4,122 research outputs found
Mean-field solution of the parity-conserving kinetic phase transition in one dimension
A two-offspring branching annihilating random walk model, with finite
reaction rates, is studied in one-dimension. The model exhibits a transition
from an active to an absorbing phase, expected to belong to the
universality class embracing systems that possess two symmetric absorbing
states, which in one-dimensional systems, is in many cases equivalent to parity
conservation. The phase transition is studied analytically through a mean-field
like modification of the so-called {\it parity interval method}. The original
method of parity intervals allows for an exact analysis of the
diffusion-controlled limit of infinite reaction rate, where there is no active
phase and hence no phase transition. For finite rates, we obtain a surprisingly
good description of the transition which compares favorably with the outcome of
Monte Carlo simulations. This provides one of the first analytical attempts to
deal with the broadly studied DP2 universality class.Comment: 4 Figures. 9 Pages. revtex4. Some comments have been improve
Seeing the Forest for the Trees: Using the Gene Ontology to Restructure Hierarchical Clustering
Motivation: There is a growing interest in improving the cluster analysis of expression data by incorporating into it prior knowledge, such as the Gene Ontology (GO) annotations of genes, in order to improve the biological relevance of the clusters that are subjected to subsequent scrutiny. The structure of the GO is another source of background knowledge that can be exploited through the use of semantic similarity. Results: We propose here a novel algorithm that integrates semantic similarities (derived from the ontology structure) into the procedure of deriving clusters from the dendrogram constructed during expression-based hierarchical clustering. Our approach can handle the multiple annotations, from different levels of the GO hierarchy, which most genes have. Moreover, it treats annotated and unannotated genes in a uniform manner. Consequently, the clusters obtained by our algorithm are characterized by significantly enriched annotations. In both cross-validation tests and when using an external index such as proteināprotein interactions, our algorithm performs better than previous approaches. When applied to human cancer expression data, our algorithm identifies, among others, clusters of genes related to immune response and glucose metabolism. These clusters are also supported by proteināprotein interaction data. Contact: [email protected] Supplementary information: Supplementary data are available at Bioinformatics online.Lynne and William Frankel Center for Computer Science; Paul Ivanier center for robotics research and production; National Institutes of Health (R01 HG003367-01A1
Quantum phase transitions, frustration, and the Fermi surface in the Kondo lattice model
The quantum phase transition from a spin-Peierls phase with a small Fermi
surface to a paramagnetic Luttinger-liquid phase with a large Fermi surface is
studied in the framework of a one-dimensional Kondo-Heisenberg model that
consists of an electron gas away from half filling, coupled to a spin-1/2 chain
by Kondo interactions. The Kondo spins are further coupled to each other with
isotropic nearest-neighbor and next-nearest-neighbor antiferromagnetic
Heisenberg interactions which are tuned to the Majumdar-Ghosh point. Focusing
on three-eighths filling and using the density-matrix renormalization-group
(DMRG) method, we show that the zero-temperature transition between the phases
with small and large Fermi momenta appears continuous, and involves a new
intermediate phase where the Fermi surface is not well defined. The
intermediate phase is spin gapped and has Kondo-spin correlations that show
incommensurate modulations. Our results appear incompatible with the local
picture for the quantum phase transition in heavy fermion compounds, which
predicts an abrupt change in the size of the Fermi momentum.Comment: 9 pages, 8 figure
Another Proof of the Total Positivity of the Discrete Spline Collocation Matrix
AbstractWe provide a different proof for Morken's result on necessary and sufficient conditions for a minor of the discrete B-spline collocation matrix to be positive and supply intuition for those conditions
Virtual dielectric waveguide mode description of a high-gain free-electron laser I: Theory
A set of mode-coupled excitation equations for the slowly-growing amplitudes
of dielectric waveguide eigenmodes is derived as a description of the
electromagnetic signal field of a high-gain free-electron laser, or FEL,
including the effects of longitudinal space-charge. This approach of describing
the field basis set has notable advantages for FEL analysis in providing an
efficient characterization of eigenmodes, and in allowing a clear connection to
free-space propagation of the input (seeding) and output radiation. The
formulation describes the entire evolution of the radiation wave through the
linear gain regime, prior to the onset of saturation, with arbitrary initial
conditions. By virtue of the flexibility in the expansion basis, this technique
can be used to find the direct coupling and amplification of a particular mode.
A simple transformation converts the derived coupled differential excitation
equations into a set of coupled algebraic equations and yields a matrix
determinant equation for the FEL eigenmodes. A quadratic index medium is used
as a model dielectric waveguide to obtain an expression for the predicted spot
size of the dominant system eigenmode, in the approximation that it is a single
gaussian mode.Comment: 14 page
A Method of Intervals for the Study of Diffusion-Limited Annihilation, A + A --> 0
We introduce a method of intervals for the analysis of diffusion-limited
annihilation, A+A -> 0, on the line. The method leads to manageable diffusion
equations whose interpretation is intuitively clear. As an example, we treat
the following cases: (a) annihilation in the infinite line and in infinite
(discrete) chains; (b) annihilation with input of single particles, adjacent
particle pairs, and particle pairs separated by a given distance; (c)
annihilation, A+A -> 0, along with the birth reaction A -> 3A, on finite rings,
with and without diffusion.Comment: RevTeX, 13 pages, 4 figures, 1 table. References Added, and some
other minor changes, to conform with final for
Preference Reversals and the Analysis of Income Distributions
It is known from the literature on uncertainty that in cases where individuals express a preference for a high win-probability bet over a bet with high winnings they nevertheless will bid more to obtain the bet with high winnings. We investigate whether a similar phenomenon applies in the parallel social-choice situation. Here decisions are to be made between a distribution with a small group of very high-income people. Results from a number of experimental designs are analysed.Preference reversals, social welfare, inequality, risk and experiments.
Cluster approximation solution of a two species annihilation model
A two species reaction-diffusion model, in which particles diffuse on a
one-dimensional lattice and annihilate when meeting each other, has been
investigated. Mean field equations for general choice of reaction rates have
been solved exactly. Cluster mean field approximation of the model is also
studied. It is shown that, the general form of large time behavior of one- and
two-point functions of the number operators, are determined by the diffusion
rates of the two type of species, and is independent of annihilation rates.Comment: 9 pages, 7 figure
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