Simplicial Kuramoto models have emerged as a diverse and intriguing class of models describing oscillators on simplices rather than nodes. In this paper, we present a unified framework to describe different variants of these models, categorized into three main groups: simple models, Hodge-coupled models, and order-coupled (Dirac) models. Our framework is based on topology, discrete differential geometry as well as gradient flows and frustrations, and permits a systematic analysis of their properties. We establish an equivalence between the simple simplicial Kuramoto model and the standard Kuramoto model on pairwise networks under the condition of manifoldness of the simplicial complex. Then, starting from simple models, we describe the notion of simplicial synchronization and derive bounds on the coupling strength necessary or sufficient for achieving it. For some variants, we generalize these results and provide new ones, such as the controllability of equilibrium solutions. Finally, we explore a potential application in the reconstruction of brain functional connectivity from structural connectomes and find that simple edge-based Kuramoto models perform competitively or even outperform complex extensions of node-based models.

Oxytocin is necessary and sufficient for social fear contagion in zebrafish supporting an evolutionary conserved role for oxytocin in emotional contagion among vertebrates.

Although ubiquitous, interactions of groups of individuals (e.g., modern messaging applications, group meetings, or even a parliament discussion) are not yet thoroughly studied. Frequently, single-groups are modeled as critical-mass dynamics, which is a widespread concept used not only by academics but also by politicians and the media. However, less explored questions are how a collection of groups will behave and how the intersection between these groups might change the global dynamics. Here, we formulate this process in terms of binary state dynamics on hypergraphs. We showed that our model has a very rich and unexpected behavior that goes beyond discontinuous transitions. In particular, we might have multistability and intermittency as a consequence of bimodal state distributions. By using artificial random models, we demonstrated that this phenomenology could be associated with community structures. Specifically, we might have multistability or intermittency by controlling the number of bridges between two communities with different densities. The introduction of bridges destroys multistability but creates an intermittent behavior. Furthermore, we provide an analytical formulation showing that the observed pattern for the order parameter and susceptibility are compatible with hybrid phase transitions. Our findings open new paths for research, ranging from physics, on the formal calculation of quantities of interest, to social sciences, where new experiments can be designed.

We introduce hypercores and show that they are important for multiple dynamical processes.

Time series analysis has proven to be a powerful method to characterize several phenomena in biology, neuroscience and economics, and to understand some of their underlying dynamical features. Several methods have been proposed for the analysis of multivariate time series, yet most of them neglect the effect of non-pairwise interactions on the emerging dynamics. Here, we propose a framework to characterize the temporal evolution of higher-order dependencies within multivariate time series. Using network analysis and topology, we show that our framework robustly differentiates various spatiotemporal regimes of coupled chaotic maps. This includes chaotic dynamical phases and various types of synchronization. Hence, using the higher-order co-fluctuation patterns in simulated dynamical processes as a guide, we highlight and quantify signatures of higher-order patterns in data from brain functional activity, financial markets and epidemics. Overall, our approach sheds light on the higher-order organization of multivariate time series, allowing a better characterization of dynamical group dependencies inherent to real-world data.

We formulate a general Kuramoto model on weighted simplicial complexes where phases oscillators are supported on simplices of any order k. Crucially, we introduce linear and non-linear frustration terms that are independent of the orientation of the k+1 simplices, providing a natural generalization of the Sakaguchi-Kuramoto model. In turn, this provides a generalized formulation of the Kuramoto higher-order parameter as a potential function to write the dynamics as a gradient flow. We study the properties of the dynamics of the simplicial Sakaguchi-Kuramoto model with oscillators on edges using a selection of simplicial complexes of increasingly complex structure, to highlight the complexity of dynamical behaviors emerging from even simple simplicial complexes. In particular, using the Hodge decomposition of the solution, we understand how the nonlinear frustration couples the dynamics in orthogonal subspaces. We discover various dynamical phenomena, such as the partial loss of synchronization in subspaces aligned with the Hodge subspaces and the emergence of simplicial phase re-locking in regimes of high frustration.

Social behavior is developed over the lifetime of an organism and the neuropeptide oxytocin (OXT) modulates social behaviors across vertebrate species, and is associated with neuro-developmental social deficits such as autism. However, whether OXT plays a role in the developmental maturation of neural systems that are necessary for social behavior remains poorly explored. We show that proper behavioral and neural response to social stimuli depends on a developmental process orchestrated by OXT neurons. Animals whose OXT system is ablated in early life show blunted neuronal and behavioral responses to social stimuli as well as wide ranging disruptions in the functional connectivity of the social brain. We provide a window into the mechanisms underlying OXT-dependent developmental processes that implement adult sociality.

Group living animals can use social and asocial cues to predict the presence of a reward or a punishment in the environment through associative learning. The degree to which social and asocial learning share the same mechanisms is still a matter of debate, and, so far, studies investigating the neuronal basis of these two types of learning are scarce and have been restricted to primates, including humans, and rodents. Here we have used a Pavlovian fear conditioning paradigm in which a social (fish image) or an asocial (circle image) conditioned stimulus (CS) have been paired with an unconditioned stimulus (US=food), and we have used the expression of the immediate early gene c-fos to map the neural circuits associated with social and asocial learning. Our results show that the learning performance is similar with social (fish image) and asocial (circle image) CSs. However, the brain regions involved in each learning type are distinct. Social learning is associated with an increased expression of c-fos in olfactory bulbs, ventral zone of ventral telencephalic area, ventral habenula and ventromedial thalamus, whereas asocial learning is associated with a decreased expression of c-fos in dorsal habenula and anterior tubercular nucleus. Using egonetworks, we further show that each learning type has an associated pattern of functional connectivity across brain regions. Moreover, a community analysis of the network data reveals four segregated functional submodules, which seem to be associated with different cognitive functions involved in the learning tasks: a generalized attention module, a visual response module, a social stimulus integration module and a learning module. Together, these results suggest that, although there are localized differences in brain activity between social and asocial learning, the two learning types share a common learning module and social learning also recruits a specific social stimulus integration module. Therefore, our results support the occurrence of a common general-purpose learning module, that is differentially modulated by localized activation in social and asocial learning.

Complex networks have become the main paradigm for modelling the dynamics of interacting systems. However, networks are intrinsically limited to describing pairwise interactions, whereas real-world systems are often characterized by higher-order interactions involving groups of three or more units. Higher-order structures, such as hypergraphs and simplicial complexes, are therefore a better tool to map the real organization of many social, biological and man-made systems. Here, we highlight recent evidence of collective behaviours induced by higher-order interactions, and we outline three key challenges for the physics of higher-order systems.

The ability to learn new tasks and generalize performance to others is one of the most remarkable characteristics of the human brain and of recent AI systems. The ability to perform multiple tasks simultaneously is also a signature characteristic of large-scale parallel architectures, that is evident in the human brain, and has been exploited effectively more traditional, massively parallel computational architectures. Here, we show that these two characteristics are in tension, reflecting a fundamental tradeoff between interactive parallelism that supports learning and generalization, and independent parallelism that supports processing efficiency through concurrent multitasking. We formally show that, while the maximum number of tasks that can be performed simultaneously grows linearly with network size, under realistic scenarios (e.g. in an unpredictable environment), the expected number that can be performed concurrently grows radically sublinearly with network size. Hence, even modest reliance on shared representation strictly constrains the number of tasks that can be performed simultaneously, implying profound consequences for the development of artificial intelligence that optimally manages the tradeoff between learning and processing, and for un- derstanding the human brain’s remarkably puzzling mix of sequential and parallel capabilities.

Until recently, little attention has been devoted to the higher-order architecture of real complex systems. However, a mounting body of evidence is showing that taking the higher-order structure of these systems into account can greatly enhance our modeling capacities and help us to understand and predict their emerging dynamical behaviors. Here, we present a complete overview of the emerging field of networks beyond pairwise interactions.

Complex networks have been successfully used to describe the spread of diseases in populations of interacting individuals. Conversely, pairwise interactions are often not enough to characterize social contagion processes such as opinion formation or the adoption of novelties, where complex mechanisms of influence and reinforcement are at work. Here we introduce a higher-order model of social contagion in which a social system is represented by a simplicial complex and contagion can occur through interactions in groups of different sizes. Numerical simulations of the model on both empirical and synthetic simplicial complexes highlight the emergence of novel phenomena such as a discontinuous transition induced by higher-order interactions. We show analytically that the transition is discontinuous and that a bistable region appears where healthy and endemic states co-exist. Our results help explain why critical masses are required to initiate social changes and contribute to the understanding of higher-order interactions in complex systems.

Infectious disease outbreaks recapitulate biology: they emerge from the multi-level interaction of hosts, pathogens, and their shared environment. As a result, predicting when, where, and how far diseases will spread requires a complex systems approach to modeling. Recent studies have demonstrated that predicting different components of outbreaks–e.g., the expected number of cases, pace and tempo of cases needing treatment, importation probability etc.–is feasible. Therefore, advancing both the science and practice of disease forecasting now requires testing for the presence of fundamental limits to outbreak prediction. To investigate the question of outbreak prediction, we study the information theoretic limits to forecasting across a broad set of infectious diseases using permutation entropy as a model independent measure of predictability. Studying the predictability of a diverse collection of historical outbreaks–including, gonorrhea, influenza, Zika, measles, polio, whooping cough, and mumps–we identify a fundamental entropy barrier for time series forecasting. However, we find that for most diseases this barrier to prediction is often well beyond the time scale of single outbreaks, implying prediction is likely to succeed. We also find that the forecast horizon varies by disease and demonstrate that both shifting model structures and social network heterogeneity are the most likely mechanisms for the observed differences in predictability across contagions. Our results highlight the importance of moving beyond time series forecasting, by embracing dynamic modeling approaches to prediction and suggest challenges for performing model selection across long disease time series. We further anticipate that our findings will contribute to the rapidly growing field of epidemiological forecasting and may relate more broadly to the predictability of complex adaptive systems.

Many complex systems find a convenient representation in terms of networks: structures made by pairwise interactions (links) of elements (nodes). For many biological and social systems, elementary interactions involve however more than two elements, and simplicial complexes are more adequate to describe such phenomena. Moreover, these interactions often change over time. Here, we propose a framework to model such an evolution: the Simplicial Activity Driven (SAD) model, in which the building block is a simplex of nodes representing a multi-agent interaction. We show analytically and numerically that the use of simplicial structures leads to crucial differences in the outcome of paradigmatic processes modelling disease propagation or social contagion, with respect to the activity-driven (AD) model, a paradigmatic temporal network model involving only binary interactions. In particular, fluctuations in the number of nodes involved in the interactions can affect the outcome of models of simple contagion processes, contrarily to what happens in the AD model. Moreover, social contagion models such as cascading processes present a much richer phenomenology and can become extremely slow when occurring on evolving simplicial complexes.