Group Structure as a Foundation for Entropies.

Entropy can signify different things. For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced, and it can be difficult to ascertain their respective importance and merits. Here, we consider entropy in an abstract sense, as a functional on a probability space, and we review how being able to handle the trivial case of non-interacting systems, together with the subtle requirement of extensivity, allows for a systematic classification of the functional form.

Information theory-based direct causality measure to assess cardiac fibrillation dynamics.

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.

Economic Trading Susceptibility: Constructing Networks of Mutual Influence through the Fitness of Countries.

The emergence of economic blocks and the level of influence countries exert on each other are fundamental features of the 21st century globally interconnected economy. However, limited quantitative research exists measuring the level of influence among countries and quantitatively determining economic blocks. This research develops a method to quantify the mutual influence of countries by making use of relatively standard procedures for complex networks in order to assemble non-trivial networks of influences and to identify symbiotic relationships. The methods are of significant help to an enhanced understanding of the global politics of trading and associations. Moreover, we develop the Mutual Influence Robustness (MIR) metric to work together with the Economic Fitness metric to provide some level of predictive modeling for the trends and future paths of countries. Our key results show the existence of a mutually influencing network around East and Southeast Asia, developed North America, and the northern and Iberian countries. Moreover, we find that it is possible to do some level of path predictability for the fitness and mutual influence of countries.

Spontaneous emergence of computation in network cascades.

Neuronal network computation and computation by avalanche supporting networks are of interest to the fields of physics, computer science (computation theory as well as statistical or machine learning) and neuroscience. Here we show that computation of complex Boolean functions arises spontaneously in threshold networks as a function of connectivity and antagonism (inhibition), computed by logic automata (motifs) in the form of computational cascades. We explain the emergent inverse relationship between the computational complexity of the motifs and their rank-ordering by function probabilities due to motifs, and its relationship to symmetry in function space. We also show that the optimal fraction of inhibition observed here supports results in computational neuroscience, relating to optimal information processing.

Spread of COVID-19 in urban neighbourhoods and slums of the developing world.

We study the spread of COVID-19 across neighbourhoods of cities in the developing world and find that small numbers of neighbourhoods account for a majority of cases (k-index approx. 0.7). We also find that the countrywide distribution of cases across states/provinces in these nations also displays similar inequality, indicating self-similarity across scales. Neighbourhoods with slums are found to contain the highest density of cases across all cities under consideration, revealing that slums constitute the most at-risk urban locations in this epidemic. We present a stochastic network model to study the spread of a respiratory epidemic through physically proximate and accidental daily human contacts in a city, and simulate outcomes for a city with two kinds of neighbourhoods-slum and non-slum. The model reproduces observed empirical outcomes for a broad set of parameter values-reflecting the potential validity of these findings for epidemic spread in general, especially across cities of the developing world. We also find that distribution of cases becomes less unequal as the epidemic runs its course, and that both peak and cumulative caseloads are worse for slum neighbourhoods than non-slums at the end of an epidemic. Large slums in the developing world, therefore, contain the most vulnerable populations in an outbreak, and the continuing growth of metropolises in Asia and Africa presents significant challenges for future respiratory outbreaks from perspectives of public health and socioeconomic equity.

Allometric Scaling of Mutual Information in Complex Networks: A Conceptual Framework and Empirical Approach.

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.

Poverty in the time of epidemic: A modelling perspective.

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.

Universality Classes and Information-Theoretic Measures of Complexity via Group Entropies.

We introduce a class of information measures based on group entropies, allowing us to describe the information-theoretical properties of complex systems. These entropic measures are nonadditive, and are mathematically deduced from a series of natural axioms. In addition, we require extensivity in order to ensure that our information measures are meaningful. The entropic measures proposed are suitably defined for describing universality classes of complex systems, each characterized by a specific state space growth rate function.

Dynamics of essential interaction between firms on financial reports.

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.

Assembling real networks from synthetic and unstructured subsets: the corporate reporting case.

The analysis of interfirm business transaction networks provides invaluable insight into the trading dynamics and economic structure of countries. However, there is a general scarcity of data available recording real, accurate and extensive information for these types of networks. As a result, and in common with other types of network studies - such as protein interactions for instance - research tends to rely on partial and incomplete datasets, i.e. subsets, with less certain conclusions. Here, we make use of unstructured financial and corporate reporting data in Japan as the base source to construct a financial reporting network, which is then compared and contrasted to the wider real business transaction network. The comparative analysis between these two rich datasets - the proxy, partially derived network and the real, complete network at macro as well as local structural levels - provides an enhanced understanding of the non trivial relationships between partial sampled subsets and fully formed networks. Furthermore, we present an elemental agent based pruning algorithm that reconciles and preserves key structural differences between these two networks, which may serve as an embryonic generic framework of potentially wider use to network research, enabling enhanced extrapolation of conclusions from partial data or subsets.

Network characterization of the Entangled Model for sustainability indicators. Analysis of the network properties for scenarios.

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.

Ethnicity and wealth: The dynamics of dual segregation.

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.

Cooperative dynamics of neighborhood economic status in cities.

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.

Appearance of Unstable Monopoly State Caused by Selective and Concentrative Mergers in Business Networks.

Recently, growth mechanism of firms in complex business networks became new targets of scientific study owing to increasing availability of high quality business firms' data. Here, we paid attention to comprehensive data of M&A events for 40 years and derived empirical laws by applying methods and concepts of aggregation dynamics of aerosol physics. It is found that the probability of merger between bigger firms is bigger than that between smaller ones, and such tendency is enhancing year by year. We introduced a numerical model simulating the whole ecosystem of firms and showed that the system is already in an unstable monopoly state in which growth of middle sized firms are suppressed.

The evolution of ecosystem ascendency in a complex systems based model.

General patterns in ecosystem development can shed light on driving forces behind ecosystem formation and recovery and have been of long interest. In recent years, the need for integrative and process oriented approaches to capture ecosystem growth, development and organisation, as well as the scope of information theory as a descriptive tool has been addressed from various sides. However data collection of ecological network flows is difficult and tedious and comprehensive models are lacking. We use a hierarchical version of the Tangled Nature Model of evolutionary ecology to study the relationship between structure, flow and organisation in model ecosystems, their development over evolutionary time scales and their relation to ecosystem stability. Our findings support the validity of ecosystem ascendency as a meaningful measure of ecosystem organisation, which increases over evolutionary time scales and significantly drops during periods of disturbance. The results suggest a general trend towards both higher integrity and increased stability driven by functional and structural ecosystem coadaptation.

Dynamics of Transformation from Segregation to Mixed Wealth Cities.

We model the dynamics of a variation of the Schelling model for agents described simply by a continuously distributed variable-wealth. Agent movement is not dictated by agent choice as in the classic Schelling model, but by their wealth status. Agents move to neighborhoods where their wealth is not lesser than that of some proportion of their neighbors, the threshold level. As in the case of the classic Schelling model, we find here that wealth-based segregation occurs and persists. However, introducing uncertainty into the decision to move-that is, with some probability, if agents are allowed to move even though the threshold condition is contravened-we find that even for small proportions of such disallowed moves, the dynamics no longer yield segregation but instead sharply transition into a persistent mixed wealth distribution, consistent with empirical findings of Benenson, Hatna, and Or. We investigate the nature of this sharp transformation, and find that it is because of a non-linear relationship between allowed moves (moves where threshold condition is satisfied) and disallowed moves (moves where it is not). For small increases in disallowed moves, there is a rapid corresponding increase in allowed moves (before the rate of increase tapers off and tends to zero), and it is the effect of this non-linearity on the dynamics of the system that causes the rapid transition from a segregated to a mixed wealth state. The contravention of the tolerance condition, sanctioning disallowed moves, could be interpreted as public policy interventions to drive de-segregation. Our finding therefore suggests that it might require limited, but continually implemented, public intervention-just sufficient to enable a small, persistently sustained fraction of disallowed moves so as to trigger the dynamics that drive the transformation from a segregated to mixed equilibrium.

Precise calculation of a bond percolation transition and survival rates of nodes in a complex network.

Through precise numerical analysis, we reveal a new type of universal loopless percolation transition in randomly removed complex networks. As an example of a real-world network, we apply our analysis to a business relation network consisting of approximately 3,000,000 links among 300,000 firms and observe the transition with critical exponents close to the mean-field values taking into account the finite size effect. We focus on the largest cluster at the critical point, and introduce survival probability as a new measure characterizing the robustness of each node. We also discuss the relation between survival probability and k-shell decomposition.

The causal inference of cortical neural networks during music improvisations.

We present an EEG study of two music improvisation experiments. Professional musicians with high level of improvisation skills were asked to perform music either according to notes (composed music) or in improvisation. Each piece of music was performed in two different modes: strict mode and "let-go" mode. Synchronized EEG data was measured from both musicians and listeners. We used one of the most reliable causality measures: conditional Mutual Information from Mixed Embedding (MIME), to analyze directed correlations between different EEG channels, which was combined with network theory to construct both intra-brain and cross-brain networks. Differences were identified in intra-brain neural networks between composed music and improvisation and between strict mode and "let-go" mode. Particular brain regions such as frontal, parietal and temporal regions were found to play a key role in differentiating the brain activities between different playing conditions. By comparing the level of degree centralities in intra-brain neural networks, we found a difference between the response of musicians and the listeners when comparing the different playing conditions.

Quantifying 'causality' in complex systems: understanding transfer entropy.

'Causal' direction is of great importance when dealing with complex systems. Often big volumes of data in the form of time series are available and it is important to develop methods that can inform about possible causal connections between the different observables. Here we investigate the ability of the Transfer Entropy measure to identify causal relations embedded in emergent coherent correlations. We do this by firstly applying Transfer Entropy to an amended Ising model. In addition we use a simple Random Transition model to test the reliability of Transfer Entropy as a measure of 'causal' direction in the presence of stochastic fluctuations. In particular we systematically study the effect of the finite size of data sets.

Forecasting transitions in systems with high-dimensional stochastic complex dynamics: a linear stability analysis of the tangled nature model.

We propose a new procedure to monitor and forecast the onset of transitions in high-dimensional complex systems. We describe our procedure by an application to the tangled nature model of evolutionary ecology. The quasistable configurations of the full stochastic dynamics are taken as input for a stability analysis by means of the deterministic mean-field equations. Numerical analysis of the high-dimensional stability matrix allows us to identify unstable directions associated with eigenvalues with a positive real part. The overlap of the instantaneous configuration vector of the full stochastic system with the eigenvectors of the unstable directions of the deterministic mean-field approximation is found to be a good early warning of the transitions occurring intermittently.