2,560 research outputs found
Simulation of stochastic network dynamics via entropic matching
The simulation of complex stochastic network dynamics arising, for instance,
from models of coupled biomolecular processes remains computationally
challenging. Often, the necessity to scan a models' dynamics over a large
parameter space renders full-fledged stochastic simulations impractical,
motivating approximation schemes. Here we propose an approximation scheme which
improves upon the standard linear noise approximation while retaining similar
computational complexity. The underlying idea is to minimize, at each time
step, the Kullback-Leibler divergence between the true time evolved probability
distribution and a Gaussian approximation (entropic matching). This condition
leads to ordinary differential equations for the mean and the covariance matrix
of the Gaussian. For cases of weak nonlinearity, the method is more accurate
than the linear method when both are compared to stochastic simulations.Comment: 23 pages, 6 figures; significantly revised versio
Artificial Sequences and Complexity Measures
In this paper we exploit concepts of information theory to address the
fundamental problem of identifying and defining the most suitable tools to
extract, in a automatic and agnostic way, information from a generic string of
characters. We introduce in particular a class of methods which use in a
crucial way data compression techniques in order to define a measure of
remoteness and distance between pairs of sequences of characters (e.g. texts)
based on their relative information content. We also discuss in detail how
specific features of data compression techniques could be used to introduce the
notion of dictionary of a given sequence and of Artificial Text and we show how
these new tools can be used for information extraction purposes. We point out
the versatility and generality of our method that applies to any kind of
corpora of character strings independently of the type of coding behind them.
We consider as a case study linguistic motivated problems and we present
results for automatic language recognition, authorship attribution and self
consistent-classification.Comment: Revised version, with major changes, of previous "Data Compression
approach to Information Extraction and Classification" by A. Baronchelli and
V. Loreto. 15 pages; 5 figure
Entropic Distance for Nonlinear Master Equation
More and more works deal with statistical systems far from equilibrium,
dominated by unidirectional stochastic processes augmented by rare resets. We
analyze the construction of the entropic distance measure appropriate for such
dynamics. We demonstrate that a power-like nonlinearity in the state
probability in the master equation naturally leads to the Tsallis
(Havrda-Charv\'at, Acz\'el-Dar\'oczy) q-entropy formula in the context of
seeking for the maximal entropy state at stationarity. A few possible
applications of a certain simple and linear master equation to phenomena
studied in statistical physics are listed at the end.Comment: Talk given by T.S.Bir\'o at BGL 2017, Gy\"ongy\"os, Hungar
Relative information entropy and Weyl curvature of the inhomogeneous Universe
Penrose conjectured a connection between entropy and Weyl curvature of the
Universe. This is plausible, as the almost homogeneous and isotropic Universe
at the onset of structure formation has negligible Weyl curvature, which then
grows (relative to the Ricci curvature) due to the formation of large-scale
structure and thus reminds us of the second law of thermodynamics. We study two
scalar measures to quantify the deviations from a homogeneous and isotropic
space-time, the relative information entropy and a Weyl tensor invariant, and
show their relation to the averaging problem. We calculate these two quantities
up to second order in standard cosmological perturbation theory and find that
they are correlated and can be linked via the kinematic backreaction of a
spatially averaged universe model.Comment: 8 pages, matches the published version in Physical Review
Optimal experimental design for mathematical models of haematopoiesis.
The haematopoietic system has a highly regulated and complex structure in which cells are organized to successfully create and maintain new blood cells. It is known that feedback regulation is crucial to tightly control this system, but the specific mechanisms by which control is exerted are not completely understood. In this work, we aim to uncover the underlying mechanisms in haematopoiesis by conducting perturbation experiments, where animal subjects are exposed to an external agent in order to observe the system response and evolution. We have developed a novel Bayesian hierarchical framework for optimal design of perturbation experiments and proper analysis of the data collected. We use a deterministic model that accounts for feedback and feedforward regulation on cell division rates and self-renewal probabilities. A significant obstacle is that the experimental data are not longitudinal, rather each data point corresponds to a different animal. We overcome this difficulty by modelling the unobserved cellular levels as latent variables. We then use principles of Bayesian experimental design to optimally distribute time points at which the haematopoietic cells are quantified. We evaluate our approach using synthetic and real experimental data and show that an optimal design can lead to better estimates of model parameters
Entropy-based parametric estimation of spike train statistics
We consider the evolution of a network of neurons, focusing on the asymptotic
behavior of spikes dynamics instead of membrane potential dynamics. The spike
response is not sought as a deterministic response in this context, but as a
conditional probability : "Reading out the code" consists of inferring such a
probability. This probability is computed from empirical raster plots, by using
the framework of thermodynamic formalism in ergodic theory. This gives us a
parametric statistical model where the probability has the form of a Gibbs
distribution. In this respect, this approach generalizes the seminal and
profound work of Schneidman and collaborators. A minimal presentation of the
formalism is reviewed here, while a general algorithmic estimation method is
proposed yielding fast convergent implementations. It is also made explicit how
several spike observables (entropy, rate, synchronizations, correlations) are
given in closed-form from the parametric estimation. This paradigm does not
only allow us to estimate the spike statistics, given a design choice, but also
to compare different models, thus answering comparative questions about the
neural code such as : "are correlations (or time synchrony or a given set of
spike patterns, ..) significant with respect to rate coding only ?" A numerical
validation of the method is proposed and the perspectives regarding spike-train
code analysis are also discussed.Comment: 37 pages, 8 figures, submitte
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