Relativistic Equilibrium Distribution by Relative Entropy Maximization

The equilibrium state of a relativistic gas has been calculated based on the maximum entropy principle. Though the relativistic equilibrium state was long believed to be the Juttner distribution, a number of papers have been published in recent years proposing alternative equilibrium states. However, some of these papers do not pay enough attention to the covariance of distribution functions, resulting confusion in equilibrium states. Starting from a fully covariant expression to avoid this confusion, it has been shown in the present paper that the Juttner distribution is the maximum entropy state if we assume the Lorentz symmetry.Comment: Six pages, no figure

A Daple-Akt feed-forward loop enhances noncanonical Wnt signals by compartmentalizing β-catenin.

Cellular proliferation is antagonistically regulated by canonical and noncanonical Wnt signals; their dysbalance triggers cancers. We previously showed that a multimodular signal transducer, Daple, enhances PI3-K→Akt signals within the noncanonical Wnt signaling pathway and antagonistically inhibits canonical Wnt responses. Here we demonstrate that the PI3-K→Akt pathway serves as a positive feedback loop that further enhances noncanonical Wnt signals by compartmentalizing β-catenin. By phosphorylating the phosphoinositide- (PI) binding domain of Daple, Akt abolishes Daple's ability to bind PI3-P-enriched endosomes that engage dynein motor complex for long-distance trafficking of β-catenin/E-cadherin complexes to pericentriolar recycling endosomes (PCREs). Phosphorylation compartmentalizes Daple/β-catenin/E-cadherin complexes to cell-cell contact sites, enhances noncanonical Wnt signals, and thereby suppresses colony growth. Dephosphorylation compartmentalizes β-catenin on PCREs, a specialized compartment for prolonged unopposed canonical Wnt signaling, and enhances colony growth. Cancer-associated Daple mutants that are insensitive to Akt mimic a constitutively dephosphorylated state. This work not only identifies Daple as a platform for cross-talk between Akt and the noncanonical Wnt pathway but also reveals the impact of such cross-talk on tumor cell phenotypes that are critical for cancer initiation and progression

Stationarity, soft ergodicity, and entropy in relativistic systems

Recent molecular dynamics simulations show that a dilute relativistic gas equilibrates to a Juettner velocity distribution if ensemble velocities are measured simultaneously in the observer frame. The analysis of relativistic Brownian motion processes, on the other hand, implies that stationary one-particle distributions can differ depending on the underlying time-parameterizations. Using molecular dynamics simulations, we demonstrate how this relativistic phenomenon can be understood within a deterministic model system. We show that, depending on the time-parameterization, one can distinguish different types of soft ergodicity on the level of the one-particle distributions. Our analysis further reveals a close connection between time parameters and entropy in special relativity. A combination of different time-parameterizations can potentially be useful in simulations that combine molecular dynamics algorithms with randomized particle creation, annihilation, or decay processes.Comment: 4 page

Establishing the substantive interpretation of the GFP by considering evidence from research on personality disorders and Animal Personality

In research on individual differences, various structural models aim at providing a comprehensive description of personality. These models assume multiple, mostly independent personality dimensions. More recently, the so-called General Factor of Personality (GFP) has become a proliferous, but contentious, topic. The notion of the GFP is based on the observations that personality dimensions are not independent, but in fact show consistent inter-correlations, leading to a relevant proportion of shared variance among them (Figueredo et al., 2006). The GFP seems to capture the socially desirable ends of personality scales, and, in terms of the Big Five model, high-GFP individuals score relatively high on openness, conscientiousness, extraversion (mainly the sociability-facet), agreeableness, and emotional stability (Rushton and Irwing, 2009; van der Linden et al., 2010a). Some authors have suggested that the GFP simply reflects methodological artifacts (Ashton et al., 2009; Backstrom et al., 2009; Hopwood et al., 2011b; Pettersson et al., 2012). However, much of this criticism has been addressed (Rushton and Erdle, 2010; Loehlin, 2012; Dunkel and van der Linden, 2014; van der Linden et al., 2014a). The objective of the present work is not to reiterate these issues, as they have been discussed extensively elsewhere (Irwing, 2013; van der Linden et al., 2016). Instead, we contend that criticism mostly offered within the specialty of personality psychology misses the bigger picture. More specific, evidence in favor of the GFP as a substantive and theoretically coherent construct has been provided in other research fields long before it became a contentious issue in personality psychology. Here we introduce two lines of evidence that may further corroborate the substantive interpretation of the GFP, specifically, findings from personality pathology as well as from animal personality. Looking at the GFP from a different perspective may help to overcome the current debates within personality psychology. In the following we will first briefly introduce work on the GFP and its theoretical foundation as social effectiveness. Afterwards we outline research from psychiatric nosology and animal ecology and discuss these in context

Single to Double Hump Transition in the Equilibrium Distribution Function of Relativistic Particles

We unveil a transition from single peaked to bimodal velocity distribution in a relativistic fluid under increasing temperature, in contrast with a non-relativistic gas, where only a monotonic broadening of the bell-shaped distribution is observed. Such transition results from the interplay between the raise in thermal energy and the constraint of maximum velocity imposed by the speed of light. We study the Bose-Einstein, the Fermi-Dirac, and the Maxwell-J\"uttner distributions, all exhibiting the same qualitative behavior. We characterize the nature of the transition in the framework of critical phenomena and show that it is either continuous or discontinuous, depending on the group velocity. We analyze the transition in one, two, and three dimensions, with special emphasis on two-dimensions, for which a possible experiment in graphene, based on the measurement of the Johnson-Nyquist noise, is proposed.Comment: 5 pages, 5 figure

Non-analytic microscopic phase transitions and temperature oscillations in the microcanonical ensemble: An exactly solvable 1d-model for evaporation

We calculate exactly both the microcanonical and canonical thermodynamic functions (TDFs) for a one-dimensional model system with piecewise constant Lennard-Jones type pair interactions. In the case of an isolated $N$-particle system, the microcanonical TDFs exhibit (N-1) singular (non-analytic) microscopic phase transitions of the formal order N/2, separating N energetically different evaporation (dissociation) states. In a suitably designed evaporation experiment, these types of phase transitions should manifest themselves in the form of pressure and temperature oscillations, indicating cooling by evaporation. In the presence of a heat bath (thermostat), such oscillations are absent, but the canonical heat capacity shows a characteristic peak, indicating the temperature-induced dissociation of the one-dimensional chain. The distribution of complex zeros (DOZ) of the canonical partition may be used to identify different degrees of dissociation in the canonical ensemble.Comment: version accepted for publication in PRE, minor additions in the text, references adde

Overlap Between the General Factor of Personality and Emotional Intelligence: A Meta-Analysis

We examine the relationship between the general factor of personality (GFP) and emotional intelligence (EI) and specifically test the hypothesis that the GFP is a social effectiveness factor overlapping conceptually with EI. Presented is an extensive meta-analysis in which the associations between the GFP, extracted from the Big Five dimensions, with various EI measures is examined. Based on a total sample of k = 142 data sources (N = 36,268) the 2 major findings from the meta-analysis were (a) a large overlap between the GFP and trait EI (r ≈ .85); and (b) a positive, but more moderate, correlation with ability EI (r ≈ .28). These findings show that high-GFP individuals score higher on trait and ability EI, supporting the notion that the GFP is a social effectiveness factor. The findings also suggest that the GFP is very similar, perhaps even synonymous, to trait EI

On Existence and Properties of Approximate Pure Nash Equilibria in Bandwidth Allocation Games

In \emph{bandwidth allocation games} (BAGs), the strategy of a player consists of various demands on different resources. The player's utility is at most the sum of these demands, provided they are fully satisfied. Every resource has a limited capacity and if it is exceeded by the total demand, it has to be split between the players. Since these games generally do not have pure Nash equilibria, we consider approximate pure Nash equilibria, in which no player can improve her utility by more than some fixed factor $\alpha$ through unilateral strategy changes. There is a threshold $\alpha_\delta$ (where $\delta$ is a parameter that limits the demand of each player on a specific resource) such that $\alpha$-approximate pure Nash equilibria always exist for $\alpha \geq \alpha_\delta$, but not for $\alpha < \alpha_\delta$. We give both upper and lower bounds on this threshold $\alpha_\delta$ and show that the corresponding decision problem is ${\sf NP}$-hard. We also show that the $\alpha$-approximate price of anarchy for BAGs is $\alpha+1$. For a restricted version of the game, where demands of players only differ slightly from each other (e.g. symmetric games), we show that approximate Nash equilibria can be reached (and thus also be computed) in polynomial time using the best-response dynamic. Finally, we show that a broader class of utility-maximization games (which includes BAGs) converges quickly towards states whose social welfare is close to the optimum

Nonlocal observables and lightcone-averaging in relativistic thermodynamics

The unification of relativity and thermodynamics has been a subject of considerable debate over the last 100 years. The reasons for this are twofold: (i) Thermodynamic variables are nonlocal quantities and, thus, single out a preferred class of hyperplanes in spacetime. (ii) There exist different, seemingly equally plausible ways of defining heat and work in relativistic systems. These ambiguities led, for example, to various proposals for the Lorentz transformation law of temperature. Traditional 'isochronous' formulations of relativistic thermodynamics are neither theoretically satisfactory nor experimentally feasible. Here, we demonstrate how these deficiencies can be resolved by defining thermodynamic quantities with respect to the backward-lightcone of an observation event. This approach yields novel, testable predictions and allows for a straightforward-extension of thermodynamics to General Relativity. Our theoretical considerations are illustrated through three-dimensional relativistic many-body simulations.Comment: typos in Eqs. (12) and (14) corrected, minor additions in the tex