32 research outputs found
Efficiency of the Incomplete Enumeration algorithm for Monte-Carlo simulation of linear and branched polymers
We study the efficiency of the incomplete enumeration algorithm for linear
and branched polymers. There is a qualitative difference in the efficiency in
these two cases. The average time to generate an independent sample of
sites for large varies as for linear polymers, but as for branched (undirected and directed) polymers, where
. On the binary tree, our numerical studies for of order
gives . We argue that exactly in this
case.Comment: replaced with published versio
The exponent of UNil
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/23710/1/0000682.pd
The stable topological-hyperbolic space form problem for complete manifolds of finite volume
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46609/1/222_2005_Article_BF01389189.pd
Population Monte Carlo algorithms
We give a cross-disciplinary survey on ``population'' Monte Carlo algorithms.
In these algorithms, a set of ``walkers'' or ``particles'' is used as a
representation of a high-dimensional vector. The computation is carried out by
a random walk and split/deletion of these objects. The algorithms are developed
in various fields in physics and statistical sciences and called by lots of
different terms -- ``quantum Monte Carlo'', ``transfer-matrix Monte Carlo'',
``Monte Carlo filter (particle filter)'',``sequential Monte Carlo'' and
``PERM'' etc. Here we discuss them in a coherent framework. We also touch on
related algorithms -- genetic algorithms and annealed importance sampling.Comment: Title is changed (Population-based Monte Carlo -> Population Monte
Carlo). A number of small but important corrections and additions. References
are also added. Original Version is read at 2000 Workshop on
Information-Based Induction Sciences (July 17-18, 2000, Syuzenji, Shizuoka,
Japan). No figure
A mathematical model for the onset of avascular tumor growth in response to the loss of p53 function
We present a mathematical model for the formation of an avascular tumor based on the loss by gene mutation of the tumor suppressor function of p53. The wild type p53 protein regulates apoptosis, cell expression of growth factor and matrix metalloproteinase, which are regulatory functions that many mutant p53 proteins do not possess. The focus is on a description of cell movement as the transport of cell population density rather than as the movement of individual cells. In contrast to earlier works on solid tumor growth, a model is proposed for the initiation of tumor growth. The central idea, taken from the mathematical theory of dynamical systems, is to view the loss of p53 function in a few cells as a small instability in a rest state for an appropriate system of differential equations describing cell movement. This instability is shown (numerically) to lead to a second, spatially inhomogeneous, solution that can be thought of as a solid tumor whose growth is nutrient diffusion limited. In this formulation, one is led to a system of nine partial differential equations. We show computationally that there can be tumor states that coexist with benign states and that are highly unstable in the sense that a slight increase in tumor size results in the tumor occupying the sample region while a slight decrease in tumor size results in its ultimate disappearance
Theta-point behavior of diluted polymer solutions: Can one observe the universal logarithmic corrections predicted by field theory?
In recent large scale Monte-Carlo simulations of various models of
Theta-point polymers in three dimensions Grassberger and Hegger found
logarithmic corrections to mean field theory with amplitudes much larger than
the universal amplitudes of the leading logarithmic corrections calculated by
Duplantier in the framework of tricritical O(n) field theory. To resolve this
issue we calculate the universal subleading correction of field theory, which
turns out to be of the same order of magnitude as the leading correction for
all chain lengths available in present days simulations. Borel resummation of
the renormalization group flow equations also shows the presence of such large
corrections. This suggests that the published simulations did not reach the
asymptotic regime. To further support this view, we present results of
Monte-Carlo simulations on a Domb-Joyce like model of weakly interacting random
walks. Again the results cannot be explained by keeping only the leading
corrections, but are in fair accord with our full theoretical result. The
corrections found for the Domb-Joyce model are much smaller than those for
other models, which clearly shows that the effective corrections are not yet in
the asymptotic regime. All together our findings show that the existing
simulations of Theta-polymers are compatible with tricritical field theory
since the crossover to the asymptotic regime is very slow. Similar results were
found earlier for self avoiding walks at their upper critical dimension d=4.Comment: 15 pages,6 figure
A review of Monte Carlo simulations of polymers with PERM
In this review, we describe applications of the pruned-enriched Rosenbluth
method (PERM), a sequential Monte Carlo algorithm with resampling, to various
problems in polymer physics. PERM produces samples according to any given
prescribed weight distribution, by growing configurations step by step with
controlled bias, and correcting "bad" configurations by "population control".
The latter is implemented, in contrast to other population based algorithms
like e.g. genetic algorithms, by depth-first recursion which avoids storing all
members of the population at the same time in computer memory. The problems we
discuss all concern single polymers (with one exception), but under various
conditions: Homopolymers in good solvents and at the point, semi-stiff
polymers, polymers in confining geometries, stretched polymers undergoing a
forced globule-linear transition, star polymers, bottle brushes, lattice
animals as a model for randomly branched polymers, DNA melting, and finally --
as the only system at low temperatures, lattice heteropolymers as simple models
for protein folding. PERM is for some of these problems the method of choice,
but it can also fail. We discuss how to recognize when a result is reliable,
and we discuss also some types of bias that can be crucial in guiding the
growth into the right directions.Comment: 29 pages, 26 figures, to be published in J. Stat. Phys. (2011
History of clinical transplantation
How transplantation came to be a clinical discipline can be pieced together by perusing two volumes of reminiscences collected by Paul I. Terasaki in 1991-1992 from many of the persons who were directly involved. One volume was devoted to the discovery of the major histocompatibility complex (MHC), with particular reference to the human leukocyte antigens (HLAs) that are widely used today for tissue matching.1 The other focused on milestones in the development of clinical transplantation.2 All the contributions described in both volumes can be traced back in one way or other to the demonstration in the mid-1940s by Peter Brian Medawar that the rejection of allografts is an immunological phenomenon.3,4 © 2008 Springer New York
Global data on earthworm abundance, biomass, diversity and corresponding environmental properties
14 p.Earthworms are an important soil taxon as ecosystem engineers, providing a variety of crucial ecosystem functions and services. Little is known about their diversity and distribution at large spatial scales, despite the availability of considerable amounts of local-scale data. Earthworm diversity data, obtained from the primary literature or provided directly by authors, were collated with information on site locations, including coordinates, habitat cover, and soil properties. Datasets were required, at a minimum, to include abundance or biomass of earthworms at a site. Where possible, site-level species lists were included, as well as the abundance and biomass of individual species and ecological groups. This global dataset contains 10,840 sites, with 184 species, from 60 countries and all continents except Antarctica. The data were obtained from 182 published articles, published between 1973 and 2017, and 17 unpublished datasets. Amalgamating data into a single global database will assist researchers in investigating and answering a wide variety of pressing questions, for example, jointly assessing aboveground and belowground biodiversity distributions and drivers of biodiversity change