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Human societies are complex systems and as such have tipping points. They can rapidly transit from one mode of operation to another and thereby change the way they function as a whole. Such transitions appear as financial or economic crises, rapid swings in collective opinion, political regime shifts, or revolutions. In physics collective transitions are known as phase transitions; for example, water exists in states of liquid, ice, and vapor. A few variables determine which state is realized: temperature, pressure, and volume. For social systems it is less clear what determines collective social states. A better understanding of social tipping points would allow us to tackle some of the big challenges more systematically, such as polarization, loss of social cohesion, fragmentation, or the green transition. The physics concept of universality might be key to understanding some tipping points in human societies and why agent-based models (ABMs) might make sense for identifying the transition points. If universality exists in social systems there is hope that relatively simple ABMs will be sufficient for understanding collective social systems in transition; if it does not exist, highly detailed computational models will be unavoidable. Both are possible. Both need new forms of collaboration between the social and natural sciences, and new types of data will be essential. [ABSTRACT FROM AUTHOR]

Complex systems with strong correlations and fat-tailed distribution functions have been argued to be incompatible with the Boltzmann-Gibbs entropy framework and alternatives, so-called generalised entropies, were proposed and studied. Here we show, that this perceived incompatibility is actually a misconception. For a broad class of processes, Boltzmann entropy –the log multiplicity– remains the valid entropy concept. However, for non-i.i.d. processes, Boltzmann entropy is not of Shannon form, −k∑ipi log pi, but takes the shape of generalised entropies. We derive this result for all processes that can be asymptotically mapped to adjoint representations reversibly where processes are i.i.d. In these representations the information production is given by the Shannon entropy. Over the original sampling space this yields functionals identical to generalised entropies. The problem of constructing adequate context-sensitive entropy functionals therefore can be translated into the much simpler problem of finding adjoint representations. The method provides a comprehensive framework for a statistical physics of strongly correlated systems and complex processes. [ABSTRACT FROM AUTHOR]

The article examines the long-term health impacts of famine, specifically how early exposure to food scarcity in Ukraine can increase the risk of developing type 2 diabetes later in life. Topics discussed include the dose-response relationship between prenatal famine exposure and diabetes risk, the critical period of exposure during early gestation, and the potential global public health consequences of current food supply disruptions due to the Russia-Ukraine conflict.

In the current COVID19 crisis many national healthcare systems are confronted with an acute shortage of tests for confirming SARS-CoV-2 infections. For low overall infection levels in the population the pooling of samples can drastically amplify the testing capacity. Here we present a formula to estimate the optimal group-size for pooling, the efficiency gain (tested persons per test), and the expected upper bound of missed infections in pooled testing, all as a function of the population-wide infection levels and the false negative/positive rates of the currently used PCR tests. Assuming an infection level of 0.1% and a false negative rate of 2%, the optimal pool-size is about 34, and an efficiency gain of about 15 tested persons per test is possible. For an infection level of 1% the optimal pool-size is 11, the efficiency gain is 5.1 tested persons per test. For an infection level of 10% the optimal pool-size reduces to about 4, the efficiency gain is about 1.7 tested persons per test. For infection levels of 30% and higher there is no more benefit from pooling. To see to what extent replicates of the pooled tests improve the estimate of the maximal number of missed infections, we present results for 1 to 5 replicates. [ABSTRACT FROM AUTHOR]

Sentence formation is a highly structured, history-dependent, and sample-space reducing (SSR) process. While the first word in a sentence can be chosen from the entire vocabulary, typically, the freedom of choosing subsequent words gets more and more constrained by grammar and context, as the sentence progresses. This sample-space reducing property offers a natural explanation of Zipf's law in word frequencies, however, it fails to capture the structure of the word-to-word transition probability matrices of English text. Here we adopt the view that grammatical constraints (such as subject–predicate–object) locally re-order the word order in sentences that are sampled by the word generation process. We demonstrate that superimposing grammatical structure–as a local word re-ordering (permutation) process–on a sample-space reducing word generation process is sufficient to explain both, word frequencies and word-to-word transition probabilities. We compare the performance of the grammatically ordered SSR model in reproducing several test statistics of real texts with other text generation models, such as the Bernoulli model, the Simon model, and the random typewriting model. [ABSTRACT FROM AUTHOR]

Many countries have passed their first COVID-19 epidemic peak. Traditional epidemiological models describe this as a result of nonpharmaceutical interventions pushing the growth rate below the recovery rate. In this phase of the pandemic many countries showed an almost linear growth of confirmed cases for extended time periods. This new containment regime is hard to explain by traditional models where either infection numbers grow explosively until herd immunity is reached or the epidemic is completely suppressed. Here we offer an explanation of this puzzling observation based on the structure of contact networks.We show that for any given transmission rate there exists a critical number of social contacts, Dc , below which linear growth and low infection prevalence must occur. Above Dc traditional epidemiological dynamics take place, e.g., as in susceptible-infected-recovered (SIR) models. When calibrating our model to empirical estimates of the transmission rate and the number of days being contagious, we find Dc ~7:2. Assuming realistic contact networks with a degree of about 5, and assuming that lockdown measures would reduce that to household size (about 2.5), we reproduce actual infection curves with remarkable precision, without fitting or fine-tuning of parameters. In particular, we compare the United States and Austria, as examples for one country that initially did not impose measures and one that responded with a severe lockdown early on. Our findings question the applicability of standard compartmental models to describe the COVID-19 containment phase. The probability to observe linear growth in these is practically zero. [ABSTRACT FROM AUTHOR]

Is it possible to tell how interdisciplinary and out-of-the-box scientific papers are, or which papers are mainstream? Here we use the bibliographic coupling network, derived from all physics papers that were published in the Physical Review journals in the past century, to try to identify them as mainstream, out-of-the-box, or interdisciplinary. We show that the network clusters into scientific fields. The position of individual papers with respect to these clusters allows us to estimate their degree of mainstreamness or interdisciplinarity. We show that over the past decades the fraction of mainstream papers increases, the fraction of out-of-the-box decreases, and the fraction of interdisciplinary papers remains constant. Studying the rewards of papers, we find that in terms of absolute citations, both, mainstream and interdisciplinary papers are rewarded. In the long run, mainstream papers perform less than interdisciplinary ones in terms of citation rates. We conclude that to avoid a unilateral trend towards mainstreamness a new incentive scheme is necessary. [ABSTRACT FROM AUTHOR]

There are practically no quantitative tools for understanding how much stress a health care system can absorb before it loses its ability to provide care. We propose to measure the resilience of health care systems with respect to changes in the density of primary care providers. We develop a computational model on a 1-to-1 scale for a countrywide primary care sector based on patientsharing networks. Nodes represent all primary care providers in a country; links indicate patient flows between them. The removal of providers could cause a cascade of patient displacements, as patients have to find alternative providers. The model is calibrated with nationwide data from Austria that includes almost all primary care contacts over 2 y. We assign 2 properties to every provider: the "CareRank" measures the average number of displacements caused by a provider's removal (systemic risk) as well as the fraction of patients a provider can absorb when others default (systemic benefit). Below a critical number of providers, large-scale cascades of patient displacements occur, and no more providers can be found in a given region. We quantify regional resilience as the maximum fraction of providers that can be removed before cascading events prevent coverage for all patients within a district. We find considerable regional heterogeneity in the critical transition point from resilient to nonresilient behavior. We demonstrate that health care resilience cannot be quantified by physician density alone but must take into account how networked systems respond and restructure in response to shocks. The approach can identify systemically relevant providers. [ABSTRACT FROM AUTHOR]

Forecasting the popularity of new songs has become a standard practice in the music industry and provides a comparative advantage for those that do it well. Considerable efforts were put into machine learning prediction models for that purpose. It is known that in these models, relevant predictive parameters include intrinsic lyrical and acoustic characteristics, extrinsic factors (e.g., publisher influence and support), and the previous popularity of the artists. Much less attention was given to the social components of the spreading of song popularity. Recently, evidence for musical homophily—the tendency that people who are socially linked also share musical tastes—was reported. Here we determine how musical homophily can be used to predict song popularity. The study is based on an extensive dataset from the last.fm online music platform from which we can extract social links between listeners and their listening patterns. To quantify the importance of networks in the spreading of songs that eventually determines their popularity, we use musical homophily to design a predictive influence parameter and show that its inclusion in state-of-the-art machine learning models enhances predictions of song popularity. The influence parameter improves the prediction precision (TP/(TP + FP)) by about 50% from 0.14 to 0.21, indicating that the social component in the spreading of music plays at least as significant a role as the artist's popularity or the impact of the genre. [ABSTRACT FROM AUTHOR]

As anthropologists study complex societies and large databases, we have to ask whether using demographic divisions within a population help or hinder our understanding of people's cognition, particularly political cognition. Using a database of 1,283 interviews gathered in Mongolia in 1998 and 2003, the authors divide the sample population by the demographic categories of location, gender, education level attained, and age. We use network analysis to note differences in network structure and textual analysis to learn how Mongolians characterize democracy as they emerge from Soviet-style socialism. We find that even though Mongolians are a rather homogeneous society, people's concept of democracy varies by demographic category. We conclude that because experience often varies with a person's position in society, demography correlates with people's perception of democracy and therefore remains a valid and helpful way to study the political culture of a population. [ABSTRACT FROM AUTHOR]

Concerns about the integrity of Turkey's elections have increased with the recent transition from a parliamentary democracy to an executive presidency under Recep Tayyip Erdoğan. Election forensics tools are used to identify statistical traces of certain types of electoral fraud, providing important information about the integrity and validity of democratic elections. Such analyses of the 2017 and 2018 Turkish elections revealed that malpractices such as ballot stuffing or voter manipulation may indeed have played a significant role in determining the election results. Here, we apply election forensic statistical tests for ballot stuffing and voter manipulation to the results of the 2023 presidential election in Turkey. We find that both rounds of the 2023 presidential election exhibit similar statistical irregularities to those observed in the 2018 presidential election, however the magnitude of these distortions has decreased. We estimate that 2.4% (SD 1.9%) and 1.9% (SD 1.7%) of electoral units may have been affected by ballot stuffing practices in favour of Erdoğan in the first and second rounds, respectively, compared to 8.5% (SD 3.9%) in 2018. Areas with smaller polling stations and fewer ballot boxes had significantly inflated votes and turnout, again, in favor of Erdoğan. Furthermore, electoral districts with two or fewer ballot boxes were more likely to show large swings in vote shares in favour of Erdoğan from the first to the second round. Based on a statistical model, it is estimated that these shifts account for 342,000 additional ballots (SD 4,900) or 0.64% for Erdoğan, which is lower than the 4.36% margin by which Erdoğan was victorious. Our results suggest that Turkish elections continue to be riddled with statistical irregularities, that may be indicative of electoral fraud. [ABSTRACT FROM AUTHOR]

Homophily, the tendency of individuals to associate with others who share similar traits, has been identified as a major driving force in the formation and evolution of social ties. In many cases, it is not clear if homophily is the result of a socialization process, where individuals change their traits according to the dominance of that trait in their local social networks, or if it results from a selection process, in which individuals reshape their social networks so that their traits match those in the new environment. Here we demonstrate the detailed temporal formation of strong homophily in academic achievements of high school and university students. We analyze a unique dataset that contains information about the detailed time evolution of a friendship network of 6,000 students across 42 months. Combining the evolving social network data with the time series of the academic performance (GPA) of individual students, we show that academic homophily is a result of selection: students prefer to gradually reorganize their social networks according to their performance levels, rather than adapting their performance to the level of their local group. We find no signs for a pull effect, where a social environment of good performers motivates bad students to improve their performance. We are able to understand the underlying dynamics of grades and networks with a simple model. The lack of a social pull effect in classical educational settings could have important implications for the understanding of the observed persistence of segregation, inequality and social immobility in societies. [ABSTRACT FROM AUTHOR]

Financial markets are exposed to systemic risk (SR), the risk that a major fraction of the system ceases to function, and collapses. It has recently become possible to quantify SR in terms of underlying financial networks where nodes represent financial institutions, and links capture the size and maturity of assets (loans), liabilities and other obligations, such as derivatives. We demonstrate that it is possible to quantify the share of SR that individual liabilities within a financial network contribute to the overall SR. We use empirical data of nationwide interbank liabilities to show that the marginal contribution to overall SR of liabilities for a given size varies by a factor of a thousand. We propose a tax on individual transactions that is proportional to their marginal contribution to overall SR. If a transaction does not increase SR, it is tax-free. With an agent-based model (ABM) (CRISIS macro-financial model), we demonstrate that the proposed ‘Systemic Risk Tax’ (SRT) leads to a self-organized restructuring of financial networks that are practically free of SR. The SRT can be seen as an insurance for the public against costs arising from cascading failure. ABM predictions are shown to be in remarkable agreement with the empirical data and can be used to understand the relation of credit risk and SR. [ABSTRACT FROM AUTHOR]

Physical interactions between particles are the result of the exchange of gauge bosons. Human interactions are mediated by the exchange of messages, goods, money, promises, hostilities, etc. While in the physical world interactions and their associated forces have immediate dynamical consequences (Newton’s laws) the situation is not clear for human interactions. Here we quantify the relative acceleration between humans who interact through the exchange of messages, goods and hostilities in a massive multiplayer online game. For this game we have complete information about all interactions (exchange events) between about 430,000 players, and about their trajectories (movements) in the metric space of the game universe at any point in time. We use this information to derive “interaction potentials" for communication, trade and attacks and show that they are harmonic in nature. Individuals who exchange messages and trade goods generally attract each other and start to separate immediately after exchange events end. The form of the interaction potential for attacks mirrors the usual “hit-and-run" tactics of aggressive players. By measuring interaction intensities as a function of distance, velocity and acceleration, we show that “forces" between players are directly related to the number of exchange events. We find an approximate power-law decay of the likelihood for interactions as a function of distance, which is in accordance with previous real world empirical work. We show that the obtained potentials can be understood with a simple model assuming an exchange-driven force in combination with a distance-dependent exchange rate. [ABSTRACT FROM AUTHOR]

Global Positioning Systems (GPS) as one of the Global Navigation Satellite Systems (GNSS) have been applied in many studies especially focusing on wildlife but there are very few studies using GPS on domesticated animals under extensive conditions combined with extreme relief such as in the Alps. Therefore, the main aim of this study was to test, evaluate and support the development of new tracking systems based on GNSS- and GSM-technology. Furthermore, movement patterns of cattle and the workload of herdsman were analysed for a possible optimization of the management of grazing animals in mountainous areas. Two newly developed prototypes of companies GNSS_L and GNSS_M and two commercially available systems GNSS_H and GNSS_T were tested on several alpine farms (AF) over the pasture season of the year 2012 and 2013. The evaluation of GNSS devices focused on position accuracy, battery life, smartphone applications as well as availability of supportive functions and application of geo-fencing. Also a standardized dynamic accuracy test of a GPS data logger and four different tracking systems was conducted. Movement pattern analyses focused on distances walked by cattle from sequenced GNSS fixes and autocorrelation of recorded information. Parallel to the previous aims the workload management of different alpine farms was analysed to support the evaluation of advantages of using GNSS tracking systems in mountainous areas. Based on the results of a comparison of the tested tracking systems we can conclude that devices GNSS_M and GNSS_T performed better under the alpine conditions compared with GNSS_L and GNSS_H, when GSM (Global System for Mobile Communications) reception was available. The standardized dynamic accuracy test showed significant differences (P≤0.001) among most of the tested GNSS collars and the GPS data logger, except between the prototypes GNSS_L and GNSS_M (P≤0.05). On average 62% of information on the distance walked by cattle was lost when GNSS fix intervals increased from 5 to 20 min. Finally, based on analyses of the workload of herdsmen this study showed potential of using GNSS tracking systems to reduce labour time requirement and workload for farming in mountainous regions. [ABSTRACT FROM AUTHOR]

This study aims to quantify whether age and sex groups in Austrian regions are equally affected by the rise of type 2 diabetes. Population-wide medical claims data was obtained for citizens in Austria aged above 50 year, who received antihyperglycemic treatments or underwent HbA1c monitoring between 2012 and 2017. Diabetes incidence was measured using an epidemiological diabetes progression model accounting for patients who discontinued antihyperglycemic therapy; the erratic group. Out of 746,184 patients, 268,680 (140,960 females) discontinued their treatment and/or monitoring for at least one year. Without adjusting for such erratic patients, incidence rates increase from 2013 to 2017 (females: from 0·5% to 1·1%, males: 0·5% to 1·2%), whereas they decrease in all groups after adjustments (females: − 0·3% to − 0·5%, males: − 0·4% to − 0·5%). Higher mortality was observed in the erratic group compared to patients on continued antihyperglycemic therapy (mean difference 12% and 14% for females and males, respectively). In summary, incidence strongly depends on age, sex and place of residency. One out of three patients with diabetes in Austria discontinued antihyperglycemic treatment or glycemic monitoring for at least one year. This newly identified subgroup raises concern regarding adherence and continuous monitoring of diabetes care and demands further evaluation. [ABSTRACT FROM AUTHOR]

Almost universally, wealth is not distributed uniformly within societies or economies. Even though wealth data have been collected in various forms for centuries, the origins for the observed wealth-disparity and social inequality are not yet fully understood. Especially the impact and connections of human behavior on wealth could so far not be inferred from data. Here we study wealth data from the virtual economy of the massive multiplayer online game (MMOG) Pardus. This data not only contains every player's wealth at every point in time, but also all actions over a timespan of almost a decade. We find that wealth distributions in the virtual world are very similar to those in Western countries. In particular we find an approximate exponential distribution for low wealth levels and a power-law tail for high levels. The Gini index is found to be , which is close to the indices of many Western countries. We find that wealth-increase rates depend on the time when players entered the game. Players that entered the game early on tend to have remarkably higher wealth-increase rates than those who joined later. Studying the players' positions within their social networks, we find that the local position in the trade network is most relevant for wealth. Wealthy people have high in- and out-degrees in the trade network, relatively low nearest-neighbor degrees, and low clustering coefficients. Wealthy players have many mutual friendships and are socially well respected by others, but spend more time on business than on socializing. Wealthy players have few personal enemies, but show animosity towards players that behave as public enemies. We find that players that are not organized within social groups are significantly poorer on average. We observe that “political” status and wealth go hand in hand. [ABSTRACT FROM AUTHOR]

The maximum entropy principle (MEP) is a method for obtaining the most likely distribution functions of observables from statistical systems by maximizing entropy under constraints. The MEP has found hundreds of applications in ergodic and Markovian systems in statistical mechanics, information theory, and statistics. For several decades there has been an ongoing controversy over whether the notion of the maximum entropy principle can be extended in a meaningful way to nonextensive, nonergodic, and complex statistical systems and processes. In this paper we start by reviewing how Boltzmann-Gibbs-Shannon entropy is related to multiplicities of independent random processes. We then show how the relaxation of independence naturally leads to the most general entropies that are compatible with the first three Shannon-Khinchin axioms, the (c,d)-entropies. We demonstrate that the MEP is a perfectly consistent concept for nonergodic and complex statistical systems if their relative entropy can be factored into a generalized multiplicity and a constraint term. The problem of finding such a factorization reduces to finding an appropriate representation of relative entropy in a linear basis. In a particular example we show that path-dependent random processes with memory naturally require specific generalized entropies. The example is to our knowledge the first exact derivation of a generalized entropy from the microscopic properties of a pathdependent random process. [ABSTRACT FROM AUTHOR]

Complex systems are often inherently non-ergodic and non-Markovian and Shannon entropy loses its applicability. Accelerating, path-dependent and aging random walks offer an intuitive picture for non-ergodic and non-Markovian systems. It was shown that the entropy of non-ergodic systems can still be derived from three of the Shannon-Khinchin axioms and by violating the fourth, the so-called composition axiom. The corresponding entropy is of the form Sc,d ~ Σi Г(1+d; 1 - cln pi) and depends on two system-specific scaling exponents, c and d. This entropy contains many recently proposed entropy functionals as special cases, including Shannon and Tsallis entropy. It was shown that this entropy is relevant for a special class of non-Markovian random walks. In this work, we generalize these walks to a much wider class of stochastic systems that can be characterized as "aging" walks. These are systems whose transition rates between states are path- and time-dependent. We show that for particular aging walks, Sc,d is again the correct extensive entropy. Before the central part of the paper, we review the concept of (c; d)-entropy in a self-contained way. [ABSTRACT FROM AUTHOR]

Social networks exhibit scaling laws for several structural characteristics, such as degree distribution, scaling of the attachment kernel and clustering coefficients as a function of node degree. A detailed understanding if and how these scaling laws are inter-related is missing so far, let alone whether they can be understood through a common, dynamical principle. We propose a simple model for stationary network formation and show that the three mentioned scaling relations follow as natural consequences of triadic closure. The validity of the model is tested on multiplex data from a well-studied massive multiplayer online game. We find that the three scaling exponents observed in the multiplex data for the friendship, communication and trading networks can simultaneously be explained by the model. These results suggest that triadic closure could be identified as one of the fundamental dynamical principles in social multiplex network formation. [ABSTRACT FROM AUTHOR]

Based on a unique dataset comprising all 325,000 Austrian patients that were under pharmaceutical treatment for diabetes during 2006 and 2007, we measured the excess risk of developing diabetes triggered by undernourishment in early life. We studied the percentage of all diabetes patients in the total population specifically for each year of birth, from 1917 to 2007. We found a massive excess risk of diabetes in people born during the times of the three major famines and immediately after, which occurred in Austria in the 20th century: 1918-1919, 1938, and 1946-1947. Depending on the region, there was an up to 40% higher chance of having diabetes when born in 1919-1921, compared with 1918 or 1922, where age-specific typical diabetes ratios are observed. The excess risk for diabetes was practically absent in those provinces of Austria that were less affected by the famines. We show that diabetes rates exhibit nontrivial, age-specific sex differences, and correlate with the economic wealth of the region. Our results might be of relevance for establishing higher awareness in the health system for those born in high-risk years, and underline the importance of ensuring sufficient nutrition in prenatal and early stages of life. [ABSTRACT FROM AUTHOR]

Our current view on how protein complexes assemble and disassemble at promoter sites is based on experimental data. For instance this data is provided by biochemical methods (e.g. ChIP-on-chip assays) or GFP-based assays. These two approaches suggest very different characteristics for protein recruitment processes that regulate and initiate gene transcription. Biochemical methods suggest a strictly ordered and consecutive protein recruitment while GFP-based assays draw a picture much closer to chaotic or stochastic recruitment. To understand the reason for these conflicting results, we design a generalized recruitment model (GRM) that allows to simulate all possible scenarios between strictly sequential recruitment and completely probabilistic recruitment. With this model we show that probabilistic, transient binding events that are visible in GFP experiments can not be detected by ChIP experiments. We demonstrate that sequential recruitment processes and probabilistic recruitment processes that contain “shortcuts” exhibit periodic dynamics and are hard to distinguish with standard ChIP measurements. Therefore we propose a simple experimental method that can be used to discriminate sequential from probabilistic recruitment processes. We discuss the limitations of this method. [ABSTRACT FROM AUTHOR]

For statistical systems that violate one of the four Shannon-Khinchin axioms, entropy takes a more general form than the Boltzmann-Gibbs entropy. The framework of superstatistics allows one to for-mulate a maximum entropy principle with these generalized entro-pies, making them useful for understanding distribution functions of non-Markovian or nonergodic complex systems. For such systems where the composability axiom is violated there exist only two ways to implement the maximum entropy principle, one using escort prob-abilities, the other not. The two ways are connected through a dual-ity. Here we show that this duality fixes a unique escort probability, which allows us to derive a complete theory of the generalized log-arithms that naturally arise from the violation of this axiom. We then show how the functional forms of these generalized logarithms are related to the asymptotic scaling behavior of the entropy. [ABSTRACT FROM AUTHOR]

Complex systems - when treated as systems accessible to natural sciences - pose tremendous requirements on data. Usually these requirements obstruct a scientific understanding of social phenomena on scientific grounds. Due to developments in IT, new collective human behavior, new dimensions of data sources are beginning to open up. Here we report on a complete data set of an entire society, consisting of over 350,000 human players of a massive multiplayer online game. All actions of all players over three years are recorded, including communication behavior and social ties. In this work we review the first steps undertaken in analyzing this vast data set, focusing on social dynamics on friend-, enemy- and communication networks. This new data-driven approach to social science allows to study socio-economic behavior of humans and human groups in specific environments with unprecedented precision. We propose two new empirical social laws which relate the network properties of link weight, overlap and betweenness centrality in a nonlinear way, and provide strong quantitative evidence for classical social balance assumptions, the weak ties hypothesis and triadic closure. In our analysis of large-scale multirelational networks we discover systematic deviations between positive and negative tie networks. Exploring such virtual "social laboratories" in the light of complexity science has the potential to lead to the discovery of systemic properties of human societies, with unforeseen impact on managing human-induced crises. [ABSTRACT FROM AUTHOR]

We build a simple model of leveraged asset purchases with margin calls. Investment funds use what is perhaps the most basic financial strategy, called ‘value investing’, i.e. systematically attempting to buy underpriced assets. When funds do not borrow, the price fluctuations of the asset are approximately normally distributed and uncorrelated across time. This changes when the funds are allowed to leverage, i.e. borrow from a bank, which allows them to purchase more assets than their wealth would otherwise permit. During good times, funds that use more leverage have higher profits, increasing their wealth and making them dominant in the market. However, if a downward price fluctuation occurs while one or more funds is fully leveraged, the resulting margin call causes them to sell into an already falling market, amplifying the downward price movement. If the funds hold large positions in the asset, this can cause substantial losses. This in turn leads to clustered volatility: before a crash, when the value funds are dominant, they damp volatility, and after the crash, when they suffer severe losses, volatility is high. This leads to power-law tails, which are both due to the leverage-induced crashes and due to the clustered volatility induced by the wealth dynamics. This is in contrast to previous explanations of fat tails and clustered volatility, which depended on ‘irrational behavior’, such as trend following. A standard (supposedly more sophisticated) risk control policy in which individual banks base leverage limits on volatility causes leverage to rise during periods of low volatility, and to contract more quickly when volatility becomes high, making these extreme fluctuations even worse. [ABSTRACT FROM AUTHOR]

We study behavioral action sequences of players in a massive multiplayer online game. In their virtual life players use eight basic actions which allow them to interact with each other. These actions are communication, trade, establishing or breaking friendships and enmities, attack, and punishment. We measure the probabilities for these actions conditional on previous taken and received actions and find a dramatic increase of negative behavior immediately after receiving negative actions. Similarly, positive behavior is intensified by receiving positive actions. We observe a tendency towards antipersistence in communication sequences. Classifying actions as positive (good) and negative (bad) allows us to define binary 'world lines' of lives of individuals. Positive and negative actions are persistent and occur in clusters, indicated by large scaling exponents α∼0:87 of the mean square displacement of the world lines. For all eight action types we find strong signs for high levels of repetitiveness, especially for negative actions. We partition behavioral sequences into segments of length n (behavioral 'words' and 'motifs') and study their statistical properties. We find two approximate power laws in the word ranking distribution, one with an exponent of κ∼-1 for the ranks up to 100, and another with a lower exponent for higher ranks. The Shannon n-tuple redundancy yields large values and increases in terms of word length, further underscoring the non-trivial statistical properties of behavioral sequences. On the collective, societal level the timeseries of particular actions per day can be understood by a simple mean-reverting log-normal model. [ABSTRACT FROM AUTHOR]

Superstatistics describes statistical systems that behave like superpositions of different inverse temperatures β. so that the probability distribution is p(ϵi)∞ ∫0∞f(β)e -βϵidβ, where the "kernel" f(β) is nonnegative and normalized [∫f(β)dβ= 1]. We discuss the relation between this distribution and the generalized entropic form S = Σis(ρi). The first three Shannon-Khinchin axioms are assumed to hold. It then turns out that for a given distribution there are two different ways to construct the entropy. One approach uses escort probabilities and the other does not; the question of which to use must be decided empirically. The two approaches are related by a duality. The thermodynamic properties of the system can be quite different for the two approaches. In that connection, we present the transformation laws for the superstatistical distributions under macroscopic state changes. The transformation group is the Euclidean group in one dimension. [ABSTRACT FROM AUTHOR]

It has often been noted that most of the major world religions espouse a version of the "golden rule." In this paper we consider the cultural evolution of such a doctrine, where the responsibility to act altruistically towards others applies universally, not just to other members of the same society. Using a game-theoretical model, we find that societies over a critical size benefit from adopting a mode of universal altruism. These "golden-rule societies" must justify violence against outsiders by formulating exceptions to this universal rule. For smaller groups, it is more efficient to adopt a rule that simply requires cooperation within the group. Data from the ethnographic record supports a correlation between group size and societal norms of universal cooperation. Our results provide an explanation for the prevalence of the golden rule among contemporary cultures. We find that universal altruism arises due to cultural selection for greater ingroup bias, and is a natural byproduct of the emergence of large-scale societies. [ABSTRACT FROM AUTHOR]

Abstract: Traditionally evolution is seen as a process where from a pool of possible variations of a population (e.g. biological species or industrial goods) a few variations get selected which survive and proliferate, whereas the others vanish. Survival probabilities and proliferation rates are typically associated with the ‘fitness’ of particular variations. In this paper we argue that the notion of fitness is an a posteriori concept, in the sense that one can assign higher fitness to species that survive but one can generally not derive or predict fitness per se. Proliferation rates can be measured, whereas fitness landscapes, i.e. the inter-dependence of proliferation rates, cannot. For this reason we think that in a physical theory of evolution such notions should be avoided. In this spirit, here we propose a random matrix model of evolution where selection mechanisms are encoded in interaction matrices of species, thereby extending the previous work of ours by a control parameter describing suppressors in the system. We are able to recover some key facts of evolution dynamics endogenously, such as punctuated equilibrium, i.e. the existence of intrinsic large extinction events, and, at the same time, periods of dramatic diversification, as known e.g. from the fossil record. Further, we comment on two fundamental technical problems of a ‘physics of evolution’, the non-closedness of its phase space and the problem of co-evolving boundary conditions, apparent in all systems subject to evolution. [Copyright &y& Elsevier]

Abstract: In statistical physics lately a specific kind of average, called the q-expectation value, has been extensively used in the context of q-generalized statistics dealing with distributions following power laws. In this context q-expectation value appear naturally. Since it was recently shown that this non-linear functional is instable, using a very strong notion of stability, it is therefore of high interest to know sufficient conditions for when the results of q-expectations are robust under small variations of the underlying distribution function and when not. We show that reasonable restrictions on the domain of admissible probability distributions restore uniform continuity for the q-expectation. Bounds on the size of admissible variations can be given. The practical usefulness of the theorems for estimating the robustness of the q-expectation value with respect to small variations is discussed. [Copyright &y& Elsevier]

Abstract: We propose a model for evolution aiming to reproduce statistical features of fossil data, in particular the distributions of extinction events, the distribution of species per genus and the distribution of lifetimes, all of which are known to be of power-law type. The model incorporates both species–species interactions and ancestral relationships. The main novelty of this work is to show the feasibility of k-core percolation as a selection mechanism. We give theoretical predictions for the observable distributions, confirm their validity by computer simulation and compare with fossil data. A key feature of the proposed model is a co-evolving fitness landscape determined by the topology of the underlying species interactions, ecological niches emerge naturally. The predicted distributions are independent of the rate of speciation, i.e. whether one adopts an gradualist or punctuated view of evolution. [Copyright &y& Elsevier]

We derive the exact form of the eigenvalue spectra of correlation matrices derived from a set of time-shifted, finite Brownian random walks (time-series). These matrices can be seen as real, asymmetric random matrices where the time-shift superimposes some structure. We demonstrate that, for large matrices, the associated eigenvalue spectrum is circular symmetric in the complex plane. This fact allows us to exactly compute the eigenvalue density via an inverse Abel-transform of the density of the symmetrized problem. We demonstrate the validity of this approach numerically. Theoretical findings are then compared with eigenvalue densities obtained from actual high-frequency (5 min) data of the S&P 500 and the observed deviations are discussed. We identify various non-trivial, non-random patterns and find asymmetric dependencies associated with eigenvalues departing strongly from the Gaussian prediction in the imaginary part. For the same time-series, with the market contribution removed, we observe strong clustering of stocks into causal sectors. We finally comment on the stability of the observed patterns. [ABSTRACT FROM AUTHOR]

We derive the exact form of the eigenvalue spectrum of correlation matrices obtained from a set of N time-shifted, iid Gaussian time-series of length T . These matrices are random, real and asymmetric matrices with a superimposed structure due to the time-lag. We demonstrate that the associated (complex) eigenvalue spectrum is circular symmetric for large matrices (lim N → ∞). This fact allows to exactly compute the eigenvalue density via the inverse Abel-transform of the density of the symmetrized problem. The validity of the approach is demonstrated by comparison to numerical realizations of random time-series. As an example, spectra of correlation matrices from time-lagged financial data are presented. [ABSTRACT FROM AUTHOR]

Abstract: We generalize the usual exponential Boltzmann factor to any reasonable and potentially observable distribution function, . By defining generalized logarithms as inverses of these distribution functions, we are led to a generalization of the classical Boltzmann–Gibbs entropy () to the expression , which contains the classical entropy as a special case. We show that this is the unique modification of entropy which is compatible with the maximum entropy principle for arbitrary, non-exponential distribution functions. We demonstrate that this entropy has two important features: first, it describes the correct thermodynamic relations of the system, and second, the observed distributions are straightforward solutions to the Jaynes maximum entropy principle with the ordinary (not escort!) constraints. Tsallis entropy is recovered as a further special case. [Copyright &y& Elsevier]

Abstract: By adopting an ensemble interpretation of non-growing rewiring networks, network theory can be reduced to a counting problem of possible network states and an identification of their associated probabilities. We present two scenarios of how different rewirement schemes can be used to control the state probabilities of the system. In particular, we review how by generalizing the linking rules of random graphs, in combination with superstatistics and quantum mechanical concepts, one can establish an exact relation between the degree distribution of any given network and the nodes’ linking probability distributions. In a second approach, we control state probabilities by a network Hamiltonian, whose characteristics are motivated by biological and socio-economical statistical systems. We demonstrate that a thermodynamics of networks becomes a fully consistent concept, allowing to study e.g. ‘phase transitions’ and computing entropies through thermodynamic relations. [Copyright &y& Elsevier]

The Erdös–Rényi classical random graph is characterized by a fixed linking probability for all pairs of vertices. Here, this concept is generalized by drawing the linking probability from a certain distribution. Such a procedure is found to lead to a static complex network with an arbitrary connectivity distribution. In particular, a scale-free network with the hierarchical organization is constructed without assuming any knowledge about the global linking structure, in contrast to the preferential attachment rule for a growing network. The hierarchical and mixing properties of the static scale-free network thus constructed are studied. The present approach establishes a bridge between a scalar characterization of individual vertices and topology of an emerging complex network. The result may offer a clue for understanding the origin of a few abundance of connectivity distributions in a wide variety of static real-world networks. [ABSTRACT FROM AUTHOR]

Abstract: We show that within classical statistical mechanics, without taking the thermodynamic limit, the most general Boltzmann factor for the canonical ensemble is a q-exponential function. The only assumption here is that microcanonical distributions have to be separated from the total system energy, which is the prerequisite for any sensible measurement. We derive that all separable distributions are parametrized by a mathematical separation constant Q, which can be related to the non-extensivity q-parameter in Tsallis distributions. We further demonstrate that nature fixes the separation constant Q to 1 for large dimensionality of Gibbs -phase space. Our results will be relevant for systems with a low-dimensional -space, for example nanosystems, comprised of a small number of particles, or for systems with a dimensionally collapsed phase space, which might be the case for a large class of complex systems. [Copyright &y& Elsevier]

Abstract: Einstein''s theory of Brownian motion is revisited in order to formulate a generalized kinetic theory of anomalous diffusion. It is shown that if the assumptions of analyticity and the existence of the second moment of the displacement distribution are relaxed, the fractional derivative naturally appears in the diffusion equation. This is the first demonstration of the physical origin of the fractional derivative, in marked contrast to the usual phenomenological introduction of it. It is also examined if Einstein''s approach can be generalized to nonlinear kinetic theory to derive a generalization of the porous-medium-type equation by the appropriate use of the escort distribution. [Copyright &y& Elsevier]

Abstract: We show that within classical statistical mechanics it is possible to naturally derive power-law distributions which are of Tsallis type. The only assumption is that microcanonical distributions have to be separable from of the total system energy, which is reasonable for any sensible measurement. We demonstrate that all separable distributions are parametrized by a separation constant Q which is one to one related to the q-parameter in Tsallis distributions. The power laws obtained are formally equivalent to those obtained by maximizing the Tsallis entropy under q constraints. We further ask why nature fixes the separation constant Q to 1 in so many cases leading to standard thermodynamics. We answer this with an explicit example where it is possible to relate Q to system size and interaction parameters, characterizing the physical system. We argue that these results might be helpful to explain the ubiquity of Tsallis distributions in nature. [Copyright &y& Elsevier]

Abstract: Using a recently proposed model Physica A 332 (2004) 566 of information transport on complex networks we study the role of network substrates on the statistics of queuing times and correlations in traffic streams. When navigation with an enlarged information horizon is applied the waiting time distribution on structured networks has a power-law tail which can be parametrized by , where the respective value of the non-extensivity parameter q increases systematically with increasing graph complexity. The corresponding distribution on the small-world graph appears to be a stretched-exponential function that cannot be classified within the same scheme. We further demonstrate by looking at the anti-persistence in flow time-series and the transit time distributions, how traffic efficiency increases with an extended information horizon. A horizon of two layers approaches the critical horizon on the correlated cyclic scale-free graph, suggesting that the mechanisms of signaling over two-to-three layers ensure efficient transport processes on networks with this organizational complexity. [Copyright &y& Elsevier]

We study diffusion of information packets on several classes of structured networks. Packets diffuse from a randomly chosen node to a specified destination in the network. As local transport rules we consider random diffusion and an improved local search method. Numerical simulations are performed in the regime of stationary workloads away from the jamming transition. We find that graph topology determines the properties of diffusion in a universal way, which is reflected by power laws in the transit time and velocity distributions of packets. With the use of multifractal scaling analysis and arguments of non-extensive statistics we find evidence that these power-laws are compatible with super-diffusive traffic on large networks. We are able to quantify the role of network topology on overall transport efficiency. Further, we demonstrate the implications of improved transport rules and discuss the importance of matching (global) topology with (local) transport rules for the optimal function of networks. The presented model should be applicable to a wide range of phenomena ranging from Internet traffic to protein transport along the cytoskeleton in biological cells. [Copyright &y& Elsevier]

We study the temporal variability of human brain activity in timeseries of functional magnetic resonance imaging (fMRI) data. We find that these timeseries show scaling behavior which is quantified by computing various scaling exponents. We demonstrate that mentally active zones are one-to-one related to large exponents, or equivalently, to highly temporally correlated processes, while mentally inactive zones are well described by a simple random walk model. Activation maps of scaling exponents are presented and compared to standard results in fMRI. In contrast to standard model-based activation analyses no prior knowledge of the experimental stimulation paradigm has to be assumed for extracting activation patterns from fMRI timeseries. We mention consequences of persistence in fMRI timeseries for standard statistical analysis. [Copyright &y& Elsevier]

In the context of understanding the nature of the risk transformation process of the financial system we propose an iterative risk-trading game between several agents who build their trading strategies based on a general utility setting. The game is studied numerically for different network topologies. Consequences of topology are shown for the wealth time-series of agents, for the safety and efficiency of various types of network. The proposed set-up allows an analysis of the effects of different approaches to banking regulation as currently suggested by the Basle Committee of Banking Supervision. We find a phase-transition-like phenomenon, where the Basle parameter plays the role of temperature and system safety serves as the order parameter. This result suggests the existence of an optimal regulation parameter. As a consequence, a tightening of the current regulatory framework does not necessarily lead to an improvement of the safety of the banking system. Moreover, we show that banking systems with local risk-sharing cooperations have higher global default rates than systems with low cyclicality. [ABSTRACT FROM AUTHOR]

We propose a model for cell migration where epithelial cells are able to detect trajectories of other cells and try to follow them. As cells move along in 2D cell culture, they mark their paths by loosing tiny parts of cytoplasm. Any cell moving on a surface where other cells have moved before faces a network of cell trajectories, which it tries to restrict its motion onto. With the Tsallis modification of classical thermodynamics one can solve the relevant Fokker–Planck like equation and obtain experimentally testable distribution functions. We compare the model to experimental data of normal mammary epithelial cells and cells which have been genetically manipulated to change their cell–cell interaction. [Copyright &y& Elsevier]

Human posture is the result of a complex control system. The joint output of several physiological — most likely nonlinearly interacting — processes leads to constant correctional movements which enable humans to stand upright. These correctional body movements reflect features of the underlying control mechanisms and have recently been shown to be multifractal processes. We analyze the movements of healthy quiet standing persons by means of wavelet-based multifractal spectra. We show that the functional form of these spectra depends on the mode of balance control. We compare the findings from a group of healthy persons to a group of patients suffering from balance disorders. As the main result we find that if balance control inputs, such as visual cues or tactile information are reduced, the dominant fractal exponent becomes smaller and the range of fractal exponents strongly narrows. We suggest to use a set of multifractal spectrum parameters as a "measure of complexity. [ABSTRACT FROM AUTHOR]