An Agent-Based Statistical Physics Model for Political Polarization: A Monte Carlo Study.

World-wide, political polarization continues unabated, undermining collective decision-making ability. In this issue, we have examined polarization dynamics using a (mean-field) model borrowed from statistical physics, assuming that each individual interacted with each of the others. We use the model to generate scenarios of polarization trends in time in the USA and explore ways to reduce it, as measured by a polarization index that we propose. Here, we extend our work using a more realistic assumption that individuals interact only with "neighbors" (short-range interactions). We use agent-based Monte Carlo simulations to generate polarization scenarios, considering again three USA political groups: Democrats, Republicans, and Independents. We find that mean-field and Monte Carlo simulation results are quite similar. The model can be applied to other political systems with similar polarization dynamics.

Statistical Mechanics of Political Polarization.

Rapidly increasing political polarization threatens democracies around the world. Scholars from several disciplines are assessing and modeling polarization antecedents, processes, and consequences. Social systems are complex and networked. Their constant shifting hinders attempts to trace causes of observed trends, predict their consequences, or mitigate them. We propose an equivalent-neighbor model of polarization dynamics. Using statistical physics techniques, we generate anticipatory scenarios and examine whether leadership and/or external events alleviate or exacerbate polarization. We consider three highly polarized USA groups: Democrats, Republicans, and Independents. We assume that in each group, each individual has a political stance s ranging between left and right. We quantify the noise in this system as a "social temperature" T. Using energy E, we describe individuals' interactions in time within their own group and with individuals of the other groups. It depends on the stance s as well as on three intra-group and six inter-group coupling parameters. We compute the probability distributions of stances at any time using the Boltzmann probability weight exp(-E/T). We generate average group-stance scenarios in time and explore whether concerted interventions or unexpected shocks can alter them. The results inform on the perils of continuing the current polarization trends, as well as on possibilities of changing course.

Sociophysics Analysis of Multi-Group Conflicts.

We present our research on the application of statistical physics techniques to multi-group social conflicts. We identify real conflict situations of which the characteristics correspond to the model. We offer realistic assumptions about conflict behaviors that get factored into model-generated scenarios. The scenarios can inform conflict research and strategies for conflict management. We discuss model applications to two- and three-group conflicts. We identify chaotic time evolution of mean attitudes and the occurrence of strange attractors. We examine the role that the range of interactions plays with respect to the occurrence of chaotic behavior.

Mixing Enhancement in Serpentine Micromixers with a Non-Rectangular Cross-Section.

In this numerical study, a new type of serpentine micromixer involving mixing units with a non-rectangular cross-section is investigated. Similar to other serpentine/spiral shaped micromixers, the design exploits the formation of transversal vortices (Dean flows) in pressure-driven systems, associated with the centrifugal forces experienced by the fluid as it is confined to move along curved geometries. In contrast with other previous designs, though, the use of non-rectangular cross-sections that change orientation between mixing units is exploited to control the center of rotation of the transversal flows formed. The associated extensional flows that thus develop between the mixing segments complement the existent rotational flows, leading to a more complex fluid motion. The fluid flow characteristics and associated mixing are determined numerically from computational solutions to Navier⁻Stokes equations and the concentration-diffusion equation. It is found that the performance of the investigated mixers exceeds that of simple serpentine channels with a more consistent behavior at low and high Reynolds numbers. An analysis of the mixing quality using an entropic mixing index indicates that maximum mixing can be achieved at Reynolds numbers as small as 20 in less than four serpentine mixing units.

Entropy Driven Phase Transition in Polymer Gels: Mean Field Theory.

We present a mean field model of a gel consisting of P polymers, each of length L and Nz polyfunctional monomers. Each polyfunctional monomer forms z covalent bonds with the 2P bifunctional monomers at the ends of the linear polymers. We find that the entropy dependence on the number of polyfunctional monomers exhibits an abrupt change at Nz = 2P/z due to the saturation of possible crosslinks. This non-analytical dependence of entropy on the number of polyfunctionals generates a first-order phase transition between two gel phases: one poor and the other rich in poly-functional molecules.

Equation of state from the Potts-percolation model of a solid.

We expand the Potts-percolation model of a solid to include stress and strain. Neighboring atoms are connected by bonds. We set the energy of a bond to be given by the Lennard-Jones potential. If the energy is larger than a threshold the bond is more likely to fail, whereas if the energy is lower than the threshold, the bond is more likely to be alive. In two dimensions we compute the equation of state: stress as a function of interatomic distance and temperature by using renormalization-group and Monte Carlo simulations. The phase diagram, the equation of state, and the isothermal modulus are determined. When the Potts heat capacity is divergent the continuous transition is replaced by a weak first-order transition through the van der Waals loop mechanism. When the Potts transition is first order the stress exhibits a large discontinuity as a function of the interatomic distance.

Reliability difference between spectral and entropic measures of erector spinae muscle fatigability.

This study investigated back muscle fatigability of the erector spinae (ES) muscles during submaximal contractions with the use of surface electromyography (sEMG). It was important to confirm the reliability of measurements for characterizing neuromuscular alterations by establishing the difference between the Shannon (information) entropy and the power spectrum analysis in subjects with low back pain (LBP). The data was collected on two different days, one week apart, and the between-days reliability of these measures was examined. Thirty-two gender-matched subjects completed the modified Sorenson test; 16 of the subjects were female while 16 were male. The entropy of the sEMG signal was more reliable than either the median frequency (MF) or the slope of the MF. The intraclass correlation coefficient (ICC) was higher for the entropy than for the MF slope. The ICC values of entropy for between-day measurements were higher (0.82-0.85) than MF (0.54-0.64) and MF slope (0.26-0.30). The standard errors of measurement (SEM) values for entropy were lower (0.04-0.05) than MF (3.10-3.60) and MF slope (0.03-0.04). The Pearson correlation coefficients of the entropy were significantly higher (0.75-0.77) than those of the MF (0.38-0.47) and the MF slope (0.15-0.18). Therefore, the results of this study indicated that the entropy analysis could provide a reliable measure of muscle fatigability.

Extended defects in the Potts-percolation model of a solid: renormalization group and Monte Carlo analysis.

We extend the model of a 2d solid to include a line of defects. Neighboring atoms on the defect line are connected by springs of different strength and different cohesive energy with respect to the rest of the system. Using the Migdal-Kadanoff renormalization group we show that the elastic energy is an irrelevant field at the bulk critical point. For zero elastic energy this model reduces to the Potts model. By using Monte Carlo simulations of the three- and four-state Potts model on a square lattice with a line of defects, we confirm the renormalization-group prediction that for a defect interaction larger than the bulk interaction the order parameter of the defect line changes discontinuously while the defect energy varies continuously as a function of temperature at the bulk critical temperature.

Gender differences in spectral and entropic measures of erector spinae muscle fatigue.

Electromyographic power spectral analysis is a valuable measurement; however, conflicting results have been reported for amplitude and frequency changes during a fatiguing submaximal muscle contraction. This study compared gender differences for two analyses in subjects with low back pain (LBP). Distinct gender differences are found in musculoskeletal illness/dysfunction, and we examined the effect of gender on entropy and median frequency (MF) slope in a cohort of subjects with LBP. A total of 44 subjects (24 female and 20 male) completed the modified Sorenson test. These subjects ranged in age from 26 to 64 years old, with an average age of 49.9 +/- 9.4 years. Overall, a significant fatigability difference was found based on MF slope (F = 21.33, p = 0.001) and entropy measures (F = 68.26, p = 0.001) of the back muscles. While the MF slope was not different (F = 0.44, p = 0.51) between genders, the entropy values were higher for the male subjects than for the female subjects (F = 6.70, p = 0.01). These results indicate that the Shannon entropy measure differentiates between genders. Further studies are needed to evaluate the effectiveness of using nonlinear analysis as a measurement tool.

Comparison of spectral and entropic measures for surface electromyography time series: a pilot study.

In a previous study, we reported that the mean square displacement calculated from the surface electromyography (sEMG) signal of low back muscles exhibits a plateaulike behavior for intermediate times 20 ms < t < 400 ms. This property indicates the existence of correlations in the signal for times much longer than the inverse of the median frequency (MF), which is calculated from the power spectrum 1/ = 1/(100 Hz) = 10 ms, where is the MF. This result suggests the use of methods from nonlinear analysis to characterize sEMG time series. In this study, we applied these techniques to sEMG signals and calculated the time-dependent entropy. The results showed that the entropy of physiological time series from nondisabled control subjects is higher than the entropy from subjects with low back pain (LBP). The entropy reveals properties of the sEMG signal that are not captured by the power spectrum. In turn, this suggests a possible benefit of entropy as a tool for the clinical assessment of LBP. Because the two groups of subjects were not matched by age, the physiological origin of the observed differences between groups could be attributed to either LBP, age, or both. Additional studies with larger sample sizes and age-matched subjects are needed to investigate the relationship between LBP and entropy.

Nonlinear analysis of electromyography time series as a diagnostic tool for low back pain.

BACKGROUND: A number of studies have evaluated lumbar spinal muscle fatigue using the electromyography (EMG) signal. However, back muscle fatigue studies do not consistently report endurance levels for patients with or without low back pain (LBP). In this case report, we investigated a nonlinear analysis of EMG time series that characterizes their complexity. MATERIAL/METHODS: A 37-year-old male with chronic LBP and an age- and gender-matched volunteer were compared. The endurance of the erector spinae muscle was determined using a modified version of the isometric Sorensen fatigue test. Nonlinear time series analysis techniques reveal the presence of long-range, power-law correlations. After checking that the signal was stationary, the original time series of 60,000 entries was reduced to 6000 entries by averaging over 10 consecutive entries. RESULTS: There was a difference between the entropy time dependence exhibited by entropy time dependence exhibited by the healthy subject and the LBP subject. The entropy associated with the LBP subject saturates at very short-times--two orders of magnitude shorter than for the healthy subject. CONCLUSIONS: The characterization of the nonlinear time series in this case study provides a consistent measure of back muscle activities. It is important to understand the potential limitations before undertaking an EMG analysis in the field of ergonomics or biomechanics. Further studies are needed to investigate the characteristics of back muscles.

Age differences in central (semantic) and peripheral processing: the importance of considering both response times and errors.

In this project we examined the effect of adult age on visual word recognition by using combined reaction time (RT) and accuracy methods based on the Hick-Hyman law. This was necessary because separate Brinley analyses of RT and errors resulted in contradicting results. We report the results of a lexical decision task experiment (with 96 younger adults and 97 older adults). We transformed the error data into entropy and then predicted RT by using entropy values separately for exposure duration (thought to influence peripheral processes) and word frequency (thought to influence central processes). For exposure duration, the entropy-RT functions indicate that older adults show higher intercepts and slopes than do younger adults, suggesting an encoding decrement for older adults. However, for word frequency, older adults show higher intercepts but not steeper slopes than younger adults. Older adults thus show a peripheral processing decrement but not a central processing decrement for lexical decision.