32 research outputs found
Sorting signed circular permutations by super short reversals
We consider the problem of sorting a circular permutation by reversals of length at most 2, a problem that finds application in comparative genomics. Polynomial-time solutions for the unsigned version of this problem are known, but the signed version remained open. In this paper, we present the first polynomial-time solution for the signed version of this problem. Moreover, we perform an experiment for inferring distances and phylogenies for published Yersinia genomes and compare the results with the phylogenies presented in previous works.We consider the problem of sorting a circular permutation by reversals of length at most 2, a problem that finds application in comparative genomics. Polynomial-time solutions for the unsigned version of this problem are known, but the signed version rema9096272283FAPESP - FUNDAĂĂO DE AMPARO Ă PESQUISA DO ESTADO DE SĂO PAULOCAPES - COORDENAĂĂO DE APERFEIĂOAMENTO DE PESSOAL DE NĂVEL SUPERIORCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTĂFICO E TECNOLĂGICO2013/08293-72014/04718-6306730/2012-0; 477692/2012-5; 483370/2013-411th International Symposium on Bioinformatics Research and Application
Sorting Signed Circular Permutations by Super Short Reversals
International audienceWe consider the problem of sorting a circular permutation by reversals of length at most 2, a problem that finds application in comparative genomics. Polynomial-time solutions for the unsigned version of this problem are known, but the signed version remained open. In this paper, we present the first polynomial-time solution for the signed version of this problem. Moreover, we perform an experiment for inferring distances and phylogenies for published Yersinia genomes and compare the results with the phylogenies presented in previous works
Exponential Time Complexity of Weighted Counting of Independent Sets
We consider weighted counting of independent sets using a rational weight x:
Given a graph with n vertices, count its independent sets such that each set of
size k contributes x^k. This is equivalent to computation of the partition
function of the lattice gas with hard-core self-repulsion and hard-core pair
interaction. We show the following conditional lower bounds: If counting the
satisfying assignments of a 3-CNF formula in n variables (#3SAT) needs time
2^{\Omega(n)} (i.e. there is a c>0 such that no algorithm can solve #3SAT in
time 2^{cn}), counting the independent sets of size n/3 of an n-vertex graph
needs time 2^{\Omega(n)} and weighted counting of independent sets needs time
2^{\Omega(n/log^3 n)} for all rational weights x\neq 0.
We have two technical ingredients: The first is a reduction from 3SAT to
independent sets that preserves the number of solutions and increases the
instance size only by a constant factor. Second, we devise a combination of
vertex cloning and path addition. This graph transformation allows us to adapt
a recent technique by Dell, Husfeldt, and Wahlen which enables interpolation by
a family of reductions, each of which increases the instance size only
polylogarithmically.Comment: Introduction revised, differences between versions of counting
independent sets stated more precisely, minor improvements. 14 page
Approximating Fixation Probabilities in the Generalized Moran Process
We consider the Moran process, as generalized by Lieberman, Hauert and Nowak
(Nature, 433:312--316, 2005). A population resides on the vertices of a finite,
connected, undirected graph and, at each time step, an individual is chosen at
random with probability proportional to its assigned 'fitness' value. It
reproduces, placing a copy of itself on a neighbouring vertex chosen uniformly
at random, replacing the individual that was there. The initial population
consists of a single mutant of fitness placed uniformly at random, with
every other vertex occupied by an individual of fitness 1. The main quantities
of interest are the probabilities that the descendants of the initial mutant
come to occupy the whole graph (fixation) and that they die out (extinction);
almost surely, these are the only possibilities. In general, exact computation
of these quantities by standard Markov chain techniques requires solving a
system of linear equations of size exponential in the order of the graph so is
not feasible. We show that, with high probability, the number of steps needed
to reach fixation or extinction is bounded by a polynomial in the number of
vertices in the graph. This bound allows us to construct fully polynomial
randomized approximation schemes (FPRAS) for the probability of fixation (when
) and of extinction (for all ).Comment: updated to the final version, which appeared in Algorithmic
Critical cluster size and droplet nucleation rate from growth and decay simulations of Lennard-Jones clusters
We study a single cluster of Lennard-Jones atoms using a novel and physically transparent Monte Carlo simulation technique. We compute the canonical ensemble averages of the grand canonical growth and decay probabilities of the cluster, and identify the critical cluster, the size for which the growth and decay probabilities are equal. The size and internal energy of the critical cluster, for different values of the temperature and chemical potential, are used together with the nucleation theorems to predict the behavior of the nucleation rate as a function of these parameters. Our results agree with those found in the literature, and roughly correspond to the predictions of classical theory. In contrast to most other simulation studies, we are able to concentrate on the properties of the clusters which are most important to the process of nucleation, namely those around the critical size. This makes our simulations computationally more efficient. (C) 2000 American Institute of Physics. [S0021- 9606(00)50209-8]