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## Distribution of infected mass in disease spreading in scale-free networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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#Condensed Matter - Disordered Systems and Neural Networks#Condensed Matter - Statistical Mechanics#Quantitative Biology

We use scale-free networks to study properties of the infected mass $M$ of
the network during a spreading process as a function of the infection
probability $q$ and the structural scaling exponent $\gamma$. We use the
standard SIR model and investigate in detail the distribution of $M$, We find
that for dense networks this function is bimodal, while for sparse networks it
is a smoothly decreasing function, with the distinction between the two being a
function of $q$. We thus recover the full crossover transition from one case to
the other. This has a result that on the same network a disease may die out
immediately or persist for a considerable time, depending on the initial point
where it was originated. Thus, we show that the disease evolution is
significantly influenced by the structure of the underlying population.; Comment: 7 pages, 3 figures, submitted to Physica A; Improved the discussion
and shifted the emphasis on the distributions of figure 2. Because of this we
had to change the title of the paper

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## Reliability of Coupled Oscillators II: Larger Networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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We study the reliability of phase oscillator networks in response to
fluctuating inputs. Reliability means that an input elicits essentially
identical responses upon repeated presentations, regardless of the network's
initial condition. In this paper, we extend previous results on two-cell
networks to larger systems. The first issue that arises is chaos in the absence
of inputs, which we demonstrate and interpret in terms of reliability. We give
a mathematical analysis of networks that can be decomposed into modules
connected by an acyclic graph. For this class of networks, we show how to
localize the source of unreliability, and address questions concerning
downstream propagation of unreliability once it is produced.; Comment: Part 2 of 2. Part 1 can be found at 0708.3061

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## Macroscopic description for networks of spiking neurons

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 22/06/2015
Português

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#Quantitative Biology - Neurons and Cognition#Condensed Matter - Disordered Systems and Neural Networks#Nonlinear Sciences - Adaptation and Self-Organizing Systems#Nonlinear Sciences - Chaotic Dynamics

A major goal of neuroscience, statistical physics and nonlinear dynamics is
to understand how brain function arises from the collective dynamics of
networks of spiking neurons. This challenge has been chiefly addressed through
large-scale numerical simulations. Alternatively, researchers have formulated
mean-field theories to gain insight into macroscopic states of large neuronal
networks in terms of the collective firing activity of the neurons, or the
firing rate. However, these theories have not succeeded in establishing an
exact correspondence between the firing rate of the network and the underlying
microscopic state of the spiking neurons. This has largely constrained the
range of applicability of such macroscopic descriptions, particularly when
trying to describe neuronal synchronization. Here we provide the derivation of
a set of exact macroscopic equations for a network of spiking neurons. Our
results reveal that the spike generation mechanism of individual neurons
introduces an effective coupling between two biophysically relevant macroscopic
quantities, the firing rate and the mean membrane potential, which together
govern the evolution of the neuronal network. The resulting equations exactly
describe all possible macroscopic dynamical states of the network...

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## Average synaptic activity and neural networks topology: a global inverse problem

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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#Condensed Matter - Disordered Systems and Neural Networks#Condensed Matter - Statistical Mechanics#Physics - Biological Physics#Quantitative Biology - Neurons and Cognition

The dynamics of neural networks is often characterized by collective behavior
and quasi-synchronous events, where a large fraction of neurons fire in short
time intervals, separated by uncorrelated firing activity. These global
temporal signals are crucial for brain functioning. They strongly depend on the
topology of the network and on the fluctuations of the connectivity. We propose
a heterogeneous mean--field approach to neural dynamics on random networks,
that explicitly preserves the disorder in the topology at growing network
sizes, and leads to a set of self-consistent equations. Within this approach,
we provide an effective description of microscopic and large scale temporal
signals in a leaky integrate-and-fire model with short term plasticity, where
quasi-synchronous events arise. Our equations provide a clear analytical
picture of the dynamics, evidencing the contributions of both periodic (locked)
and aperiodic (unlocked) neurons to the measurable average signal. In
particular, we formulate and solve a global inverse problem of reconstructing
the in-degree distribution from the knowledge of the average activity field.
Our method is very general and applies to a large class of dynamical models on
dense random networks.

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## Heterogeneous Bond Percolation on Multitype Networks with an Application to Epidemic Dynamics

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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Considerable attention has been paid, in recent years, to the use of networks
in modeling complex real-world systems. Among the many dynamical processes
involving networks, propagation processes -- in which final state can be
obtained by studying the underlying network percolation properties -- have
raised formidable interest. In this paper, we present a bond percolation model
of multitype networks with an arbitrary joint degree distribution that allows
heterogeneity in the edge occupation probability. As previously demonstrated,
the multitype approach allows many non-trivial mixing patterns such as
assortativity and clustering between nodes. We derive a number of useful
statistical properties of multitype networks as well as a general phase
transition criterion. We also demonstrate that a number of previous models
based on probability generating functions are special cases of the proposed
formalism. We further show that the multitype approach, by naturally allowing
heterogeneity in the bond occupation probability, overcomes some of the
correlation issues encountered by previous models. We illustrate this point in
the context of contact network epidemiology.; Comment: 10 pages, 5 figures. Minor modifications were made in figures 3...

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## Efficient transmission of subthreshold signals in complex networks of spiking neurons

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

45.57%

#Physics - Biological Physics#Condensed Matter - Disordered Systems and Neural Networks#Quantitative Biology - Neurons and Cognition

We investigate the efficient transmission and processing of weak,
subthreshold signals in a realistic neural medium in the presence of different
levels of the underlying noise. Assuming Hebbian weights for maximal synaptic
conductances -- that naturally balances the network with excitatory and
inhibitory synapses -- and considering short-term synaptic plasticity affecting
such conductances, we found different dynamic phases in the system. This
includes a memory phase where population of neurons remain synchronized, an
oscillatory phase where transitions between different synchronized populations
of neurons appears and an asynchronous or noisy phase. When a weak stimulus
input is applied to each neuron, increasing the level of noise in the medium we
found an efficient transmission of such stimuli around the transition and
critical points separating different phases for well-defined different levels
of stochasticity in the system. We proved that this intriguing phenomenon is
quite robust, as it occurs in different situations including several types of
synaptic plasticity, different type and number of stored patterns and diverse
network topologies, namely, diluted networks and complex topologies such as
scale-free and small-world networks. We conclude that the robustness of the
phenomenon in different realistic scenarios...

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## Stability of Spreading Processes over Time-Varying Large-Scale Networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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#Computer Science - Social and Information Networks#Mathematics - Dynamical Systems#Mathematics - Optimization and Control#Physics - Physics and Society#Quantitative Biology - Populations and Evolution

In this paper, we analyze the dynamics of spreading processes taking place
over time-varying networks. A common approach to model time-varying networks is
via Markovian random graph processes. This modeling approach presents the
following limitation: Markovian random graphs can only replicate switching
patterns with exponential inter-switching times, while in real applications
these times are usually far from exponential. In this paper, we introduce a
flexible and tractable extended family of processes able to replicate, with
arbitrary accuracy, any distribution of inter-switching times. We then study
the stability of spreading processes in this extended family. We first show
that a direct analysis based on It\^o's formula provides stability conditions
in terms of the eigenvalues of a matrix whose size grows exponentially with the
number of edges. To overcome this limitation, we derive alternative stability
conditions involving the eigenvalues of a matrix whose size grows linearly with
the number of nodes. Based on our results, we also show that heuristics based
on aggregated static networks approximate the epidemic threshold more
accurately as the number of nodes grows, or the temporal volatility of the
random graph process is reduced. Finally...

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## Robustness of cooperation on scale-free networks under continuous topological change

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

45.57%

#Physics - Physics and Society#Computer Science - Social and Information Networks#Quantitative Biology - Populations and Evolution

In this paper, we numerically investigate the robustness of cooperation
clusters in prisoner's dilemma played on scale-free networks, where the network
topologies change by continuous removal and addition of nodes. Each removal and
addition can be either random or intentional. We therefore have four different
strategies in changing network topology: random removal and random addition
(RR), random removal and preferential addition (RP), targeted removal and
random addition (TR), and targeted removal and preferential addition (TP). We
find that cooperation clusters are most fragile against TR, while they are most
robust against RP, even for large values of the temptation coefficient for
defection. The effect of the degree mixing pattern of the network is not the
primary factor for the robustness of cooperation under continuous change in
network topology, which is quite different from the cases observed in static
networks. Cooperation clusters become more robust as the number of links of
hubs occupied by cooperators increase. Our results might infer the fact that a
huge variety of individuals is needed for maintaining global cooperation in
social networks in the real world where each node representing an individual is
constantly removed and added.; Comment: 6 pages...

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## Epidemic fronts in complex networks with metapopulation structure

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

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Infection dynamics have been studied extensively on complex networks,
yielding insight into the effects of heterogeneity in contact patterns on
disease spread. Somewhat separately, metapopulations have provided a paradigm
for modeling systems with spatially extended and "patchy" organization. In this
paper we expand on the use of multitype networks for combining these paradigms,
such that simple contagion models can include complexity in the agent
interactions and multiscale structure. We first present a generalization of the
Volz-Miller mean-field approximation for Susceptible-Infected-Recovered (SIR)
dynamics on multitype networks. We then use this technique to study the special
case of epidemic fronts propagating on a one-dimensional lattice of
interconnected networks - representing a simple chain of coupled population
centers - as a necessary first step in understanding how macro-scale disease
spread depends on micro-scale topology. Using the formalism of front
propagation into unstable states, we derive the effective transport
coefficients of the linear spreading: asymptotic speed, characteristic
wavelength, and diffusion coefficient for the leading edge of the pulled
fronts, and analyze their dependence on the underlying graph structure. We also
derive the epidemic threshold for the system and study the front profile for
various network configurations. To our knowledge...

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## Multifractal Characterization of Protein Contact Networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

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The multifractal detrended fluctuation analysis of time series is able to
reveal the presence of long-range correlations and, at the same time, to
characterize the self-similarity of the series. The rich information derivable
from the characteristic exponents and the multifractal spectrum can be further
analyzed to discover important insights about the underlying dynamical process.
In this paper, we employ multifractal analysis techniques in the study of
protein contact networks. To this end, initially a network is mapped to three
different time series, each of which is generated by a stationary unbiased
random walk. To capture the peculiarities of the networks at different levels,
we accordingly consider three observables at each vertex: the degree, the
clustering coefficient, and the closeness centrality. To compare the results
with suitable references, we consider also instances of three well-known
network models and two typical time series with pure monofractal and
multifractal properties. The first result of notable interest is that time
series associated to proteins contact networks exhibit long-range correlations
(strong persistence), which are consistent with signals in-between the typical
monofractal and multifractal behavior. Successively...

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## Uniqueness, intractability and exact algorithms: reflections on level-k phylogenetic networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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Phylogenetic networks provide a way to describe and visualize evolutionary
histories that have undergone so-called reticulate evolutionary events such as
recombination, hybridization or horizontal gene transfer. The level k of a
network determines how non-treelike the evolution can be, with level-0 networks
being trees. We study the problem of constructing level-k phylogenetic networks
from triplets, i.e. phylogenetic trees for three leaves (taxa). We give, for
each k, a level-k network that is uniquely defined by its triplets. We
demonstrate the applicability of this result by using it to prove that (1) for
all k of at least one it is NP-hard to construct a level-k network consistent
with all input triplets, and (2) for all k it is NP-hard to construct a level-k
network consistent with a maximum number of input triplets, even when the input
is dense. As a response to this intractability we give an exact algorithm for
constructing level-1 networks consistent with a maximum number of input
triplets.

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## Spike Synchronization Dynamics of Small-World Networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 22/09/2013
Português

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#Computer Science - Neural and Evolutionary Computing#Nonlinear Sciences - Adaptation and Self-Organizing Systems#Quantitative Biology - Neurons and Cognition

In this research report, we examine the effects of small-world network
organization on spike synchronization dynamics in networks of Izhikevich
spiking units. We interpolate network organizations from regular ring lattices,
through the small-world region, to random networks, and measure global spike
synchronization dynamics. We examine how average path length and clustering
effect the dynamics of global and neighborhood clique spike organization and
propagation. We show that the emergence of global synchronization undergoes a
phase transition in the small-world region, between the clustering and path
length phase transitions that are known to exist. We add additional realistic
constraints on the dynamics by introducing propagation delays of spiking
signals proportional to wiring length. The addition of delays interferes with
the ability of random networks to sustain global synchronization, in relation
to the breakdown of clustering in the networks. The addition of delays further
enhances the finding that small-world organization is beneficial for balancing
neighborhood synchronized waves of organization with global synchronization
dynamics.; Comment: 22 pages, 6 figures

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## Biased imitation in coupled evolutionary games in interdependent networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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We explore the evolutionary dynamics of two games - the Prisoner's Dilemma
and the Snowdrift Game - played within distinct networks (layers) of
interdependent networks. In these networks imitation and interaction between
individuals of opposite layers is established through interlinks. We explore an
update rule in which revision of strategies is a biased imitation process:
individuals imitate neighbors from the same layer with probability p, and
neighbors from the second layer with complementary probability 1 - p. We
demonstrate that a small decrease of p from p = 1 (which corresponds to
forbidding strategy transfer between layers) is sufficient to promote
cooperation in the Prisoner's Dilemma subpopulation. This, on the other hand,
is detrimental for cooperation in the Snowdrift Game subpopulation. We provide
results of extensive computer simulations for the case in which layers are
modelled as regular random networks, and support this study with analytical
results for coupled well-mixed populations.; Comment: 20 pages, 8 figures

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## Rhythmic inhibition allows neural networks to search for maximally consistent states

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 10/03/2015
Português

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Gamma-band rhythmic inhibition is a ubiquitous phenomenon in neural circuits
yet its computational role still remains elusive. We show that a model of
Gamma-band rhythmic inhibition allows networks of coupled cortical circuit
motifs to search for network configurations that best reconcile external inputs
with an internal consistency model encoded in the network connectivity. We show
that Hebbian plasticity allows the networks to learn the consistency model by
example. The search dynamics driven by rhythmic inhibition enable the described
networks to solve difficult constraint satisfaction problems without making
assumptions about the form of stochastic fluctuations in the network. We show
that the search dynamics are well approximated by a stochastic sampling
process. We use the described networks to reproduce perceptual multi-stability
phenomena with switching times that are a good match to experimental data and
show that they provide a general neural framework which can be used to model
other 'perceptual inference' phenomena.

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## The diplomat's dilemma: Maximal power for minimal effort in social networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 26/05/2008
Português

Relevância na Pesquisa

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Closeness is a global measure of centrality in networks, and a proxy for how
influential actors are in social networks. In most network models, and many
empirical networks, closeness is strongly correlated with degree. However, in
social networks there is a cost of maintaining social ties. This leads to a
situation (that can occur in the professional social networks of executives,
lobbyists, diplomats and so on) where agents have the conflicting objectives of
aiming for centrality while simultaneously keeping the degree low. We
investigate this situation in an adaptive network-evolution model where agents
optimize their positions in the network following individual strategies, and
using only local information. The strategies are also optimized, based on the
success of the agent and its neighbors. We measure and describe the time
evolution of the network and the agents' strategies.; Comment: Submitted to Adaptive Networks: Theory, Models and Applications, to
be published from Springer

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## Griffiths phases and the stretching of criticality in brain networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

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#Condensed Matter - Disordered Systems and Neural Networks#Quantitative Biology - Neurons and Cognition

Hallmarks of criticality, such as power-laws and scale invariance, have been
empirically found in cortical networks and it has been conjectured that
operating at criticality entails functional advantages, such as optimal
computational capabilities, memory, and large dynamical ranges. As critical
behavior requires a high degree of fine tuning to emerge, some type of
self-tuning mechanism needs to be invoked. Here we show that, taking into
account the complex hierarchical-modular architecture of cortical networks, the
singular critical point is replaced by an extended critical-like region which
corresponds --in the jargon of statistical mechanics-- to a Griffiths phase.
Using computational and analytical approaches, we find Griffiths phases in
synthetic hierarchical networks and also in empirical brain networks such as
the human connectome and the caenorhabditis elegans one. Stretched critical
regions, stemming from structural disorder, yield enhanced functionality in a
generic way, facilitating the task of self-organizing, adaptive, and
evolutionary mechanisms selecting for criticality.; Comment: Final version. A misprint in Equation (2) was corrected.
Supplementary Information included

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## Social insect colony as a biological regulatory system: Information flow in dominance networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 16/03/2014
Português

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Social insects provide an excellent platform to investigate flow of
information in regulatory systems since their successful social organization is
essentially achieved by effective information transfer through complex
connectivity patterns among the colony members. Network representation of such
behavioural interactions offers a powerful tool for structural as well as
dynamical analysis of the underlying regulatory systems. In this paper, we
focus on the dominance interaction networks in the tropical social wasp
\textit{Ropalidia marginata} - a species where behavioural observations
indicate that such interactions are principally responsible for the transfer of
information between individuals about their colony needs, resulting in a
regulation of their own activities. Our research reveals that the dominance
networks of \textit{R. marginata} are structurally similar to a class of
naturally evolved information processing networks, a fact confirmed also by the
predominance of a specific substructure - the `feed-forward loop' - a key
functional component in many other information transfer networks. The dynamical
analysis through Boolean modeling confirms that the networks are sufficiently
stable under small fluctuations and yet capable of more efficient information
transfer compared to their randomized counterparts. Our results suggest the
involvement of a common structural design principle in different biological
regulatory systems and a possible similarity with respect to the effect of
selection on the organization levels of such systems. The findings are also
consistent with the hypothesis that dominance behaviour has been shaped by
natural selection to co-opt the information transfer process in such social
insect species...

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## Climatic seasonality may affect ecological network structure: Food webs and mutualistic networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 02/06/2014
Português

Relevância na Pesquisa

45.58%

#Quantitative Biology - Populations and Evolution#Physics - Data Analysis, Statistics and Probability#Physics - Physics and Society

Ecological networks exhibit non-random structural patterns, such as
modularity and nestedness, which indicate ecosystem stability, species
diversity, and connectance. Such structure-stability relationships are well
known. However, another important perspective is less well understood: the
relationship between the environment and structure. Inspired by theoretical
studies that suggest that network structure can change due to environmental
variability, we collected data on a number of empirical food webs and
mutualistic networks and evaluated the effect of climatic seasonality on
ecological network structure. As expected, we found that climatic seasonality
affects ecological network structure. In particular, an increase in modularity
due to climatic seasonality was observed in food webs; however, it is debatable
whether this occurs in mutualistic networks. Interestingly, the type of
climatic seasonality that affects network structure differs with ecosystem
type. Rainfall and temperature seasonality influence freshwater food webs and
mutualistic networks, respectively; food webs are smaller, and more modular,
with increasing rainfall seasonality. Mutualistic networks exhibit a higher
diversity (particularly of animals) with increasing temperature seasonality.
These results confirm the theoretical prediction that stability increases with
greater perturbation. Although these results are still debatable because of
several limitations in the data analysis...

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## Special homomorphisms between Probabilistic Gene Regulatory Networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 13/03/2006
Português

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45.58%

#Mathematics - Dynamical Systems#Mathematics - Probability#Quantitative Biology - Genomics#03C60#00A71

In this paper we study finite dynamical systems with $n$ functions acting on
the same set $X$, and probabilities assigned to these functions, that it is
called Probabilistic Regulatory Gene Networks (PRN. his concept is the same or
a natural generalization of the concept Probabilistic Boolean Networks (PBN),
introduced by I. Shmulevich, E. Dougherty, and W. Zhang, particularly the model
PBN has been using to describe genetic networks and has therapeutic
applications. In PRNs the most important question is to describe the steady
states of the systems, so in this paper we pay attention to the idea of
transforming a network to another without lost all the properties, in
particular the probability distribution. Following this objective we develop
the concepts of homomorphism and $\epsilon$-homomorphism of probabilistic
regulatory networks, since these concepts bring the properties from one
networks to another. Projections are special homomorphisms, and they always
induce invariant subnetworks that contain all cycles and steady states in the
network.

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## Robust Detection of Dynamic Community Structure in Networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

45.58%

#Physics - Data Analysis, Statistics and Probability#Condensed Matter - Disordered Systems and Neural Networks#Computer Science - Social and Information Networks#Physics - Biological Physics#Physics - Physics and Society#Quantitative Biology - Neurons and Cognition

We describe techniques for the robust detection of community structure in
some classes of time-dependent networks. Specifically, we consider the use of
statistical null models for facilitating the principled identification of
structural modules in semi-decomposable systems. Null models play an important
role both in the optimization of quality functions such as modularity and in
the subsequent assessment of the statistical validity of identified community
structure. We examine the sensitivity of such methods to model parameters and
show how comparisons to null models can help identify system scales. By
considering a large number of optimizations, we quantify the variance of
network diagnostics over optimizations (`optimization variance') and over
randomizations of network structure (`randomization variance'). Because the
modularity quality function typically has a large number of nearly-degenerate
local optima for networks constructed using real data, we develop a method to
construct representative partitions that uses a null model to correct for
statistical noise in sets of partitions. To illustrate our results, we employ
ensembles of time-dependent networks extracted from both nonlinear oscillators
and empirical neuroscience data.; Comment: 18 pages...

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