The dynamics of meaningful social interactions and the emergence of collective knowledge

Nonlocal models in biology and life sciences: Sources, developments, and applications

Mathematical modeling is one of the fundamental techniques for understanding biophysical mechanisms in developmental biology. It helps researchers to analyze complex physiological processes and connect like a bridge between theoretical and experimental observations. Various groups of mathematical models have been studied to analyze these processes, and the nonlocal models are one of them. Nonlocality is important in realistic mathematical models of physical and biological systems when local models fail to capture the essential dynamics and interactions that occur over a range of distances (e.g., cell-cell, cell-tissue adhesions, neural networks, the spread of diseases, intra-specific competition, nanobeams, etc.). This review illustrates different nonlocal mathematical models applied to biology and life sciences. The major focus has been given to sources, developments, and applications of such models. Among other things, a systematic discussion has been provided for the conditions of pattern formations in biological systems of population dynamics. Special attention has also been given to nonlocal interactions on networks, network coupling and integration, including brain dynamics models that provide an important tool to understand neurodegenerative diseases better. In addition, we have discussed nonlocal modeling approaches for cancer stem cells and tumor cells that are widely applied in the cell migration processes, growth, and avascular tumors in any organ. Furthermore, the discussed nonlocal continuum models can go sufficiently smaller scales, including nanotechnology, where classical local models often fail to capture the complexities of nanoscale interactions, applied to build biosensors to sense biomaterial and its concentration. Piezoelectric and other smart materials are among them, and these devices are becoming increasingly important in the digital and physical world that is intrinsically interconnected with biological systems. Additionally, we have reviewed a nonlocal theory of peridynamics, which deals with continuous and discrete media and applies to model the relationship between fracture and healing in cortical bone, tissue growth and shrinkage, and other areas increasingly important in biomedical and bioengineering applications. Finally, we provided a comprehensive summary of emerging trends and highlighted future directions in this rapidly expanding field.

Fractal information dissemination and clustering evolution on social hypernetwork

The complexity of systems stems from the richness of the group interactions among their units. Classical networks exhibit identified limits in the study of complex systems, where links connect pairs of nodes, inability to comprehensively describe higher-order interactions in networks. Higher-order networks can enhance modeling capacities of group interaction networks and help understand and predict network dynamical behavior. This paper constructs a social hypernetwork with a group structure by analyzing a community overlapping structure and a network iterative relationship, and the overlapping relationship between communities is logically separated. Considering the different group behavior pattern and attention focus, we defined the group cognitive disparity, group credibility, group cohesion index, hyperedge strength to study the relationship between information dissemination and network evolution. This study shows that groups can alter the connected network through information propagation, and users in social networks tend to form highly connected groups or communities in information dissemination. Propagation networks with high clustering coefficients promote the fractal information dissemination, which in itself drives the fractal evolution of groups within the network. This study emphasizes the significant role of "key groups" with overlapping structures among communities in group network propagation. Real cases provide evidence for the clustering phenomenon and fractal evolution of networks.

A taxonomy of innovation spaces from the innovation networks lens

Collaborative innovation addresses intricate, multifaceted problems of a systemic nature involving a multitude of actors with diverse and often unknown expectations. To facilitate this collaboration, innovation spaces—such as Makerspaces, Hackerspaces, Fablabs, among others—have emerged as arenas where networks of actors interconnect and solidify. Understanding the diverse nature of these innovation spaces poses a challenge, particularly in distinguishing their specific characteristics and assessing how each contributes to fostering innovative networks. This article aims to address the question: how can we classify innovation spaces based on the innovation networks they constitute? To tackle this query, we initially conducted an in-depth exploration of various innovation spaces through web content analysis, scrutinizing their individual value propositions. Subsequently, employing innovation network theory alongside domain analysis methodology, we proposed a taxonomy designed to classify the distinct types of innovation spaces under scrutiny. Our taxonomy reveals three types of spaces—learn-and-explore, partner-and impact, and transitory—as well as convergent and divergent spaces, showing the diversity and complexity of networks they constitute. The findings also show that while the majority of innovation spaces unite diverse actors to drive collaboration and innovation, many resulting networks have a medium level of formality and are project-centric. These networks tend to be synthetic in nature, seeking to apply existing knowledge, and represent exploration networks wherein the adaptability and diversity of initiatives foster learning, the acquisition of new knowledge, and the development of fresh capacities through interactions.

Associative linking for collaborative thinking: Self-organization of content in online Q&A communities via user-generated links

Virtual collaborative Q&A communities generate shared knowledge through the interaction of people and content. This knowledge is often fragmented, and its value as a collective, collaboratively formed product, is largely overlooked. Inspired by work on individual mental semantic networks, the current study explores the networks formed by user-added associative links as reflecting an aspect of self-organization within the communities' collaborative knowledge sharing. Using eight Q&A topic-centered discussions from the Stack Exchange platform, it investigated how associative links form internal structures within the networks. Network analysis tools were used to derive topological indicator metrics of complex structures from associatively-linked networks. Similar metrics extracted from 1000 simulated randomly linked networks of comparable sizes and growth patterns were used to generate estimated sampling distributions through bootstrap resampling, and 99% confidence intervals were constructed for each metric. The discussion-network indicators were compared against these. Results showed that participant-added associative links largely led to networks that were more clustered, integrated, and included posts with more connections than those that would be expected in random networks of similar size and growth pattern. The differences were observed to increase over time. Also, the largest connected subgraphs within the discussion networks were found to be modular. Limited qualitative observations have also pointed to the impacts of external content-related events on the network structures. The findings strengthen the notion that the networks emerging from associative link sharing resemble other information networks that are characterized by internal structures suggesting self-organization, laying the ground for further exploration of collaborative linking as a form of collective knowledge organization. It underscores the importance of recognizing and leveraging this latent mechanism in both theory and practice.

Bursts of communication increase opinion diversity in the temporal Deffuant model

Human interactions create social networks forming the backbone of societies. Individuals adjust their opinions by exchanging information through social interactions. Two recurrent questions are whether social structures promote opinion polarisation or consensus and whether polarisation can be avoided, particularly on social media. In this paper, we hypothesise that not only network structure but also the timings of social interactions regulate the emergence of opinion clusters. We devise a temporal version of the Deffuant opinion model where pairwise social interactions follow temporal patterns. Individuals may self-organise into a multi-partisan society due to network clustering promoting the reinforcement of local opinions. Burstiness has a similar effect and is alone sufficient to refrain the population from consensus and polarisation by also promoting the reinforcement of local opinions. The diversity of opinions in socially clustered networks thus increases with burstiness, particularly, and counter-intuitively, when individuals have low tolerance and prefer to adjust to similar peers. The emergent opinion landscape is well-balanced regarding groups' size, with relatively short differences between groups, and a small fraction of extremists. We argue that polarisation is more likely to emerge in social media than offline social networks because of the relatively low social clustering observed online, despite the observed online burstiness being sufficient to promote more diversity than would be expected offline. Increasing the variance of burst activation times, e.g. by being less active on social media, could be a venue to reduce polarisation. Furthermore, strengthening online social networks by increasing social redundancy, i.e. triangles, may also promote diversity.

Collective patterns and stable misunderstandings in networks striving for consensus without a common value system

Collective phenomena in systems of interacting agents have helped us understand diverse social, ecological and biological observations. The corresponding explanations are challenged by incorrect information processing. In particular, the models typically assume a shared understanding of signals or a common truth or value system, i.e., an agreement of whether the measurement or perception of information is ‘right’ or ‘wrong’. It is an open question whether a collective consensus can emerge without these conditions. Here we introduce a model of interacting agents that strive for consensus, however, each with only a subjective perception of the world. Our communication model does not presuppose a definition of right or wrong and the actors can hence not distinguish between correct and incorrect observations. Depending on a single parameter that governs how responsive the agents are to changing their world-view we observe a transition between an unordered phase of individuals that are not able to communicate with each other and a phase of an emerging shared signalling framework. We find that there are two types of convention-aligned clusters: one, where all social actors in the cluster have the same set of conventions, and one, where neighbouring actors have different but compatible conventions (‘stable misunderstandings’).

Interacting Discovery Processes on Complex Networks

Innovation is the driving force of human progress. Recent urn models reproduce well the dynamics through which the discovery of a novelty may trigger further ones, in an expanding space of opportunities, but neglect the effects of social interactions. Here we focus on the mechanisms of collective exploration, and we propose a model in which many urns, representing different explorers, are coupled through the links of a social network and exploit opportunities coming from their contacts. We study different network structures showing, both analytically and numerically, that the pace of discovery of an explorer depends on its centrality in the social network. Our model sheds light on the role that social structures play in discovery processes.

Modeling latent infection transmissions through biosocial stochastic dynamics

The events of the recent SARS-CoV-2 epidemics have shown the importance of social factors, especially given the large number of asymptomatic cases that effectively spread the virus, which can cause a medical emergency to very susceptible individuals. Besides, the SARS-CoV-2 virus survives for several hours on different surfaces, where a new host can contract it with a delay. These passive modes of infection transmission remain an unexplored area for traditional mean-field epidemic models. Here, we design an agent-based model for simulations of infection transmission in an open system driven by the dynamics of social activity; the model takes into account the personal characteristics of individuals, as well as the survival time of the virus and its potential mutations. A growing bipartite graph embodies this biosocial process, consisting of active carriers (host) nodes that produce viral nodes during their infectious period. With its directed edges passing through viral nodes between two successive hosts, this graph contains complete information about the routes leading to each infected individual. We determine temporal fluctuations of the number of exposed and the number of infected individuals, the number of active carriers and active viruses at hourly resolution. The simulated processes underpin the latent infection transmissions, contributing significantly to the spread of the virus within a large time window. More precisely, being brought by social dynamics and exposed to the currently existing infection, an individual passes through the infectious state until eventually spontaneously recovers or otherwise is moves to a controlled hospital environment. Our results reveal complex feedback mechanisms that shape the dependence of the infection curve on the intensity of social dynamics and other sociobiological factors. In particular, the results show how the lockdown effectively reduces the spread of infection and how it increases again after the lockdown is removed. Furthermore, a reduced level of social activity but prolonged exposure of susceptible individuals have adverse effects. On the other hand, virus mutations that can gradually reduce the transmission rate by hopping to each new host along the infection path can significantly reduce the extent of the infection, but can not stop the spreading without additional social strategies. Our stochastic processes, based on graphs at the interface of biology and social dynamics, provide a new mathematical framework for simulations of various epidemic control strategies with high temporal resolution and virus traceability.

Emergence of complex structures from nonlinear interactions and noise in coevolving networks

We study the joint effect of the non-linearity of interactions and noise on coevolutionary dynamics. We choose the coevolving voter model as a prototype framework for this problem. By numerical simulations and analytical approximations we find three main phases that differ in the absolute magnetisation and the size of the largest component: a consensus phase, a coexistence phase, and a dynamical fragmentation phase. More detailed analysis reveals inner differences in these phases, allowing us to divide two of them further. In the consensus phase we can distinguish between a weak or alternating consensus and a strong consensus, in which the system remains in the same state for the whole realisation of the stochastic dynamics. In the coexistence phase we distinguish a fully-mixing phase and a structured coexistence phase, where the number of active links drops significantly due to the formation of two homogeneous communities. Our numerical observations are supported by an analytical description using a pair approximation approach and an ad-hoc calculation for the transition between the coexistence and dynamical fragmentation phases. Our work shows how simple interaction rules including the joint effect of non-linearity, noise, and coevolution lead to complex structures relevant in the description of social systems.

Efficient team structures in an open-ended cooperative creativity experiment

Creativity is progressively acknowledged as the main driver for progress in all sectors of humankind's activities: arts, science, technology, business, and social policies. Nowadays, many creative processes rely on many actors collectively contributing to an outcome. The same is true when groups of people collaborate in the solution of a complex problem. Despite the critical importance of collective actions in human endeavors, few works have tackled this topic extensively and quantitatively. Here we report about an experimental setting to single out some of the key determinants of efficient teams committed to an open-ended creative task. In this experiment, dynamically forming teams were challenged to create several artworks using LEGO bricks. The growth rate of the artworks, the dynamical network of social interactions, and the interaction patterns between the participants and the artworks were monitored in parallel. The experiment revealed that larger working teams are building at faster rates and that higher commitment leads to higher growth rates. Even more importantly, there exists an optimal number of weak ties in the social network of creators that maximizes the growth rate. Finally, the presence of influencers within the working team dramatically enhances the building efficiency. The generality of the approach makes it suitable for application in very different settings, both physical and online, whenever a creative collective outcome is required.

Ordered Avalanches on the Bethe Lattice

We discuss deterministic sequences of avalanches on a directed Bethe lattice. The approach is motivated by the phenomenon of self-organized criticality. Grains are added only at one node of the network. When the number of grains at any node exceeds a threshold b, each of k out-neighbors gets one grain. The probability of an avalanche of size s is proportional to s−τ. When the avalanche mass is conserved (k=b), we get τ=1. For an application of the model to social phenomena, the conservation condition can be released. Then, the exponent τ is found to depend on the model parameters; τ ≈ log(b)/log(k). The distribution of the time duration of avalanches is exponential. Multifractal analysis of the avalanche sequences reveals their strongly non-uniform fractal organization. Maximal value of the singularity strength αmax in the bifractal spectrum is found to be 1/τ.

The central role of peripheral nodes in directed network dynamics

Many social, technological, and biological systems with asymmetric interactions display a variety of collective phenomena, such as opinion formation and synchronization. This has motivated much research on the dynamical impact of local and mesoscopic structure in directed networks. However, the unique constraints imposed by the global organization of directed networks remain largely undiscussed. Here, we control the global organization of directed Erdős–Rényi networks, and study its impact on the emergence of synchronization and ferromagnetic ordering, using Kuramoto and Ising dynamics. In doing so, we demonstrate that source nodes – peripheral nodes without incoming links – can disrupt or entirely suppress the emergence of collective states in directed networks. This effect is imposed by the bow-tie organization of directed networks, where a large connected core does not uniquely ensure the emergence of collective states, as it does for undirected networks.

Network Dynamics of Innovation Processes

We introduce a model for the emergence of innovations, in which cognitive processes are described as random walks on the network of links among ideas or concepts, and an innovation corresponds to the first visit of a node. The transition matrix of the random walk depends on the network weights, while in turn the weight of an edge is reinforced by the passage of a walker. The presence of the network naturally accounts for the mechanism of the "adjacent possible," and the model reproduces both the rate at which novelties emerge and the correlations among them observed empirically. We show this by using synthetic networks and by studying real data sets on the growth of knowledge in different scientific disciplines. Edge-reinforced random walks on complex topologies offer a new modeling framework for the dynamics of correlated novelties and are another example of coevolution of processes and networks.

Mechanisms of self-organized criticality in social processes of knowledge creation

In online social dynamics, a robust scale invariance appears as a key feature of collaborative efforts that lead to new social value. The underlying empirical data thus offers a unique opportunity to study the origin of self-organized criticality (SOC) in social systems. In contrast to physical systems in the laboratory, various human attributes of the actors play an essential role in the process along with the contents (cognitive, emotional) of the communicated artifacts. As a prototypical example, we consider the social endeavor of knowledge creation via Questions and Answers (Q&A). Using a large empirical data set from one of such Q&A sites and theoretical modeling, we reveal fundamental characteristics of SOC by investigating the temporal correlations at all scales and the role of cognitive contents to the avalanches of the knowledge-creation process. Our analysis shows that the universal social dynamics with power-law inhomogeneities of the actions and delay times provides the primary mechanism for self-tuning towards the critical state; it leads to the long-range correlations and the event clustering in response to the external driving by the arrival of new users. In addition, the involved cognitive contents (systematically annotated in the data and observed in the model) exert important constraints that identify unique classes of the knowledge-creation avalanches. Specifically, besides determining a fine structure of the developing knowledge networks, they affect the values of scaling exponents and the geometry of large avalanches and shape the multifractal spectrum. Furthermore, we find that the level of the activity of the communities that share the knowledge correlates with the fluctuations of the innovation rate, implying that the increase of innovation may serve as the active principle of self-organization. To identify relevant parameters and unravel the role of the network evolution underlying the process in the social system under consideration, we compare the social avalanches to the avalanche sequences occurring in the field-driven physical model of disordered solids, where the factors contributing to the collective dynamics are better understood.

Associative nature of event participation dynamics: A network theory approach

The affiliation with various social groups can be a critical factor when it comes to quality of life of each individual, making such groups an essential element of every society. The group dynamics, longevity and effectiveness strongly depend on group’s ability to attract new members and keep them engaged in group activities. It was shown that high heterogeneity of scientist’s engagement in conference activities of the specific scientific community depends on the balance between the numbers of previous attendances and non-attendances and is directly related to scientist’s association with that community. Here we show that the same holds for leisure groups of the Meetup website and further quantify individual members’ association with the group. We examine how structure of personal social networks is evolving with the event attendance. Our results show that member’s increasing engagement in the group activities is primarily associated with the strengthening of already existing ties and increase in the bonding social capital. We also show that Meetup social networks mostly grow trough big events, while small events contribute to the groups cohesiveness.

Mitigating Herding in Hierarchical Crowdsourcing Networks

Hierarchical crowdsourcing networks (HCNs) provide a useful mechanism for social mobilization. However, spontaneous evolution of the complex resource allocation dynamics can lead to undesirable herding behaviours in which a small group of reputable workers are overloaded while leaving other workers idle. Existing herding control mechanisms designed for typical crowdsourcing systems are not effective in HCNs. In order to bridge this gap, we investigate the herding dynamics in HCNs and propose a Lyapunov optimization based decision support approach - the Reputation-aware Task Sub-delegation approach with dynamic worker effort Pricing (RTS-P) - with objective functions aiming to achieve superlinear time-averaged collective productivity in an HCN. By considering the workers' current reputation, workload, eagerness to work, and trust relationships, RTS-P provides a systematic approach to mitigate herding by helping workers make joint decisions on task sub-delegation, task acceptance, and effort pricing in a distributed manner. It is an individual-level decision support approach which results in the emergence of productive and robust collective patterns in HCNs. High resolution simulations demonstrate that RTS-P mitigates herding more effectively than state-of-the-art approaches.

A Statistical Physics Characterization of the Complex Systems Dynamics: Quantifying Complexity from Spatio-Temporal Interactions

Biological systems are frequently categorized as complex systems due to their capabilities of generating spatio-temporal structures from apparent random decisions. In spite of research on analyzing biological systems, we lack a quantifiable framework for measuring their complexity. To fill this gap, in this paper, we develop a new paradigm to study a collective group of N agents moving and interacting in a three-dimensional space. Our paradigm helps to identify the spatio-temporal states of the motion of the group and their associated transition probabilities. This framework enables the estimation of the free energy landscape corresponding to the identified states. Based on the energy landscape, we quantify missing information, emergence, self-organization and complexity for a collective motion. We show that the collective motion of the group of agents evolves to reach the most probable state with relatively lowest energy level and lowest missing information compared to other possible states. Our analysis demonstrates that the natural group of animals exhibit a higher degree of emergence, self-organization and complexity over time. Consequently, this algorithm can be integrated into new frameworks to engineer collective motions to achieve certain degrees of emergence, self-organization and complexity.

Topology of Innovation Spaces in the Knowledge Networks Emerging through Questions-And-Answers

The communication processes of knowledge creation represent a particular class of human dynamics where the expertise of individuals plays a substantial role, thus offering a unique possibility to study the structure of knowledge networks from online data. Here, we use the empirical evidence from questions-and-answers in mathematics to analyse the emergence of the network of knowledge contents (or tags) as the individual experts use them in the process. After removing extra edges from the network-associated graph, we apply the methods of algebraic topology of graphs to examine the structure of higher-order combinatorial spaces in networks for four consecutive time intervals. We find that the ranking distributions of the suitably scaled topological dimensions of nodes fall into a unique curve for all time intervals and filtering levels, suggesting a robust architecture of knowledge networks. Moreover, these networks preserve the logical structure of knowledge within emergent communities of nodes, labeled according to a standard mathematical classification scheme. Further, we investigate the appearance of new contents over time and their innovative combinations, which expand the knowledge network. In each network, we identify an innovation channel as a subgraph of triangles and larger simplices to which new tags attach. Our results show that the increasing topological complexity of the innovation channels contributes to network’s architecture over different time periods, and is consistent with temporal correlations of the occurrence of new tags. The methodology applies to a wide class of data with the suitable temporal resolution and clearly identified knowledge-content units.