Session E55: Statistical Mechanics of Social Systems

Statistical mechanics of Twitter

From fads to residential segregation, social processes depend on interactions among many individuals. Social phenomena are prototypically emergent, leading some to ask if we can build a statistical mechanics for these systems. We construct such models directly from data on individual participation in Twitter communities. We identify communities and topics of conversation within those communities, allowing the definition of binary (tweet/silent) variables for each individual during each conversation. We then build maximum entropy models that match the pairwise correlations among these variables, predicting the joint distribution of the binary variables across the entire community. These simple Ising-like models give an accurate quantitative description of many higher order features in the data, and lie near a critical surface in the space of possible models. Finally, we systematically coarse-grain the observed network states, finding hints that the macroscopic behavior is controlled by a non-trivial fixed point in the sense of the renormalization group.   

Empirical scaling and dynamical regimes for GDP: challenges and opportunities

Analysis of GDP data and per capita GDP data from 1980 and 2016 finds three scaling regions. The GDP of the largest ~25 economies (nations, EU) follows a power law GDP ~ 1/rank; this is followed by a second scaling region in which GDP falls off exponentially with rank and finally a third scaling region in which the GDP falls off exponentially with the square of rank. The distribution of per capita GDP also displays these three scaling regions. Both patterns hold despite significant changes in technology, the size of the world economy, emergence of new economic powers such, and world trade (almost free communication, containerized shipping yielding sharp declines in shipping costs). Thus, empirically, these patterns may be universal [1-5]; in which case one of the targets for growth of those in the second and third scaling regions may be to identify and target causative differences between these economies and those in the first (power law) scaling region.
References
1. Solomon S and Richmond P 2002. Eur Phys J B 27, 257
2. Solomon S and Richmond P 2001. Physica A 299, 188.
3. Mitzenmacher M 2004. Internet Math 1, 226.
4. Yakovenko VM 2009. In Encyclopedia of Complexity and Systems Science (p 2800-2826), Springer.
5. Yakovenko VM and Rosser Jr JB 2009. Rev Modern Phys 81, 1703   

Three-state Voter Model on Barab\'asi-Albert Networks and the Unitary Relation for Critical Exponents

We investigate the three-state majority-vote model with noise on scale-free 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. 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 ∼ 3. Using Q finite-size scaling for any dimensions and the finite-size scaling for complex networks, we show that the critical exponents associated to the magnetization and to the susceptibility are related by 2β/ν + γ/ν = 1, regardless the dimension of the complex network. Using Monte Carlo simulations we obtain the phase diagram of the model and we verify the unitary relation for the critical exponents numerically by calculating β/ν, γ/ν and 1/ν for several values of the parameter z.   

Robust design from systems physics

Ensuring robust outcomes and designs is a crucial challenge in the engineering of modern integrated systems that are comprised of many heterogeneous subsystems. Coupling among heterogeneous subsystems leads to the complex response of design elements to changes in whole-system specifications. Here, we show that the response of design elements to whole-system specification changes can be characterized, as materials are, using strong/weak and brittle/ductile dichotomies. We find these dichotomies emerge from a mesoscale treatment of early stage design problems that we cast in terms of stress--strain relationships. We illustrate the use of this approach with examples from naval engineering, however our approach is immediately applicable to a broad range of problems in integrated systems design.   

Coarse-graining armed conflict

Large-scale armed conflict between groups is a defining phenomenon of modern human civilization, but the absence of a compelling model of conflict that agrees with the data means that prediction of conflict remains rudimentary. In a simple model, the spread of conflict might be described as a propagating avalanche or percolating component that extends across time and space and through a network of related actors. The presence of near power-law statistics in the sizes, durations, and actor network components of conflict suggests that such an abstracted model could provide both useful intuition and quantitative predictions about the structure of conflict on large scales. We explore this perspective in detail by performing a renormalization scheme on the surface of the Earth to generate statistics of conflict avalanches along coarse-grained spatiotemporal scales. We show that some kinds of armed conflict may obey scaling laws that could provide a basis for a predictive theory of conflict based on ideas from statistical physics.   

Impact Factors and the Central Limit Theorem: Why citation averages are scale dependent

We apply the Central Limit Theorem to study how citation averages, and Impact Factors (IFs) in particular, depend on scale. For a journal of n papers randomly selected from a population, we expect from the Theorem that its IF fluctuates around the population average μ, and spans a range of values proportional to σ/√n, where σ² is the variance of the population's citation distribution. The 1/√n dependence has profound implications for IF rankings: The larger a journal, the narrower the range around μ where its IF lies. IF rankings therefore allocate an unfair advantage to smaller journals in the high IF ranks, and to larger journals in the low IF ranks. This implies a scale-dependent stratification of journals in IF rankings, whereby small journals occupy all ranks, mid-sized journals occupy the middle ranks, and very large journals have IFs that asymptotically approach μ. We confirm these predictions by analyzing 20 years of Impact-Factor and journal-size data, and the citation distributions of 11,000 journals. We propose the Φ index, a rescaled IF that accounts for size effects, and which can be readily generalized to account also for different citation practices across research fields [1].

[1] M. Antonoyiannakis, J. Informetrics 12, 1072 (2018).   

Higher-Order Correlations in Bursty Temporal Patterns

Temporal inhomogeneities in event sequences of natural and social phenomena have been characterized in terms of interevent times and correlations between interevent times. The inhomogeneities of interevent times have been extensively studied, while the correlations between interevent times, correlated bursts (CB), are far from being fully understood. Firstly, we numerically show that the strong CB, depicted by power-law burst size distributions, violates the well-established scaling relation between the power-law decaying autocorrelation function and the power-law interevent time distribution (PRE 2017). Next, for understanding empirical data sets for human activities showing power-law burst size distributions but negligible memory coefficient, we derive an analytic form of the memory coefficient between consecutive interevent times as a function of parameters describing interevent time and burst size statistics, to conclude that the memory coefficient might have some limits in quantifying CB (PRE 2018). Finally, in order to completely characterize the event sequence, we develop a detection method of the hierarchical burst structure by exactly mapping the event sequence onto a rooted tree, implying no loss of information on the original event sequence (in preparation).   

A Generalized Asset Exchange Model With Economic Growth and Wealth Distribution

An agent-based yard-sale model of the economy is generalized to incorporate economic growth and its distribution to the agents according to their wealth as determined by a parameter λ. In addition to providing insight into the relation between the nature of economic growth and wealth inequality, we find that the model has a phase transition at λ = 1 between a equilibrium phase with economic mobility and a non-stationary phase for which there is no mobility and wealth is concentrated among a few agents. We show that the critical exponents obtained for a fixed number of agents do not obey the usual scaling laws. However, the critical exponents are consistent with the scaling laws and mean-field theory if the Ginzburg parameter, which controls the accuracy of the mean-field approximation, is held fixed as the transition is approached and is much greater than one. The transition raises questions about whether the methods of equilibrium statistical mechanics can be applied to economic systems. We also discuss possible implications of our results for economic systems and for understanding critical point behavior in systems with long, but finite, range interactions such as metals, biological systems and polymers.   

Statistical Mechanics of Intractable Conflicts

We extend a statistical physics model of two-group conflicts (H. T. Diep, et al Physica A 469, 183 (2017) to three conflicting groups. We apply mean field theory (for long range interactions) and Monte-Carlo simulations (for short range interactions) to study the time dependence of the mean attitudes in each group. Using the mean field approach, we observe that at some intermediate temperatures the means of group attitudes oscillate in time. Independent of initial conditions, attitude trajectories converge over time to an attractor in the three-dimensional space of group mean attitudes. In contrast, chaotic unpredictable time variation of attitudes is observed for short range interactions. This model with attractors and chaos is proposed as a tool for understanding intractable conflict dynamics. It can be used to generate scenarios of possible trajectories in time, which can be empoyed for managing intractable conflicts.   

Understanding the extreme Thouless effect in a simple, dynamic social network - the XIE model

A system undergoing a phase transition which exhibits the characteristics of both first and second order transitions is said to display the Thouless effect, e.g., the order parameter suffering a discontinuity and fluctuates through all values within the jump. In a simple of model extreme introverts and extroverts, the former/latter cuts/adds a random link when chosen to act (the XIE model, EPL 100, 66007 and PRE91, 042102). The steady state consists of a networks of crosslinks between the i's and e's.. The fraction of these, f, serves as an order parameter jumping from ~0 to ~1 as the ratio of i's to e's drops through unity. At unity, f wanders between "soft walls" at f₀ and 1- f₀. With f₀ →0, the system is said to exhibit an “extreme Thouless effect.” We present a novel approach based on a self-consistent mean field theory. The predictions agree spectacularly well with all simulation data. Further, we obtain the analytic form of the asymptotic behavior of f₀ : It vanishes as [(lnL² )/L]^1/2, where L is the size of each subgroup. Though this form sets in as late as L~10²⁰⁰, very good bounds (e.g., ~1%) for more accessible L’s (e.g., 2000) can be found by solving a transcendental equation: x+lnx = ln(L²/2π).   

Price Measurement in Financial Markets and Quantum Coupled-Wave Model of Price Dynamics

We present a theory of bid and ask price dynamics in financial markets where the two prices form as a result of quantum-chaotic interaction between buy and sell orders. In this model the two prices are represented by eigenvalues of a 2x2 price operator corresponding to "bid" and "ask" eigenstates. We will present the trading process from physics point of view, discuss how each trade represents an elementary act of price measurement and demonstrate how the theory is built from this argument. We will show that the coupled-wave theory reflects important characteristics of bid and ask price dynamics and order density in the limit order book. Calibration examples will be provided for stocks at various time scales. This theory opens a new dimension in financial modeling providing a framework for liquidity pricing, illiquidity risk evaluation, position management, as well as brings up a discussion about the nature of processes in financial markets.   

Congested Equilibria in Large-Scale Traffic Networks: Existence, Stability and Robustness through Chemical Reaction Network Analogues

Discrete fluid-like models such as the Cell Transmission Model (CTM) have proven successful in modeling traffic networks. In general, these models employ discontinuous dynamics or nonlinear terms to describe phenomena like shock waves and phantom jams. Given the complexity of the dynamics, it is not surprising that the stability properties of these models are not yet well characterized. Recent results prove the existence of a unique equilibrium in the free flow regime for certain classes of networks modeled by the CTM; however, these results restrict network demands and hold only for acyclic network topologies. Further, it is of interest to understand network behavior in congested regimes, since practical networks are often congested. We propose a new modeling paradigm for traffic networks, where an analogy between discrete fluid-like traffic models and a class of chemical reaction networks is constructed by suitable relaxations of key conservation laws in the CTM. Using this analogy, we provide structural conditions on the network graph topology for the existence of equilibria in congested regimes. Drawing upon entropy-like Lyapunov functions from chemical reaction network theory, we prove that the network admits multiple stable and robust congested equilibria.   

Individual-Trait-Based Assortative Mixing in a Large Scientific Collaboration Network

Understanding the underlying mechanism of collaborative network formation is highly relying on the property of assortative/disassortative mixing patterns. Recent studies have shown that both of assortative and disassortative mixing patterns are widely existing in many social networks. However, it's not always been well-confirmed that people tend to connect with someone who has similar or dissimilar individual traits. In this study, we build a scientific collaboration network by the common publishing relationship with the APS journal papers and measure the scholars' degree assortativity and research interest assortativity. Our study has shown that the extent of assortative mixing behaviors of scholars may diversify from the different physics fields, or the social ties. In addition, the middle-level degree scholars play a vital role in bridging the collaborative communities and research fields, while this large group of members have not received adequate attention in the study of the science of science.   

A Vector Threshold Model for the Simultaneous Spread of Correlated Influence

Most existing works modeling influence propagation assume that there is only one content spreading over networks. However, an influence propagation process could have multiple correlated contents spreading simultaneously and exhibiting positive (e.g., opinions on same-sex marriage and gun control) or negative (e.g., opinions on universal healthcare and tax-relief for the ``rich") correlation. In a nutshell, few researchers model an influence propagation with the simultaneous spread of multiple correlated contents. Thus,for this scenario, we first propose a new model, the vector threshold model. For this model, we analyze the expected size of global cascades and find the condition of the existence of global cascades. Then, we confirm the correctness of our analysis by numerical studies. Next, we discuss how the correlation among contents affects the expected size of global cascades. In particular, when the mean degree of nodes is at a low level, the competitive, independent, and cooperative relationships produce global cascades with similar size. Only when the mean degree is at a high level do we see significant differences between these relationships on the expected size of global cascades.   

A stochastic microscopic model describing the continuous Generalized Voter Model

We present a stochastic microscopic model that exhibits the same properties as the Generalized Voter Model in its Langevin description. Building on a model introduced in 2011 by Blythe et al. for the investigation of ordering dynamics in the presence of symmetric absorbing states, we show that our model exhibits phase transitions belonging to three different universality classes: Voter, Ising, and Directed Percolation. These different universality classes are identified through a systematic investigation of various static and dynamic quantities. We also present some data on the aging processes taking place at Voter critical points and show that, depending on the values of some system parameters, properties of linear or non-linear voter models are recovered.