arXiv subjects

Stefan Thurner

Publications and source records attributed to Stefan Thurner.

At least 127 records · Page 7Linked to original sources

arXiv2011

Experimental characterization of a broadband transmission-line cloak in free space

The cloaking efficiency of a finite-size cylindrical transmission-line cloak operating in the X-band is verified with bistatic free space measurements. The cloak is designed and optimized with numerical full-wave simulations. The reduction of the total scattering width of a metal object, enabled by the cloak, is clearly observed from the bistatic free space measurements. The numerical and experimental results are compared resulting in good agreement with each other.

physics.class-ph↗

arXiv2011

Emergence of good conduct, scaling and Zipf laws in human behavioral sequences in an online world

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 anti-persistence 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 alpha~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 kappa-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.

physics.soc-ph↗

arXiv2011

What do generalized entropies look like? An axiomatic approach for complex, non-ergodic systems

Shannon and Khinchin showed that assuming four information theoretic axioms the entropy must be of Boltzmann-Gibbs type, $S=-\sum_i p_i \log p_i$. Here we note that in physical systems one of these axioms may be violated. For non-ergodic systems the so called separation axiom (Shannon-Khinchin axiom 4) will in general not be valid. We show that when this axiom is violated the entropy takes a more general form, $S_{c,d}\propto \sum_i ^W Γ(d+1, 1- c \log p_i)$, where $c$ and $d$ are scaling exponents and $Γ(a,b)$ is the incomplete gamma function. The exponents $(c,d)$ define equivalence classes for all interacting and non interacting systems and unambiguously characterize any statistical system in its thermodynamic limit. The proof is possible because of two newly discovered scaling laws which any entropic form has to fulfill, if the first three Shannon-Khinchin axioms hold. $(c,d)$ can be used to define equivalence classes of statistical systems. A series of known entropies can be classified in terms of these equivalence classes. We show that the corresponding distribution functions are special forms of Lambert-${\cal W}$ exponentials containing -- as special cases -- Boltzmann, stretched exponential and Tsallis distributions (power-laws). In the derivation we assume trace form entropies, $S=\sum_i g(p_i)$, with $g$ some function, however more general entropic forms can be classified along the same scaling analysis.

cond-mat.stat-mech↗

arXiv2011

When do generalized entropies apply? How phase space volume determines entropy

We show how the dependence of phase space volume $Ω(N)$ of a classical system on its size $N$ uniquely determines its extensive entropy. We give a concise criterion when this entropy is not of Boltzmann-Gibbs type but has to assume a {\em generalized} (non-additive) form. We show that generalized entropies can only exist when the dynamically (statistically) relevant fraction of degrees of freedom in the system vanishes in the thermodynamic limit. These are systems where the bulk of the degrees of freedom is frozen and is practically statistically inactive. Systems governed by generalized entropies are therefore systems whose phase space volume effectively collapses to a lower-dimensional 'surface'. We explicitly illustrate the situation for binomial processes and argue that generalized entropies could be relevant for self organized critical systems such as sand piles, for spin systems which form meta-structures such as vortices, domains, instantons, etc., and for problems associated with anomalous diffusion.

cond-mat.stat-mech↗

arXiv2011

Generalized entropies and the transformation group of superstatistics

Superstatistics describes statistical systems that behave like superpositions of different inverse temperatures $β$, so that the probability distribution is $p(ε_i) \propto \int_{0}^{\infty} f(β) e^{-βε_i}dβ$, where the `kernel' $f(β)$ is nonnegative and normalized ($\int f(β)d β=1$). We discuss the relation between this distribution and the generalized entropic form $S=\sum_i s(p_i)$. 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.

cond-mat.stat-mech↗

arXiv2011

The blogosphere as an excitable social medium: Richter's and Omori's Law in media coverage

We study the dynamics of public media attention by monitoring the content of online blogs. Social and media events can be traced by the propagation of word frequencies of related keywords. Media events are classified as exogenous - where blogging activity is triggered by an external news item - or endogenous where word frequencies build up within a blogging community without external influences. We show that word occurrences show statistical similarities to earthquakes. The size distribution of media events follows a Gutenberg-Richter law, the dynamics of media attention before and after the media event follows Omori's law. We present further empirical evidence that for media events of endogenous origin the overall public reception of the event is correlated with the behavior of word frequencies at the beginning of the event, and is to a certain degree predictable. These results may imply that the process of opinion formation in a human society might be related to effects known from excitable media.

physics.soc-ph↗

arXiv2010

Peer-review in a world with rational scientists: Toward selection of the average

One of the virtues of peer review is that it provides a self-regulating selection mechanism for scientific work, papers and projects. Peer review as a selection mechanism is hard to evaluate in terms of its efficiency. Serious efforts to understand its strengths and weaknesses have not yet lead to clear answers. In theory peer review works if the involved parties (editors and referees) conform to a set of requirements, such as love for high quality science, objectiveness, and absence of biases, nepotism, friend and clique networks, selfishness, etc. If these requirements are violated, what is the effect on the selection of high quality work? We study this question with a simple agent based model. In particular we are interested in the effects of rational referees, who might not have any incentive to see high quality work other than their own published or promoted. We find that a small fraction of incorrect (selfish or rational) referees can drastically reduce the quality of the published (accepted) scientific standard. We quantify the fraction for which peer review will no longer select better than pure chance. Decline of quality of accepted scientific work is shown as a function of the fraction of rational and unqualified referees. We show how a simple quality-increasing policy of e.g. a journal can lead to a loss in overall scientific quality, and how mutual support-networks of authors and referees deteriorate the system.

physics.soc-ph↗

arXiv2010

Multirelational Organization of Large-scale Social Networks in an Online World

The capacity to collect fingerprints of individuals in online media has revolutionized the way researchers explore human society. Social systems can be seen as a non-linear superposition of a multitude of complex social networks, where nodes represent individuals and links capture a variety of different social relations. Much emphasis has been put on the network topology of social interactions, however, the multi-dimensional nature of these interactions has largely been ignored in empirical studies, mostly because of lack of data. Here, for the first time, we analyze a complete, multi-relational, large social network of a society consisting of the 300,000 odd players of a massive multiplayer online game. We extract networks of six different types of one-to-one interactions between the players. Three of them carry a positive connotation (friendship, communication, trade), three a negative (enmity, armed aggression, punishment). We first analyze these types of networks as separate entities and find that negative interactions differ from positive interactions by their lower reciprocity, weaker clustering and fatter-tail degree distribution. We then proceed to explore how the inter-dependence of different network types determines the organization of the social system. In particular we study correlations and overlap between different types of links and demonstrate the tendency of individuals to play different roles in different networks. As a demonstration of the power of the approach we present the first empirical large-scale verification of the long-standing structural balance theory, by focusing on the specific multiplex network of friendship and enmity relations.

physics.soc-ph↗

arXiv2010

A comprehensive classification of complex statistical systems and an ab-initio derivation of their entropy and distribution functions

To characterize strongly interacting statistical systems within a thermodynamical framework - complex systems in particular - it might be necessary to introduce generalized entropies, $S_g$. A series of such entropies have been proposed in the past, mainly to accommodate important empirical distribution functions to a maximum ignorance principle. Until now the understanding of the fundamental origin of these entropies and its deeper relations to complex systems is limited. Here we explore this questions from first principles. We start by observing that the 4th Khinchin axiom (separability axiom) is violated by strongly interacting systems in general and ask about the consequences of violating the 4th axiom while assuming the first three Khinchin axioms (K1-K3) to hold and $S_g=\sum_ig(p_i)$. We prove by simple scaling arguments that under these requirements {\em each} statistical system is uniquely characterized by a distinct pair of scaling exponents $(c,d)$ in the large size limit. The exponents define equivalence classes for all interacting and non interacting systems. This allows to derive a unique entropy, $S_{c,d}\propto \sum_i Γ(d+1, 1- c \ln p_i)$, which covers all entropies which respect K1-K3 and can be written as $S_g=\sum_ig(p_i)$. Known entropies can now be classified within these equivalence classes. The corresponding distribution functions are special forms of Lambert-$W$ exponentials containing as special cases Boltzmann, stretched exponential and Tsallis distributions (power-laws) -- all widely abundant in nature. This is, to our knowledge, the first {\em ab initio} justification for the existence of generalized entropies. Even though here we assume $S_g=\sum_ig(p_i)$, we show that more general entropic forms can be classified along the same lines.

physics.class-ph↗

arXiv2010

Living on the edge of chaos: minimally nonlinear models of genetic regulatory dynamics

Linearized catalytic reaction equations modeling e.g. the dynamics of genetic regulatory networks under the constraint that expression levels, i.e. molecular concentrations of nucleic material are positive, exhibit nontrivial dynamical properties, which depend on the average connectivity of the reaction network. In these systems the inflation of the edge of chaos and multi-stability have been demonstrated to exist. The positivity constraint introduces a nonlinearity which makes chaotic dynamics possible. Despite the simplicity of such minimally nonlinear systems, their basic properties allow to understand fundamental dynamical properties of complex biological reaction networks. We analyze the Lyapunov spectrum, determine the probability to find stationary oscillating solutions, demonstrate the effect of the nonlinearity on the effective in- and out-degree of the active interaction network and study how the frequency distributions of oscillatory modes of such system depend on the average connectivity.

cond-mat.dis-nn↗

arXiv2010

Leverage Causes Fat Tails and Clustered Volatility

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 normally distributed and uncorrelated across time. All this changes when the funds are allowed to leverage, i.e. borrow from a bank, to purchase more assets than their wealth would otherwise permit. During good times competition drives investors to funds that use more leverage, because they have higher profits. As leverage increases price fluctuations become heavy tailed and display clustered volatility, similar to what is observed in real markets. Previous explanations of fat tails and clustered volatility depended on "irrational behavior", such as trend following. Here instead this comes from the fact that leverage limits cause funds to sell into a falling market: A prudent bank makes itself locally safer by putting a limit to leverage, so when a fund exceeds its leverage limit, it must partially repay its loan by selling the asset. Unfortunately this sometimes happens to all the funds simultaneously when the price is already falling. The resulting nonlinear feedback amplifies large downward price movements. At the extreme this causes crashes, but the effect is seen at every time scale, producing a power law of price disturbances. 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 gets high, making these extreme fluctuations even worse.

q-fin.ST↗

arXiv2009

Evolutionary dynamics from a variational principle

We demonstrate with a thought experiment that fitness-based population dynamical approaches to evolution are not able to make quantitative, falsifiable predictions about the long-term behavior of evolutionary systems. A key characteristic of evolutionary systems is the ongoing endogenous production of new species. These novel entities change the conditions for already existing species. Even {\em Darwin's Demon}, a hypothetical entity with exact knowledge of the abundance of all species and their fitness functions at a given time, could not pre-state the impact of these novelties on established populations. We argue that fitness is always {\it a posteriori} knowledge -- it measures but does not explain why a species has reproductive success or not. To overcome these conceptual limitations, a variational principle is proposed in a spin-model-like setup of evolutionary systems. We derive a functional which is minimized under the most general evolutionary formulation of a dynamical system, i.e. evolutionary trajectories causally emerge as a minimization of a functional. This functional allows the derivation of analytic solutions of the asymptotic diversity for stochastic evolutionary systems within a mean-field approximation. We test these approximations by numerical simulations of the corresponding model and find good agreement in the position of phase transitions in diversity curves. The model is further able to reproduce stylized facts of timeseries from several man-made and natural evolutionary systems. Light will be thrown on how species and their fitness landscapes dynamically co-evolve.

q-bio.PE↗

arXiv2009

Measuring social dynamics in a massive multiplayer online game

Quantification of human group-behavior has so far defied an empirical, falsifiable approach. This is due to tremendous difficulties in data acquisition of social systems. Massive multiplayer online games (MMOG) provide a fascinating new way of observing hundreds of thousands of simultaneously socially interacting individuals engaged in virtual economic activities. We have compiled a data set consisting of practically all actions of all players over a period of three years from a MMOG played by 300,000 people. This large-scale data set of a socio-economic unit contains all social and economic data from a single and coherent source. Players have to generate a virtual income through economic activities to `survive' and are typically engaged in a multitude of social activities offered within the game. Our analysis of high-frequency log files focuses on three types of social networks, and tests a series of social-dynamics hypotheses. In particular we study the structure and dynamics of friend-, enemy- and communication networks. We find striking differences in topological structure between positive (friend) and negative (enemy) tie networks. All networks confirm the recently observed phenomenon of network densification. We propose two approximate social laws in communication networks, the first expressing betweenness centrality as the inverse square of the overlap, the second relating communication strength to the cube of the overlap. These empirical laws provide strong quantitative evidence for the Weak ties hypothesis of Granovetter. Further, the analysis of triad significance profiles validates well-established assertions from social balance theory. We find overrepresentation (underrepresentation) of complete (incomplete) triads in networks of positive ties, and vice versa for networks of negative ties...

physics.soc-ph↗

arXiv2009

Schumpeterian economic dynamics as a quantifiable minimum model of evolution

We propose a simple quantitative model of Schumpeterian economic dynamics. New goods and services are endogenously produced through combinations of existing goods. As soon as new goods enter the market they may compete against already existing goods, in other words new products can have destructive effects on existing goods. As a result of this competition mechanism existing goods may be driven out from the market - often causing cascades of secondary defects (Schumpeterian gales of destruction). The model leads to a generic dynamics characterized by phases of relative economic stability followed by phases of massive restructuring of markets - which could be interpreted as Schumpeterian business `cycles'. Model timeseries of product diversity and productivity reproduce several stylized facts of economics timeseries on long timescales such as GDP or business failures, including non-Gaussian fat tailed distributions, volatility clustering etc. The model is phrased in an open, non-equilibrium setup which can be understood as a self organized critical system. Its diversity dynamics can be understood by the time-varying topology of the active production networks.

physics.soc-ph↗

arXiv2009

Limit distributions of scale-invariant probabilistic models of correlated random variables with the q-Gaussian as an explicit example

Extremization of the Boltzmann-Gibbs (BG) entropy under appropriate norm and width constraints yields the Gaussian distribution. Also, the basic solutions of the standard Fokker-Planck (FP) equation (related to the Langevin equation with additive noise), as well as the Central Limit Theorem attractors, are Gaussians. The simplest stochastic model with such features is N to infinity independent binary random variables, as first proved by de Moivre and Laplace. What happens for strongly correlated random variables? Such correlations are often present in physical situations as e.g. systems with long range interactions or memory. Frequently q-Gaussians become observed. This is typically so if the Langevin equation includes multiplicative noise, or the FP equation to be nonlinear. Scale-invariance, i.e. exchangeable binary stochastic processes, allow a systematical analysis of the relation between correlations and non-Gaussian distributions. In particular, a generalized stochastic model yielding q-Gaussians for all q (including q>1) was missing. This is achieved here by using the Laplace-de Finetti representation theorem, which embodies strict scale-invariance of interchangeable random variables. We demonstrate that strict scale invariance together with q-Gaussianity mandates the associated extensive entropy to be BG.

cond-mat.stat-mech↗

arXiv2008

On the robustness of q-expectation values and Renyi entropy

We study the robustness of functionals of probability distributions such as the Rényi and nonadditive S_q entropies, as well as the q-expectation values under small variations of the distributions. We focus on three important types of distribution functions, namely (i) continuous bounded (ii) discrete with finite number of states, and (iii) discrete with infinite number of states. The physical concept of robustness is contrasted with the mathematically stronger condition of stability and Lesche-stability for functionals. We explicitly demonstrate that, in the case of continuous distributions, once unbounded distributions and those leading to negative entropy are excluded, both Renyi and nonadditive S_q entropies as well as the q-expectation values are robust. For the discrete finite case, the Renyi and nonadditive S_q entropies and the q-expectation values are robust. For the infinite discrete case, where both Renyi entropy and q-expectations are known to violate Lesche-stability and stability respectively, we show that one can nevertheless state conditions which guarantee physical robustness.

cond-mat.stat-mech↗

arXiv2008

Stability criteria for q-expectation values

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 values appear naturally. After it has been recently shown that this non-linear functional is instable, under 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. 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.

cond-mat.stat-mech↗

arXiv2008

Socio-economical dynamics as a solvable spin system on co-evolving networks

We consider social systems in which agents are not only characterized by their states but also have the freedom to choose their interaction partners to maximize their utility. We map such systems onto an Ising model in which spins are dynamically coupled by links in a dynamical network. In this model there are two dynamical quantities which arrange towards a minimum energy state in the canonical framework: the spins, s_i, and the adjacency matrix elements, c_{ij}. The model is exactly solvable because microcanonical partition functions reduce to products of binomial factors as a direct consequence of the c_{ij} minimizing energy. We solve the system for finite sizes and for the two possible thermodynamic limits and discuss the phase diagrams.

cond-mat.stat-mech↗