542 research outputs found
Bose-Einstein distribution, condensation transition and multiple stationary states in multiloci evolution of diploid population
The mapping between genotype and phenotype is encoded in the complex web of
epistatic interaction between genetic loci. In this rugged fitness landscape,
recombination processes, which tend to increase variation in the population,
compete with selection processes that tend to reduce genetic variation. Here we
show that the Bose-Einstein distribution describe the multiple stationary
states of a diploid population under this multi-loci evolutionary dynamics.
Moreover, the evolutionary process might undergo an interesting condensation
phase transition in the universality class of a Bose-Einstein condensation when
a finite fraction of pairs of linked loci, is fixed into given allelic states.
Below this phase transition the genetic variation within a species is
significantly reduced and only maintained by the remaining polymorphic loci.Comment: (12 pages, 7 figures
Does hardcore interaction change absorbing type critical phenomena?
It has been generally believed that hardcore interaction is irrelevant to
absorbing type critical phenomena because the particle density is so low near
an absorbing phase transition. We study the effect of hardcore interaction on
the N species branching annihilating random walks with two offspring and report
that hardcore interaction drastically changes the absorbing type critical
phenomena in a nontrivial way. Through Langevin equation type approach, we
predict analytically the values of the scaling exponents, in one dimension for all N > 1. Direct numerical
simulations confirm our prediction. When the diffusion coefficients for
different species are not identical, and vary
continuously with the ratios between the coefficients.Comment: 4 pages, 1 figur
Robustness and Generalization
We derive generalization bounds for learning algorithms based on their
robustness: the property that if a testing sample is "similar" to a training
sample, then the testing error is close to the training error. This provides a
novel approach, different from the complexity or stability arguments, to study
generalization of learning algorithms. We further show that a weak notion of
robustness is both sufficient and necessary for generalizability, which implies
that robustness is a fundamental property for learning algorithms to work
Critical behavior of a one-dimensional monomer-dimer reaction model with lateral interactions
A monomer-dimer reaction lattice model with lateral repulsion among the same
species is studied using a mean-field analysis and Monte Carlo simulations. For
weak repulsions, the model exhibits a first-order irreversible phase transition
between two absorbing states saturated by each different species. Increasing
the repulsion, a reactive stationary state appears in addition to the saturated
states. The irreversible phase transitions from the reactive phase to any of
the saturated states are continuous and belong to the directed percolation
universality class. However, a different critical behavior is found at the
point where the directed percolation phase boundaries meet. The values of the
critical exponents calculated at the bicritical point are in good agreement
with the exponents corresponding to the parity-conserving universality class.
Since the adsorption-reaction processes does not lead to a non-trivial local
parity-conserving dynamics, this result confirms that the twofold symmetry
between absorbing states plays a relevant role in determining the universality
class. The value of the exponent , which characterizes the
fluctuations of an interface at the bicritical point, supports the
Bassler-Brown's conjecture which states that this is a new exponent in the
parity-conserving universality class.Comment: 19 pages, 22 figures, to be published in Phys. Rev
Unsupervised fuzzy pattern discovery in gene expression data
2010-2011 > Academic research: refereed > Publication in refereed journalpublished_fina
The non-equilibrium phase transition of the pair-contact process with diffusion
The pair-contact process 2A->3A, 2A->0 with diffusion of individual particles
is a simple branching-annihilation processes which exhibits a phase transition
from an active into an absorbing phase with an unusual type of critical
behaviour which had not been seen before. Although the model has attracted
considerable interest during the past few years it is not yet clear how its
critical behaviour can be characterized and to what extent the diffusive
pair-contact process represents an independent universality class. Recent
research is reviewed and some standing open questions are outlined.Comment: Latexe2e, 53 pp, with IOP macros, some details adde
The Hilbertian Tensor Norm and Entangled Two-Prover Games
We study tensor norms over Banach spaces and their relations to quantum
information theory, in particular their connection with two-prover games. We
consider a version of the Hilbertian tensor norm and its dual
that allow us to consider games with arbitrary output alphabet
sizes. We establish direct-product theorems and prove a generalized
Grothendieck inequality for these tensor norms. Furthermore, we investigate the
connection between the Hilbertian tensor norm and the set of quantum
probability distributions, and show two applications to quantum information
theory: firstly, we give an alternative proof of the perfect parallel
repetition theorem for entangled XOR games; and secondly, we prove a new upper
bound on the ratio between the entangled and the classical value of two-prover
games.Comment: 33 pages, some of the results have been obtained independently in
arXiv:1007.3043v2, v2: an error in Theorem 4 has been corrected; Section 6
rewritten, v3: completely rewritten in order to improve readability; title
changed; references added; published versio
Absorbing-state phase transitions in fixed-energy sandpiles
We study sandpile models as closed systems, with conserved energy density
playing the role of an external parameter. The critical energy density,
, marks a nonequilibrium phase transition between active and absorbing
states. Several fixed-energy sandpiles are studied in extensive simulations of
stationary and transient properties, as well as the dynamics of roughening in
an interface-height representation. Our primary goal is to identify the
universality classes of such models, in hopes of assessing the validity of two
recently proposed approaches to sandpiles: a phenomenological continuum
Langevin description with absorbing states, and a mapping to driven interface
dynamics in random media. Our results strongly suggest that there are at least
three distinct universality classes for sandpiles.Comment: 41 pages, 23 figure
Very Important Pool (VIP) genes – an application for microarray-based molecular signatures
<p>Abstract</p> <p>Background</p> <p>Advances in DNA microarray technology portend that molecular signatures from which microarray will eventually be used in clinical environments and personalized medicine. Derivation of biomarkers is a large step beyond hypothesis generation and imposes considerably more stringency for accuracy in identifying informative gene subsets to differentiate phenotypes. The inherent nature of microarray data, with fewer samples and replicates compared to the large number of genes, requires identifying informative genes prior to classifier construction. However, improving the ability to identify differentiating genes remains a challenge in bioinformatics.</p> <p>Results</p> <p>A new hybrid gene selection approach was investigated and tested with nine publicly available microarray datasets. The new method identifies a Very Important Pool (VIP) of genes from the broad patterns of gene expression data. The method uses a bagging sampling principle, where the re-sampled arrays are used to identify the most informative genes. Frequency of selection is used in a repetitive process to identify the VIP genes. The putative informative genes are selected using two methods, t-statistic and discriminatory analysis. In the t-statistic, the informative genes are identified based on p-values. In the discriminatory analysis, disjoint Principal Component Analyses (PCAs) are conducted for each class of samples, and genes with high discrimination power (DP) are identified. The VIP gene selection approach was compared with the p-value ranking approach. The genes identified by the VIP method but not by the p-value ranking approach are also related to the disease investigated. More importantly, these genes are part of the pathways derived from the common genes shared by both the VIP and p-ranking methods. Moreover, the binary classifiers built from these genes are statistically equivalent to those built from the top 50 p-value ranked genes in distinguishing different types of samples.</p> <p>Conclusion</p> <p>The VIP gene selection approach could identify additional subsets of informative genes that would not always be selected by the p-value ranking method. These genes are likely to be additional true positives since they are a part of pathways identified by the p-value ranking method and expected to be related to the relevant biology. Therefore, these additional genes derived from the VIP method potentially provide valuable biological insights.</p
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