40 research outputs found
Distribution of the resistance of nanowires with strong impurities
Motivated by recent experiments on nanowires and carbon nanotubes, we study
theoretically the effect of strong, point-like impurities on the linear
electrical resistance R of finite length quantum wires. Charge transport is
limited by Coulomb blockade and cotunneling. ln R is slowly self-averaging and
non Gaussian. Its distribution is Gumbel with finite-size corrections which we
compute. At low temperature, the distribution is similar to the variable range
hopping (VRH) behaviour found long ago in doped semiconductors. We show that a
result by Raikh and Ruzin does not apply. The finite-size corrections decay
with the length L like 1/ln L. At higher temperatures, this regime is replaced
by new laws and the shape of the finite-size corrections changes strongly: if
the electrons interact weakly, the corrections vanish already for wires with a
few tens impurities.Comment: 4 pages, 3 figure
Criticality and Universality in the Unit-Propagation Search Rule
The probability Psuccess(alpha, N) that stochastic greedy algorithms
successfully solve the random SATisfiability problem is studied as a function
of the ratio alpha of constraints per variable and the number N of variables.
These algorithms assign variables according to the unit-propagation (UP) rule
in presence of constraints involving a unique variable (1-clauses), to some
heuristic (H) prescription otherwise. In the infinite N limit, Psuccess
vanishes at some critical ratio alpha\_H which depends on the heuristic H. We
show that the critical behaviour is determined by the UP rule only. In the case
where only constraints with 2 and 3 variables are present, we give the phase
diagram and identify two universality classes: the power law class, where
Psuccess[alpha\_H (1+epsilon N^{-1/3}), N] ~ A(epsilon)/N^gamma; the stretched
exponential class, where Psuccess[alpha\_H (1+epsilon N^{-1/3}), N] ~
exp[-N^{1/6} Phi(epsilon)]. Which class is selected depends on the
characteristic parameters of input data. The critical exponent gamma is
universal and calculated; the scaling functions A and Phi weakly depend on the
heuristic H and are obtained from the solutions of reaction-diffusion equations
for 1-clauses. Computation of some non-universal corrections allows us to match
numerical results with good precision. The critical behaviour for constraints
with >3 variables is given. Our results are interpreted in terms of dynamical
graph percolation and we argue that they should apply to more general
situations where UP is used.Comment: 30 pages, 13 figure
Exclusion processes: short range correlations induced by adhesion and contact interactions
We analyze the out-of-equilibrium behavior of exclusion processes where
agents interact with their nearest neighbors, and we study the short-range
correlations which develop because of the exclusion and other contact
interactions. The form of interactions we focus on, including adhesion and
contact-preserving interactions, is especially relevant for migration processes
of living cells. We show the local agent density and nearest-neighbor two-point
correlations resulting from simulations on two dimensional lattices in the
transient regime where agents invade an initially empty space from a source and
in the stationary regime between a source and a sink. We compare the results of
simulations with the corresponding quantities derived from the master equation
of the exclusion processes, and in both cases, we show that, during the
invasion of space by agents, a wave of correlations travels with velocity v(t)
~ t^(-1/2). The relative placement of this wave to the agent density front and
the time dependence of its height may be used to discriminate between different
forms of contact interactions or to quantitatively estimate the intensity of
interactions. We discuss, in the stationary density profile between a full and
an empty reservoir of agents, the presence of a discontinuity close to the
empty reservoir. Then, we develop a method for deriving approximate
hydrodynamic limits of the processes. From the resulting systems of partial
differential equations, we recover the self-similar behavior of the agent
density and correlations during space invasion
Automatic quantification of the microvascular density on whole slide images, applied to paediatric brain tumours
Angiogenesis is a key phenomenon for tumour progression, diagnosis and
treatment in brain tumours and more generally in oncology. Presently, its
precise, direct quantitative assessment can only be done on whole tissue
sections immunostained to reveal vascular endothelial cells. But this is a
tremendous task for the pathologist and a challenge for the computer since
digitised whole tissue sections, whole slide images (WSI), contain typically
around ten gigapixels.
We define and implement an algorithm that determines automatically, on a WSI
at objective magnification , the regions of tissue, the regions
without blur and the regions of large puddles of red blood cells, and
constructs the mask of blur-free, significant tissue on the WSI. Then it
calibrates automatically the optical density ratios of the immunostaining of
the vessel walls and of the counterstaining, performs a colour deconvolution
inside the regions of blur-free tissue, and finds the vessel walls inside these
regions by selecting, on the image resulting from the colour deconvolution,
zones which satisfy a double-threshold criterion. A mask of vessel wall regions
on the WSI is produced. The density of microvessels is finally computed as the
fraction of the area of significant tissue which is occupied by vessel walls.
We apply this algorithm to a set of 186 WSI of paediatric brain tumours from
World Health Organisation grades I to IV. The segmentations are of very good
quality although the set of slides is very heterogeneous. The computation time
is of the order of a fraction of an hour for each WSI on a modest computer. The
computed microvascular density is found to be robust and strongly correlates
with the tumour grade.
This method requires no training and can easily be applied to other tumour
types and other stainings
Stack or trash? Quality assessment of virtual slides
International audienc
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
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 stochastic individual-based model to explore the role of spatial interactions and antigen recognition in the immune response against solid tumours
FRM is funded by the Engineering and Physical Sciences Research Council (EPSRC).Spatial interactions between cancer and immune cells, as well as the recognition of tumour antigens by cells of the immune system, play a key role in the immune response against solid tumours. The existing mathematical models generally focus only on one of these key aspects. We present here a spatial stochastic individual-based model that explicitly captures antigen expression and recognition. In our model, each cancer cell is characterised by an antigen profile which can change over time due to either epimutations or mutations. The immune response against the cancer cells is initiated by the dendritic cells that recognise the tumour antigens and present them to the cytotoxic T cells. Consequently, T cells become activated against the tumour cells expressing such antigens. Moreover, the differences in movement between inactive and active immune cells are explicitly taken into account by the model. Computational simulations of our model clarify the conditions for the emergence of tumour clearance, dormancy or escape, and allow us to assess the impact of antigenic heterogeneity of cancer cells on the efficacy of immune action. Ultimately, our results highlight the complex interplay between spatial interactions and adaptive mechanisms that underpins the immune response against solid tumours, and suggest how this may be exploited to further develop cancer immunotherapies.PostprintPeer reviewe