75 research outputs found
Maximal entropy random walk in community finding
The aim of this paper is to check feasibility of using the maximal-entropy
random walk in algorithms finding communities in complex networks. A number of
such algorithms exploit an ordinary or a biased random walk for this purpose.
Their key part is a (dis)similarity matrix, according to which nodes are
grouped. This study encompasses the use of the stochastic matrix of a random
walk, its mean first-passage time matrix, and a matrix of weighted paths count.
We briefly indicate the connection between those quantities and propose
substituting the maximal-entropy random walk for the previously chosen models.
This unique random walk maximises the entropy of ensembles of paths of given
length and endpoints, which results in equiprobability of those paths. We
compare performance of the selected algorithms on LFR benchmark graphs. The
results show that the change in performance depends very strongly on the
particular algorithm, and can lead to slight improvements as well as
significant deterioration.Comment: 7 pages, 4 figures, submitted to European Physical Journal Special
Topics following the 4-th Conference on Statistical Physics: Modern Trends
and Applications, July 3-6, 2012 Lviv, Ukrain
Maximal-entropy random walk unifies centrality measures
In this paper analogies between different (dis)similarity matrices are
derived. These matrices, which are connected to path enumeration and random
walks, are used in community detection methods or in computation of centrality
measures for complex networks. The focus is on a number of known centrality
measures, which inherit the connections established for similarity matrices.
These measures are based on the principal eigenvector of the adjacency matrix,
path enumeration, as well as on the stationary state, stochastic matrix or mean
first-passage times of a random walk. Particular attention is paid to the
maximal-entropy random walk, which serves as a very distinct alternative to the
ordinary random walk used in network analysis.
The various importance measures, defined both with the use of ordinary random
walk and the maximal-entropy random walk, are compared numerically on a set of
benchmark graphs. It is shown that groups of centrality measures defined with
the two random walks cluster into two separate families. In particular, the
group of centralities for the maximal-entropy random walk, connected to the
eigenvector centrality and path enumeration, is strongly distinct from all the
other measures and produces largely equivalent results.Comment: 7 pages, 2 figure
Co-occurrence of resonant activation and noise-enhanced stability in a model of cancer growth in the presence of immune response
We investigate a stochastic version of a simple enzymatic reaction which
follows the generic Michaelis-Menten kinetics. At sufficiently high
concentrations of reacting species, the molecular fluctuations can be
approximated as a realization of a Brownian dynamics for which the model
reaction kinetics takes on the form of a stochastic differential equation.
After eliminating a fast kinetics, the model can be rephrased into a form of a
one-dimensional overdamped Langevin equation. We discuss physical aspects of
environmental noises acting in such a reduced system, pointing out the
possibility of coexistence of dynamical regimes where noise-enhanced stability
and resonant activation phenomena can be observed together.Comment: 18 pages, 11 figures, published in Physical Review E 74, 041904
(2006
Seeking for a fingerprint: analysis of point processes in actigraphy recording
Motor activity of humans displays complex temporal fluctuations which can be
characterized by scale-invariant statistics, thus documenting that structure
and fluctuations of such kinetics remain similar over a broad range of time
scales. Former studies on humans regularly deprived of sleep or suffering from
sleep disorders predicted change in the invariant scale parameters with respect
to those representative for healthy subjects. In this study we investigate the
signal patterns from actigraphy recordings by means of characteristic measures
of fractional point processes. We analyse spontaneous locomotor activity of
healthy individuals recorded during a week of regular sleep and a week of
chronic partial sleep deprivation. Behavioural symptoms of lack of sleep can be
evaluated by analysing statistics of duration times during active and resting
states, and alteration of behavioural organization can be assessed by analysis
of power laws detected in the event count distribution, distribution of waiting
times between consecutive movements and detrended fluctuation analysis of
recorded time series. We claim that among different measures characterizing
complexity of the actigraphy recordings and their variations implied by chronic
sleep distress, the exponents characterizing slopes of survival functions in
resting states are the most effective biomarkers distinguishing between healthy
and sleep-deprived groups.Comment: Communicated at UPON2015, 14-17 July 2015, Barcelona. 21 pages, 11
figures; updated: figures 4-7, text revised, expanded Sec. 1,3,
Noise-assisted spike propagation in myelinated neurons
We consider noise-assisted spike propagation in myelinated axons within a
multi-compartment stochastic Hodgkin-Huxley model. The noise originates from a
finite number of ion channels in each node of Ranvier. For the subthreshold
internodal electric coupling, we show that (i) intrinsic noise removes the
sharply defined threshold for spike propagation from node to node, and (ii)
there exists an optimum number of ion channels which allows for the most
efficient signal propagation and it corresponds to the actual physiological
values.Comment: 8 pages, 12 figures, accepted for publication in Phys. Rev.
Shift of percolation thresholds for epidemic spread between static and dynamic small-world networks
The aim of the study was to compare the epidemic spread on static and dynamic
small-world networks. The network was constructed as a 2-dimensional
Watts-Strogatz model (500x500 square lattice with additional shortcuts), and
the dynamics involved rewiring shortcuts in every time step of the epidemic
spread. The model of the epidemic is SIR with latency time of 3 time steps. The
behaviour of the epidemic was checked over the range of shortcut probability
per underlying bond 0-0.5. The quantity of interest was percolation threshold
for the epidemic spread, for which numerical results were checked against an
approximate analytical model. We find a significant lowering of percolation
thresholds for the dynamic network in the parameter range given. The result
shows that the behaviour of the epidemic on dynamic network is that of a static
small world with the number of shortcuts increased by 20.7 +/- 1.4%, while the
overall qualitative behaviour stays the same. We derive corrections to the
analytical model which account for the effect. For both dynamic and static
small-world we observe suppression of the average epidemic size dependence on
network size in comparison with finite-size scaling known for regular lattice.
We also study the effect of dynamics for several rewiring rates relative to
latency time of the disease.Comment: 13 pages, 6 figure
There are no non-zero Stable Fixed Points for dense networks in the homogeneous Kuramoto model
This paper is concerned with the existence of multiple stable fixed point
solutions of the homogeneous Kuramoto model. We develop a necessary condition
for the existence of stable fixed points for the general network Kuramoto
model. This condition is applied to show that for sufficiently dense n-node
networks, with node degrees at least 0.9395(n-1), the homogeneous (equal
frequencies) model has no non-zero stable fixed point solution over the full
space of phase angles in the range -Pi to Pi. This result together with
existing research proves a conjecture of Verwoerd and Mason (2007) that for the
complete network and homogeneous model the zero fixed point has a basin of
attraction consisting of the entire space minus a set of measure zero. The
necessary conditions are also tested to see how close to sufficiency they might
be by applying them to a class of regular degree networks studied by Wiley,
Strogatz and Girvan (2006).Comment: 15 pages 8 figures. arXiv admin note: text overlap with
arXiv:1010.076
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