model of public opinion…

Physics and Society · Physics 2020-10-14 Felix Gaisbauer , Eckehard Olbrich , Sven Banisch

Collective leadership and herding may arise in standard models of opinion dynamics as an interplay of a strong separation of time scales within the population and its hierarchical organization. Using the voter model as a simple opinion…

Physics and Society · Physics 2017-07-12 Liudmila Rozanova , Marian Boguna

A broad range of dynamical systems involve multi-body interactions, or group interactions, which may not be encoded in traditional graphical structures. In this work, we focus on a canonical example from opinion dynamics, the Majority Rule,…

Physics and Society · Physics 2021-09-01 James Noonan , Renaud Lambiotte

A system responding to a stochastic driving signal can be interpreted as computing, by means of its dynamics, an implicit model of the environmental variables. The system's state retains information about past environmental fluctuations,…

Statistical Mechanics · Physics 2012-10-09 Susanne Still , David A. Sivak , Anthony J. Bell , Gavin E. Crooks

In this work, we introduce an information-theoretic approach for considering changes in dynamics of finitely dimensional open quantum systems governed by master equations. This experimentally motivated approach arises from considering how…

Quantum Physics · Physics 2021-05-03 Katarzyna Macieszczak

Dynamics of complex systems is often hierarchically organized on different time scales. To understand the physics of such hierarchy, here Brownian motion of a particle moving through a fluctuating medium with slowly varying temperature is…

Statistical Mechanics · Physics 2014-02-14 Sumiyoshi Abe

We propose a general scenario to analyze social and economic changes in modern environments. We illustrate the ideas with a model that incorporating the main trends is simple enough to extract analytical results and, at the same time,…

Statistical Mechanics · Physics 2009-10-31 A. Arenas , A. Diaz-Guilera , C. J. Perez , F. Vega-Redondo

We study systems of interacting reinforced stochastic processes, where agents' decisions evolve under reinforcement, network-mediated interactions, and environmental influences. In competitive environments with irreducible networks, we…

Probability · Mathematics 2025-09-18 Michele Aleandri , Paolo Dai Pra , Ida Germana Minelli

We propose and discuss some toy models of stock markets using the same operatorial approach adopted in quantum mechanics. Our models are suggested by the discrete nature of the number of shares and of the cash which are exchanged in a real…

General Finance · Quantitative Finance 2009-11-13 F. Bagarello

We describe a diagrammatic technique for non-Hermitian fermionic systems that is applicable in the steady state, and which allows addressing correlations effects by systematic expansion. Applying this method to exceptional points or rings,…

Mesoscale and Nanoscale Physics · Physics 2020-01-29 Johan Carlström

Social dynamics determined by voting in a stochastic environment is analyzed for a society composed of two cohesive groups of similar size. Within the model of random walks determined by voting, explicit formulas are derived for the capital…

Multiagent Systems · Computer Science 2011-09-21 P. Yu. Chebotarev , A. K. Loginov , Ya. Yu. Tsodikova , Z. M. Lezina , V. I. Borzenko

We have limited our interaction scope to those involving particle-s spin. We then develop operators for handling a many-body treatment of the spin interactions. The results presented show how to promote the particles of the system into the…

Strongly Correlated Electrons · Physics 2013-01-01 R. O. Akande , O. E. Oyewande

It is important to study how strategic agents can affect the outcome of an election. There has been a long line of research in the computational study of elections on the complexity of manipulative actions such as manipulation and bribery.…

Computer Science and Game Theory · Computer Science 2023-07-24 Zack Fitzsimmons , Edith Hemaspaandra