Methods Of Statistical Physics Research Articles

Asymmetric games on networks: Mapping to Ising models and bounded rationality

We investigate the dynamics of coordination and consensus in an agent population. Considering agents endowed with bounded rationality, we study asymmetric coordination games using a mapping to random field Ising models. In doing so, we investigate the relationship between group coordination and agent rationality. Analytical calculations and numerical simulations of the proposed model lead to novel insight into opinion dynamics. For instance, we find that bounded rationality and preference intensity can determine a series of possible scenarios with different levels of opinion polarization. To conclude, we deem our investigation opens a new avenue for studying game dynamics through methods of statistical physics.

Highly efficient batch adsorption of anionic dye in wastewater using nanocomposite: Experimental and theoretical studies

The adsorptive properties of the Erionyl Red (ER) dye on bentonite (B) intercalated with cetyltrimethylammonium bromide (HDTMA-B) were investigated using experimental and statistical physics methods. The dye was then taken up by the intercalated bentonite from a real water sample. After intercalation, X-ray diffraction analysis indicates an increase in HDTMA-B basal spacing to 15.2 Ả. Scanning electron microscopy images show the formation of large particles and many cavities. The results revealed that the material had high properties to adsorb organic molecules (greater than 99 %). The Langmuir-Freundlich model, described the isotherms, whereas the second-order model better captured the kinetic of dye adsorption. The maximum ER uptake observed was 478 mg g−1 at a temperature of 328 K. Reusability of nanocomposite showed stability, over five cycles. Thermodynamic analysis suggested spontaneous (negative ΔG°) and endothermic (positive ΔH°) adsorption processes. The statistical physics model was also used to estimate the orientation of ER adsorption on the material. The oxygens connected to the dye in the HDTMA-B structure played in particular an important role in the adsorption mechanisms of dye. This study combines experiment data with a theoretical approach to provide a new explanation for the mechanism. The removal of dyes from wastewater, in particular Erionyl red, is vital for the protection of the environment and public health. Nanocomposite appears to be an effective, durable, and environmentally friendly adsorbent for the removal of Erionyl red dye from synthetic solutions and real wastewater.

Reconfigurable Intelligent Surfaces and Capacity Optimization: A Large System Analysis

Reconfigurable Intelligent Surfaces (RISs) have been recently proposed as an enabling technology for programmable wireless environments. In this paper, we present asymptotic closed-form expressions for the mean and variance of the mutual information for a multi-antenna transmitter-receiver pair in the presence of RISs, using statistical physics methods. While nominally valid in the large-system limit, we show that the derived Gaussian approximation for the mutual information can be quite accurate, even for modest-sized antenna arrays and metasurfaces. The above results are particularly useful when fast-fading conditions are present, which renders channel estimation challenging. We find that, when the channel close to an RIS is correlated, for instance due to small angle spread, which is reasonable for wireless systems with increasing carrier frequencies, the communication link benefits significantly from statistical RIS optimization, resulting in gains that are surprisingly higher than the nearly uncorrelated case. Using our novel asymptotic properties of the correlation matrices of the impinging and outgoing signals at the RISs, we can optimize the metasurfaces without brute-force numerical optimization. When the desired reflection from any of the RISs departs significantly from geometrical optics, the metasurfaces can be optimized to provide robust communication links, without significant need for their optimal placement.

Effect of collaborative-filtering-based recommendation algorithms on opinion polarization.

A central role in shaping the experience of users online is played by recommendation algorithms. On the one hand they help retrieving content that best suits users taste, but on the other hand they may give rise to the so-called "filter bubble" effect, favoring the rise of polarization. In the present paper we study how a user-user collaborative-filtering algorithm affects the behavior of a group of agents repeatedly exposed to it. By means of analytical and numerical techniques we show how the system stationary state depends on the strength of the similarity and popularity biases, quantifying respectively the weight given to the most similar users and to the best rated items. In particular, we derive a phase diagram of the model, where we observe three distinct phases: disorder, consensus, and polarization. In the last users spontaneously split into different groups, each focused on a single item. We identify, at the boundary between the disorder and polarization phases, a region where recommendations are nontrivially personalized without leading to filter bubbles. Finally, we show that our model well reproduces the behavior of users on the online music platform last.fm. This analysis paves the way to a systematic analysis of recommendation algorithms by means of statistical physics methods and opens the possibility of devising less polarizing recommendation algorithms.

Fermionic physics from abinitio path integral Monte Carlo simulations of fictitious identical particles.

The abinitio path integral Monte Carlo (PIMC) method is one of the most successful methods in statistical physics, quantum chemistry and related fields, but its application to quantum degenerate Fermi systems is severely hampered by an exponential computational bottleneck: the notorious fermion signproblem. Very recently, Xiong and Xiong [J. Chem. Phys. 157, 094112 (2022)] have suggested to partially circumvent the signproblem by carrying out simulations of fictitious systems guided by an interpolating continuous variable ξ ∈ [-1, 1], with the physical Fermi- and Bose-statistics corresponding to ξ = -1 and ξ = 1. It has been proposed that information about the fermionic limit might be obtained by calculations within the bosonic sector ξ > 0 combined with an extrapolation throughout the fermionic sector ξ < 0, essentially bypassing the signproblem. Here, we show how the inclusion of the artificial parameter ξ can be interpreted as an effective penalty on the formation of permutation cycles in the PIMC simulation. We demonstrate that the proposed extrapolation method breaks down for moderate to high quantum degeneracy. Instead, the method constitutes a valuable tool for the description of large Fermi-systems of weak quantum degeneracy. This is demonstrated for electrons in a 2D harmonic trap and for the uniform electron gas (UEG), where we find excellent agreement (∼0.5%) with exact configuration PIMC results in the high-density regime while attaining a speed-up exceeding 11 orders of magnitude. Finally, we extend the idea beyond the energy and analyze the radial density distribution (2D trap), as well as the static structure factor and imaginary-time density-density correlation function (UEG).

Surface modification of natural clay with H2O2 for high adsorption of acid Red 114: Experimental and modelling studies

The water contamination problem caused by dyes and the understanding of their adsorption mechanism in aqueous media is still significant nowadays. This study investigates the adsorption performance of natural montmorillonite clay treated with H2O2 (MMT-H2O2) and employed as an adsorbent to remove Acid Red 114 (AR-114) from aqueous solutions. MMT-H2O2 and the natural clay without treatment (MMT) were analysed using different analytical techniques such as XRF, XRD, FESEM, EDS, FTIR, TGA/DTG, N2-adsorption/desorption curves, CHNS/O analysis, hydrophobicity Index (HI). It also provides a theoretical analysis of the adsorption phenomenon utilising Statistical Physics methods to understand the adsorption mechanism between AR-114 and MMT-H2O2 adsorbent associated with batch adsorption conditions and adsorption equilibrium. The treated clay with H2O2 showed a higher oxygen content and a better adsorption capacity than the untreated one. The maximum adsorption capacity (Qmax) values obtained with the best-fitted model (Liu) ranged from 421.9 and 1178.5 mg g−1. This high adsorption capacity for AR-114 dye can be explained by considering the remarkable characteristics of the MMTH2O2 material, such as high oxygen content, variety of surface functional groups, porous interlayer structure, and hydrophilicity. The computational adsorption results suggest that the AR-114 molecules adsorbed onto the surface site of the MMTH2O2 adsorbent in a perpendicular orientation. This indicates that the n2 values increased as the operating temperature was raised, demonstrating the endothermic accumulation of dye molecules on the treated clay mineral surface. Moreover, the temperature-dependent adsorption energies (E1 and E2) levels were less than 40 kJ mol−1, highlighting the primary physical interactions between AR-114 and MMTH2O2 clay mineral by electrostatic attraction and hydrogen bonding.

Compositional Structure of the Genome: A Review.

As the genome carries the historical information of a species' biotic and environmental interactions, analyzing changes in genome structure over time by using powerful statistical physics methods (such as entropic segmentation algorithms, fluctuation analysis in DNA walks, or measures of compositional complexity) provides valuable insights into genome evolution. Nucleotide frequencies tend to vary along the DNA chain, resulting in a hierarchically patchy chromosome structure with heterogeneities at different length scales that range from a few nucleotides to tens of millions of them. Fluctuation analysis reveals that these compositional structures can be classified into three main categories: (1) short-range heterogeneities (below a few kilobase pairs (Kbp)) primarily attributed to the alternation of coding and noncoding regions, interspersed or tandem repeats densities, etc.; (2) isochores, spanning tens to hundreds of tens of Kbp; and (3) superstructures, reaching sizes of tens of megabase pairs (Mbp) or even larger. The obtained isochore and superstructure coordinates in the first complete T2T human sequence are now shared in a public database. In this way, interested researchers can use T2T isochore data, as well as the annotations for different genome elements, to check a specific hypothesis about genome structure. Similarly to other levels of biological organization, a hierarchical compositional structure is prevalent in the genome. Once the compositional structure of a genome is identified, various measures can be derived to quantify the heterogeneity of such structure. The distribution of segment G+C content has recently been proposed as a new genome signature that proves to be useful for comparing complete genomes. Another meaningful measure is the sequence compositional complexity (SCC), which has been used for genome structure comparisons. Lastly, we review the recent genome comparisons in species of the ancient phylum Cyanobacteria, conducted by phylogenetic regression of SCC against time, which have revealed positive trends towards higher genome complexity. These findings provide the first evidence for a driven progressive evolution of genome compositional structure.

原子論的スピンモデルによる永久磁石の磁気特性の研究 ―熱揺らぎおよび温度効果の取り扱いと将来展望―

We review atomistic spin model studies, a new approach for theoretical investigations, on magnetic properties of permanent magnets. In the atomistic modeling, the microscopic details of magnetic parameters and lattice structures are realistically considered, and the temperature effect, including thermal fluctuation, is properly treated based on statistical physics methods: Monte Caro methods and stochastic Landau-Lifshitz-Gilbert equation methods. We introduce how to treat thermal effects for static and dynamical properties using these methods. Focusing especially on neodymium permanent magnets, we discuss features of magnetization, domain wall, coercivity of a grain, nucleation and pinning fields, and dysprosium substitution effect, which were first elucidated with those methods.

Stratifications and foliations in phase portraits of gene network models.

Periodic processes of gene network functioning are described with good precision by periodic trajectories (limit cycles) of multidimensional systems of kinetic-type differential equations. In the literature, such systems are often called dynamical, they are composed according to schemes of positive and negative feedback between components of these networks. The variables in these equations describe concentrations of these components as functions of time. In the preparation of numerical experiments with such mathematical models, it is useful to start with studies of qualitative behavior of ensembles of trajectories of the corresponding dynamical systems, in particular, to estimate the highest likelihood domain of the initial data, to solve inverse problems of parameter identification, to list the equilibrium points and their characteristics, to localize cycles in the phase portraits, to construct stratification of the phase portraits to subdomains with different qualities of trajectory behavior, etc. Such an à priori geometric analysis of the dynamical systems is quite analogous to the basic section "Investigation of functions and plot of their graphs" of Calculus, where the methods of qualitative studies of shapes of curves determined by equations are exposed. In the present paper, we construct ensembles of trajectories in phase portraits of some dynamical systems. These ensembles are 2-dimensional surfaces invariant with respect to shifts along the trajectories. This is analogous to classical construction in analytic mechanics, i. e. the level surfaces of motion integrals (energy, kinetic moment, etc.). Such surfaces compose foliations in phase portraits of dynamical systems of Hamiltonian mechanics. In contrast with this classical mechanical case, the foliations considered in this paper have singularities: all their leaves have a non-empty intersection, they contain limit cycles on their boundaries. Description of the phase portraits of these systems at the level of their stratifications, and that of ensembles of trajectories allows one to construct more realistic gene network models on the basis of methods of statistical physics and the theory of stochastic differential equations.

Precision Measurement of the Return Distribution Property of the Chinese Stock Market Index.

In econophysics, the analysis of the return distribution of a financial asset using statistical physics methods is a long-standing and important issue. This paper systematically conducts an analysis of composite index 1 min datasets over a 17-year period (2005−2021) for both the Shanghai and Shenzhen stock exchanges. To reveal the differences between Chinese and mature stock markets, we precisely measure the property of the return distribution of the composite index over the time scale Δt, which ranges from 1 min to almost 4000 min. The main findings are as follows: (1) The return distribution presents a leptokurtic, fat-tailed, and almost symmetrical shape that is similar to that of mature markets. (2) The central part of the return distribution is described by the symmetrical Lévy α-stable process, with a stability parameter comparable with a value of about 1.4, which was extracted for the U.S. stock market. (3) The return distribution can be described well by Student’s t-distribution within a wider return range than the Lévy α-stable distribution. (4) Distinctively, the stability parameter shows a potential change when Δt increases, and thus a crossover region at 15 <Δt< 60 min is observed. This is different from the finding in the U.S. stock market that a single value of about 1.4 holds over 1 ≤Δt≤ 1000 min. (5) The tail distribution of returns at small Δt decays as an asymptotic power law with an exponent of about 3, which is a widely observed value in mature markets. However, it decays exponentially when Δt≥ 240 min, which is not observed in mature markets. (6) Return distributions gradually converge to a normal distribution as Δt increases. This observation is different from the finding of a critical Δt= 4 days in the U.S. stock market.

Solutions of the Ortvay Rudolf International Competition in Physics: Phase-Transition in Collective Aggression (1991/22 Problem)

This paper is the third in a series of published solutions 1 , 2 discussing problems of the Ortvay Rudolf international competition. The problem treated below is an exercise in building a qualitative model for complex systems, applying statistical physics methods. Accounting for the simplifications, it is also possible to express corrections in the results due to otherwise neglected properties. The problem is appropriate for university students, especially for future physics teachers, as it helps to demonstrate the power of using physical reasoning in interdisciplinary fields.

On the Characterization of a Finite Random Field by Conditional Distribution and its Gibbs Form

In this paper, we show that the methods of mathematical statistical physics can be successfully applied to random fields in finite volumes. As a result, we obtain simple necessary and sufficient conditions for the existence and uniqueness of a finite random field with a given system of one-point conditional distributions. Using the axiomatic (without the notion of potential) definition of Hamiltonian, we show that any finite random field is Gibbsian. We also apply the proposed approach to Markov random fields.

An analytical theory of curriculum learning in teacher–student networks* *This article was also accepted in NeurIPS2022 Proceedings.

In animals and humans, curriculum learning—presenting data in a curated order—is critical to rapid learning and effective pedagogy. A long history of experiments has demonstrated the impact of curricula in a variety of animals but, despite its ubiquitous presence, a theoretical understanding of the phenomenon is still lacking. Surprisingly, in contrast to animal learning, curricula strategies are not widely used in machine learning and recent simulation studies reach the conclusion that curricula are moderately effective or even ineffective in most cases. This stark difference in the importance of curriculum raises a fundamental theoretical question: when and why does curriculum learning help? In this work, we analyse a prototypical neural network model of curriculum learning in the high-dimensional limit, employing statistical physics methods. We study a task in which a sparse set of informative features are embedded amidst a large set of noisy features. We analytically derive average learning trajectories for simple neural networks on this task, which establish a clear speed benefit for curriculum learning in the online setting. However, when training experiences can be stored and replayed (for instance, during sleep), the advantage of curriculum in standard neural networks disappears, in line with observations from the deep learning literature. Inspired by synaptic consolidation techniques developed to combat catastrophic forgetting, we propose curriculum-aware algorithms that consolidate synapses at curriculum change points and investigate whether this can boost the benefits of curricula. We derive generalisation performance as a function of consolidation strength (implemented as an L 2 regularisation/elastic coupling connecting learning phases), and show that curriculum-aware algorithms can yield a large improvement in test performance. Our reduced analytical descriptions help reconcile apparently conflicting empirical results, trace regimes where curriculum learning yields the largest gains, and provide experimentally-accessible predictions for the impact of task parameters on curriculum benefits. More broadly, our results suggest that fully exploiting a curriculum may require explicit adjustments in the loss.

Efficient adsorption of Rhodamine B using a composite of Fe3O4@zif-8: Synthesis, characterization, modeling analysis, statistical physics and mechanism of interaction

ABSTRACT. The utilization of a metal organic framework (ZIF-8) modified by Fe3O4 nanoparticles was used to accomplish adsorption of Rhodamine B (RB) from aqueous solutions. SEM, XRD, IR, and BET analyses were all used to characterize the composite (Fe3O4@ZIF-8). The surface area of this adsorbent was 478.4 m2/g. X-Ray diffraction spectroscopy was used to detect surface modification utilizing electron microscopy (SEM) scanning with 48 nm in diameter average particle size according to a statistical physics method. Fe3O4@ZIF-8 appears to have dispersive interactions and pore characteristics, according to quantum chemistry simulations. On the adsorption of RB, the influences of contact time, adsorbent quantity, dye concentration, and temperature were studied. The Langmuir and Freundlich adsorption isotherm models were used to study the adsorption isotherms. Anticipated overall adsorption potential was 647.5 mg/g, with a zero-charge point (pHPZC) of 4.3. The adsorption isotherm was fitted using Langmuir whereas pseudo second order was used to match the kinetics. Energy of adsorption (Ea) is 28.7 kJ/mol, indicating a chemisorption phase. The adsorption process is endothermic and unpredictable, according to thermodynamic experiments. It was also looked into using ethanol as a solvent in the desorption of deposited cationic dye.&#x0D; &#x0D; KEY WORDS: Fe3O4@ZIF-8, Rhodamine B, Adsorption models, Thermodynamics&#x0D; &#x0D; Bull. Chem. Soc. Ethiop. 2023, 37(1), 211-229. &#x0D; DOI: https://dx.doi.org/10.4314/bcse.v37i1.17

Economic System Research by Using Statistical Physics

Physicists’ research in finance and economics began in the 1990s and has been applied to the challenges of this field ever since. One of the challenging issues of econophysics is to answer the questions: Can we solve the economic challenges? How does the statistical physics method contribute with the problem in the asset pricing model? How does the economics network structure and the global financial crisis co-evolve? To answer that questions, several theoretical and empirical studies have already been conducted on the anomalous phenomena of the economy and financial markets. Moreover, at the forefront of recent financial crisis research, extensive and rapid development has been achieved by combining text information and machine learning methodologies. Here, we discuss financial time series analysis and outline the future prospects for econophysics research.

Modeling of Air Traffic Flow Using Cellular Automata

Fast simulation technology is very important to explore the consequences of air traffic management decision. Although a variety of simulation tools have been developed to make decisions for air traffic controllers, the cognitive process of air traffic controllers is not effectively integrated into these tools. This article studies a probabilistic cellular automata (CA) model for air traffic flow simulation. By introducing the safety distance parameter into the CA model, the equilibrium property of air traffic system is studiedusing the statistical physics method. The simulation results show that the data are in good agreement with the measured results.

Evolution of cooperation with time-varying tags and heterogeneous immigration dynamics

Cooperation in an open dynamic system fundamentally depends upon information distributed across its components. Yet in an environment with rapidly evolving complexity, this information may need to change adaptively to enable cooperative interactions. Combining the methods of evolutionary game theory, agent-based simulation, and statistical physics, we develop a model of the evolution of cooperation in an ageing population of artificial decision makers playing spatial tag-mediated prisoner’s dilemma games with their ingroup neighbors and with genetically unrelated immigrant agents. We introduce the concept of time-varying tags such that the phenotypic features of ‘new’ agents can change into ‘approved’ following variable approval times. In the standard 4-strategy model with fixed tags, we identified a critical cost [Formula: see text] above which cooperation transitioned abruptly into the phase of pure defection. In our generalized 6-strategy model with time-varying tags, the maintenance of elevated cooperation was observed for a much wider region of the parameter space, peaking at intermediate approval times and cost values above [Formula: see text]. Our findings reveal the existence of optimal approval times leading to high levels of cooperation if a fraction of the population adopts the strategy with an egalitarian generosity directed towards both native and approved agents, regardless of their actual origin.

Introducing simple models of social systems

Learning to model social systems can foster critical thinking about the applications of mathematical methods to social issues and also lead to professional opportunities. I introduce an intriguing simple model proposed by Thomas Schelling to understand urban segregation. It shows that even when individual agents seek mixed neighborhoods, they can collectively create a segregated city that makes everyone unhappy. The model can be presented as a simple role-playing game or by a computer program. At a more advanced level, the methods of statistical physics provide a way to calculate equilibrium states corresponding to segregated configurations. I also discuss why physics inspired models have difficulties in understanding the complex dynamics of real social systems.

Completed Review of Various Solar Power Forecasting Techniques Considering Different Viewpoints

Solar power has rapidly become an increasingly important energy source in many countries over recent years; however, the intermittent nature of photovoltaic (PV) power generation has a significant impact on existing power systems. To reduce this uncertainty and maintain system security, precise solar power forecasting methods are required. This study summarizes and compares various PV power forecasting approaches, including time-series statistical methods, physical methods, ensemble methods, and machine and deep learning methods, the last of which there is a particular focus. In addition, various optimization algorithms for model parameters are summarized, the crucial factors that influence PV power forecasts are investigated, and input selection for PV power generation forecasting models are discussed. Probabilistic forecasting is expected to play a key role in the PV power forecasting required to meet the challenges faced by modern grid systems, and so this study provides a comparative analysis of existing deterministic and probabilistic forecasting models. Additionally, the importance of data processing techniques that enhance forecasting performance are highlighted. In comparison with the extant literature, this paper addresses more of the issues concerning the application of deep and machine learning to PV power forecasting. Based on the survey results, a complete and comprehensive solar power forecasting process must include data processing and feature extraction capabilities, a powerful deep learning structure for training, and a method to evaluate the uncertainty in its predictions.

FRACTAL MODELING OF STOCHASTIC PROCESSES AND DEVELOPMENT OF STATISTICAL REPRESENTATIONS

The effectiveness of using fractal models to consider complex multicomponent systems, especially those whose functioning is based on stochastic processes, is well known. In particular, they also include molecular systems, the study of which was considered the exclusive prerogative of the well-known methods of statistical physics. At first glance, it seems that the imposition of fractal modeling on a statistical problem is a kind of double simplification, which should narrow the area of applicability of such an approach. However, fractal modeling only tightened the requirements for a clearer and more precise formulation of statistical problems, refinement of basic concepts, ideas about distinguishing particles, etc. The paper shows for the first time that the statistics of molecular systems should be based on two statistical factors Gn and Fm. The basis for the factor Gn is the difference in the nature of the motion and interaction of particles, and the factor Fm is the difference in the ways of filling the phase cells. They together form physical statistics that are sensitive to changes in the nature of interactions in the system. At the same time, mathematical methods of statistics, insensitive to the nuances of interactions, describe the maximum chaos in the system, in fact, an ideal gas. One of the achievements of the study is the establishment of the fact that both quantum statistics are based only on the statistical factor Fm, based on the difference in the ways of filling the phase cells.