Characterizing unstructured data with the nearest neighbor permutation entropy.

Permutation entropy and its associated frameworks are remarkable examples of physics-inspired techniques adept at processing complex and extensive datasets. Despite substantial progress in developing and applying these tools, their use has been predominantly limited to structured datasets such as time series or images. Here, we introduce the k-nearest neighbor permutation entropy, an innovative extension of the permutation entropy tailored for unstructured data, irrespective of their spatial or temporal configuration and dimensionality. Our approach builds upon nearest neighbor graphs to establish neighborhood relations and uses random walks to extract ordinal patterns and their distribution, thereby defining the k-nearest neighbor permutation entropy. This tool not only adeptly identifies variations in patterns of unstructured data but also does so with a precision that significantly surpasses conventional measures such as spatial autocorrelation. Additionally, it provides a natural approach for incorporating amplitude information and time gaps when analyzing time series or images, thus significantly enhancing its noise resilience and predictive capabilities compared to the usual permutation entropy. Our research substantially expands the applicability of ordinal methods to more general data types, opening promising research avenues for extending the permutation entropy toolkit for unstructured data.

Dynamics of parkinsonian oscillations mediated by transmission delays in a mean-field model of the basal ganglia.

Introduction: Neural interactions in the brain are affected by transmission delays which may critically alter signal propagation across different brain regions in both normal and pathological conditions. The effect of interaction delays on the dynamics of the generic neural networks has been extensively studied by theoretical and computational models. However, the role of transmission delays in the development of pathological oscillatory dynamics in the basal ganglia (BG) in Parkinson's disease (PD) is overlooked. Methods: Here, we investigate the effect of transmission delays on the discharge rate and oscillatory power of the BG networks in control (normal) and PD states by using a Wilson-Cowan (WC) mean-field firing rate model. We also explore how transmission delays affect the response of the BG to cortical stimuli in control and PD conditions. Results: Our results show that the BG oscillatory response to cortical stimulation in control condition is robust against the changes in the inter-population delays and merely depends on the phase of stimulation with respect to cortical activity. In PD condition, however, transmission delays crucially contribute to the emergence of abnormal alpha (8-13 Hz) and beta band (13-30 Hz) oscillations, suggesting that delays play an important role in abnormal rhythmogenesis in the parkinsonian BG. Discussion: Our findings indicate that in addition to the strength of connections within and between the BG nuclei, oscillatory dynamics of the parkinsonian BG may also be influenced by inter-population transmission delays. Moreover, phase-specificity of the BG response to cortical stimulation may provide further insight into the potential role of delays in the computational optimization of phase-specific brain stimulation therapies.

EEG-based finger movement classification with intrinsic time-scale decomposition.

Introduction: Brain-computer interfaces (BCIs) are systems that acquire the brain's electrical activity and provide control of external devices. Since electroencephalography (EEG) is the simplest non-invasive method to capture the brain's electrical activity, EEG-based BCIs are very popular designs. Aside from classifying the extremity movements, recent BCI studies have focused on the accurate coding of the finger movements on the same hand through their classification by employing machine learning techniques. State-of-the-art studies were interested in coding five finger movements by neglecting the brain's idle case (i.e., the state that brain is not performing any mental tasks). This may easily cause more false positives and degrade the classification performances dramatically, thus, the performance of BCIs. This study aims to propose a more realistic system to decode the movements of five fingers and the no mental task (NoMT) case from EEG signals. Methods: In this study, a novel praxis for feature extraction is utilized. Using Proper Rotational Components (PRCs) computed through Intrinsic Time Scale Decomposition (ITD), which has been successfully applied in different biomedical signals recently, features for classification are extracted. Subsequently, these features were applied to the inputs of well-known classifiers and their different implementations to discriminate between these six classes. The highest classifier performances obtained in both subject-independent and subject-dependent cases were reported. In addition, the ANOVA-based feature selection was examined to determine whether statistically significant features have an impact on the classifier performances or not. Results: As a result, the Ensemble Learning classifier achieved the highest accuracy of 55.0% among the tested classifiers, and ANOVA-based feature selection increases the performance of classifiers on five-finger movement determination in EEG-based BCI systems. Discussion: When compared with similar studies, proposed praxis achieved a modest yet significant improvement in classification performance although the number of classes was incremented by one (i.e., NoMT).

Topological features of spike trains in recurrent spiking neural networks that are trained to generate spatiotemporal patterns.

In this study, we focus on training recurrent spiking neural networks to generate spatiotemporal patterns in the form of closed two-dimensional trajectories. Spike trains in the trained networks are examined in terms of their dissimilarity using the Victor-Purpura distance. We apply algebraic topology methods to the matrices obtained by rank-ordering the entries of the distance matrices, specifically calculating the persistence barcodes and Betti curves. By comparing the features of different types of output patterns, we uncover the complex relations between low-dimensional target signals and the underlying multidimensional spike trains.

Success-driven opinion formation determines social tensions.

Polarization is common in politics and public opinion. It is believed to be shaped by media as well as ideologies, and often incited by misinformation. However, little is known about the microscopic dynamics behind polarization and the resulting social tensions. By coupling opinion formation with the strategy selection in different social dilemmas, we reveal how success at an individual level transforms to global consensus or lack thereof. When defection carries with it the fear of punishment in the absence of greed, as in the stag-hunt game, opinion fragmentation is the smallest. Conversely, if defection promises a higher payoff and also evokes greed, like in the prisoner's dilemma and snowdrift game, consensus is more difficult to attain. Our research thus challenges the top-down narrative of social tensions, showing they might originate from fundamental principles at individual level, like the desire to prevail in pairwise evolutionary comparisons.

Language-based game theory in the age of artificial intelligence.

Understanding human behaviour in decision problems and strategic interactions has wide-ranging applications in economics, psychology and artificial intelligence. Game theory offers a robust foundation for this understanding, based on the idea that individuals aim to maximize a utility function. However, the exact factors influencing strategy choices remain elusive. While traditional models try to explain human behaviour as a function of the outcomes of available actions, recent experimental research reveals that linguistic content significantly impacts decision-making, thus prompting a paradigm shift from outcome-based to language-based utility functions. This shift is more urgent than ever, given the advancement of generative AI, which has the potential to support humans in making critical decisions through language-based interactions. We propose sentiment analysis as a fundamental tool for this shift and take an initial step by analysing 61 experimental instructions from the dictator game, an economic game capturing the balance between self-interest and the interest of others, which is at the core of many social interactions. Our meta-analysis shows that sentiment analysis can explain human behaviour beyond economic outcomes. We discuss future research directions. We hope this work sets the stage for a novel game-theoretical approach that emphasizes the importance of language in human decisions.

Assortative mixing of opinions about COVID-19 vaccination in personal networks.

Many countries worldwide had difficulties reaching a sufficiently high vaccination uptake during the COVID-19 pandemic. Given this context, we collected data from a panel of 30,000 individuals, which were representative of the population of Romania (a country in Eastern Europe with a low 42.6% vaccination rate) to determine whether people are more likely to be connected to peers displaying similar opinions about COVID-19 vaccination. We extracted 443 personal networks, amounting to 4430 alters. We estimated multilevel logistic regression models with random-ego-level intercepts to predict individual opinions about COVID-19 vaccination. Our evidence indicates positive opinions about the COVID-19 vaccination cluster. Namely, the likelihood of having a positive opinion about COVID-19 vaccination increases when peers have, on average, a more positive attitude than the rest of the nodes in the network (OR 1.31, p < 0.001). We also found that individuals with higher education and age are more likely to hold a positive opinion about COVID-19 vaccination. With the given empirical data, our study cannot reveal whether this assortative mixing of opinions is due to social influence or social selection. However, it may nevertheless have implications for public health interventions, especially in countries that strive to reach higher uptake rates. Understanding opinions about vaccination can act as an early warning system for potential outbreaks, inform predictions about vaccination uptake, or help supply chain management for vaccine distribution.

Synchronization in simplicial complexes of memristive Rulkov neurons.

Simplicial complexes are mathematical constructions that describe higher-order interactions within the interconnecting elements of a network. Such higher-order interactions become increasingly significant in neuronal networks since biological backgrounds and previous outcomes back them. In light of this, the current research explores a higher-order network of the memristive Rulkov model. To that end, the master stability functions are used to evaluate the synchronization of a network with pure pairwise hybrid (electrical and chemical) synapses alongside a network with two-node electrical and multi-node chemical connections. The findings provide good insight into the impact of incorporating higher-order interaction in a network. Compared to two-node chemical synapses, higher-order interactions adjust the synchronization patterns to lower multi-node chemical coupling parameter values. Furthermore, the effect of altering higher-order coupling parameter value on the dynamics of neurons in the synchronization state is researched. It is also shown how increasing network size can enhance synchronization by lowering the value of coupling parameters whereby synchronization occurs. Except for complete synchronization, cluster synchronization is detected for higher electrical coupling strength values wherein the neurons are out of the completed synchronization state.

Self-organization in Slovenian public spending.

Private businesses are often entrusted with public contracts, wherein public money is allocated to a private company. This process raises concerns about transparency, even in the most developed democracies. But are there any regularities guiding this process? Do all private companies benefit equally from the state budgets? Here, we tackle these questions focusing on the case of Slovenia, which keeps excellent records of this kind of public spending. We examine a dataset detailing every transfer of public money to the private sector from January 2003 to May 2020. During this time, Slovenia has conducted business with no less than 248 989 private companies. We find that the cumulative distribution of money received per company can be reasonably well explained by a power-law or lognormal fit. We also show evidence for the first-mover advantage, and determine that companies receive new funding in a way that is roughly linear over time. These results indicate that, despite all human factors involved, Slovenian public spending is at least to some extent regulated by emergent self-organizing principles.

Time delays shape the eco-evolutionary dynamics of cooperation.

We study the intricate interplay between ecological and evolutionary processes through the lens of the prisoner's dilemma game. But while previous studies on cooperation amongst selfish individuals often assume instantaneous interactions, we take into consideration delays to investigate how these might affect the causes underlying prosocial behavior. Through analytical calculations and numerical simulations, we demonstrate that delays can lead to oscillations, and by incorporating also the ecological variable of altruistic free space and the evolutionary strategy of punishment, we explore how these factors impact population and community dynamics. Depending on the parameter values and the initial fraction of each strategy, the studied eco-evolutionary model can mimic a cyclic dominance system and even exhibit chaotic behavior, thereby highlighting the importance of complex dynamics for the effective management and conservation of ecological communities. Our research thus contributes to the broader understanding of group decision-making and the emergence of moral behavior in multidimensional social systems.

Complexity of the COVID-19 pandemic in Maringá.

While extensive literature exists on the COVID-19 pandemic at regional and national levels, understanding its dynamics and consequences at the city level remains limited. This study investigates the pandemic in Maringá, a medium-sized city in Brazil's South Region, using data obtained by actively monitoring the disease from March 2020 to June 2022. Despite prompt and robust interventions, COVID-19 cases increased exponentially during the early spread of COVID-19, with a reproduction number lower than that observed during the initial outbreak in Wuhan. Our research demonstrates the remarkable impact of non-pharmaceutical interventions on both mobility and pandemic indicators, particularly during the onset and the most severe phases of the emergency. However, our results suggest that the city's measures were primarily reactive rather than proactive. Maringá faced six waves of cases, with the third and fourth waves being the deadliest, responsible for over two-thirds of all deaths and overwhelming the local healthcare system. Excess mortality during this period exceeded deaths attributed to COVID-19, indicating that the burdened healthcare system may have contributed to increased mortality from other causes. By the end of the fourth wave, nearly three-quarters of the city's population had received two vaccine doses, significantly decreasing deaths despite the surge caused by the Omicron variant. Finally, we compare these findings with the national context and other similarly sized cities, highlighting substantial heterogeneities in the spread and impact of the disease.

Profiling of patients with type 2 diabetes based on medication adherence data.

Introduction: Type 2 diabetes mellitus (T2DM) is a complex, chronic disease affecting multiple organs with varying symptoms and comorbidities. Profiling patients helps identify those with unfavorable disease progression, allowing for tailored therapy and addressing special needs. This study aims to uncover different T2DM profiles based on medication intake records and laboratory measurements, with a focus on how individuals with diabetes move through disease phases. Methods: We use medical records from databases of the last 20 years from the Department of Endocrinology and Diabetology of the University Medical Center in Maribor. Using the standard ATC medication classification system, we created a patient-specific drug profile, created using advanced natural language processing methods combined with data mining and hierarchical clustering. Results: Our results show a well-structured profile distribution characterizing different age groups of individuals with diabetes. Interestingly, only two main profiles characterize the early 40-50 age group, and the same is true for the last 80+ age group. One of these profiles includes individuals with diabetes with very low use of various medications, while the other profile includes individuals with diabetes with much higher use. The number in both groups is reciprocal. Conversely, the middle-aged groups are characterized by several distinct profiles with a wide range of medications that are associated with the distinct concomitant complications of T2DM. It is intuitive that the number of profiles increases in the later age groups, but it is not obvious why it is reduced later in the 80+ age group. In this context, further studies are needed to evaluate the contributions of a range of factors, such as drug development, drug adoption, and the impact of mortality associated with all T2DM-related diseases, which characterize these middle-aged groups, particularly those aged 55-75. Conclusion: Our approach aligns with existing studies and can be widely implemented without complex or expensive analyses. Treatment and drug use data are readily available in healthcare facilities worldwide, allowing for profiling insights into individuals with diabetes. Integrating data from other departments, such as cardiology and renal disease, may provide a more sophisticated understanding of T2DM patient profiles.

Statistically significant features improve binary and multiple Motor Imagery task predictions from EEGs.

In recent studies, in the field of Brain-Computer Interface (BCI), researchers have focused on Motor Imagery tasks. Motor Imagery-based electroencephalogram (EEG) signals provide the interaction and communication between the paralyzed patients and the outside world for moving and controlling external devices such as wheelchair and moving cursors. However, current approaches in the Motor Imagery-BCI system design require effective feature extraction methods and classification algorithms to acquire discriminative features from EEG signals due to the non-linear and non-stationary structure of EEG signals. This study investigates the effect of statistical significance-based feature selection on binary and multi-class Motor Imagery EEG signal classifications. In the feature extraction process performed 24 different time-domain features, 15 different frequency-domain features which are energy, variance, and entropy of Fourier transform within five EEG frequency subbands, 15 different time-frequency domain features which are energy, variance, and entropy of Wavelet transform based on five EEG frequency subbands, and 4 different Poincare plot-based non-linear parameters are extracted from each EEG channel. A total of 1,364 Motor Imagery EEG features are supplied from 22 channel EEG signals for each input EEG data. In the statistical significance-based feature selection process, the best one among all possible combinations of these features is tried to be determined using the independent t-test and one-way analysis of variance (ANOVA) test on binary and multi-class Motor Imagery EEG signal classifications, respectively. The whole extracted feature set and the feature set that contain statistically significant features only are classified in this study. We implemented 6 and 7 different classifiers in multi-class and binary (two-class) classification tasks, respectively. The classification process is evaluated using the five-fold cross-validation method, and each classification algorithm is tested 10 times. These repeated tests provide to check the repeatability of the results. The maximum of 61.86 and 47.36% for the two-class and four-class scenarios, respectively, are obtained with Ensemble Subspace Discriminant among all these classifiers using selected features including only statistically significant features. The results reveal that the introduced statistical significance-based feature selection approach improves the classifier performances by achieving higher classifier performances with fewer relevant components in Motor Imagery task classification. In conclusion, the main contribution of the presented study is two-fold evaluation of non-linear parameters as an alternative to the commonly used features and the prediction of multiple Motor Imagery tasks using statistically significant features.

Reputation and reciprocity.

Reputation and reciprocity are key mechanisms for cooperation in human societies, often going hand in hand to favor prosocial behavior over selfish actions. Here we review recent researches at the interface of physics and evolutionary game theory that explored these two mechanisms. We focus on image scoring as the bearer of reputation, as well as on various types of reciprocity, including direct, indirect, and network reciprocity. We review different definitions of reputation and reciprocity dynamics, and we show how these affect the evolution of cooperation in social dilemmas. We consider first-order, second-order, as well as higher-order models in well-mixed and structured populations, and we review experimental works that support and inform the results of mathematical modeling and simulations. We also provide a synthesis of the reviewed researches along with an outlook in terms of six directions that seem particularly promising to explore in the future.

Complex evolutionary interactions in multiple populations.

In competitive settings that entail several populations, individuals often engage in intra- and interpopulation interactions that determine their fitness and evolutionary success. With this simple motivation, we here study a multipopulation model where individuals engage in group interactions within their own population and in pairwise interactions with individuals from different populations. We use the evolutionary public goods game and the prisoner's dilemma game to describe these group and pairwise interactions, respectively. We also take into account asymmetry in the extent to which group and pairwise interactions determine the fitness of individuals. We find that interactions across multiple populations reveal new mechanisms through which the evolution of cooperation can be promoted, but this depends on the level of interaction asymmetry. If inter- and intrapopulation interactions are symmetric, the sole presence of multiple populations promotes the evolution of cooperation. Asymmetry in the interactions can further promote cooperation at the expense of the coexistence of the competing strategies. An in-depth analysis of the spatiotemporal dynamics reveals loop-dominated structures and pattern formation that can explain the various evolutionary outcomes. Thus, complex evolutionary interactions in multiple populations reveal an intricate interplay between cooperation and coexistence, and they also open up the path toward further explorations of multipopulation games and biodiversity.

The dynamics of a duopoly Stackelberg game with marginal costs among heterogeneous players.

One of the famous economic models in game theory is the duopoly Stackelberg model, in which a leader and a follower firm manufacture a single product in the market. Their goal is to obtain the maximum profit while competing with each other. The desired dynamics for a firm in a market is the convergence to its Nash equilibrium, but the dynamics of real-world markets are not always steady and can result in unpredictable market changes that exhibit chaotic behaviors. On the other hand, to approach reality more, the two firms in the market can be considered heterogeneous. The leader firm is bounded rationale, and the follower firm is adaptable. Modifying the cost function that affects the firms' profit by adding the marginal cost term is another step toward reality. We propose a Stackelberg model with heterogeneous players and marginal costs, which exhibits chaotic behavior. This model's equilibrium points, including the Nash equilibrium, are calculated by the backward induction method, and their stability analyses are obtained. The influence of changing each model parameter on the consequent dynamics is investigated through one-dimensional and two-dimensional bifurcation diagrams, Lyapunov exponents spectra, and Kaplan-Yorke dimension. Eventually, using a combination of state feedback and parameter adjustment methods, the chaotic solutions of the model are successfully tamed, and the model converges to its Nash equilibrium.

Determinants of collective failure in excitable networks.

We study collective failures in biologically realistic networks that consist of coupled excitable units. The networks have broad-scale degree distribution, high modularity, and small-world properties, while the excitable dynamics is determined by the paradigmatic FitzHugh-Nagumo model. We consider different coupling strengths, bifurcation distances, and various aging scenarios as potential culprits of collective failure. We find that for intermediate coupling strengths, the network remains globally active the longest if the high-degree nodes are first targets for inactivation. This agrees well with previously published results, which showed that oscillatory networks can be highly fragile to the targeted inactivation of low-degree nodes, especially under weak coupling. However, we also show that the most efficient strategy to enact collective failure does not only non-monotonically depend on the coupling strength, but it also depends on the distance from the bifurcation point to the oscillatory behavior of individual excitable units. Altogether, we provide a comprehensive account of determinants of collective failure in excitable networks, and we hope this will prove useful for better understanding breakdowns in systems that are subject to such dynamics.

Deterrence through punishment can resolve collective risk dilemmas in carbon emission games.

Collective risk social dilemmas are at the heart of the most pressing global challenges we are facing today, including climate change mitigation and the overuse of natural resources. Previous research has framed this problem as a public goods game (PGG), where a dilemma arises between short-term interests and long-term sustainability. In the PGG, subjects are placed in groups and asked to choose between cooperation and defection, while keeping in mind their personal interests as well as the commons. Here, we explore how and to what extent the costly punishment of defectors is successful in enforcing cooperation by means of human experiments. We show that an apparent irrational underestimation of the risk of being punished plays an important role, and that for sufficiently high punishment fines, this vanishes and the threat of deterrence suffices to preserve the commons. Interestingly, however, we find that high fines not only avert freeriders, but they also demotivate some of the most generous altruists. As a consequence, the tragedy of the commons is predominantly averted due to cooperators that contribute only their "fair share" to the common pool. We also find that larger groups require larger fines for the deterrence of punishment to have the desired prosocial effect.