42 research outputs found
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
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
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,
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
Mean first-passage times of non-Markovian random walkers in confinement
The first-passage time (FPT), defined as the time a random walker takes to
reach a target point in a confining domain, is a key quantity in the theory of
stochastic processes. Its importance comes from its crucial role to quantify
the efficiency of processes as varied as diffusion-limited reactions, target
search processes or spreading of diseases. Most methods to determine the FPT
properties in confined domains have been limited to Markovian (memoryless)
processes. However, as soon as the random walker interacts with its
environment, memory effects can not be neglected. Examples of non Markovian
dynamics include single-file diffusion in narrow channels or the motion of a
tracer particle either attached to a polymeric chain or diffusing in simple or
complex fluids such as nematics \cite{turiv2013effect}, dense soft colloids or
viscoelastic solution. Here, we introduce an analytical approach to calculate,
in the limit of a large confining volume, the mean FPT of a Gaussian
non-Markovian random walker to a target point. The non-Markovian features of
the dynamics are encompassed by determining the statistical properties of the
trajectory of the random walker in the future of the first-passage event, which
are shown to govern the FPT kinetics.This analysis is applicable to a broad
range of stochastic processes, possibly correlated at long-times. Our
theoretical predictions are confirmed by numerical simulations for several
examples of non-Markovian processes including the emblematic case of the
Fractional Brownian Motion in one or higher dimensions. These results show, on
the basis of Gaussian processes, the importance of memory effects in
first-passage statistics of non-Markovian random walkers in confinement.Comment: Submitted version. Supplementary Information can be found on the
Nature website :
http://www.nature.com/nature/journal/v534/n7607/full/nature18272.htm
Comparative study of fungal cell disruption—scope and limitations of the methods
Simple and effective protocols of cell wall disruption were elaborated for tested fungal strains: Penicillium citrinum, Aspergillus fumigatus, Rhodotorula gracilis. Several techniques of cell wall disintegration were studied, including ultrasound disintegration, homogenization in bead mill, application of chemicals of various types, and osmotic shock. The release of proteins from fungal cells and the activity of a cytosolic enzyme, glucose-6-phosphate dehydrogenase, in the crude extracts were assayed to determine and compare the efficacy of each method. The presented studies allowed adjusting the particular method to a particular strain. The mechanical methods of disintegration appeared to be the most effective for the disintegration of yeast, R. gracilis, and filamentous fungi, A. fumigatus and P. citrinum. Ultrasonication and bead milling led to obtaining fungal cell-free extracts containing high concentrations of soluble proteins and active glucose-6-phosphate dehydrogenase systems
Speed, Sensitivity, and Bistability in Auto-activating Signaling Circuits
Cells employ a myriad of signaling circuits to detect environmental signals and drive specific gene expression responses. A common motif in these circuits is inducible auto-activation: a transcription factor that activates its own transcription upon activation by a ligand or by post-transcriptional modification. Examples range from the two-component signaling systems in bacteria and plants to the genetic circuits of animal viruses such as HIV. We here present a theoretical study of such circuits, based on analytical calculations, numerical computations, and simulation. Our results reveal several surprising characteristics. They show that auto-activation can drastically enhance the sensitivity of the circuit's response to input signals: even without molecular cooperativity, an ultra-sensitive threshold response can be obtained. However, the increased sensitivity comes at a cost: auto-activation tends to severely slow down the speed of induction, a stochastic effect that was strongly underestimated by earlier deterministic models. This slow-induction effect again requires no molecular cooperativity and is intimately related to the bimodality recently observed in non-cooperative auto-activation circuits. These phenomena pose strong constraints on the use of auto-activation in signaling networks. To achieve both a high sensitivity and a rapid induction, an inducible auto-activation circuit is predicted to acquire low cooperativity and low fold-induction. Examples from Escherichia coli's two-component signaling systems support these predictions
How Noisy Adaptation of Neurons Shapes Interspike Interval Histograms and Correlations
Channel noise is the dominant intrinsic noise source of neurons causing variability in the timing of action potentials and interspike intervals (ISI). Slow adaptation currents are observed in many cells and strongly shape response properties of neurons. These currents are mediated by finite populations of ionic channels and may thus carry a substantial noise component. Here we study the effect of such adaptation noise on the ISI statistics of an integrate-and-fire model neuron by means of analytical techniques and extensive numerical simulations. We contrast this stochastic adaptation with the commonly studied case of a fast fluctuating current noise and a deterministic adaptation current (corresponding to an infinite population of adaptation channels). We derive analytical approximations for the ISI density and ISI serial correlation coefficient for both cases. For fast fluctuations and deterministic adaptation, the ISI density is well approximated by an inverse Gaussian (IG) and the ISI correlations are negative. In marked contrast, for stochastic adaptation, the density is more peaked and has a heavier tail than an IG density and the serial correlations are positive. A numerical study of the mixed case where both fast fluctuations and adaptation channel noise are present reveals a smooth transition between the analytically tractable limiting cases. Our conclusions are furthermore supported by numerical simulations of a biophysically more realistic Hodgkin-Huxley type model. Our results could be used to infer the dominant source of noise in neurons from their ISI statistics