629 research outputs found
A central partition of molecular conformational space. II. Embedding 3D structures
A combinatorial model of molecular conformational space that was previously
developped (J. Gabarro-Arpa, Comp. Biol. and Chem. 27, (2003) 153-159), had the
drawback that structures could not be properly embedded beacause it lacked
explicit rotational symmetry. The problem can be circumvented by sorting the
elementary 3D components of a molecular system into a finite set of classes
that can be separately embedded. This also opens up the possibility of encoding
the dynamical states into a graph structure
A Central Partition of Molecular Conformational Space. IV. Extracting information from the graph of cells
In previous works [physics/0204035, physics/0404052, physics/0509126] a
procedure was described for dividing the -dimensional
conformational space of a molecular system into a number of discrete cells,
this partition allowed the building of a combinatorial structure from data
sampled in molecular dynamics trajectories: the graph of cells, that encodes
the set of cells in conformational space that are visited by the system in its
thermal wandering. Here we outline a set of procedures for extracting useful
information from this structure: 1st) interesting regions in the volume
occupied by the system in conformational space can be bounded by a polyhedral
cone whose faces are determined empirically from a set of relations between the
coordinates of the molecule, 2nd) it is also shown that this cone can be
decomposed into a hierarchical set of smaller cones, 3rd) the set of cells in a
cone can be encoded by a simple combinatorial sequence.Comment: added an intrduction and reference
Analytic urns
This article describes a purely analytic approach to urn models of the
generalized or extended P\'olya-Eggenberger type, in the case of two types of
balls and constant ``balance,'' that is, constant row sum. The treatment starts
from a quasilinear first-order partial differential equation associated with a
combinatorial renormalization of the model and bases itself on elementary
conformal mapping arguments coupled with singularity analysis techniques.
Probabilistic consequences in the case of ``subtractive'' urns are new
representations for the probability distribution of the urn's composition at
any time n, structural information on the shape of moments of all orders,
estimates of the speed of convergence to the Gaussian limit and an explicit
determination of the associated large deviation function. In the general case,
analytic solutions involve Abelian integrals over the Fermat curve x^h+y^h=1.
Several urn models, including a classical one associated with balanced trees
(2-3 trees and fringe-balanced search trees) and related to a previous study of
Panholzer and Prodinger, as well as all urns of balance 1 or 2 and a sporadic
urn of balance 3, are shown to admit of explicit representations in terms of
Weierstra\ss elliptic functions: these elliptic models appear precisely to
correspond to regular tessellations of the Euclidean plane.Comment: Published at http://dx.doi.org/10.1214/009117905000000026 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Stressed web environments as strategic games: risk profiles and Weltanschauung
We consider the behaviour of a set of services in a stressed
web environment where performance patterns may be di cult to pre-
dict. In stressed environments the performances of some providers may
degrade while the performances of others, with elastic resources, may
improve. The allocation of web-based providers to users (brokering) is
modelled by a strategic non-cooperative angel-daemon game with risk
pro les. A risk pro le speci es a bound on the number of unreliable ser-
vice providers within an environment without identifying the names of
these providers. Risk pro les o er a means of analysing the behaviour of
broker agents which allocate service providers to users. A Nash equilib-
rium is a xed point of such a game in which no user can locally improve
their choice of provider { thus, a Nash equilibrium is a viable solution
to the provider/user allocation problem. Angel daemon games provide a
means of reasoning about stressed environments and o er the possibility
of designing brokers using risk pro les and Nash equilibria.Postprint (author’s final draft
- …