13,417 research outputs found
Algorithmic and enumerative aspects of the Moser-Tardos distribution
Moser & Tardos have developed a powerful algorithmic approach (henceforth
"MT") to the Lovasz Local Lemma (LLL); the basic operation done in MT and its
variants is a search for "bad" events in a current configuration. In the
initial stage of MT, the variables are set independently. We examine the
distributions on these variables which arise during intermediate stages of MT.
We show that these configurations have a more or less "random" form, building
further on the "MT-distribution" concept of Haeupler et al. in understanding
the (intermediate and) output distribution of MT. This has a variety of
algorithmic applications; the most important is that bad events can be found
relatively quickly, improving upon MT across the complexity spectrum: it makes
some polynomial-time algorithms sub-linear (e.g., for Latin transversals, which
are of basic combinatorial interest), gives lower-degree polynomial run-times
in some settings, transforms certain super-polynomial-time algorithms into
polynomial-time ones, and leads to Las Vegas algorithms for some coloring
problems for which only Monte Carlo algorithms were known.
We show that in certain conditions when the LLL condition is violated, a
variant of the MT algorithm can still produce a distribution which avoids most
of the bad events. We show in some cases this MT variant can run faster than
the original MT algorithm itself, and develop the first-known criterion for the
case of the asymmetric LLL. This can be used to find partial Latin transversals
-- improving upon earlier bounds of Stein (1975) -- among other applications.
We furthermore give applications in enumeration, showing that most applications
(where we aim for all or most of the bad events to be avoided) have many more
solutions than known before by proving that the MT-distribution has "large"
min-entropy and hence that its support-size is large
Learning mutational graphs of individual tumour evolution from single-cell and multi-region sequencing data
Background. A large number of algorithms is being developed to reconstruct
evolutionary models of individual tumours from genome sequencing data. Most
methods can analyze multiple samples collected either through bulk multi-region
sequencing experiments or the sequencing of individual cancer cells. However,
rarely the same method can support both data types.
Results. We introduce TRaIT, a computational framework to infer mutational
graphs that model the accumulation of multiple types of somatic alterations
driving tumour evolution. Compared to other tools, TRaIT supports multi-region
and single-cell sequencing data within the same statistical framework, and
delivers expressive models that capture many complex evolutionary phenomena.
TRaIT improves accuracy, robustness to data-specific errors and computational
complexity compared to competing methods.
Conclusions. We show that the application of TRaIT to single-cell and
multi-region cancer datasets can produce accurate and reliable models of
single-tumour evolution, quantify the extent of intra-tumour heterogeneity and
generate new testable experimental hypotheses
Slingshot: cell lineage and pseudotime inference for single-cell transcriptomics.
BackgroundSingle-cell transcriptomics allows researchers to investigate complex communities of heterogeneous cells. It can be applied to stem cells and their descendants in order to chart the progression from multipotent progenitors to fully differentiated cells. While a variety of statistical and computational methods have been proposed for inferring cell lineages, the problem of accurately characterizing multiple branching lineages remains difficult to solve.ResultsWe introduce Slingshot, a novel method for inferring cell lineages and pseudotimes from single-cell gene expression data. In previously published datasets, Slingshot correctly identifies the biological signal for one to three branching trajectories. Additionally, our simulation study shows that Slingshot infers more accurate pseudotimes than other leading methods.ConclusionsSlingshot is a uniquely robust and flexible tool which combines the highly stable techniques necessary for noisy single-cell data with the ability to identify multiple trajectories. Accurate lineage inference is a critical step in the identification of dynamic temporal gene expression
Parallel Peeling Algorithms
The analysis of several algorithms and data structures can be framed as a
peeling process on a random hypergraph: vertices with degree less than k are
removed until there are no vertices of degree less than k left. The remaining
hypergraph is known as the k-core. In this paper, we analyze parallel peeling
processes, where in each round, all vertices of degree less than k are removed.
It is known that, below a specific edge density threshold, the k-core is empty
with high probability. We show that, with high probability, below this
threshold, only (log log n)/log(k-1)(r-1) + O(1) rounds of peeling are needed
to obtain the empty k-core for r-uniform hypergraphs. Interestingly, we show
that above this threshold, Omega(log n) rounds of peeling are required to find
the non-empty k-core. Since most algorithms and data structures aim to peel to
an empty k-core, this asymmetry appears fortunate. We verify the theoretical
results both with simulation and with a parallel implementation using graphics
processing units (GPUs). Our implementation provides insights into how to
structure parallel peeling algorithms for efficiency in practice.Comment: Appears in SPAA 2014. Minor typo corrections relative to previous
versio
Damage segregation at fissioning may increase growth rates: A superprocess model
A fissioning organism may purge unrepairable damage by bequeathing it
preferentially to one of its daughters. Using the mathematical formalism of
superprocesses, we propose a flexible class of analytically tractable models
that allow quite general effects of damage on death rates and splitting rates
and similarly general damage segregation mechanisms. We show that, in a
suitable regime, the effects of randomness in damage segregation at fissioning
are indistinguishable from those of randomness in the mechanism of damage
accumulation during the organism's lifetime. Moreover, the optimal population
growth is achieved for a particular finite, non-zero level of combined
randomness from these two sources. In particular, when damage accumulates
deterministically, optimal population growth is achieved by a moderately
unequal division of damage between the daughters. Too little or too much
division is sub-optimal. Connections are drawn both to recent experimental
results on inheritance of damage in protozoans, to theories of the evolution of
aging, and to models of resource division between siblings.Comment: Version 2 had significant conceptual and organizational changes,
though only minor changes to the mathematics. Version 3 has minor
proofreading corrections, and a few new references. The paper will appear in
Theoretical Population Biolog
Limit theorems for Markov processes indexed by continuous time Galton--Watson trees
We study the evolution of a particle system whose genealogy is given by a
supercritical continuous time Galton--Watson tree. The particles move
independently according to a Markov process and when a branching event occurs,
the offspring locations depend on the position of the mother and the number of
offspring. We prove a law of large numbers for the empirical measure of
individuals alive at time t. This relies on a probabilistic interpretation of
its intensity by mean of an auxiliary process. The latter has the same
generator as the Markov process along the branches plus additional jumps,
associated with branching events of accelerated rate and biased distribution.
This comes from the fact that choosing an individual uniformly at time t favors
lineages with more branching events and larger offspring number. The central
limit theorem is considered on a special case. Several examples are developed,
including applications to splitting diffusions, cellular aging, branching
L\'{e}vy processes.Comment: Published in at http://dx.doi.org/10.1214/10-AAP757 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Kidney regeneration: common themes from the embryo to the adult
The vertebrate kidney has an inherent ability to regenerate following acute damage. Successful regeneration of the injured kidney requires the rapid replacement of damaged tubular epithelial cells and reconstitution of normal tubular function. Identifying the cells that participate in the regeneration process as well as the molecular mechanisms involved may reveal therapeutic targets for the treatment of kidney disease. Renal regeneration is associated with the expression of genetic pathways that are necessary for kidney organogenesis, suggesting that the regenerating tubular epithelium may be “reprogrammed” to a less-differentiated, progenitor state. This review will highlight data from various vertebrate models supporting the hypothesis that nephrogenic genes are reactivated as part of the process of kidney regeneration following acute kidney injury (AKI). Emphasis will be placed on the reactivation of developmental pathways and how our understanding of the resulting regeneration process may be enhanced by lessons learned in the embryonic kidney.Fil: Cirio, Maria Cecilia. University of Pittsburgh; Estados Unidos. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: de Groh, Eric D.. University of Pittsburgh; Estados UnidosFil: de Caestecker, Mark P.. Vanderbilt University; Estados UnidosFil: Davidson, Alan J.. The University of Auckland; Nueva ZelandaFil: Hukriede, Neil A.. University of Pittsburgh; Estados Unido
Microscopic structure of travelling wave solutions in a class of stochastic interacting particle systems
We obtain exact travelling wave solutions for three families of stochastic
one-dimensional nonequilibrium lattice models with open boundaries. These
solutions describe the diffusive motion and microscopic structure of (i) of
shocks in the partially asymmetric exclusion process with open boundaries, (ii)
of a lattice Fisher wave in a reaction-diffusion system, and (iii) of a domain
wall in non-equilibrium Glauber-Kawasaki dynamics with magnetization current.
For each of these systems we define a microscopic shock position and calculate
the exact hopping rates of the travelling wave in terms of the transition rates
of the microscopic model. In the steady state a reversal of the bias of the
travelling wave marks a first-order non-equilibrium phase transition, analogous
to the Zel'dovich theory of kinetics of first-order transitions. The stationary
distributions of the exclusion process with shocks can be described in
terms of -dimensional representations of matrix product states.Comment: 27 page
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In vivo manipulation of the extracellular matrix induces vascular regression in a basal chordate.
We investigated the physical role of the extracellular matrix (ECM) in vascular homeostasis in the basal chordate Botryllus schlosseri, which has a large, transparent, extracorporeal vascular network encompassing an area >100 cm2 We found that the collagen cross-linking enzyme lysyl oxidase is expressed in all vascular cells and that in vivo inhibition using β-aminopropionitrile (BAPN) caused a rapid, global regression of the entire network, with some vessels regressing >10 mm within 16 h. BAPN treatment changed the ultrastructure of collagen fibers in the vessel basement membrane, and the kinetics of regression were dose dependent. Pharmacological inhibition of both focal adhesion kinase (FAK) and Raf also induced regression, and levels of phosphorylated FAK in vascular cells decreased during BAPN treatment and FAK inhibition but not Raf inhibition, suggesting that physical changes in the vessel ECM are detected via canonical integrin signaling pathways. Regression is driven by apoptosis and extrusion of cells through the basal lamina, which are then engulfed by blood-borne phagocytes. Extrusion and regression occurred in a coordinated manner that maintained vessel integrity, with no loss of barrier function. This suggests the presence of regulatory mechanisms linking physical changes to a homeostatic, tissue-level response
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