Publications
179 results found
Shi X, Sau A, Li X, et al., 2023, Information theory-based direct causality measure to assess cardiac fibrillation dynamics, Journal of the Royal Society Interface, Vol: 20, ISSN: 1742-5662
Understanding the mechanism sustaining cardiac fibrillation can facilitate the personalization of treatment. Granger causality analysis can be used to determine the existence of a hierarchical fibrillation mechanism that is more amenable to ablation treatment in cardiac time-series data. Conventional Granger causality based on linear predictability may fail if the assumption is not met or given sparsely sampled, high-dimensional data. More recently developed information theory-based causality measures could potentially provide a more accurate estimate of the nonlinear coupling. However, despite their successful application to linear and nonlinear physical systems, their use is not known in the clinical field. Partial mutual information from mixed embedding (PMIME) was implemented to identify the direct coupling of cardiac electrophysiology signals. We show that PMIME requires less data and is more robust to extrinsic confounding factors. The algorithms were then extended for efficient characterization of fibrillation organization and hierarchy using clinical high-dimensional data. We show that PMIME network measures correlate well with the spatio-temporal organization of fibrillation and demonstrated that hierarchical type of fibrillation and drivers could be identified in a subset of ventricular fibrillation patients, such that regions of high hierarchy are associated with high dominant frequency.
Rajpal H, Martinez Mediano PA, Rosas De Andraca FE, et al., 2022, Psychedelics and schizophrenia: Distinct alterations to Bayesian inference, NeuroImage, Vol: 263, ISSN: 1053-8119
Schizophrenia and states induced by certain psychotomimetic drugs may share some physiological and phenomenological properties, but they differ in fundamental ways: one is a crippling chronic mental disease, while the others are temporary, pharmacologically-induced states presently being explored as treatments for mental illnesses. Building towards a deeper understanding of these different alterations of normal consciousness, here we compare the changes in neural dynamics induced by LSD and ketamine (in healthy volunteers) against those associated with schizophrenia, as observed in resting-state M/EEG recordings. While both conditions exhibit increased neural signal diversity, our findings reveal that this is accompanied by an increased transfer entropy from the front to the back of the brain in schizophrenia, versus an overall reduction under the two drugs. Furthermore, we show that these effects can be reproduced via different alterations of standard Bayesian inference applied on a computational model based on the predictive processing framework. In particular, the effects observed under the drugs are modelled as a reduction of the precision of the priors, while the effects of schizophrenia correspond to an increased precision of sensory information. These findings shed new light on the similarities and differences between schizophrenia and two psychotomimetic drug states, and have potential implications for the study of consciousness and future mental health treatments.
Mediano PAM, Rosas FE, Luppi AI, et al., 2022, Greater than the parts: a review of the information decomposition approach to causal emergence., Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol: 380, Pages: 20210246-20210246, ISSN: 1364-503X
Emergence is a profound subject that straddles many scientific disciplines, including the formation of galaxies and how consciousness arises from the collective activity of neurons. Despite the broad interest that exists on this concept, the study of emergence has suffered from a lack of formalisms that could be used to guide discussions and advance theories. Here, we summarize, elaborate on, and extend a recent formal theory of causal emergence based on information decomposition, which is quantifiable and amenable to empirical testing. This theory relates emergence with information about a system's temporal evolution that cannot be obtained from the parts of the system separately. This article provides an accessible but rigorous introduction to the framework, discussing the merits of the approach in various scenarios of interest. We also discuss several interpretation issues and potential misunderstandings, while highlighting the distinctive benefits of this formalism. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.
Rosas FE, Mediano PAM, Luppi AI, et al., 2022, Disentangling high-order mechanisms and high-order behaviours in complex systems, NATURE PHYSICS, Vol: 18, Pages: 476-477, ISSN: 1745-2473
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- Citations: 14
Pazuki R, Jensen HJ, 2021, New probability distribution describing emergence in state space, Journal of Physics Communications, Vol: 5, Pages: 1-24, ISSN: 2399-6528
We revisit the pairing model of state spaces with new emergent states introduced in J. Phys. A: Math. Theor. 51 375002, 2018. We facilitate our analysis by introducing a simplified pairing model consisting of balls able to form pairs but without any internal structure. For both the simplified and the original model we compute exactly the probability distribution for observing a state with $n_p$ pairs. We show this distribution satisfies a large deviation principle with speed $n \ln(n)$. We present closed form expressions for a variety of statistical quantities including moments and marginal distributions.
Jensen HJ, 2021, What is critical about criticality: in praise of the correlation function, JOURNAL OF PHYSICS-COMPLEXITY, Vol: 2
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- Citations: 3
Sahasranaman A, Jensen HJ, 2021, Spread of COVID-19 in urban neighbourhoods and slums of the developing world, JOURNAL OF THE ROYAL SOCIETY INTERFACE, Vol: 18, ISSN: 1742-5689
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- Citations: 20
Sibani P, Boettcher S, Jensen HJ, 2021, Record dynamics of evolving metastable systems: theory and applications, European Physical Journal B: Condensed Matter and Complex Systems, Vol: 94, Pages: 1-23, ISSN: 1434-6028
Record Dynamics (RD) deals with complex systems evolving through a sequence of metastable stages. These are macroscopically distinguishable and appear stationary, except for the sudden and rapid changes, called quakes, which induce the transitions from one stage to the next. This phenomenology is well known in physics as “physical aging”, but from the vantage point of RD, the evolution of a class of systems of physical, biological, and cultural origin is rooted in a hierarchically structured configuration space and can, therefore, be analyzed by similar statistical tools. This colloquium paper strives to present in a coherent fashion methods and ideas that have gradually evolved over time. To this end, it first describes the differences and similarities between RD and two widespread paradigms of complex dynamics, Self-Organized Criticality and Continuous Time Random Walks. It then outlines the Poissonian nature of records events in white noise time-series, and connects it to the statistics of quakes in metastable hierarchical systems, arguing that the relaxation effects of quakes can generally be described by power laws unrelated to criticality. Several different applications of RD have been developed over the years. Some of these are described, showing the basic RD hypothesis and how the log-time homogeneity of quake dynamics, can be empirically verified in a given context. The discussion summarizes the paper and briefly mentions applications not discussed in detail. Finally, the outlook points to possible improvements and to new areas of research where RD could be of use.
Rosas FE, Mediano PAM, Jensen HJ, et al., 2020, Reconciling emergences: an information-theoretic approach to identify causal emergence in multivariate data, PLoS Computational Biology, Vol: 16, ISSN: 1553-734X
The broad concept of emergence is instrumental in various of the most challenging open scientific questions—yet, few quantitative theories of what constitutes emergent phenomena have been proposed. This article introduces a formal theory of causal emergence in multivariate systems, which studies the relationship between the dynamics of parts of a system and macroscopic features of interest. Our theory provides a quantitative definition of downward causation, and introduces a complementary modality of emergent behaviour—which we refer to as causal decoupling. Moreover, the theory allows practical criteria that can be efficiently calculated in large systems, making our framework applicable in a range of scenarios of practical interest. We illustrate our findings in a number of case studies, including Conway’s Game of Life, Reynolds’ flocking model, and neural activity as measured by electrocorticography.
Sahasranaman A, Jensen HJ, 2020, Poverty in the time of epidemic: A modelling perspective, PLoS One, Vol: 15, Pages: 1-16, ISSN: 1932-6203
We create a network model to study the spread of an epidemic through physically proximate and accidental daily human contacts in a city, and simulate outcomes for two kinds of agents—poor and non-poor. Under non-intervention, peak caseload is maximised, but no differences are observed in infection rates across poor and non-poor. Introducing interventions to control spread, peak caseloads are reduced, but both cumulative infection rates and current infection rates are systematically higher for the poor than for non-poor, across all scenarios. Larger populations, higher fractions of poor, and longer durations of intervention are found to progressively worsen outcomes for the poor; and these are of particular concern for economically vulnerable populations in cities of the developing world. Addressing these challenges requires a deeper, more rigorous understanding of the relationships between structural poverty and epidemy, as well as effective utilization of extant community level infrastructure for primary care in developing cities. Finally, improving iniquitous outcomes for the poor creates better outcomes for the whole population, including the non-poor.
Palmieri L, Jensen HJ, 2020, The forest fire model: the subtleties of criticality and scale invariance, Frontiers in Physics, Vol: 8, Pages: 1-8, ISSN: 2296-424X
Amongst the numerous models introduced with SOC, the Forest Fire Model (FFM) is particularly attractive for its close relationship to stochastic spreading, which is central to the study of systems as diverse as epidemics, rumors, or indeed, fires. However, since its introduction, the nature of the model's scale invariance has been controversial, and the lack of scaling observed in many studies diminished its theoretical attractiveness. In this study, we analyse the behavior of the tree density, the average cluster size and the largest cluster and show that the model could be of high practical relevance for the activation dynamics seen in brain and rain studies. From this perspective, its peculiar scaling properties should be regarded as an asset rather than a limitation.
Jensen H, 2020, Universality classes and information-theoretic measures of complexity via group entropies, Scientific Reports, Vol: 10, Pages: 1-11, ISSN: 2045-2322
We introduce a class of information measures based on group entropies, allowing us to describe the information-theoreticalproperties of complex systems. These entropic measures are nonadditive, and are mathematically deduced from a seriesof natural axioms. In addition, we require extensivity in order to ensure that our information measures are meaningful. Theinformation measures proposed are suitably defined for describing universality classes of complex systems, each characterizedby a specific state space growth rate function.
Palmieri L, Jensen HJ, 2020, Investigating critical systems via the distribution of correlation lengths, PHYSICAL REVIEW RESEARCH, Vol: 2
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- Citations: 5
Viegas E, Goto H, Kobayashi Y, et al., 2020, Allometric scaling of mutual information in complex networks: a conceptual framework and empirical approach, Entropy: international and interdisciplinary journal of entropy and information studies, Vol: 22, Pages: 1-14, ISSN: 1099-4300
Complexity and information theory are two very valuable but distinct fields of research, yet sharing the same roots. Here, we develop a complexity framework inspired by the allometric scaling laws of living biological systems in order to evaluate the structural features of networks. This is done by aligning the fundamental building blocks of information theory (entropy and mutual information) with the core concepts in network science such as the preferential attachment and degree correlations. In doing so, we are able to articulate the meaning and significance of mutual information as a comparative analysis tool for network activity. When adapting and applying the framework to the specific context of the business ecosystem of Japanese firms, we are able to highlight the key structural differences and efficiency levels of the economic activities within each prefecture in Japan. Moreover, we propose a method to quantify the distance of an economic system to its efficient free market configuration by distinguishing and quantifying two particular types of mutual information, total and structural.
Goto H, Viegas E, Takayasu H, et al., 2019, Dynamics of essential interaction between firms on financial reports, PLoS One, Vol: 14, Pages: 1-16, ISSN: 1932-6203
Companies tend to publish financial reports in order to articulate strategies, disclose key performance measurements as well as summarise the complex relationships with external stakeholders as a result of their business activities. Therefore, any major changes to business models or key relationships will be naturally reflected within these documents, albeit in an unstructured manner. In this research, we automatically scan through a large and rich database, containing over 400,000 reports of companies in Japan, in order to generate structured sets of data that capture the essential features, interactions and resulting relationships among these firms. In doing so, we generate a citation type network where we empirically observe that node creation, annihilation and link rewiring to be the dominant processes driving its structure and formation. These processes prompt the network to rapidly evolve, with over a quarter of the interactions between firms being altered within every single calendar year. In order to confirm our empirical observations and to highlight and replicate the essential dynamics of each of the three processes separately, we borrow inspiration from ecosystems and evolutionary theory. Specifically, we construct a network evolutionary model where we adapt and incorporate the concept of fitness within our numerical analysis to be a proxy real measure of a company’s importance. By making use of parameters estimated from the real data, we find that our model reliably replicates degree distributions and motif formations of the citation network, and therefore reproducing both macro as well as micro, local level, structural features. This is done with the exception of the real frequency of bidirectional links, which are primarily formed as a result of an entirely separate and distinct process, namely the equity investments from one company into another.
Rajpal H, Rosas De Andraca FE, Jensen HJ, 2019, Tangled worldview model of opinion dynamics, Frontiers in Physics, Vol: 7, ISSN: 2296-424X
We study the joint evolution of worldviews by proposing a model of opinion dynamics, which is inspired in notions fromevolutionary ecology. Agents update their opinion on a specific issue based on their propensity to change – asserted by thesocial neighbours – weighted by their mutual similarity on other issues. Agents are, therefore, more influenced by neighbourswith similar worldviews (set of opinions on various issues), resulting in a complex co-evolution of each opinion. Simulationsshow that the worldview evolution exhibits events of intermittent polarization when the social network is scale-free. This, in turn,triggers extreme crashes and surges in the popularity of various opinions. Using the proposed model, we highlight the role ofnetwork structure, bounded rationality of agents, and the role of key influential agents in causing polarization and intermittentreformation of worldviews on scale-free networks.
Rosas FE, Mediano PAM, Gastpar M, et al., 2019, Quantifying high-order interdependencies via multivariate extensions of the mutual information, Physical Review E, Vol: 100, ISSN: 2470-0045
This paper introduces a model-agnostic approach to study statistical synergy, a form of emergence in which patterns at large scales are not traceable from lower scales. Our framework leverages various multivariate extensions of Shannon's mutual information, and introduces the O-information as a metric that is capable of characterizing synergy- and redundancy-dominated systems. The O-information is a symmetric quantity, and can assess intrinsic properties of a system without dividing its parts into “predictors” and “targets.” We develop key analytical properties of the O-information, and study how it relates to other metrics of high-order interactions from the statistical mechanics and neuroscience literature. Finally, as a proof of concept, we present an exploration on the relevance of statistical synergy in Baroque music scores.
Viegas EM, Goto H, Takayasu H, et al., 2019, Assembling real networks from synthetic and unstructured subsets: the corporate reporting case, Scientific Reports, Vol: 9, ISSN: 2045-2322
The analysis of interfirm business transaction networks provides invaluable insight into the trading dynamics and economicstructure of countries. However, there is a general scarcity of data available recording real, accurate and extensive informationfor these types of networks. As a result, and in common with other types of network studies - such as protein interactions forinstance - research tends to rely on partial and incomplete datasets, i.e. subsets, with less certain conclusions. Hereh, wemake use of unstructured financial and corporate reporting data in Japan as the base source to construct a financial reportingnetwork, which is then compared and contrasted to the wider real business transaction network. The comparative analysisbetween these two rich datasets - the proxy, partially derived network and the real, complete network at macro as well as localstructural levels - provides an enhanced understanding of the non trivial relationships between partial sampled subsets andfully formed networks. Furthermore, we present an elemental agent based pruning algorithm that reconciles and preserves keystructural differences between these two networks, which may serve as an embryonic generic framework of potentially wideruse to network research, enabling enhanced extrapolation of conclusions from partial data or subsets.
Sahasranaman A, Jensen H, 2019, Rapid migrations and dynamics of citizen response, Royal Society Open Science, Vol: 6, Pages: 1-13, ISSN: 2054-5703
One of the pressing social concerns of our timeis the need for meaningful responses to migrantsand refugees fleeing conflict and environmentalcatastrophe. We develop a computational model tomodel the influx of migrants into a city, varyingthe rates of entry, and find a non-linear inverserelationship between the fraction of resident populationwhose tolerance levels are breached due to migrantentry and the average time to such tolerancebreach. Essentially, beyond a certain rate of migrantentry, there is a rapid rise in the fraction ofresidents whose tolerances are breached, even as theaverage time to breach decreases. We also modelan analytical approximation of the computationalmodel and find qualitative correspondence in theobserved phenomenology, with caveats. The sharpincrease in the fraction of residents with tolerancebreach could potentially underpin the intensity ofresident responses to bursts of migrant entry intotheir cities. Given this non-linear relationship, it isperhaps essential that responses to refugee situationsare multi-country or global efforts so that sharpspikes of refugee migrations are equitably distributedamong nations, potentially enabling all participatingcountries to avoid impacting resident tolerancesbeyond limits that are socially sustainable.
Vazquez P, del Rio JA, Cedano KG, et al., 2018, Network characterization of the Entangled Model for sustainability indicators. Analysis of the network properties for scenarios, PLoS ONE, Vol: 13, ISSN: 1932-6203
Policy-makers require strategies to select a set of sustainability indicators that are useful for monitoring sustainability. For this reason, we have developed a model where sustainability indicators compete for the attention of society. This model has shown to have steady situations where a set of sustainability indicators are stable. To understand the role of the network configuration, in this paper we analyze the network properties of the Entangled Sustainability model. We have used the degree distribution, the clustering coefficient, and the interaction strength distribution as main measures. We also analyze the network properties for scenarios compared against randomly generated scenarios. We found that the stable situations show different characteristics from the unstable transitions present in the model. We also found that the complex emergent feature of sustainability shown in the model is an attribute of the scenarios, however, the randomly generated scenarios do not present the same network properties.
Jensen H, 2018, Tangled nature: A model of emergent structure and temporal mode among co-evolving agents, European Journal of Physics, Vol: 40, ISSN: 0143-0807
Understanding systems level behaviour of many interacting agents is challenging in various ways. In this review we will focus on how the interaction between components can lead to hierarchical structures with different types of dynamics, or causations, at different levels. We use the Tangled Nature model to discuss the co-evolutionary aspects of the connection between the microscopic level of the individual and the macroscopic systems level. At the microscopic level the individual agent may undergo evolutionary changes due to 'mutations of strategies'. The micro-dynamics always run at a constant rate. Nevertheless, the systems level dynamics exhibit a completely different type of intermittent abrupt dynamics where major upheavals keep throwing the system between metastable configurations. These dramatic transitions are described by a log-Poisson time statistics. The long time effect is a collective adaptation of the ecological networks. We discuss the ecological and macro-evolutionary consequences of the adaptive dynamics and briefly describe work using the Tangled Nature framework to analyse problems in economics, sociology, innovation and sustainability.
Jensen H, Tempesta P, 2018, Group entropies: from phase space geometry to entropy functionals via group theory, Entropy, Vol: 20, ISSN: 1099-4300
The 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.
Rosas 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: 1099-4300
Self-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.
Sahasranaman A, Jensen HJ, 2018, Ethnicity and wealth: the dynamics of dual segregation, PLoS ONE, Vol: 13, ISSN: 1932-6203
Creating 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.
Dolan 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: 1664-1078
The 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
Jensen 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: 1751-8113
The 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.
Palmieri L, Jensen HJ, 2018, The emergence of weak criticality in SOC systems, EPL, Vol: 123, ISSN: 0295-5075
Since 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.
Goto 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: 1572-9613
The 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.
Siddiqui M, Wedemann RS, Jensen HJ, 2018, Avalanches and generalized memory associativity in a network model for conscious and unconscious mental functioning, Physica A: Statistical Mechanics and its Applications, Vol: 490, Pages: 127-138, ISSN: 0378-4371
We explore statistical characteristics of avalanches associated with the dynamics of a complex-network model, where two modules corresponding to sensorial and symbolic memories interact, representing unconscious and conscious mental processes. The model illustrates Freud’s ideas regarding the neuroses and that consciousness is related with symbolic and linguistic memory activity in the brain. It incorporates the Stariolo–Tsallis generalization of the Boltzmann Machine in order to model memory retrieval and associativity. In the present work, we define and measure avalanche size distributions during memory retrieval, in order to gain insight regarding basic aspects of the functioning of these complex networks. The avalanche sizes defined for our model should be related to the time consumed and also to the size of the neuronal region which is activated, during memory retrieval. This allows the qualitative comparison of the behaviour of the distribution of cluster sizes, obtained during fMRI measurements of the propagation of signals in the brain, with the distribution of avalanche sizes obtained in our simulation experiments. This comparison corroborates the indication that the Nonextensive Statistical Mechanics formalism may indeed be more well suited to model the complex networks which constitute brain and mental structure.
Sahasranaman A, Jensen HJ, 2017, Cooperative dynamics of neighborhood economic status in cities, PLoS ONE, Vol: 12, ISSN: 1932-6203
We significantly extend our earlier variant of the Schelling model, incorporating a neighborhood Potential function as well as an agent wealth gain function to study the long term evolution of the economic status of neighborhoods in cities. We find that the long term patterns of neighborhood relative economic status (RES) simulated by this model reasonably replicate the empirically observed patterns from American cities. Specifically, we find that larger fractions of rich and poor neighborhoods tend to, on average, retain status for longer than lower- and upper-middle wealth neighborhoods. The use of a Potential function that measures the relative wealth of neighborhoods as the basis for agent wealth gain and agent movement appears critical to explaining these emergent patterns of neighborhood RES. This also suggests that the empirically observed RES patterns could indeed be universal and that we would expect to see these patterns repeated for cities around the world. Observing RES behavior over even longer periods of time, the model predicts that the fraction of poor neighborhoods retaining status remains almost constant over extended periods of time, while the fraction of middle-wealth and rich neighborhoods retaining status reduces significantly over time, tending to zero.
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