Empirical social triad statistics can be explained with dyadic homophylic interactions.

The remarkable robustness of many social systems has been associated with a peculiar triangular structure in the underlying social networks. Triples of people that have three positive relations (e.g., friendship) between each other are strongly overrepresented. Triples with two negative relations (e.g., enmity) and one positive relation are also overrepresented, and triples with one or three negative relations are drastically suppressed. For almost a century, the mechanism behind these very specific ("balanced") triad statistics remained elusive. Here, we propose a simple realistic adaptive network model, where agents tend to minimize social tension that arises from dyadic interactions. Both opinions of agents and their signed links (positive or negative relations) are updated in the dynamics. The key aspect of the model resides in the fact that agents only need information about their local neighbors in the network and do not require (often unrealistic) higher-order network information for their relation and opinion updates. We demonstrate the quality of the model on detailed temporal relation data of a society of thousands of players of a massive multiplayer online game where we can observe triangle formation directly. It not only successfully predicts the distribution of triangle types but also explains empirical group size distributions, which are essential for social cohesion. We discuss the details of the phase diagrams behind the model and their parameter dependence, and we comment on to what extent the results might apply universally in societies.

Homophily-Based Social Group Formation in a Spin Glass Self-Assembly Framework.

Homophily, the tendency of humans to attract each other when sharing similar features, traits, or opinions, has been identified as one of the main driving forces behind the formation of structured societies. Here we ask to what extent homophily can explain the formation of social groups, particularly their size distribution. We propose a spin-glass-inspired framework of self-assembly, where opinions are represented as multidimensional spins that dynamically self-assemble into groups; individuals within a group tend to share similar opinions (intragroup homophily), and opinions between individuals belonging to different groups tend to be different (intergroup heterophily). We compute the associated nontrivial phase diagram by solving a self-consistency equation for "magnetization" (combined average opinion). Below a critical temperature, there exist two stable phases: one ordered with nonzero magnetization and large clusters, the other disordered with zero magnetization and no clusters. The system exhibits a first-order transition to the disordered phase. We analytically derive the group-size distribution that successfully matches empirical group-size distributions from online communities.

A network-based explanation of why most COVID-19 infection curves are linear.

Many countries have passed their first COVID-19 epidemic peak. Traditional epidemiological models describe this as a result of nonpharmaceutical interventions pushing the growth rate below the recovery rate. In this phase of the pandemic many countries showed an almost linear growth of confirmed cases for extended time periods. This new containment regime is hard to explain by traditional models where either infection numbers grow explosively until herd immunity is reached or the epidemic is completely suppressed. Here we offer an explanation of this puzzling observation based on the structure of contact networks. We show that for any given transmission rate there exists a critical number of social contacts, [Formula: see text], below which linear growth and low infection prevalence must occur. Above [Formula: see text] traditional epidemiological dynamics take place, e.g., as in susceptible-infected-recovered (SIR) models. When calibrating our model to empirical estimates of the transmission rate and the number of days being contagious, we find [Formula: see text] Assuming realistic contact networks with a degree of about 5, and assuming that lockdown measures would reduce that to household size (about 2.5), we reproduce actual infection curves with remarkable precision, without fitting or fine-tuning of parameters. In particular, we compare the United States and Austria, as examples for one country that initially did not impose measures and one that responded with a severe lockdown early on. Our findings question the applicability of standard compartmental models to describe the COVID-19 containment phase. The probability to observe linear growth in these is practically zero.

Balancing Quarantine and Self-Distancing Measures in Adaptive Epidemic Networks.

We study the relative importance of two key control measures for epidemic spreading: endogenous social self-distancing and exogenous imposed quarantine. We use the framework of adaptive networks, moment-closure, and ordinary differential equations to introduce new model types of susceptible-infected-recovered (SIR) dynamics. First, we compare computationally expensive, adaptive network simulations with their corresponding computationally efficient ODE equivalents and find excellent agreement. Second, we discover that there exists a critical curve in parameter space for the epidemic threshold, which suggests a mutual compensation effect between the two mitigation strategies: as long as social distancing and quarantine measures are both sufficiently strong, large outbreaks are prevented. Third, we study the total number of infected and the maximum peak during large outbreaks using a combination of analytical estimates and numerical simulations. Also for large outbreaks we find a similar compensation mechanism as for the epidemic threshold. This means that if there is little incentive for social distancing in a population, drastic quarantining is required, and vice versa. Both pure scenarios are unrealistic in practice. The new models show that only a combination of measures is likely to succeed to control epidemic spreading. Fourth, we analytically compute an upper bound for the total number of infected on adaptive networks, using integral estimates in combination with a moment-closure approximation on the level of an observable. Our method allows us to elegantly and quickly check and cross-validate various conjectures about the relevance of different network control measures. In this sense it becomes possible to adapt also other models rapidly to new epidemic challenges.

Quantification of the resilience of primary care networks by stress testing the health care system.

There are practically no quantitative tools for understanding how much stress a health care system can absorb before it loses its ability to provide care. We propose to measure the resilience of health care systems with respect to changes in the density of primary care providers. We develop a computational model on a 1-to-1 scale for a countrywide primary care sector based on patient-sharing networks. Nodes represent all primary care providers in a country; links indicate patient flows between them. The removal of providers could cause a cascade of patient displacements, as patients have to find alternative providers. The model is calibrated with nationwide data from Austria that includes almost all primary care contacts over 2 y. We assign 2 properties to every provider: the "CareRank" measures the average number of displacements caused by a provider's removal (systemic risk) as well as the fraction of patients a provider can absorb when others default (systemic benefit). Below a critical number of providers, large-scale cascades of patient displacements occur, and no more providers can be found in a given region. We quantify regional resilience as the maximum fraction of providers that can be removed before cascading events prevent coverage for all patients within a district. We find considerable regional heterogeneity in the critical transition point from resilient to nonresilient behavior. We demonstrate that health care resilience cannot be quantified by physician density alone but must take into account how networked systems respond and restructure in response to shocks. The approach can identify systemically relevant providers.

Relative risk of arterial and venous thromboembolism in persons with cancer vs. persons without cancer-a nationwide analysis.

AIMS: An interrelation between cancer and thrombosis is known, but population-based studies on the risk of both arterial thromboembolism (ATE) and venous thromboembolism (VTE) have not been performed. METHODS AND RESULTS: International Classification of Disease 10th Revision (ICD-10) diagnosis codes of all publicly insured persons in Austria (0-90 years) were extracted from the Austrian Association of Social Security Providers dataset covering the years 2006-07 (n = 8 306 244). Patients with a history of cancer or active cancer were defined as having at least one ICD-10 'C' diagnosis code, and patients with ATE and/or VTE as having at least one of I21/I24 (myocardial infarction), I63/I64 (stroke), I74 (arterial embolism), and I26/I80/I82 (venous thromboembolism) diagnosis code. Among 158 675 people with cancer, 8559 (5.4%) had an ATE diagnosis code and 7244 (4.6%) a VTE diagnosis code. In contrast, among 8 147 569 people without cancer, 69 381 (0.9%) had an ATE diagnosis code and 29 307 (0.4%) a VTE diagnosis code. This corresponds to age-stratified random-effects relative risks (RR) of 6.88 [95% confidence interval (CI) 4.81-9.84] for ATE and 14.91 (95% CI 8.90-24.95) for VTE. ATE proportion was highest in patients with urinary tract malignancies (RR: 7.16 [6.74-7.61]) and lowest in patients with endocrine cancer (RR: 2.49 [2.00-3.10]). The corresponding VTE proportion was highest in cancer of the mesothelium/soft tissue (RR: 19.35 [17.44-21.47]) and lowest in oropharyngeal cancer (RR: 6.62 [5.61-7.81]). CONCLUSION: The RR of both ATE and VTE are significantly higher in persons with cancer. Our population-level meta-data indicate a strong association between cancer, ATE and VTE, and support the concept of shared risk factors and pathobiology between these diseases.Relative risk of ATE and VTE in persons with a cancer diagnosis code versus persons without a cancer diagnosis code.

Bali's Ancient Rice Terraces: A Hamiltonian Approach.

We propose a Hamiltonian approach to reproduce the relevant elements of the centuries-old Subak irrigation system in Bali, showing a cluster-size distribution of rice-field patches that is a power-law with an exponent of ∼2. Besides this exponent, the resulting system presents two equilibria. The first originates from a balance between energy and entropy contributions. The second arises from the specific energy contribution through a local Potts-type interaction in combination with a long-range antiferromagnetic interaction without attenuation. Finite-size scaling analysis shows that, as a result of the second equilibrium, the critical transition balancing energy and entropy contributions at the Potts (local ferromagnetic) regime is absorbed by the transition driven by the global-antiferromagnetic interactions, as the system size increases. The phase transition balancing energy and entropy contributions at the global-antiferromagnetic regime also shows signs of criticality. Our study extends the Hamiltonian framework to a new domain of coupled human-environmental interactions.

High-risk multimorbidity patterns on the road to cardiovascular mortality.

BACKGROUND: Multimorbidity, the co-occurrence of two or more diseases in one patient, is a frequent phenomenon. Understanding how different diseases condition each other over the lifetime of a patient could significantly contribute to personalised prevention efforts. However, most of our current knowledge on the long-term development of the health of patients (their disease trajectories) is either confined to narrow time spans or specific (sets of) diseases. Here, we aim to identify decisive events that potentially determine the future disease progression of patients. METHODS: Health states of patients are described by algorithmically identified multimorbidity patterns (groups of included or excluded diseases) in a population-wide analysis of 9,000,000 patient histories of hospital diagnoses observed over 17 years. Over time, patients might acquire new diagnoses that change their health state; they describe a disease trajectory. We measure the age- and sex-specific risks for patients that they will acquire certain sets of diseases in the future depending on their current health state. RESULTS: In the present analysis, the population is described by a set of 132 different multimorbidity patterns. For elderly patients, we find 3 groups of multimorbidity patterns associated with low (yearly in-hospital mortality of 0.2-0.3%), medium (0.3-1%) and high in-hospital mortality (2-11%). We identify combinations of diseases that significantly increase the risk to reach the high-mortality health states in later life. For instance, in men (women) aged 50-59 diagnosed with diabetes and hypertension, the risk for moving into the high-mortality region within 1 year is increased by the factor of 1.96 ± 0.11 (2.60 ± 0.18) compared with all patients of the same age and sex, respectively, and by the factor of 2.09 ± 0.12 (3.04 ± 0.18) if additionally diagnosed with metabolic disorders. CONCLUSIONS: Our approach can be used both to forecast future disease burdens, as well as to identify the critical events in the careers of patients which strongly determine their disease progression, therefore constituting targets for efficient prevention measures. We show that the risk for cardiovascular diseases increases significantly more in females than in males when diagnosed with diabetes, hypertension and metabolic disorders.

Healthcare utilization, psychiatric medication and risk of rehospitalization in suicide-attempting patients with common mental disorders.

OBJECTIVE: Common mental disorders are strong risk factors for suicide attempt. We compared common mental disorder patients with and without suicide attempt regarding health care utilization and psychiatric medication, assessed gender differences and identified how psychotropic medication of attempters is associated with subsequent rehospitalization. METHODS: We used administrative claims data of 22,276 common mental disorder patients with inpatient care in Lower Austria between 1 January 2006 and 31 December 2011. Suicide attempters (cases, n = 615) and non-attempters (controls, n = 21,661) were compared regarding specific healthcare utilization by calculating mean differences of time-dependent contact probabilities and psychiatric medication (i.e. prescribed defined daily doses) ± 0.5 years around their suicide attempt (cases)/common mental disorder diagnosis (controls). Cluster analysis was used to group suicide attempters according to their psychiatric medication. The risk of rehospitalization 0.5-3 years after the attempt was calculated with regression analysis controlling for sex, age and morbidity-related factors. RESULTS: Contacts with general practitioners were lower for attempters than non-attempters (mean difference of contact probabilities over observation period, males = -0.05, 95% confidence interval = [-0.07, -0.03]; females: mean difference = -0.04, 95% confidence interval = [-0.05, -0.03]). Regarding psychiatrists, female attempters had markedly higher contact probabilities after the attempt compared to female non-attempters (mean difference = 0.02, 95% confidence interval = [0.007, 0.04]); male attempters had lower contact probabilities before the attempt compared to male non-attempters (mean difference = -0.01, 95% confidence interval = [-0.004, -0.02]). Attempters had higher dosages of psychiatric medication across the entire period. Antidepressant and antipsychotic medication peaked at the time of common mental disorder diagnosis/attempt. Benzodiazepine prescriptions were considerably higher for male attempters than their female counterparts and were constantly elevated for male attempters across the observation period. A cluster of attempters with long-term benzodiazepine prescriptions had an increased risk of rehospitalization (adjusted odds ratio = 2.4, 95% confidence interval = [1.1, 5.5]). CONCLUSION: Despite lower contact probabilities, common mental disorder patients with suicide attempt are prescribed more psychiatric medication, particularly benzodiazepines, with an elevated risk of rehospitalization. Strong sex differences were found.

Adaptive self-organization of Bali's ancient rice terraces.

Spatial patterning often occurs in ecosystems as a result of a self-organizing process caused by feedback between organisms and the physical environment. Here, we show that the spatial patterns observable in centuries-old Balinese rice terraces are also created by feedback between farmers' decisions and the ecology of the paddies, which triggers a transition from local to global-scale control of water shortages and rice pests. We propose an evolutionary game, based on local farmers' decisions that predicts specific power laws in spatial patterning that are also seen in a multispectral image analysis of Balinese rice terraces. The model shows how feedbacks between human decisions and ecosystem processes can evolve toward an optimal state in which total harvests are maximized and the system approaches Pareto optimality. It helps explain how multiscale cooperation from the community to the watershed scale could persist for centuries, and why the disruption of this self-organizing system by the Green Revolution caused chaos in irrigation and devastating losses from pests. The model shows that adaptation in a coupled human-natural system can trigger self-organized criticality (SOC). In previous exogenously driven SOC models, adaptation plays no role, and no optimization occurs. In contrast, adaptive SOC is a self-organizing process where local adaptations drive the system toward local and global optima.

Kinship structures create persistent channels for language transmission.

Languages are transmitted through channels created by kinship systems. Given sufficient time, these kinship channels can change the genetic and linguistic structure of populations. In traditional societies of eastern Indonesia, finely resolved cophylogenies of languages and genes reveal persistent movements between stable speech communities facilitated by kinship rules. When multiple languages are present in a region and postmarital residence rules encourage sustained directional movement between speech communities, then languages should be channeled along uniparental lines. We find strong evidence for this pattern in 982 individuals from 25 villages on two adjacent islands, where different kinship rules have been followed. Core groups of close relatives have stayed together for generations, while remaining in contact with, and marrying into, surrounding groups. Over time, these kinship systems shaped their gene and language phylogenies: Consistently following a postmarital residence rule turned social communities into speech communities.

Diagnosis of osteoporosis in statin-treated patients is dose-dependent.

OBJECTIVE: Whether HMG-CoA-reductase inhibition, the main mechanism of statins, plays a role in the pathogenesis of osteoporosis, is not entirely known so far. Consequently, this study was set out to investigate the relationship of different kinds and dosages of statins with osteoporosis, hypothesising that the inhibition of the synthesis of cholesterol could influence sex-hormones and therefore the diagnosis of osteoporosis. METHODS: Medical claims data of all Austrians from 2006 to 2007 was used to identify all patients treated with statins to compute their daily defined dose averages of six different types of statins. We applied multiple logistic regression to analyse the dose-dependent risks of being diagnosed with osteoporosis for each statin individually. RESULTS: In the general study population, statin treatment was associated with an overrepresentation of diagnosed osteoporosis compared with controls (OR: 3.62, 95% CI 3.55 to 3.69, p<0.01). There was a highly non-trivial dependence of statin dosage with the ORs of osteoporosis. Osteoporosis was underrepresented in low-dose statin treatment (0-10 mg per day), including lovastatin (OR: 0.39, CI 0.18 to 0.84, p<0.05), pravastatin (OR: 0.68, 95% CI 0.52 to 0.89, p<0.01), simvastatin (OR: 0.70, 95% CI 0.56 to 0.86, p<0.01) and rosuvastatin (OR: 0.69, 95% CI 0.55 to 0.87, p<0.01). However, the exceeding of the 40 mg threshold for simvastatin (OR: 1.64, 95% CI 1.31 to 2.07, p<0.01), and the exceeding of a 20 mg threshold for atorvastatin (OR: 1.78, 95% CI 1.41 to 2.23, p<0.01) and for rosuvastatin (OR: 2.04, 95% CI 1.31 to 3.18, p<0.01) was related to an overrepresentation of osteoporosis. CONCLUSION: Our results show that the diagnosis of osteoporosis in statin-treated patients is dose-dependent. Thus, osteoporosis is underrepresented in low-dose and overrepresented in high-dose statin treatment, demonstrating the importance of future studies' taking dose-dependency into account when investigating the relationship between statins and osteoporosis.

Information Geometric Duality of ϕ-Deformed Exponential Families.

In the world of generalized entropies-which, for example, play a role in physical systems with sub- and super-exponential phase space growth per degree of freedom-there are two ways for implementing constraints in the maximum entropy principle: linear and escort constraints. Both appear naturally in different contexts. Linear constraints appear, e.g., in physical systems, when additional information about the system is available through higher moments. Escort distributions appear naturally in the context of multifractals and information geometry. It was shown recently that there exists a fundamental duality that relates both approaches on the basis of the corresponding deformed logarithms (deformed-log duality). Here, we show that there exists another duality that arises in the context of information geometry, relating the Fisher information of ϕ -deformed exponential families that correspond to linear constraints (as studied by J.Naudts) to those that are based on escort constraints (as studied by S.-I. Amari). We explicitly demonstrate this information geometric duality for the case of ( c , d ) -entropy, which covers all situations that are compatible with the first three Shannon-Khinchin axioms and that include Shannon, Tsallis, Anteneodo-Plastino entropy, and many more as special cases. Finally, we discuss the relation between the deformed-log duality and the information geometric duality and mention that the escort distributions arising in these two dualities are generally different and only coincide for the case of the Tsallis deformation.

Nonadditive Entropies and Complex Systems.

An entropic functional S is said additive if it satisfies, for any two probabilistically independent systems A and B, that S ( A + B ) = S ( A ) + S ( B ) [...].

Understanding scaling through history-dependent processes with collapsing sample space.

History-dependent processes are ubiquitous in natural and social systems. Many such stochastic processes, especially those that are associated with complex systems, become more constrained as they unfold, meaning that their sample space, or their set of possible outcomes, reduces as they age. We demonstrate that these sample-space-reducing (SSR) processes necessarily lead to Zipf's law in the rank distributions of their outcomes. We show that by adding noise to SSR processes the corresponding rank distributions remain exact power laws, p(x) ~ x(-λ), where the exponent directly corresponds to the mixing ratio of the SSR process and noise. This allows us to give a precise meaning to the scaling exponent in terms of the degree to which a given process reduces its sample space as it unfolds. Noisy SSR processes further allow us to explain a wide range of scaling exponents in frequency distributions ranging from α = 2 to ∞. We discuss several applications showing how SSR processes can be used to understand Zipf's law in word frequencies, and how they are related to diffusion processes in directed networks, or aging processes such as in fragmentation processes. SSR processes provide a new alternative to understand the origin of scaling in complex systems without the recourse to multiplicative, preferential, or self-organized critical processes.

Maximum Configuration Principle for Driven Systems with Arbitrary Driving.

Depending on context, the term entropy is used for a thermodynamic quantity, a measure of available choice, a quantity to measure information, or, in the context of statistical inference, a maximum configuration predictor. For systems in equilibrium or processes without memory, the mathematical expression for these different concepts of entropy appears to be the so-called Boltzmann-Gibbs-Shannon entropy, H. For processes with memory, such as driven- or self- reinforcing-processes, this is no longer true: the different entropy concepts lead to distinct functionals that generally differ from H. Here we focus on the maximum configuration entropy (that predicts empirical distribution functions) in the context of driven dissipative systems. We develop the corresponding framework and derive the entropy functional that describes the distribution of observable states as a function of the details of the driving process. We do this for sample space reducing (SSR) processes, which provide an analytically tractable model for driven dissipative systems with controllable driving. The fact that a consistent framework for a maximum configuration entropy exists for arbitrarily driven non-equilibrium systems opens the possibility of deriving a full statistical theory of driven dissipative systems of this kind. This provides us with the technical means needed to derive a thermodynamic theory of driven processes based on a statistical theory. We discuss the Legendre structure for driven systems.

Identifying Systemically Important Companies by Using the Credit Network of an Entire Nation.

The notions of systemic importance and systemic risk of financial institutions are closely related to the topology of financial liability networks. In this work, we reconstruct and analyze the financial liability network of an entire economy using data of 50,159 firms and banks. Our analysis contains 80.2% of the total liabilities of firms towards banks and all interbank liabilities in the Austrian banking system. The combination of firm-bank networks and interbank networks allows us to extend the concept of systemic risk to the real economy. In particular, the systemic importance of individual companies can be assessed, and for the first time, the financial ties between the financial and the real economy become explicitly visible. We find that firms contribute to systemic risk in similar ways as banks do. We identify a set of mid-sized companies that carry substantial systemic risk. Their default would affect up to 40% of the Austrian financial market. We find that all firms together create more systemic risk than the entire financial sector. In 2008, the total systemic risk of the Austrian interbank network amounted to only 29% of the total systemic risk of the entire financial network consisting of firms and banks. The work demonstrates that the notions of systemically important financial institutions (SIFIs) can be directly extended to firms.

How multiplicity determines entropy and the derivation of the maximum entropy principle for complex systems.

The maximum entropy principle (MEP) is a method for obtaining the most likely distribution functions of observables from statistical systems by maximizing entropy under constraints. The MEP has found hundreds of applications in ergodic and Markovian systems in statistical mechanics, information theory, and statistics. For several decades there has been an ongoing controversy over whether the notion of the maximum entropy principle can be extended in a meaningful way to nonextensive, nonergodic, and complex statistical systems and processes. In this paper we start by reviewing how Boltzmann-Gibbs-Shannon entropy is related to multiplicities of independent random processes. We then show how the relaxation of independence naturally leads to the most general entropies that are compatible with the first three Shannon-Khinchin axioms, the (c,d)-entropies. We demonstrate that the MEP is a perfectly consistent concept for nonergodic and complex statistical systems if their relative entropy can be factored into a generalized multiplicity and a constraint term. The problem of finding such a factorization reduces to finding an appropriate representation of relative entropy in a linear basis. In a particular example we show that path-dependent random processes with memory naturally require specific generalized entropies. The example is to our knowledge the first exact derivation of a generalized entropy from the microscopic properties of a path-dependent random process.

Dealing with femtorisks in international relations.

The contemporary global community is increasingly interdependent and confronted with systemic risks posed by the actions and interactions of actors existing beneath the level of formal institutions, often operating outside effective governance structures. Frequently, these actors are human agents, such as rogue traders or aggressive financial innovators, terrorists, groups of dissidents, or unauthorized sources of sensitive or secret information about government or private sector activities. In other instances, influential "actors" take the form of climate change, communications technologies, or socioeconomic globalization. Although these individual forces may be small relative to state governments or international institutions, or may operate on long time scales, the changes they catalyze can pose significant challenges to the analysis and practice of international relations through the operation of complex feedbacks and interactions of individual agents and interconnected systems. We call these challenges "femtorisks," and emphasize their importance for two reasons. First, in isolation, they may be inconsequential and semiautonomous; but when embedded in complex adaptive systems, characterized by individual agents able to change, learn from experience, and pursue their own agendas, the strategic interaction between actors can propel systems down paths of increasing, even global, instability. Second, because their influence stems from complex interactions at interfaces of multiple systems (e.g., social, financial, political, technological, ecological, etc.), femtorisks challenge standard approaches to risk assessment, as higher-order consequences cascade across the boundaries of socially constructed complex systems. We argue that new approaches to assessing and managing systemic risk in international relations are required, inspired by principles of evolutionary theory and development of resilient ecological systems.