How rare are power-law networks really?
Ontology highlight
ABSTRACT:
SUBMITTER: Artico I
PROVIDER: S-EPMC7544363 | biostudies-literature | 2020 Sep
REPOSITORIES: biostudies-literature
Similar Datasets
Project description:The energy dissipation rate in a nonequilibrium reaction system can be determined by the reaction rates in the underlying reaction network. By developing a coarse-graining process in state space and a corresponding renormalization procedure for reaction rates, we find that energy dissipation rate has an inverse power-law dependence on the number of microscopic states in a coarse-grained state. The dissipation scaling law requires self-similarity of the underlying network, and the scaling exponent depends on the network structure and the probability flux correlation. Existence of the inverse dissipation scaling law is shown in realistic biochemical systems such as biochemical oscillators and microtubule-kinesin active flow systems.
| S-EPMC8286115 | biostudies-literature
Project description:The study of complex networks has pursued an understanding of macroscopic behaviour by focusing on power-laws in microscopic observables. Here, we uncover two universal fundamental physical principles that are at the basis of complex network generation. These principles together predict the generic emergence of deviations from ideal power laws, which were previously discussed away by reference to the thermodynamic limit. Our approach proposes a paradigm shift in the physics of complex networks, toward the use of power-law deviations to infer meso-scale structure from macroscopic observations.
| S-EPMC4512011 | biostudies-other
Project description:Darwin observed that multiple, lowly organized, rudimentary, or exaggerated structures show increased relative variability. However, the cellular basis for these laws has never been investigated. Some animals, such as the nematode Caenorhabditis elegans, are famous for having organs that possess the same number of cells in all individuals, a property known as eutely. But for most multicellular creatures, the extent of cell number variability is unknown. Here we estimate variability in organ cell number for a variety of animals, plants, slime moulds, and volvocine algae. We find that the mean and variance in cell number obey a power law with an exponent of 2, comparable to Taylor's law in ecological processes. Relative cell number variability, as measured by the coefficient of variation, differs widely across taxa and tissues, but is generally independent of mean cell number among homologous tissues of closely related species. We show that the power law for cell number variability can be explained by stochastic branching process models based on the properties of cell lineages. We also identify taxa in which the precision of developmental control appears to have evolved. We propose that the scale independence of relative cell number variability is maintained by natural selection.
| S-EPMC33276 | biostudies-literature
Project description:A common two-tier structure for social networks is based on partitioning society into two parts, referred to as the elite and the periphery, where the "elite" is the relatively small but well-connected and highly influential group of powerful individuals around which the society is centered, and the "periphery" consists of the rest of society. It is observed that the relative sizes of economic and social elites in various societies appear to be continually declining. One possible explanation is that this is a natural social phenomenon, resembling Price's "square root" law for the fraction of good scientists in the scientific community. We try to assess the validity of this explanation by studying the elite-periphery structure via introducing a novel axiom-based model for representing and measuring the influence between the elite and the periphery. The model is accompanied by a set of axioms that capture the elite's dominance, robustness and density, as well as a compactness property. Relying on the model and the accompanying axioms, we are able to draw a number of insightful conclusions about the elite-periphery structure. In particular, we show that in social networks that respect our axioms, the size of a compact elite is sublinear in the network size. This agrees with Price's principle but appears to contradict the common belief that the elite size tends to a linear fraction of society (recently claimed to be around 1%). We propose a natural method to create partitions with nice properties, based on the key observation that an elite-periphery partition is at what we call a 'balance point', where the elite and the periphery maintain a balance of powers. Our method is based on setting the elite to be the k most influential nodes in the network and suggest the balance point as a tool for choosing k and therefore the size of the elite. When using nodes degrees to order the nodes, the resulting k-rich club at the balance point is the elite of a partition we refer to as the balanced edge-based partition. We accompany these findings with an empirical study on 32 real-world social networks, which provides evidence that balanced edge-based partitions which satisfying our axioms commonly exist.
| S-EPMC6200247 | biostudies-literature
Project description:Covariance analysis of protein sequence alignments uses coevolving pairs of sequence positions to predict features of protein structure and function. However, current methods ignore the phylogenetic relationships between sequences, potentially corrupting the identification of covarying positions. Here, we use random matrix theory to demonstrate the existence of a power law tail that distinguishes the spectrum of covariance caused by phylogeny from that caused by structural interactions. The power law is essentially independent of the phylogenetic tree topology, depending on just two parameters-the sequence length and the average branch length. We demonstrate that these power law tails are ubiquitous in the large protein sequence alignments used to predict contacts in 3D structure, as predicted by our theory. This suggests that to decouple phylogenetic effects from the interactions between sequence distal sites that control biological function, it is necessary to remove or down-weight the eigenvectors of the covariance matrix with largest eigenvalues. We confirm that truncating these eigenvectors improves contact prediction.
| S-EPMC5789915 | biostudies-literature
Project description:The probability distribution of number of ties of an individual in a social network follows a scale-free power-law. However, how this distribution arises has not been conclusively demonstrated in direct analyses of people's actions in social networks. Here, we perform a causal inference analysis and find an underlying cause for this phenomenon. Our analysis indicates that heavy-tailed degree distribution is causally determined by similarly skewed distribution of human activity. Specifically, the degree of an individual is entirely random - following a "maximum entropy attachment" model - except for its mean value which depends deterministically on the volume of the users' activity. This relation cannot be explained by interactive models, like preferential attachment, since the observed actions are not likely to be caused by interactions with other people.
| S-EPMC3646275 | biostudies-other
Project description:We generalize the Susceptible-Infected-Removed (SIR) model for epidemics to take into account generic effects of heterogeneity in the degree of susceptibility to infection in the population. We introduce a single new parameter corresponding to a power-law exponent of the susceptibility distribution at small susceptibilities. We find that for this class of distributions the gamma distribution is the attractor of the dynamics. This allows us to identify generic effects of population heterogeneity in a model as simple as the original SIR model which is contained as a limiting case. Because of this simplicity, numerical solutions can be generated easily and key properties of the epidemic wave can still be obtained exactly. In particular, we present exact expressions for the herd immunity level, the final size of the epidemic, as well as for the shape of the wave and for observables that can be quantified during an epidemic. In strongly heterogeneous populations, the herd immunity level can be much lower than in models with homogeneous populations as commonly used for example to discuss effects of mitigation. Using our model to analyze data for the SARS-CoV-2 epidemic in Germany shows that the reported time course is consistent with several scenarios characterized by different levels of immunity. These scenarios differ in population heterogeneity and in the time course of the infection rate, for example due to mitigation efforts or seasonality. Our analysis reveals that quantifying the effects of mitigation requires knowledge on the degree of heterogeneity in the population. Our work shows that key effects of population heterogeneity can be captured without increasing the complexity of the model. We show that information about population heterogeneity will be key to understand how far an epidemic has progressed and what can be expected for its future course.
| S-EPMC7556502 | biostudies-literature
Project description:This research addresses the long-standing debate about the determinants of sex/gender differences. Evolutionary theorists trace many sex/gender differences back to natural selection and sex-specific adaptations. Sociocultural and biosocial theorists, in contrast, emphasize how societal roles and social power contribute to sex/gender differences beyond any biological distinctions. By connecting two empirical advances over the past two decades-6-fold increases in sex/gender difference meta-analyses and in experiments conducted on the psychological effects of power-the current research offers a novel empirical examination of whether power differences play an explanatory role in sex/gender differences. Our analyses assessed whether experimental manipulations of power and sex/gender differences produce similar psychological and behavioral effects. We first identified 59 findings from published experiments on power. We then conducted a P-curve of the experimental power literature and established that it contained evidential value. We next subsumed these effects of power into 11 broad categories and compared them to 102 similar meta-analytic sex/gender differences. We found that high-power individuals and men generally display higher agency, lower communion, more positive self-evaluations, and similar cognitive processes. Overall, 71% (72/102) of the sex/gender differences were consistent with the effects of experimental power differences, whereas only 8% (8/102) were opposite, representing a 9:1 ratio of consistent-to-inconsistent effects. We also tested for discriminant validity by analyzing whether power corresponds more strongly to sex/gender differences than extraversion: although extraversion correlates with power, it has different relationships with sex/gender differences. These results offer novel evidence that many sex/gender differences may be explained, in part, by power differences.
| S-EPMC10898859 | biostudies-literature
Project description:Many growth models have been published to model the behavior of real complex networks. These models are able to reproduce several of the topological properties of such networks. However, in most of these growth models, the number of outgoing links (i.e., out-degree) of nodes added to the network is constant, that is all nodes in the network are born with the same number of outgoing links. In other models, the resultant out-degree distribution decays as a poisson or an exponential distribution. However, it has been found that in real complex networks, the out-degree distribution decays as a power-law. In order to obtain out-degree distribution with power-law behavior some models have been proposed. This work introduces a new model that allows to obtain out-degree distributions that decay as a power-law with an exponent in the range from 0 to 1.
| S-EPMC4286734 | biostudies-other
Project description:Whether real-world complex networks are scale free or not has long been controversial. Recently, in Broido and Clauset [A. D. Broido, A. Clauset, Nat. Commun. 10, 1017 (2019)], it was claimed that the degree distributions of real-world networks are rarely power law under statistical tests. Here, we attempt to address this issue by defining a fundamental property possessed by each link, the degree-degree distance, the distribution of which also shows signs of being power law by our empirical study. Surprisingly, although full-range statistical tests show that degree distributions are not often power law in real-world networks, we find that in more than half of the cases the degree-degree distance distributions can still be described by power laws. To explain these findings, we introduce a bidirectional preferential selection model where the link configuration is a randomly weighted, two-way selection process. The model does not always produce solid power-law distributions but predicts that the degree-degree distance distribution exhibits stronger power-law behavior than the degree distribution of a finite-size network, especially when the network is dense. We test the strength of our model and its predictive power by examining how real-world networks evolve into an overly dense stage and how the corresponding distributions change. We propose that being scale free is a property of a complex network that should be determined by its underlying mechanism (e.g., preferential attachment) rather than by apparent distribution statistics of finite size. We thus conclude that the degree-degree distance distribution better represents the scale-free property of a complex network.
| S-EPMC7334507 | biostudies-literature