Divisibility patterns of natural numbers on a complex network.
Ontology highlight
ABSTRACT:
SUBMITTER: Shekatkar SM
PROVIDER: S-EPMC4571582 | biostudies-other | 2015
REPOSITORIES: biostudies-other
Similar Datasets
Project description:Congruence theory has many applications in physical, social, biological and technological systems. Congruence arithmetic has been a fundamental tool for data security and computer algebra. However, much less attention was devoted to the topological features of congruence relations among natural numbers. Here, we explore the congruence relations in the setting of a multiplex network and unveil some unique and outstanding properties of the multiplex congruence network. Analytical results show that every layer therein is a sparse and heterogeneous subnetwork with a scale-free topology. Counterintuitively, every layer has an extremely strong controllability in spite of its scale-free structure that is usually difficult to control. Another amazing feature is that the controllability is robust against targeted attacks to critical nodes but vulnerable to random failures, which also differs from ordinary scale-free networks. The multi-chain structure with a small number of chain roots arising from each layer accounts for the strong controllability and the abnormal feature. The multiplex congruence network offers a graphical solution to the simultaneous congruences problem, which may have implication in cryptography based on simultaneous congruences. Our work also gains insight into the design of networks integrating advantages of both heterogeneous and homogeneous networks without inheriting their limitations.
| S-EPMC4814780 | biostudies-other
Project description:The identification of relationships in complex networks is critical in a variety of scientific contexts. This includes the identification of globally central nodes and analysing the importance of pairwise relationships between nodes. In this paper, we consider the concept of topological proximity (or 'closeness') between nodes in a weighted network using the generalized Erdős numbers (GENs). This measure satisfies a number of desirable properties for networks with nodes that share a finite resource. These include: (i) real-valuedness, (ii) non-locality and (iii) asymmetry. We show that they can be used to define a personalized measure of the importance of nodes in a network with a natural interpretation that leads to new methods to measure centrality. We show that the square of the leading eigenvector of an importance matrix defined using the GENs is strongly correlated with well-known measures such as PageRank, and define a personalized measure of centrality that is also well correlated with other existing measures. The utility of this measure of topological proximity is demonstrated by showing the asymmetries in both the dynamics of random walks and the mean infection time in epidemic spreading are better predicted by the topological definition of closeness provided by the GENs than they are by other measures.
| S-EPMC6124095 | biostudies-other
Project description:The Erdős-Rényi (ER) random graph G(n, p) analytically characterizes the behaviors in complex networks. However, attempts to fit real-world observations need more sophisticated structures (e.g., multilayer networks), rules (e.g., Achlioptas processes), and projections onto geometric, social, or geographic spaces. The p-adic number system offers a natural representation of hierarchical organization of complex networks. The p-adic random graph interprets n as the cardinality of a set of p-adic numbers. Constructing a vast space of hierarchical structures is equivalent for combining number sequences. Although the giant component is vital in dynamic evolution of networks, the structure of multiple big components is also essential. Fitting the sizes of the few largest components to empirical data was rarely demonstrated. The p-adic ultrametric enables the ER model to simulate multiple big components from the observations of genetic interaction networks, social networks, and epidemics. Community structures lead to multimodal distributions of the big component sizes in networks, which have important implications in intervention of spreading processes.
| S-EPMC7794417 | biostudies-literature
Project description:The vertebrate central nervous system is organized in modules that independently execute sophisticated tasks. Such modules are flexibly controlled and operate with a considerable degree of autonomy. One example is locomotion generated by spinal central pattern generator networks (CPGs) that shape the detailed motor output. The level of activity is controlled from brainstem locomotor command centers, which in turn, are under the control of the basal ganglia. By using a biophysically detailed, full-scale computational model of the lamprey CPG (10,000 neurons) and its brainstem/forebrain control, we demonstrate general control principles that can adapt the network to different demands. Forward or backward locomotion and steering can be flexibly controlled by local synaptic effects limited to only the very rostral part of the network. Variability in response properties within each neuronal population is an essential feature and assures a constant phase delay along the cord for different locomotor speeds.
| S-EPMC2785286 | biostudies-other
Project description:The exploitation of high volume of geolocalized data from social sport tracking applications of outdoor activities can be useful for natural resource planning and to understand the human mobility patterns during leisure activities. This geolocalized data represents the selection of hike activities according to subjective and objective factors such as personal goals, personal abilities, trail conditions or weather conditions. In our approach, human mobility patterns are analysed from trajectories which are generated by hikers. We propose the generation of the trail network identifying special points in the overlap of trajectories. Trail crossings and trailheads define our network and shape topological features. We analyse the trail network of Balearic Islands, as a case of study, using complex weighted network theory. The analysis is divided into the four seasons of the year to observe the impact of weather conditions on the network topology. The number of visited places does not decrease despite the large difference in the number of samples of the two seasons with larger and lower activity. It is in summer season where it is produced the most significant variation in the frequency and localization of activities from inland regions to coastal areas. Finally, we compare our model with other related studies where the network possesses a different purpose. One finding of our approach is the detection of regions with relevant importance where landscape interventions can be applied in function of the communities.
| S-EPMC5443505 | biostudies-literature
Project description:Celiac disease is a common small intestinal inflammatory condition induced by wheat gluten and related proteins from rye and barley. Left untreated, the clinical presentation of CD can include failure to thrive, malnutrition, and distension in juveniles. The disease can additionally lead to vitamin deficiencies, anemia, and osteoporosis. Therefore, CD potentially negatively affected fitness in past populations utilizing wheat, barley, and rye. Previous analyses of CD risk variants have uncovered evidence for positive selection on some of these loci. These studies also suggest the possibility that risk for common autoimmune conditions such as CD may be the result of positive selection on immune related loci in the genome to fight infection. Under this evolutionary scenario, disease phenotypes may be a trade-off from positive selection on immunity. If this hypothesis is generally true, we can expect to find a signal of natural selection when we survey across the network of loci known to influence CD risk. This study examines the non-HLA autosomal network of gene loci associated with CD risk in Europe. We reject the null hypothesis of neutrality on this network of CD risk loci. Additionally, we can localize evidence of selection in time and space by adding information from the genome of the Tyrolean Iceman. While we can show significant differentiation between continental regions across the CD network, the pattern of evidence is not consistent with primarily recent (Holocene) selection across this network in Europe. Further localization of ancient selection on this network may illuminate the ecological pressures acting on the immune system during this critically interesting phase of our evolution.
| S-EPMC3729812 | biostudies-literature
Project description:Understanding, predicting, and controlling outbreaks of waterborne diseases are crucial goals of public health policies, but pose challenging problems because infection patterns are influenced by spatial structure and temporal asynchrony. Although explicit spatial modeling is made possible by widespread data mapping of hydrology, transportation infrastructure, population distribution, and sanitation, the precise condition under which a waterborne disease epidemic can start in a spatially explicit setting is still lacking. Here we show that the requirement that all the local reproduction numbers R0 be larger than unity is neither necessary nor sufficient for outbreaks to occur when local settlements are connected by networks of primary and secondary infection mechanisms. To determine onset conditions, we derive general analytical expressions for a reproduction matrix G0, explicitly accounting for spatial distributions of human settlements and pathogen transmission via hydrological and human mobility networks. At disease onset, a generalized reproduction number ?0 (the dominant eigenvalue of G0) must be larger than unity. We also show that geographical outbreak patterns in complex environments are linked to the dominant eigenvector and to spectral properties of G0. Tests against data and computations for the 2010 Haiti and 2000 KwaZulu-Natal cholera outbreaks, as well as against computations for metapopulation networks, demonstrate that eigenvectors of G0 provide a synthetic and effective tool for predicting the disease course in space and time. Networked connectivity models, describing the interplay between hydrology, epidemiology, and social behavior sustaining human mobility, thus prove to be key tools for emergency management of waterborne infections.
| S-EPMC3511721 | biostudies-literature
Project description:Molecular interactions affect the evolution of complex traits. For instance, adaptation may be constrained by pleiotropic or epistatic effects, both of which can be reflected in the structure of molecular interaction networks. To date, empirical studies investigating the role of molecular interactions in phenotypic evolution have been idiosyncratic, offering no clear patterns. Here, we investigated the network topology of genes putatively involved in local adaptation to two abiotic stressors-drought and cold-in Arabidopsis thaliana Our findings suggest that the gene-interaction topologies for both cold and drought stress response are non-random, with genes that show genetic variation in drought expression response (eGxE) being significantly more peripheral and cold response genes being significantly more central than genes which do not show GxE. We suggest that the observed topologies reflect different constraints on the genetic pathways involved in environmental response. The approach presented here may inform predictive models linking genetic variation in molecular signalling networks with phenotypic variation, specifically traits involved in environmental response.
| S-EPMC5474086 | biostudies-literature
Project description:Artificial reefs act as high-rugosity habitats and are often deployed to enhance fishing; however, the effects of man-made features on fish communities can be unpredictable and are poorly understood in deeper waters. In this study, we used a submersible to describe a deep-water artificial reef complex (93-245 m) off of Ewa Beach, Oahu, Hawaii, USA, and evaluated possible conservation and/or fisheries-related contributions. Sixty-eight species were recorded, with larger features supporting greater diversity of species. Species composition changed strongly with depth and a faunal break was detected from 113-137 m. While the features supported diverse fish communities, they were not similar to those on natural substrates, and were numerically dominated by only two species, Lutjanis kasmira and Chromis verater. Depth-generalist and endemic species were present at levels comparable to natural substrates, but were less abundant and species-rich than at biogenic Leptoseris reefs at similar depths. While the non-native L. kasmira was highly abundant, its presence and abundance were not associated with discernable changes in the fish community, and was not present deeper than 120 m. Finally, five species of commercially- and recreationally-important 'Deep 7' fisheries species were also observed, but the artificial reef complex was mostly too shallow to provide meaningful benefits.
| S-EPMC7182438 | biostudies-literature
Project description:Critical events in society or biological systems can be understood as large-scale self-emergent phenomena due to deteriorating stability. We often observe peculiar patterns preceding these events, posing a question of-how to interpret the self-organized patterns to know more about the imminent crisis. We start with a very general description - of interacting population giving rise to large-scale emergent behaviors that constitute critical events. Then we pose a key question: is there a quantifiable relation between the network of interactions and the emergent patterns? Our investigation leads to a fundamental understanding to: 1. Detect the system's transition based on the principal mode of the pattern dynamics; 2. Identify its evolving structure based on the observed patterns. The main finding of this study is that while the pattern is distorted by the network of interactions, its principal mode is invariant to the distortion even when the network constantly evolves. Our analysis on real-world markets show common self-organized behavior near the critical transitions, such as housing market collapse and stock market crashes, thus detection of critical events before they are in full effect is possible.
| S-EPMC4378512 | biostudies-literature