218 research outputs found
Random Planar Lattices and Integrated SuperBrownian Excursion
In this paper, a surprising connection is described between a specific brand
of random lattices, namely planar quadrangulations, and Aldous' Integrated
SuperBrownian Excursion (ISE). As a consequence, the radius r_n of a random
quadrangulation with n faces is shown to converge, up to scaling, to the width
r=R-L of the support of the one-dimensional ISE. More generally the
distribution of distances to a random vertex in a random quadrangulation is
described in its scaled limit by the random measure ISE shifted to set the
minimum of its support in zero.
The first combinatorial ingredient is an encoding of quadrangulations by
trees embedded in the positive half-line, reminiscent of Cori and Vauquelin's
well labelled trees. The second step relates these trees to embedded (discrete)
trees in the sense of Aldous, via the conjugation of tree principle, an
analogue for trees of Vervaat's construction of the Brownian excursion from the
bridge.
From probability theory, we need a new result of independent interest: the
weak convergence of the encoding of a random embedded plane tree by two contour
walks to the Brownian snake description of ISE.
Our results suggest the existence of a Continuum Random Map describing in
term of ISE the scaled limit of the dynamical triangulations considered in
two-dimensional pure quantum gravity.Comment: 44 pages, 22 figures. Slides and extended abstract version are
available at http://www.loria.fr/~schaeffe/Pub/Diameter/ and
http://www.iecn.u-nancy.fr/~chassain
The maximum of the local time of a diffusion process in a drifted Brownian potential
We consider a one-dimensional diffusion process in a
-drifted Brownian potential for . We are interested
in the maximum of its local time, and study its almost sure asymptotic
behaviour, which is proved to be different from the behaviour of the maximum
local time of the transient random walk in random environment. We also obtain
the convergence in law of the maximum local time of under the annealed law
after suitable renormalization when . Moreover, we characterize
all the upper and lower classes for the hitting times of , in the sense of
Paul L\'evy, and provide laws of the iterated logarithm for the diffusion
itself. To this aim, we use annealed technics.Comment: 38 pages, new version, merged with hal-00013040 (arXiv:math/0511053),
with some additional result
Information inequalities and Generalized Graph Entropies
In this article, we discuss the problem of establishing relations between
information measures assessed for network structures. Two types of entropy
based measures namely, the Shannon entropy and its generalization, the
R\'{e}nyi entropy have been considered for this study. Our main results involve
establishing formal relationship, in the form of implicit inequalities, between
these two kinds of measures when defined for graphs. Further, we also state and
prove inequalities connecting the classical partition-based graph entropies and
the functional-based entropy measures. In addition, several explicit
inequalities are derived for special classes of graphs.Comment: A preliminary version. To be submitted to a journa
String Matching and 1d Lattice Gases
We calculate the probability distributions for the number of occurrences
of a given letter word in a random string of letters. Analytical
expressions for the distribution are known for the asymptotic regimes (i) (Gaussian) and such that is finite
(Compound Poisson). However, it is known that these distributions do now work
well in the intermediate regime . We show that the
problem of calculating the string matching probability can be cast into a
determining the configurational partition function of a 1d lattice gas with
interacting particles so that the matching probability becomes the
grand-partition sum of the lattice gas, with the number of particles
corresponding to the number of matches. We perform a virial expansion of the
effective equation of state and obtain the probability distribution. Our result
reproduces the behavior of the distribution in all regimes. We are also able to
show analytically how the limiting distributions arise. Our analysis builds on
the fact that the effective interactions between the particles consist of a
relatively strong core of size , the word length, followed by a weak,
exponentially decaying tail. We find that the asymptotic regimes correspond to
the case where the tail of the interactions can be neglected, while in the
intermediate regime they need to be kept in the analysis. Our results are
readily generalized to the case where the random strings are generated by more
complicated stochastic processes such as a non-uniform letter probability
distribution or Markov chains. We show that in these cases the tails of the
effective interactions can be made even more dominant rendering thus the
asymptotic approximations less accurate in such a regime.Comment: 44 pages and 8 figures. Major revision of previous version. The
lattice gas analogy has been worked out in full, including virial expansion
and equation of state. This constitutes the main part of the paper now.
Connections with existing work is made and references should be up to date
now. To be submitted for publicatio
Minimal Absent Words in Four Human Genome Assemblies
Minimal absent words have been computed in genomes of organisms from all domains of life. Here, we aim to contribute to the catalogue of human genomic variation by investigating the variation in number and content of minimal absent words within a species, using four human genome assemblies. We compare the reference human genome GRCh37 assembly, the HuRef assembly of the genome of Craig Venter, the NA12878 assembly from cell line GM12878, and the YH assembly of the genome of a Han Chinese individual. We find the variation in number and content of minimal absent words between assemblies more significant for large and very large minimal absent words, where the biases of sequencing and assembly methodologies become more pronounced. Moreover, we find generally greater similarity between the human genome assemblies sequenced with capillary-based technologies (GRCh37 and HuRef) than between the human genome assemblies sequenced with massively parallel technologies (NA12878 and YH). Finally, as expected, we find the overall variation in number and content of minimal absent words within a species to be generally smaller than the variation between species
Decomposition cross-correlation for analysis of collagen matrix deformation by single smooth muscle cells
Microvascular remodeling is known to depend on cellular interactions with matrix tissue. However, it is difficult to study the role of specific cells or matrix elements in an in vivo setting. The aim of this study is to develop an automated technique that can be employed to obtain and analyze local collagen matrix remodeling by single smooth muscle cells. We combined a motorized microscopic setup and time-lapse video microscopy with a new cross-correlation based image analysis algorithm to enable automated recording of cell-induced matrix reorganization. This method rendered 60–90 single cell studies per experiment, for which collagen deformation over time could be automatically derived. Thus, the current setup offers a tool to systematically study different components active in matrix remodeling
Two refreshing views of Fluctuation Theorems through Kinematics Elements and Exponential Martingale
In the context of Markov evolution, we present two original approaches to
obtain Generalized Fluctuation-Dissipation Theorems (GFDT), by using the
language of stochastic derivatives and by using a family of exponential
martingales functionals. We show that GFDT are perturbative versions of
relations verified by these exponential martingales. Along the way, we prove
GFDT and Fluctuation Relations (FR) for general Markov processes, beyond the
usual proof for diffusion and pure jump processes. Finally, we relate the FR to
a family of backward and forward exponential martingales.Comment: 41 pages, 7 figures; version2: 45 pages, 7 figures, minor revisions,
new results in Section
Optimal designs for rational function regression
We consider optimal non-sequential designs for a large class of (linear and
nonlinear) regression models involving polynomials and rational functions with
heteroscedastic noise also given by a polynomial or rational weight function.
The proposed method treats D-, E-, A-, and -optimal designs in a
unified manner, and generates a polynomial whose zeros are the support points
of the optimal approximate design, generalizing a number of previously known
results of the same flavor. The method is based on a mathematical optimization
model that can incorporate various criteria of optimality and can be solved
efficiently by well established numerical optimization methods. In contrast to
previous optimization-based methods proposed for similar design problems, it
also has theoretical guarantee of its algorithmic efficiency; in fact, the
running times of all numerical examples considered in the paper are negligible.
The stability of the method is demonstrated in an example involving high degree
polynomials. After discussing linear models, applications for finding locally
optimal designs for nonlinear regression models involving rational functions
are presented, then extensions to robust regression designs, and trigonometric
regression are shown. As a corollary, an upper bound on the size of the support
set of the minimally-supported optimal designs is also found. The method is of
considerable practical importance, with the potential for instance to impact
design software development. Further study of the optimality conditions of the
main optimization model might also yield new theoretical insights.Comment: 25 pages. Previous version updated with more details in the theory
and additional example
Harmonic Systems With Bulk Noises
We consider a harmonic chain in contact with thermal reservoirs at different
temperatures and subject to bulk noises of different types: velocity flips or
self-consistent reservoirs. While both systems have the same covariances in the
nonequilibrium stationary state (NESS) the measures are very different. We
study hydrodynamical scaling, large deviations, fluctuations, and long range
correlations in both systems. Some of our results extend to higher dimensions
Improving postpartum care delivery and uptake by implementing context-specific interventions in four countries in Africa: a realist evaluation of the Missed Opportunities in Maternal and Infant Health (MOMI) project.
Postpartum care (PPC) has remained relatively neglected in many interventions designed to improve maternal and neonatal health in sub-Saharan Africa. The Missed Opportunities in Maternal and Infant Health project developed and implemented a context-specific package of health system strengthening and demand generation in four African countries, aiming to improve access and quality of PPC. A realist evaluation was conducted to enable nuanced understanding of the influence of different contextual factors on both the implementation and impacts of the interventions. Mixed methods were used to collect data and test hypothesised context-mechanism-outcome configurations: 16 case studies (including interviews, observations, monitoring data on key healthcare processes and outcomes), monitoring data for all study health facilities and communities, document analysis and participatory evaluation workshops. After evaluation in individual countries, a cross-country analysis was conducted that led to the development of four middle-range theories. Community health workers (CHWs) were key assets in shifting demand for PPC by 'bridging' communities and facilities. Because they were chosen from the community they served, they gained trust from the community and an intrinsic sense of responsibility. Furthermore, if a critical mass of women seek postpartum healthcare as a result of the CHWs bridging function, a 'buzz' for change is created, leading eventually to the acceptability and perceived value of attending for PPC that outweighs the costs of attending the health facility. On the supply side, rigid vertical hierarchies and defined roles for health facility workers (HFWs) impede integration of maternal and infant health services. Additionally, HFWs fear being judged negatively which overrides the self-efficacy that could potentially be gained from PPC training. Instead the main driver of HFWs' motivation to provide comprehensive PPC is dependent on accountability systems for delivering PPC created by other programmes. The realist evaluation offers insights into some of the contextual factors that can be pivotal in enabling the community-level and service-level interventions to be effective
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