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Journal articleJensen H, Tempesta P, 2018,
Group entropies: from phase space geometry to entropy functionals via group theory
, Entropy, Vol: 20, ISSN: 1099-4300The entropy of Boltzmann-Gibbs, as proved by Shannon and Khinchin, is based on four axioms, where the fourth one concerns additivity. The group theoretic entropies make use of formal group theory to replace this axiom with a more general composability axiom. As has been pointed out before, generalised entropies crucially depend on the number of allowed degrees of freedom N. The functional form of group entropies is restricted (though not uniquely determined) by assuming extensivity on the equal probability ensemble, which leads to classes of functionals corresponding to sub-exponential, exponential or super-exponential dependence of the phase space volume W on N. We review the ensuing entropies, discuss the composability axiom and explain why group entropies may be particularly relevant from an information-theoretical perspective.
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Journal articleRosas De Andraca FE, Martinez Mediano P, Ugarte M, et al., 2018,
An information-theoretic approach to self-organisation: Emergence of complex interdependencies in coupled dynamical systems
, Entropy, Vol: 20, ISSN: 1099-4300Self-organisation lies at the core of fundamental but still unresolved scientific questions, and holds the promise of de-centralised paradigms crucial for future technological developments. While self-organising processes have been traditionally explained by the tendency of dynamical systems to evolve towards specific configurations, or attractors, we see self-organisation as a consequence of the interdependencies that those attractors induce. Building on this intuition, in this work we develop a theoretical framework for understanding and quantifying self-organisation based on coupled dynamical systems and multivariate information theory. We propose a metric of global structural strength that identifies when self-organisation appears, and a multi-layered decomposition that explains the emergent structure in terms of redundant and synergistic interdependencies. We illustrate our framework on elementary cellular automata, showing how it can detect and characterise the emergence of complex structures.
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Journal articleSahasranaman A, Jensen HJ, 2018,
Ethnicity and wealth: the dynamics of dual segregation
, PLoS ONE, Vol: 13, ISSN: 1932-6203Creating inclusive cities requires meaningful responses to inequality and segregation. We build an agent-based model of interactions between wealth and ethnicity of agents to investigate ‘dual’ segregations—due to ethnicity and due to wealth. As agents are initially allowed to move into neighbourhoods they cannot afford, we find a regime where there is marginal increase in both wealth segregation and ethnic segregation. However, as more agents are progressively allowed entry into unaffordable neighbourhoods, we find that both wealth and ethnic segregations undergo sharp, non-linear transformations, but in opposite directions—wealth segregation shows a dramatic decline, while ethnic segregation an equally sharp upsurge. We argue that the decrease in wealth segregation does not merely accompany, but actually drives the increase in ethnic segregation. Essentially, as agents are progressively allowed into neighbourhoods in contravention of affordability, they create wealth configurations that enable a sharp decline in wealth segregation, which at the same time allow co-ethnics to spatially congregate despite differences in wealth, resulting in the abrupt worsening of ethnic segregation.
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Journal articleDolan D, Jensen H, Martinez Mediano P, et al., 2018,
The improvisational state of mind: a multidisciplinary study of an improvisatory approach to classical music repertoire performance
, Frontiers in Psychology, Vol: 9, ISSN: 1664-1078The recent re-introduction of improvisation as a professional practice within classical music, however cautious and still rare, allows direct and detailed contemporary comparison between improvised and “standard” approaches to performances of the same composition, comparisons which hitherto could only be inferred from impressionistic historical accounts. This study takes an interdisciplinary multi-method approach to discovering the contrasting nature and effects of prepared and improvised approaches during live chamber-music concert performances of a movement from Franz Schubert’s “Shepherd on the Rock”, given by a professional trio consisting of voice, flute, and piano, in the presence of an invited audience of 22 adults with varying levels of musical experience and training. The improvised performances were found to be differ systematically from prepared performances in their timing, dynamic, and timbral features as well as in the degree of risk-taking and “mind reading” between performers including during moments of added extemporised notes. Post-performance critical reflection by the performers characterised distinct mental states underlying the two modes of performance. The amount of overall body movements was reduced in the improvised performances, which showed less unco-ordinated movements between performers when compared to the prepared performance. Audience members, who were told only that the two performances would be different, but not how, rated the improvised version as more emotionally compelling and musically convincing than the prepared version. The size of this effect was not affected by whether or not the audience could see the performers, or by levels of musical training. EEG measurements from 19 scalp locations showed higher levels of Lempel-Ziv complexity (associated with awareness and alertness) in the improvised version in both performers and audience. Results are discussed in terms of their potential
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Journal articleJensen HJ, Pazuki RH, Pruessner G, et al., 2018,
Statistical mechanics of exploding phase spaces: ontic open systems
, Journal of Physics A: Mathematical and Theoretical, Vol: 51, ISSN: 1751-8113The volume of phase space may grow super-exponentially ('explosively') with the number of degrees of freedom for certain types of complex systems such as those encountered in biology and neuroscience, where components interact and create new emergent states. Standard ensemble theory can break down as we demonstrate in a simple model reminiscent of complex systems where new collective states emerge. We present an axiomatically defined entropy and argue that it is extensive in the micro-canonical, equal probability, and canonical (max-entropy) ensemble for super-exponentially growing phase spaces. This entropy may be useful in determining probability measures in analogy with how statistical mechanics establishes statistical ensembles by maximising entropy.
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Journal articlePalmieri L, Jensen HJ, 2018,
The emergence of weak criticality in SOC systems
, EPL, Vol: 123, ISSN: 0295-5075Since Self-Organised Criticality (SOC) was introduced in 1987, both the nature of the self-organisation and the criticality have remained controversial. Besides, SOC-like dynamics has recently been observed in many natural processes like brain activity and rain precipitations, making a better understanding of such systems more urgent. Here we focus on the Drossel-Schwabl forest-fire model (FFM) of SOC and show that despite the model is not critical, it nevertheless exhibits a behaviour that justifies the introduction of a new kind of weak criticality. We present a method that allows to quantify the degree of criticality of a system and to introduce a new class of critical systems. This method can be easily adapted to experimental settings and contribute to a better understanding of real systems.
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Journal articleCofré R, Maldonado C, Rosas F, 2018,
Large Deviations Properties of Maximum Entropy Markov Chains from Spike Trains
, Entropy, Vol: 20, Pages: 573-573<jats:p>We consider the maximum entropy Markov chain inference approach to characterize the collective statistics of neuronal spike trains, focusing on the statistical properties of the inferred model. To find the maximum entropy Markov chain, we use the thermodynamic formalism, which provides insightful connections with statistical physics and thermodynamics from which large deviations properties arise naturally. We provide an accessible introduction to the maximum entropy Markov chain inference problem and large deviations theory to the community of computational neuroscience, avoiding some technicalities while preserving the core ideas and intuitions. We review large deviations techniques useful in spike train statistics to describe properties of accuracy and convergence in terms of sampling size. We use these results to study the statistical fluctuation of correlations, distinguishability, and irreversibility of maximum entropy Markov chains. We illustrate these applications using simple examples where the large deviation rate function is explicitly obtained for maximum entropy models of relevance in this field.</jats:p>
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Journal articleCofré R, Maldonado C, Rosas De Andraca F, 2018,
Large deviations properties of maximum entropy Markov chains from spike trains
, Entropy, Vol: 20, ISSN: 1099-4300We consider the maximum entropy Markov chain inference approach to characterize the collective statistics of neuronal spike trains, focusing on the statistical properties of the inferred model. To find the maximum entropy Markov chain, we use the thermodynamic formalism, which provides insightful connections with statistical physics and thermodynamics from which large deviations properties arise naturally. We provide an accessible introduction to the maximum entropy Markov chain inference problem and large deviations theory to the community of computational neuroscience, avoiding some technicalities while preserving the core ideas and intuitions. We review large deviations techniques useful in spike train statistics to describe properties of accuracy and convergence in terms of sampling size. We use these results to study the statistical fluctuation of correlations, distinguishability, and irreversibility of maximum entropy Markov chains. We illustrate these applications using simple examples where the large deviation rate function is explicitly obtained for maximum entropy models of relevance in this field.
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Journal articleGoto H, Viegas E, Jensen HJ, et al., 2018,
Smoluchowski equation for networks: merger induced intermittent giant node formation and degree gap
, Journal of Statistical Physics, Vol: 172, Pages: 1086-1100, ISSN: 1572-9613The dynamical phase diagram of a network undergoing annihilation, creation, and coagulation of nodes is found to exhibit two regimes controlled by the combined effect of preferential attachment for initiator and target nodes during coagulation and for link assignment to new nodes. The first regime exhibits smooth dynamics and power law degree distributions. In the second regime, giant degree nodes and gaps in the degree distribution are formed intermittently. Data for the Japanese firm network in 1994 and 2014 suggests that this network is moving towards the intermittent switching region.
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Conference paperAzari MM, Rosas De Andraca FE, Pollin S, 2018,
Reshaping cellular networks for the sky: major factors and feasibility
, 2018 IEEE International Conference on Communications (ICC), Publisher: IEEE, ISSN: 1938-1883This paper studies the feasibility of supporting drone operations using existent cellular infrastructure. We propose an analytical framework that includes the effects of base station (BS) height and antenna radiation pattern, drone antenna directivity and various propagation environments. With this framework, we derive an exact expression for the coverage probability of ground and drone users through a practical cell association strategy. Our results show that a carefully designed network can control the radiated interference that is received by the drones, and therefore guarantees a satisfactory quality of service. Moreover, as the network density grows the increasing level of interference can be partially managed by lowering the drone flying altitude. However, even at optimal conditions the drone coverage performance converges to zero considerably fast, suggesting that ultra-dense networks might be poor candidates for serving aerial users.
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