Browse
Submit Data
Databases
API
Help

Dataset Information

39 Views

0 Connections

0 Citations

0 Reanalyses

0 Downloads

Omics score: 0

Optimal partition and effective dynamics of complex networks.

ABSTRACT: Given a large and complex network, we would like to find the best partition of this network into a small number of clusters. This question has been addressed in many different ways. Here we propose a strategy along the lines of optimal prediction for the Markov chains associated with the dynamics on these networks. We develop the necessary ingredients for such an optimal partition strategy, and we compare our strategy with the previous ones. We show that when the Markov chain is lumpable, we recover the partition with respect to which the chain is lumpable. We also discuss the case of well-clustered networks. Finally, we illustrate our strategy on several examples.

SUBMITTER: E W

PROVIDER: S-EPMC2786939 | biostudies-literature | 2008 Jun

REPOSITORIES: biostudies-literature

ACCESS DATA

Json Xml

Publications

Optimal partition and effective dynamics of complex networks.

E Weinan W Li Tiejun T Vanden-Eijnden Eric E

Proceedings of the National Academy of Sciences of the United States of America 20080226 23

Given a large and complex network, we would like to find the best partition of this network into a small number of clusters. This question has been addressed in many different ways. Here we propose a strategy along the lines of optimal prediction for the Markov chains associated with the dynamics on these networks. We develop the necessary ingredients for such an optimal partition strategy, and we compare our strategy with the previous ones. We show that when the Markov chain is lumpable, we rec ...[more]

PMID: 18303119

Similar Datasets

Optimal control of transient dynamics in balanced networks supports generation of complex movements.

Project description:Populations of neurons in motor cortex engage in complex transient dynamics of large amplitude during the execution of limb movements. Traditional network models with stochastically assigned synapses cannot reproduce this behavior. Here we introduce a class of cortical architectures with strong and random excitatory recurrence that is stabilized by intricate, fine-tuned inhibition, optimized from a control theory perspective. Such networks transiently amplify specific activity states and can be used to reliably execute multidimensional movement patterns. Similar to the experimental observations, these transients must be preceded by a steady-state initialization phase from which the network relaxes back into the background state by way of complex internal dynamics. In our networks, excitation and inhibition are as tightly balanced as recently reported in experiments across several brain areas, suggesting inhibitory control of complex excitatory recurrence as a generic organizational principle in cortex.

| S-EPMC6364799 | biostudies-literature

Effective Augmentation of Complex Networks.

Project description:Networks science plays an enormous role in many aspects of modern society from distributing electrical power across nations to spreading information and social networking amongst global populations. While modern networks constantly change in size, few studies have sought methods for the difficult task of optimising this growth. Here we study theoretical requirements for augmenting networks by adding source or sink nodes, without requiring additional driver-nodes to accommodate the change i.e., conserving structural controllability. Our "effective augmentation" algorithm takes advantage of clusters intrinsic to the network topology, and permits rapidly and efficient augmentation of a large number of nodes in one time-step. "Effective augmentation" is shown to work successfully on a wide range of model and real networks. The method has numerous applications (e.g. study of biological, social, power and technological networks) and potentially of significant practical and economic value.

| S-EPMC4863250 | biostudies-literature

Optimal control of aging in complex networks.

Project description:Many complex systems experience damage accumulation, which leads to aging, manifest as an increasing probability of system collapse with time. This naturally raises the question of how to maximize health and longevity in an aging system at minimal cost of maintenance and intervention. Here, we pose this question in the context of a simple interdependent network model of aging in complex systems and show that it exhibits cascading failures. We then use both optimal control theory and reinforcement learning alongside a combination of analysis and simulation to determine optimal maintenance protocols. These protocols may motivate the rational design of strategies for promoting longevity in aging complex systems with potential applications in therapeutic schedules and engineered system maintenance.

| S-EPMC7456090 | biostudies-literature

Optimal localization of diffusion sources in complex networks.

Project description:Locating sources of diffusion and spreading from minimum data is a significant problem in network science with great applied values to the society. However, a general theoretical framework dealing with optimal source localization is lacking. Combining the controllability theory for complex networks and compressive sensing, we develop a framework with high efficiency and robustness for optimal source localization in arbitrary weighted networks with arbitrary distribution of sources. We offer a minimum output analysis to quantify the source locatability through a minimal number of messenger nodes that produce sufficient measurement for fully locating the sources. When the minimum messenger nodes are discerned, the problem of optimal source localization becomes one of sparse signal reconstruction, which can be solved using compressive sensing. Application of our framework to model and empirical networks demonstrates that sources in homogeneous and denser networks are more readily to be located. A surprising finding is that, for a connected undirected network with random link weights and weak noise, a single messenger node is sufficient for locating any number of sources. The framework deepens our understanding of the network source localization problem and offers efficient tools with broad applications.

| S-EPMC5414272 | biostudies-literature

Optimal search strategies on complex multi-linked networks.

Project description:In this paper we consider the problem of optimal search strategies on multi-linked networks, i.e. graphs whose nodes are endowed with several independent sets of links. We focus preliminarily on agents randomly hopping along the links of a graph, with the additional possibility of performing non-local hops to randomly chosen nodes with a given probability. We show that an optimal combination of the two jump rules exists that maximises the efficiency of target search, the optimum reflecting the topology of the network. We then generalize our results to multi-linked networks with an arbitrary number of mutually interfering link sets.

| S-EPMC4423499 | biostudies-literature

Competitive dynamics on complex networks.

Project description:We consider a dynamical network model in which two competitors have fixed and different states, and each normal agent adjusts its state according to a distributed consensus protocol. The state of each normal agent converges to a steady value which is a convex combination of the competitors' states, and is independent of the initial states of agents. This implies that the competition result is fully determined by the network structure and positions of competitors in the network. We compute an Influence Matrix (IM) in which each element characterizing the influence of an agent on another agent in the network. We use the IM to predict the bias of each normal agent and thus predict which competitor will win. Furthermore, we compare the IM criterion with seven node centrality measures to predict the winner. We find that the competitor with higher Katz Centrality in an undirected network or higher PageRank in a directed network is most likely to be the winner. These findings may shed new light on the role of network structure in competition and to what extent could competitors adjust network structure so as to win the competition.

| S-EPMC5376163 | biostudies-literature

Targeting the dynamics of complex networks.

Project description:We report on a generic procedure to steer (target) a network's dynamics towards a given, desired evolution. The problem is here tackled through a Master Stability Function approach, assessing the stability of the aimed dynamics, and through a selection of nodes to be targeted. We show that the degree of a node is a crucial element in this selection process, and that the targeting mechanism is most effective in heterogeneous scale-free architectures. This makes the proposed approach applicable to the large majority of natural and man-made networked systems.

| S-EPMC3343324 | biostudies-other

Energy scaling of targeted optimal control of complex networks.

Project description:Recently it has been shown that the control energy required to control a dynamical complex network is prohibitively large when there are only a few control inputs. Most methods to reduce the control energy have focused on where, in the network, to place additional control inputs. Here, in contrast, we show that by controlling the states of a subset of the nodes of a network, rather than the state of every node, while holding the number of control signals constant, the required energy to control a portion of the network can be reduced substantially. The energy requirements exponentially decay with the number of target nodes, suggesting that large networks can be controlled by a relatively small number of inputs as long as the target set is appropriately sized. We validate our conclusions in model and real networks to arrive at an energy scaling law to better design control objectives regardless of system size, energy restrictions, state restrictions, input node choices and target node choices.

| S-EPMC5413984 | biostudies-literature

Steering complex networks toward desired dynamics.

Project description:We consider networks of dynamical units that evolve in time according to different laws, and are coupled to each other in highly irregular ways. Studying how to steer the dynamics of such systems towards a desired evolution is of great practical interest in many areas of science, as well as providing insight into the interplay between network structure and dynamical behavior. We propose a pinning protocol for imposing specific dynamic evolutions compatible with the equations of motion on a networked system. The method does not impose any restrictions on the local dynamics, which may vary from node to node, nor on the interactions between nodes, which may adopt in principle any nonlinear mathematical form and be represented by weighted, directed or undirected links. We first explore our method on small synthetic networks of chaotic oscillators, which allows us to unveil a correlation between the ordered sequence of pinned nodes and their topological influence in the network. We then consider a 12-species trophic web network, which is a model of a mammalian food web. By pinning a relatively small number of species, one can make the system abandon its spontaneous evolution from its (typically uncontrolled) initial state towards a target dynamics, or periodically control it so as to make the populations evolve within stipulated bounds. The relevance of these findings for environment management and conservation is discussed.

| S-EPMC7695727 | biostudies-literature

Adaptive contact networks change effective disease infectiousness and dynamics.

Project description:Human societies are organized in complex webs that are constantly reshaped by a social dynamic which is influenced by the information individuals have about others. Similarly, epidemic spreading may be affected by local information that makes individuals aware of the health status of their social contacts, allowing them to avoid contact with those infected and to remain in touch with the healthy. Here we study disease dynamics in finite populations in which infection occurs along the links of a dynamical contact network whose reshaping may be biased based on each individual's health status. We adopt some of the most widely used epidemiological models, investigating the impact of the reshaping of the contact network on the disease dynamics. We derive analytical results in the limit where network reshaping occurs much faster than disease spreading and demonstrate numerically that this limit extends to a much wider range of time scales than one might anticipate. Specifically, we show that from a population-level description, disease propagation in a quickly adapting network can be formulated equivalently as disease spreading on a well-mixed population but with a rescaled infectiousness. We find that for all models studied here--SI, SIS and SIR--the effective infectiousness of a disease depends on the population size, the number of infected in the population, and the capacity of healthy individuals to sever contacts with the infected. Importantly, we indicate how the use of available information hinders disease progression, either by reducing the average time required to eradicate a disease (in case recovery is possible), or by increasing the average time needed for a disease to spread to the entire population (in case recovery or immunity is impossible).

| S-EPMC2924249 | biostudies-literature

OmicsDI is part of the ELIXIR infrastructure

OmicsDI is an Elixir interoperability service. Learn more ›

Tweets

OmicsDI Databases

PRIDE
PeptideAtlas
MassIVE
JPOST Repository
Physiome Model Repository

EGA
EVA
ENA
LINCS
PAXDB
Cell Collective

MetaboLights
Metabolomics Workbench
MetabolomeExpress
GNPS
BioModels
FAIRDOMHub

ArrayExpress
dbGaP
ExpressionAtlas
GEO
NODE

Information

Databases
Help
API
Contact us
Code on GitHub
Terms of use
Submit Data