31 research outputs found
Critical behaviour of combinatorial search algorithms, and the unitary-propagation universality class
The probability P(alpha, N) that search algorithms for random Satisfiability
problems successfully find a solution is studied as a function of the ratio
alpha of constraints per variable and the number N of variables. P is shown to
be finite if alpha lies below an algorithm--dependent threshold alpha\_A, and
exponentially small in N above. The critical behaviour is universal for all
algorithms based on the widely-used unitary propagation rule: P[ (1 + epsilon)
alpha\_A, N] ~ exp[-N^(1/6) Phi(epsilon N^(1/3)) ]. Exponents are related to
the critical behaviour of random graphs, and the scaling function Phi is
exactly calculated through a mapping onto a diffusion-and-death problem.Comment: 7 pages; 3 figure
Critical Behavior and Lack of Self Averaging in the Dynamics of the Random Potts Model in Two Dimensions
We study the dynamics of the q-state random bond Potts ferromagnet on the
square lattice at its critical point by Monte Carlo simulations with single
spin-flip dynamics. We concentrate on q=3 and q=24 and find, in both cases,
conventional, rather than activated, dynamics. We also look at the distribution
of relaxation times among different samples, finding different results for the
two q values. For q=3 the relative variance of the relaxation time tau at the
critical point is finite. However, for q=24 this appears to diverge in the
thermodynamic limit and it is ln(tau) which has a finite relative variance. We
speculate that this difference occurs because the transition of the
corresponding pure system is second order for q=3 but first order for q=24.Comment: 9 pages, 13 figures, final published versio
Hyperbolic traveling waves driven by growth
We perform the analysis of a hyperbolic model which is the analog of the
Fisher-KPP equation. This model accounts for particles that move at maximal
speed (\epsilon\textgreater{}0), and proliferate according to
a reaction term of monostable type. We study the existence and stability of
traveling fronts. We exhibit a transition depending on the parameter
: for small the behaviour is essentially the same as for
the diffusive Fisher-KPP equation. However, for large the traveling
front with minimal speed is discontinuous and travels at the maximal speed
. The traveling fronts with minimal speed are linearly stable in
weighted spaces. We also prove local nonlinear stability of the traveling
front with minimal speed when is smaller than the transition
parameter.Comment: 24 page
Modeling tumor cell migration: from microscopic to macroscopic
It has been shown experimentally that contact interactions may influence the
migration of cancer cells. Previous works have modelized this thanks to
stochastic, discrete models (cellular automata) at the cell level. However, for
the study of the growth of real-size tumors with several millions of cells, it
is best to use a macroscopic model having the form of a partial differential
equation (PDE) for the density of cells. The difficulty is to predict the
effect, at the macroscopic scale, of contact interactions that take place at
the microscopic scale. To address this we use a multiscale approach: starting
from a very simple, yet experimentally validated, microscopic model of
migration with contact interactions, we derive a macroscopic model. We show
that a diffusion equation arises, as is often postulated in the field of glioma
modeling, but it is nonlinear because of the interactions. We give the explicit
dependence of diffusivity on the cell density and on a parameter governing
cell-cell interactions. We discuss in details the conditions of validity of the
approximations used in the derivation and we compare analytic results from our
PDE to numerical simulations and to some in vitro experiments. We notice that
the family of microscopic models we started from includes as special cases some
kinetically constrained models that were introduced for the study of the
physics of glasses, supercooled liquids and jamming systems.Comment: Final published version; 14 pages, 7 figure
Thermodynamic formalism for systems with Markov dynamics
The thermodynamic formalism allows one to access the chaotic properties of
equilibrium and out-of-equilibrium systems, by deriving those from a dynamical
partition function. The definition that has been given for this partition
function within the framework of discrete time Markov chains was not suitable
for continuous time Markov dynamics. Here we propose another interpretation of
the definition that allows us to apply the thermodynamic formalism to
continuous time.
We also generalize the formalism --a dynamical Gibbs ensemble construction--
to a whole family of observables and their associated large deviation
functions. This allows us to make the connection between the thermodynamic
formalism and the observable involved in the much-studied fluctuation theorem.
We illustrate our approach on various physical systems: random walks,
exclusion processes, an Ising model and the contact process. In the latter
cases, we identify a signature of the occurrence of dynamical phase
transitions. We show that this signature can already be unravelled using the
simplest dynamical ensemble one could define, based on the number of
configuration changes a system has undergone over an asymptotically large time
window.Comment: 64 pages, LaTeX; version accepted for publication in Journal of
Statistical Physic
Field theoretic approach to metastability in the contact process
A quantum field theoretic formulation of the dynamics of the Contact Process
on a regular graph of degree z is introduced. A perturbative calculation in
powers of 1/z of the effective potential for the density of particles phi(t)
and an instantonic field psi(t) emerging from the quantum formalism is
performed. Corrections to the mean-field distribution of densities of particles
in the out-of-equilibrium stationary state are derived in powers of 1/z.
Results for typical (e.g. average density) and rare fluctuation (e.g. lifetime
of the metastable state) properties are in very good agreement with numerical
simulations carried out on D-dimensional hypercubic (z=2D) and Cayley lattices.Comment: Final published version; 20 pages, 5 figure
A Deep Learning based Pipeline for Efficient Oral Cancer Screening on Whole Slide Images
Oral cancer incidence is rapidly increasing worldwide. The most important
determinant factor in cancer survival is early diagnosis. To facilitate large
scale screening, we propose a fully automated pipeline for oral cancer
detection on whole slide cytology images. The pipeline consists of fully
convolutional regression-based nucleus detection, followed by per-cell focus
selection, and CNN based classification. Our novel focus selection step
provides fast per-cell focus decisions at human-level accuracy. We demonstrate
that the pipeline provides efficient cancer classification of whole slide
cytology images, improving over previous results both in terms of accuracy and
feasibility. The complete source code is available at
https://github.com/MIDA-group/OralScreen.Comment: Accepted to ICIAR 202
QuPath:Open source software for digital pathology image analysis
Abstract QuPath is new bioimage analysis software designed to meet the growing need for a user-friendly, extensible, open-source solution for digital pathology and whole slide image analysis. In addition to offering a comprehensive panel of tumor identification and high-throughput biomarker evaluation tools, QuPath provides researchers with powerful batch-processing and scripting functionality, and an extensible platform with which to develop and share new algorithms to analyze complex tissue images. Furthermore, QuPath’s flexible design makes it suitable for a wide range of additional image analysis applications across biomedical research