arXiv subjects

Rudolf Hanel

Publications and source records attributed to Rudolf Hanel.

67 records · Page 4Linked to original sources

arXiv2008

To how many politicians should government be left?

The quality of governance of institutions, corporations and countries depends on the ability of efficient decision making within the respective boards or cabinets. Opinion formation processes within groups are size dependent. It is often argued - as now e.g. in the discussion of the future size of the European Commission - that decision making bodies of a size beyond 20 become strongly inefficient. We report empirical evidence that the performance of national governments declines with increasing membership and undergoes a qualitative change in behavior at a particular group size. We use recent UNDP, World Bank and CIA data on overall government efficacy, i.e. stability, the quality of policy formulation as well as human development indices of individual countries and relate it to the country's cabinet size. We are able to understand our findings through a simple physical model of opinion dynamics in groups.

physics.soc-ph↗

arXiv2007

The window at the edge of chaos in a simple model of gene interaction networks

As a model for gene and protein interactions we study a set for molecular catalytic reactions. The model is based on experimentally motivated interaction network topologies, and is designed to capture some key statistics of gene expression statistics. We impose a non-linearity to the system by a boundary condition which guarantees non-negative concentrations of chemical concentrations and study the system stability quantified by maximum Lyapunov exponents. We find that the non-negativity constraint leads to a drastic inflation of those regions in parameter space where the Lyapunov exponent exactly vanishes. We explain the finding as a self-organized critical phenomenon. The robustness of this finding with respect to different network topologies and the role of intrinsic molecular- and external noise is discussed. We argue that systems with inflated 'edges of chaos' could be much more easily favored by natural selection than systems where the Lyapunov exponent vanishes only on a parameter set of measure zero.

q-bio.MN↗

arXiv2007

Studies in the physics of evolution: creation, formation, destruction

The concept of (auto)catalytic systems has become a cornerstone in understanding evolutionary processes in various fields. The common ground is the observation that for the production of new species/goods/ideas/elements etc. the pre-existence of specific other elements is a necessary condition. In previous work some of us showed that the dynamics of the catalytic network equation can be understood in terms of topological recurrence relations paving a path towards the analytic tractability of notoriously high dimensional evolution equations. We apply this philosophy to studies in socio-physics, bio-diversity and massive events of creation and destruction in technological and biological networks. Cascading events, triggered by small exogenous fluctuations, lead to dynamics strongly resembling the qualitative picture of Schumpeterian economic evolution. Further we show that this new methodology allows to mathematically treat a variant of the threshold voter-model of opinion formation on networks. For fixed topology we find distinct phases of mixed opinions and consensus.

q-bio.PE↗

arXiv2007

Entropies for complex systems: generalized-generalized entropies

Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann) we demonstrate how the corresponding entropy has to look like, given the form of the corresponding distribution functions. By two natural assumptions that (i) the maximum entropy principle should hold and that (ii) entropy should describe the correct thermodynamics of a system (which produces non-Boltzmann distributions) the existence of a class of fully consistent entropies can be deduced. Classical Boltzmann-Gibbs entropy is recovered as a special case for the observed distribution being the exponential, Tsallis entropy is the special case for q-exponential observations.

cond-mat.stat-mech↗

arXiv2007

Solution of the Unanimity Rule on exponential, uniform and scalefree networks: A simple model for biodiversity collapse in foodwebs

We solve the Unanimity Rule on networks with exponential, uniform and scalefree degree distributions. In particular we arrive at equations relating the asymptotic number of nodes in one of two states to the initial fraction of nodes in this state. The solutions for exponential and uniform networks are exact, the approximation for the scalefree case is in perfect agreement with simulation results. We use these solutions to provide a theoretical understanding for experimental data on biodiversity loss in foodwebs, which is available for the three network types discussed. The model allows in principle to estimate the critical value of species that have to be removed from the system to induce its complete collapse.

physics.bio-ph↗

arXiv2007

Towards a physics of evolution: Existence of gales of creative deconstruction in evolving technological networks

Systems evolving according to the standard concept of biological or technological evolution are often described by catalytic evolution equations. We study the structure of these equations and find a deep relationship to classical thermodynamics. In particular we can demonstrate the existence of several distinct phases of evolutionary dynamics: a phase of fast growing diversity, one of stationary, finite diversity, and one of rapidly decaying diversity. While the first two phases have been subject to previous work, here we focus on the destructive aspects - in particular the phase diagram - of evolutionary dynamics. We further propose a dynamical model of diversity which captures spontaneous creation and destruction processes fully respecting the phase diagrams of evolutionary systems. The emergent timeseries show a Zipf law in the diversity dynamics, which is e.g. observable in actual economical data, e.g. in firm bankruptcy data. We believe the present model is a way to cast the famous qualitative picture of Schumpeterian economic evolution, into a quantifiable and testable framework.

physics.soc-ph↗

arXiv2006

Unanimity Rule on networks

We introduce a model for innovation-, evolution- and opinion dynamics whose spreading is dictated by unanimity rules, i.e. a node will change its (binary) state only if all of its neighbours have the same corresponding state. It is shown that a transition takes place depending on the initial condition of the problem. In particular, a critical number of initially activated nodes is needed so that the whole system gets activated in the long-time limit. The influence of the degree distribution of the nodes is naturally taken into account. For simple network topologies we solve the model analytically, the cases of random, small-world and scale-free are studied in detail.

physics.soc-ph↗

arXiv2006

Generalized Boltzmann factors and the maximum entropy principle

We generalize the usual exponential Boltzmann factor to any reasonable and potentially observable distribution function, $B(E)$. By defining generalized logarithms $Λ$ as inverses of these distribution functions, we are led to a generalization of the classical Boltzmann-Gibbs entropy, $S_{BG}= -\int d εω(ε) B(ε) \log B(ε)$ to the expression $S\equiv -\int d εω(ε) \int_0^{B(ε)} dx Λ(x)$, which contains the classical entropy as a special case. 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 straight forward solutions to the Jaynes maximum entropy principle with the ordinary (not escort!) constraints. Tsallis entropy is recovered as a further special case.

cond-mat.stat-mech↗

arXiv2005

On the derivation of power-law distributions within classical statistical mechanics far from the thermodynamic limit

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 separable from of 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 Gamma-phase space. Our results will be relevant for systems with a low-dimensional Gamma-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.

cond-mat.stat-mech↗

arXiv2005

The phase transition in random catalytic sets

The notion of (auto) catalytic networks has become a cornerstone in understanding the possibility of a sudden dramatic increase of diversity in biological evolution as well as in the evolution of social and economical systems. Here we study catalytic random networks with respect to the final outcome diversity of products. We show that an analytical treatment of this longstanding problem is possible by mapping the problem onto a set of non-linear recurrence equations. The solution of these equations show a crucial dependence of the final number of products on the initial number of products and the density of catalytic production rules. For a fixed density of rules we can demonstrate the existence of a phase transition from a practically unpopulated regime to a fully populated and diverse one. The order parameter is the number of final products. We are able to further understand the origin of this phase transition as a crossover from one set of solutions from a quadratic equation to the other.

cond-mat.other↗

arXiv2004

On the Derivation of power-law distributions within standard statistical mechanics

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 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 sytem 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.

cond-mat.stat-mech↗

arXiv2003

Risk trading, network topology, and banking regulation

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 networks. The proposed setup 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.

cond-mat↗

arXiv2002

Anomalous diffusion on dynamical networks: A model for interacting epithelial cell migration

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 degree of cell-cell interaction.

cond-mat↗