Abstract.- We study the robustness of functionals of probability distributions such as the Rényi ... more Abstract.- We study the robustness of functionals of probability distributions such as the Rényi and nonadditive Sq 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 Rényi and nonadditive Sq entropies as well as the q-expectation values are robust. For the discrete finite case, the Rényi and nonadditive Sq entropies and the q-expectation values are robust. For the infinite discrete case, where both Rényi entropy and q-expectations are known to violate Lesche-stab...
Evolutionary processes combine many features of complex systems: they are algorithmic; states co-... more Evolutionary processes combine many features of complex systems: they are algorithmic; states co-evolve with interactions; they show power law statistics; they are selforganized critical; and they are driven non-equilibrium systems. Evolution is a dynamical process that changes the composition of large sets of interconnected elements, entities, or species over time. The essence of evolutionary processes is that, through the interaction of existing entities with each other and with their environment, they give rise to an open-ended process of creation and destruction of new entities. Evolutionary processes are critical, co-evolutionary, and combinatorial, meaning that thew entities are created from combinations of existing ones. We review the concepts of the replicator equation, fitness landscapes, cascading events, the adjacent possible. We review several classical quantitative approaches to evolutionary dynamics such as the NK model and the Bak–Snappen model. We propose a general a...
Understanding the interactions between the components of a system is key to understanding it. In ... more Understanding the interactions between the components of a system is key to understanding it. In complex systems, interactions are usually not uniform, not isotropic and not homogeneous: each interaction can be specific between elements.Networks are a tool for keeping track of who is interacting with whom, at what strength, when, and in what way. Networks are essential for understanding of the co-evolution and phase diagrams of complex systems. Here we provide a self-contained introduction to the field of network science. We introduce ways of representing and handle networks mathematically and introduce the basic vocabulary and definitions. The notions of random- and complex networks are reviewed as well as the notions of small world networks, simple preferentially grown networks, community detection, and generalized multilayer networks.
Scaling appears practically everywhere in science; it basically quantifies how the properties or ... more Scaling appears practically everywhere in science; it basically quantifies how the properties or shapes of an object change with the scale of the object. Scaling laws are always associated with power laws. The scaling object can be a function, a structure, a physical law, or a distribution function that describes the statistics of a system or a temporal process. We focus on scaling laws that appear in the statistical description of stochastic complex systems, where scaling appears in the distribution functions of observable quantities of dynamical systems or processes. The distribution functions exhibit power laws, approximate power laws, or fat-tailed distributions. Understanding their origin and how power law exponents can be related to the particular nature of a system, is one of the aims of the book.We comment on fitting power laws.
Proceedings IEEE and ACM International Symposium on Augmented Reality
Computer-aided surgery (CAS), the intraoperative application of biomedical visualization techniqu... more Computer-aided surgery (CAS), the intraoperative application of biomedical visualization techniques, appears to be one of the most promising fields of application for augmented reality (AR), the display of additional computer generated graphics over a real-world scene. Typically a device such as a head-mounted display (HMD) is used for AR. However considerable technical problems connected with AR have limited the intraoperative
Complex systems with strong correlations and fat-tailed distribution functions have been argued t... more 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 si...
Even though irreversibility is one of the major hallmarks of any real life process, an actual und... more Even though irreversibility is one of the major hallmarks of any real life process, an actual understanding of irreversible processes remains still mostly semi-empirical. In this paper, we formulate a thermodynamic uncertainty principle for irreversible heat engines operating with an ideal gas as a working medium. In particular, we show that the time needed to run through such an irreversible cycle multiplied by the irreversible work lost in the cycle, is bounded from below by an irreducible and process-dependent constant that has the dimension of an action. The constant in question depends on a typical scale of the process and becomes comparable to Planck's constant at the length scale of the order Bohr-radius, i.e. the scale that corresponds to the smallest distance on which the ideal gas paradigm realistically applies.This article is part of the theme issue 'Fundamental aspects of non-equilibrium thermodynamics'.
As anthropologists study complex societies and large databases, we have to ask whether using demo... more 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.
The chapter contains the most important mathematical forumas that are used throughout the book. T... more The chapter contains the most important mathematical forumas that are used throughout the book. This collection should make the book self-contained. The chapter also contains some useful approximations that are used several times in the text.
Proceedings IEEE and ACM International Symposium on Augmented Reality (ISAR 2000)
In computer-aided surgery (CAS), an undesired side-effect of the necessity of handling sophistica... more In computer-aided surgery (CAS), an undesired side-effect of the necessity of handling sophisticated equipment in the operating room is the fact that the surgeon's attention is drawn from the operating field, since surgical progress is partially monitored on the computer's screen. Augmented reality (AR), the overlay of computer-generated graphics over a real-world scene, provides a possibility to solve this problem.
We show with two simple examples, one—an autocorrelated random walk, the other—an accelerated ran... more We show with two simple examples, one—an autocorrelated random walk, the other—an accelerated random walk, that two processes that are fundamentally different on a microscopical level, so different in fact that the two processes implement different types of entropic concepts, still can be indistinguishable from a probabilistic point of view, i.e. all finite moments of the two processes may coincide. The immediate consequence of this observation is that entropy primarily is a property associated with the structure of phase-space rather than a consequence of specific observable distribution functions.
In the context of understanding risk-regulatory behavior of financial institutions we propose a g... more In the context of understanding risk-regulatory behavior of financial institutions we propose a general dynamical game between several agents who pick their trading strategies depending on their individual risk-to-wealth ratio. 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 model yields realistic-looking time-series of wealth and the cost of safety increases as a power-like function. The relevant model parameters should be controllable in reality. This setup allows a stringent analysis of the effects of different approaches of banking regulation as currently suggested by the Basle Committee of Banking Supervision. We find evidence that a tightening of the current regulatory framework does not necessarily lead to an improvement of the safety of the banking system. Moreover, the potential impact of catastrophic events like September 11, 2001, on the financial system can be measured within this framework.
Abstract.- We study the robustness of functionals of probability distributions such as the Rényi ... more Abstract.- We study the robustness of functionals of probability distributions such as the Rényi and nonadditive Sq 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 Rényi and nonadditive Sq entropies as well as the q-expectation values are robust. For the discrete finite case, the Rényi and nonadditive Sq entropies and the q-expectation values are robust. For the infinite discrete case, where both Rényi entropy and q-expectations are known to violate Lesche-stab...
Evolutionary processes combine many features of complex systems: they are algorithmic; states co-... more Evolutionary processes combine many features of complex systems: they are algorithmic; states co-evolve with interactions; they show power law statistics; they are selforganized critical; and they are driven non-equilibrium systems. Evolution is a dynamical process that changes the composition of large sets of interconnected elements, entities, or species over time. The essence of evolutionary processes is that, through the interaction of existing entities with each other and with their environment, they give rise to an open-ended process of creation and destruction of new entities. Evolutionary processes are critical, co-evolutionary, and combinatorial, meaning that thew entities are created from combinations of existing ones. We review the concepts of the replicator equation, fitness landscapes, cascading events, the adjacent possible. We review several classical quantitative approaches to evolutionary dynamics such as the NK model and the Bak–Snappen model. We propose a general a...
Understanding the interactions between the components of a system is key to understanding it. In ... more Understanding the interactions between the components of a system is key to understanding it. In complex systems, interactions are usually not uniform, not isotropic and not homogeneous: each interaction can be specific between elements.Networks are a tool for keeping track of who is interacting with whom, at what strength, when, and in what way. Networks are essential for understanding of the co-evolution and phase diagrams of complex systems. Here we provide a self-contained introduction to the field of network science. We introduce ways of representing and handle networks mathematically and introduce the basic vocabulary and definitions. The notions of random- and complex networks are reviewed as well as the notions of small world networks, simple preferentially grown networks, community detection, and generalized multilayer networks.
Scaling appears practically everywhere in science; it basically quantifies how the properties or ... more Scaling appears practically everywhere in science; it basically quantifies how the properties or shapes of an object change with the scale of the object. Scaling laws are always associated with power laws. The scaling object can be a function, a structure, a physical law, or a distribution function that describes the statistics of a system or a temporal process. We focus on scaling laws that appear in the statistical description of stochastic complex systems, where scaling appears in the distribution functions of observable quantities of dynamical systems or processes. The distribution functions exhibit power laws, approximate power laws, or fat-tailed distributions. Understanding their origin and how power law exponents can be related to the particular nature of a system, is one of the aims of the book.We comment on fitting power laws.
Proceedings IEEE and ACM International Symposium on Augmented Reality
Computer-aided surgery (CAS), the intraoperative application of biomedical visualization techniqu... more Computer-aided surgery (CAS), the intraoperative application of biomedical visualization techniques, appears to be one of the most promising fields of application for augmented reality (AR), the display of additional computer generated graphics over a real-world scene. Typically a device such as a head-mounted display (HMD) is used for AR. However considerable technical problems connected with AR have limited the intraoperative
Complex systems with strong correlations and fat-tailed distribution functions have been argued t... more 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 si...
Even though irreversibility is one of the major hallmarks of any real life process, an actual und... more Even though irreversibility is one of the major hallmarks of any real life process, an actual understanding of irreversible processes remains still mostly semi-empirical. In this paper, we formulate a thermodynamic uncertainty principle for irreversible heat engines operating with an ideal gas as a working medium. In particular, we show that the time needed to run through such an irreversible cycle multiplied by the irreversible work lost in the cycle, is bounded from below by an irreducible and process-dependent constant that has the dimension of an action. The constant in question depends on a typical scale of the process and becomes comparable to Planck's constant at the length scale of the order Bohr-radius, i.e. the scale that corresponds to the smallest distance on which the ideal gas paradigm realistically applies.This article is part of the theme issue 'Fundamental aspects of non-equilibrium thermodynamics'.
As anthropologists study complex societies and large databases, we have to ask whether using demo... more 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.
The chapter contains the most important mathematical forumas that are used throughout the book. T... more The chapter contains the most important mathematical forumas that are used throughout the book. This collection should make the book self-contained. The chapter also contains some useful approximations that are used several times in the text.
Proceedings IEEE and ACM International Symposium on Augmented Reality (ISAR 2000)
In computer-aided surgery (CAS), an undesired side-effect of the necessity of handling sophistica... more In computer-aided surgery (CAS), an undesired side-effect of the necessity of handling sophisticated equipment in the operating room is the fact that the surgeon's attention is drawn from the operating field, since surgical progress is partially monitored on the computer's screen. Augmented reality (AR), the overlay of computer-generated graphics over a real-world scene, provides a possibility to solve this problem.
We show with two simple examples, one—an autocorrelated random walk, the other—an accelerated ran... more We show with two simple examples, one—an autocorrelated random walk, the other—an accelerated random walk, that two processes that are fundamentally different on a microscopical level, so different in fact that the two processes implement different types of entropic concepts, still can be indistinguishable from a probabilistic point of view, i.e. all finite moments of the two processes may coincide. The immediate consequence of this observation is that entropy primarily is a property associated with the structure of phase-space rather than a consequence of specific observable distribution functions.
In the context of understanding risk-regulatory behavior of financial institutions we propose a g... more In the context of understanding risk-regulatory behavior of financial institutions we propose a general dynamical game between several agents who pick their trading strategies depending on their individual risk-to-wealth ratio. 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 model yields realistic-looking time-series of wealth and the cost of safety increases as a power-like function. The relevant model parameters should be controllable in reality. This setup allows a stringent analysis of the effects of different approaches of banking regulation as currently suggested by the Basle Committee of Banking Supervision. We find evidence that a tightening of the current regulatory framework does not necessarily lead to an improvement of the safety of the banking system. Moreover, the potential impact of catastrophic events like September 11, 2001, on the financial system can be measured within this framework.
Uploads
Papers by Rudolf hanel