179 research outputs found
Optimizing experimental parameters for tracking of diffusing particles
We describe how a single-particle tracking experiment should be designed in
order for its recorded trajectories to contain the most information about a
tracked particle's diffusion coefficient. The precision of estimators for the
diffusion coefficient is affected by motion blur, limited photon statistics,
and the length of recorded time-series. We demonstrate for a particle
undergoing free diffusion that precision is negligibly affected by motion blur
in typical experiments, while optimizing photon counts and the number of
recorded frames is the key to precision. Building on these results, we describe
for a wide range of experimental scenarios how to choose experimental
parameters in order to optimize the precision. Generally, one should choose
quantity over quality: experiments should be designed to maximize the number of
frames recorded in a time-series, even if this means lower information content
in individual frames
Temporal Gillespie algorithm: Fast simulation of contagion processes on time-varying networks
Stochastic simulations are one of the cornerstones of the analysis of
dynamical processes on complex networks, and are often the only accessible way
to explore their behavior. The development of fast algorithms is paramount to
allow large-scale simulations. The Gillespie algorithm can be used for fast
simulation of stochastic processes, and variants of it have been applied to
simulate dynamical processes on static networks. However, its adaptation to
temporal networks remains non-trivial. We here present a temporal Gillespie
algorithm that solves this problem. Our method is applicable to general Poisson
(constant-rate) processes on temporal networks, stochastically exact, and up to
multiple orders of magnitude faster than traditional simulation schemes based
on rejection sampling. We also show how it can be extended to simulate
non-Markovian processes. The algorithm is easily applicable in practice, and as
an illustration we detail how to simulate both Poissonian and non-Markovian
models of epidemic spreading. Namely, we provide pseudocode and its
implementation in C++ for simulating the paradigmatic
Susceptible-Infected-Susceptible and Susceptible-Infected-Recovered models and
a Susceptible-Infected-Recovered model with non-constant recovery rates. For
empirical networks, the temporal Gillespie algorithm is here typically from 10
to 100 times faster than rejection sampling.Comment: Minor changes and updates to reference
How memory generates heterogeneous dynamics in temporal networks
Empirical temporal networks display strong heterogeneities in their dynamics,
which profoundly affect processes taking place on these networks, such as rumor
and epidemic spreading. Despite the recent wealth of data on temporal networks,
little work has been devoted to the understanding of how such heterogeneities
can emerge from microscopic mechanisms at the level of nodes and links. Here we
show that long-term memory effects are present in the creation and
disappearance of links in empirical networks. We thus consider a simple
generative modeling framework for temporal networks able to incorporate these
memory mechanisms. This allows us to study separately the role of each of these
mechanisms in the emergence of heterogeneous network dynamics. In particular,
we show analytically and numerically how heterogeneous distributions of contact
durations, of inter-contact durations and of numbers of contacts per link
emerge. We also study the individual effect of heterogeneities on dynamical
processes, such as the paradigmatic Susceptible-Infected epidemic spreading
model. Our results confirm in particular the crucial role of the distributions
of inter-contact durations and of the numbers of contacts per link
Compensating for population sampling in simulations of epidemic spread on temporal contact networks
Data describing human interactions often suffer from incomplete sampling of
the underlying population. As a consequence, the study of contagion processes
using data-driven models can lead to a severe underestimation of the epidemic
risk. Here we present a systematic method to alleviate this issue and obtain a
better estimation of the risk in the context of epidemic models informed by
high-resolution time-resolved contact data. We consider several such data sets
collected in various contexts and perform controlled resampling experiments. We
show how the statistical information contained in the resampled data can be
used to build a series of surrogate versions of the unknown contacts. We
simulate epidemic processes on the resulting reconstructed data sets and show
that it is possible to obtain good estimates of the outcome of simulations
performed using the complete data set. We discuss limitations and potential
improvements of our method
Impact of spatially constrained sampling of temporal contact networks on the evaluation of the epidemic risk
The ability to directly record human face-to-face interactions increasingly
enables the development of detailed data-driven models for the spread of
directly transmitted infectious diseases at the scale of individuals. Complete
coverage of the contacts occurring in a population is however generally
unattainable, due for instance to limited participation rates or experimental
constraints in spatial coverage. Here, we study the impact of spatially
constrained sampling on our ability to estimate the epidemic risk in a
population using such detailed data-driven models. The epidemic risk is
quantified by the epidemic threshold of the
susceptible-infectious-recovered-susceptible model for the propagation of
communicable diseases, i.e. the critical value of disease transmissibility
above which the disease turns endemic. We verify for both synthetic and
empirical data of human interactions that the use of incomplete data sets due
to spatial sampling leads to the underestimation of the epidemic risk. The bias
is however smaller than the one obtained by uniformly sampling the same
fraction of contacts: it depends nonlinearly on the fraction of contacts that
are recorded and becomes negligible if this fraction is large enough. Moreover,
it depends on the interplay between the timescales of population and spreading
dynamics.Comment: 21 pages, 7 figure
Data on face-to-face contacts in an office building suggests a low-cost vaccination strategy based on community linkers
Empirical data on contacts between individuals in social contexts play an
important role in providing information for models describing human behavior
and how epidemics spread in populations. Here, we analyze data on face-to-face
contacts collected in an office building. The statistical properties of
contacts are similar to other social situations, but important differences are
observed in the contact network structure. In particular, the contact network
is strongly shaped by the organization of the offices in departments, which has
consequences in the design of accurate agent-based models of epidemic spread.
We consider the contact network as a potential substrate for infectious disease
spread and show that its sparsity tends to prevent outbreaks of rapidly
spreading epidemics. Moreover, we define three typical behaviors according to
the fraction of links each individual shares outside its own department:
residents, wanderers and linkers. Linkers () act as bridges in the
network and have large betweenness centralities. Thus, a vaccination strategy
targeting linkers efficiently prevents large outbreaks. As such a behavior may
be spotted a priori in the offices' organization or from surveys, without the
full knowledge of the time-resolved contact network, this result may help the
design of efficient, low-cost vaccination or social-distancing strategies
Intracellular signaling by diffusion: can waves of hydrogen peroxide transmit intracellular information in plant cells?
Amplitude- and frequency-modulated waves of Ca(2+) ions transmit information inside cells. Reactive Oxygen Species (ROS), specifically hydrogen peroxide, have been proposed to have a similar role in plant cells. We consider the feasibility of such an intracellular communication system in view of the physical and biochemical conditions in plant cells. As model system, we use a H(2)O(2) signal originating at the plasma membrane (PM) and spreading through the cytosol. We consider two maximally simple types of signals, isolated pulses and harmonic oscillations. First we consider the basic limits on such signals as regards signal origin, frequency, amplitude, and distance. Then we establish the impact of ROS-removing enzymes on the ability of H(2)O(2) to transmit signals. Finally, we consider to what extent cytoplasmic streaming distorts signals. This modeling allows us to predict the conditions under which diffusion-mediated signaling is possible. We show that purely diffusive transmission of intracellular information by H(2)O(2) over a distance of 1 μm (typical distance between organelles, which may function as relay stations) is possible at frequencies well above 1 Hz, which is the highest frequency observed experimentally. This allows both frequency and amplitude modulation of the signal. Signaling over a distance of 10 μm (typical distance between the PM and the nucleus) may be possible, but requires high signal amplitudes or, equivalently, a very low detection threshold. Furthermore, at this longer distance a high rate of enzymatic degradation is required to make signaling at frequencies above 0.1 Hz possible. In either case, cytoplasmic streaming does not seriously disturb signals. We conclude that although purely diffusion-mediated signaling without relaying stations is theoretically possible, it is unlikely to work in practice, since it requires a much faster enzymatic degradation and a much lower cellular background concentration of H(2)O(2) than observed experimentally
Compression-based inference of network motif sets
Physical and functional constraints on biological networks lead to complex
topological patterns across multiple scales in their organization. A particular
type of higher-order network feature that has received considerable interest is
network motifs, defined as statistically regular subgraphs. These may implement
fundamental logical and computational circuits and are referred as ``building
blocks of complex networks''. Their well-defined structures and small sizes
also enables the testing of their functions in synthetic and natural biological
experiments. The statistical inference of network motifs is however fraught
with difficulties, from defining and sampling the right null model to
accounting for the large number of possible motifs and their potential
correlations in statistical testing. Here we develop a framework for motif
mining based on lossless network compression using subgraph contractions. The
minimum description length principle allows us to select the most significant
set of motifs as well as other prominent network features in terms of their
combined compression of the network. The approach inherently accounts for
multiple testing and correlations between subgraphs and does not rely on a
priori specification of an appropriate null model. This provides an alternative
definition of motif significance which guarantees more robust statistical
inference. Our approach overcomes the common problems in classic testing-based
motif analysis. We apply our methodology to perform comparative connectomics by
evaluating the compressibility and the circuit motifs of a range of
synaptic-resolution neural connectomes
Estimation of motility parameters from trajectory data:A condensate of our recent results
International audienceGiven a theoretical model for a self-propelled particle or micro-organism, how does one optimally determine the parameters of the model from experimental data in the form of a time-lapse recorded trajectory? For very long trajectories, one has very good statistics, and optimality may matter little. However, for biological micro-organisms, one may not control the duration of recordings, and then optimality can matter. This is especially the case if one is interested in individuality and hence cannot improve statistics by taking population averages over many trajectories. One can learn much about this problem by studying its simplest case, pure diffusion with no self-propagation. This is an interesting problem also in its own right for the very same reasons: interest in individuality and short trajectories. We summarize our recent results on this latter issue here and speculate about the extent to which similar results may be obtained also for self-propelled particles
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