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To better understand the temporal characteristics and the lifetime of fluctuations in stochastic processes in networks, we investigated diffusive persistence in various graphs. Global diffusive persistence is defined as the fraction of nodes for which the diffusive field at a site (or node) has not changed sign up to time t (or, in general, that the node remained active or inactive in discrete models). Here we investigate disordered and random networks and show that the behavior of the persistence depends on the topology of the network. In two-dimensional (2D) disordered networks, we find that above the percolation threshold diffusive persistence scales similarly as in the original 2D regular lattice, according to a power law P(t , L) ∼ t−θ with an exponent θ ~ 0.186, in the limit of large linear system size L. At the percolation threshold, however, the scaling exponent changes to θ ~ 0.141, as the result of the interplay of diffusive persistence and the underlying structural transition in the disordered lattice at the percolation threshold. Moreover, studying finite-size effects for 2D lattices at and above the percolation threshold, we find that at the percolation threshold, the long-time asymptotic value obeys a power law P(t , L) ∼ L−zθ with z ~ 2.86 instead of the value of z = 2 normally associated with finite-size effects on 2D regular lattices. In contrast, we observe that in random networks without a local regular structure, such as Erdos-Rényi networks, no simple power-law scaling behavior exists above the percolation threshold 

Clustering molecular data into informative groups is a primary step in extracting robust conclusions from big data. However, due to foundational issues in how they are defined and detected, such clusters are not always reliable, leading to unstable conclusions. We compare popular clustering algorithms across thousands of synthetic and real biological datasets, including a new consensus clustering algorithm—SpeakEasy2: Champagne. These tests identify trends in performance, show no single method is universally optimal, and allow us to examine factors behind variation in performance. Multiple metrics indicate SpeakEasy2 generally provides robust, scalable, and informative clusters for a range of applications.

 

We are now exposed daily to more information than we can process and this has substantial costs. We argue that the information space should be recognized as part of our environment and call for research into the effects and management of information overload. 

Most of studied social interactions arise from dyadic relations. An exception is Heider Balance Theory that postulates the existence of triad dynamics, which however has been elusive to observe. Here, we discover a sufficient condition for the Heider dynamics observability: assigning the edge signs according to multiple opinions of connected agents. Using longitudinal records of university student mutual contacts and opinions, we create a coevolving network on which we introduce models of student interactions. These models account for: multiple topics of individual student opinions, influence of such opinions on dyadic relations, and influence of triadic relations on opinions. We show that the triadic influence is empirically measurable for static and dynamic observables when signs of edges are defined by multidimensional differences between opinions on all topics. Yet, when these signs are defined by a difference between opinions on each topic separately, the triadic interactions’ influence is indistinguishable from noise.

 

Social media has been transforming political communication dynamics for over a decade. Here using nearly a billion tweets, we analyse the change in Twitter’s news media landscape between the 2016 and 2020 US presidential elections. Using political bias and fact-checking tools, we measure the volume of politically biased content and the number of users propagating such information. We then identify influencers—users with the greatest ability to spread news in the Twitter network. We observe that the fraction of fake and extremely biased content declined between 2016 and 2020. However, results show increasing echo chamber behaviours and latent ideological polarization across the two elections at the user and influencer levels.

 

Research has documented increasing partisan division and extremist positions that are more pronounced among political elites than among voters. Attention has now begun to focus on how polarization might be attenuated. We use a general model of opinion change to see if the self-reinforcing dynamics of influence and homophily may be characterized by tipping points that make reversibility problematic. The model applies to a legislative body or other small, densely connected organization, but does not assume country-specific institutional arrangements that would obscure the identification of fundamental regularities in the phase transitions. Agents in the model have initially random locations in a multidimensional issue space consisting of membership in one of two equal-sized parties and positions on 10 issues. Agents then update their issue positions by moving closer to nearby neighbors and farther from those with whom they disagree, depending on the agents’ tolerance of disagreement and strength of party identification compared to their ideological commitment to the issues. We conducted computational experiments in which we manipulated agents’ tolerance for disagreement and strength of party identification. Importantly, we also introduced exogenous shocks corresponding to events that create a shared interest against a common threat (e.g., a global pandemic). Phase diagrams of political polarization reveal difficult-to-predict transitions that can be irreversible due to asymmetric hysteresis trajectories. We conclude that future empirical research needs to pay much closer attention to the identification of tipping points and the effectiveness of possible countermeasures. 

Many systems may switch to an undesired state due to internal failures or external perturbations, of which critical transitions toward degraded ecosystem states are prominent examples. Resilience restoration focuses on the ability of spatially-extended systems and the required time to recover to their desired states under stochastic environmental conditions. The difficulty is rooted in the lack of mathematical tools to analyze systems with high dimensionality, nonlinearity, and stochastic effects. Here we show that nucleation theory can be employed to advance resilience restoration in spatially-embedded ecological systems. We find that systems may exhibit single-cluster or multi-cluster phases depending on their sizes and noise strengths. We also discover a scaling law governing the restoration time for arbitrary system sizes and noise strengths in two-dimensional systems. This approach is not limited to ecosystems and has applications in various dynamical systems, from biology to infrastructural systems.

 

Abstract Despite the advances in discovering new nuclei, modeling microscopic nuclear structure, nuclear reactors, and stellar nucleosynthesis, we still lack a systemic tool, such as a network approach, to understand the structure and dynamics of over 70 thousands reactions compiled in JINA REACLIB. To this end, we develop an analysis framework, under which it is simple to know which reactions generally are possible and which are not, by counting neutrons and protons incoming to and outgoing from any target nucleus. Specifically, we assemble here a nuclear reaction network in which a node represents a nuclide, and a link represents a direct reaction between nuclides. Interestingly, the degree distribution of nuclear network exhibits a bimodal distribution that significantly deviates from the common power-law distribution of scale-free networks and Poisson distribution of random networks. Based on the dynamics from the cross section parameterizations in REACLIB, we surprisingly find that the distribution is universal for reactions with a rate below the threshold, λ < e − T γ , where T is the temperature and γ ≈ 1.05. Moreover, we discover three rules that govern the structure pattern of nuclear reaction network: (i) reaction-type is determined by linking choices, (ii) network distances between the reacting nuclides on 2D grid of Z vs N of nuclides are short, and (iii) each node in- and out-degrees are close to each other. By incorporating these three rules, our model universally unveils the underlying nuclear reaction patterns hidden in a large and dense nuclear reaction network regardless of nuclide chart expansions. It enables us to predict missing links that represent possible new nuclear reactions not yet discovered.