1,062 research outputs found
Meander, Folding and Arch Statistics
The statistics of meander and related problems are studied as particular
realizations of compact polymer chain foldings. This paper presents a general
discussion of these topics, with a particular emphasis on three points: (i) the
use of a direct recursive relation for building (semi) meanders (ii) the
equivalence with a random matrix model (iii) the exact solution of simpler
related problems, such as arch configurations or irreducible meanders.Comment: 82 pages, uuencoded, uses harvmac (l mode) and epsf, 26+7 figures
include
Meanders: A Direct Enumeration Approach
We study the statistics of semi-meanders, i.e. configurations of a set of
roads crossing a river through n bridges, and possibly winding around its
source, as a toy model for compact folding of polymers. By analyzing the
results of a direct enumeration up to n=29, we perform on the one hand a large
n extrapolation and on the other hand we reformulate the available data into a
large q expansion, where q is a weight attached to each road. We predict a
transition at q=2 between a low-q regime with irrelevant winding, and a large-q
regime with relevant winding.Comment: uses harvmac (l), epsf, 16 figs included, uuencoded, tar compresse
Monotone Hurwitz numbers in genus zero
Hurwitz numbers count branched covers of the Riemann sphere with specified
ramification data, or equivalently, transitive permutation factorizations in
the symmetric group with specified cycle types. Monotone Hurwitz numbers count
a restricted subset of the branched covers counted by the Hurwitz numbers, and
have arisen in recent work on the the asymptotic expansion of the
Harish-Chandra-Itzykson-Zuber integral. In this paper we begin a detailed study
of monotone Hurwitz numbers. We prove two results that are reminiscent of those
for classical Hurwitz numbers. The first is the monotone join-cut equation, a
partial differential equation with initial conditions that characterizes the
generating function for monotone Hurwitz numbers in arbitrary genus. The second
is our main result, in which we give an explicit formula for monotone Hurwitz
numbers in genus zero.Comment: 22 pages, submitted to the Canadian Journal of Mathematic
Flight control system rapid prototyping for the remotely-controlled elettra-twin-flyer airship
Nautilus S.p. A. is a small company investing in the design and development of a low-cost multipurpose multi-mission platform, known as Elettra-Twin-Flyer, which is a very innovative radio-controled airship, equipped with high precision sensors and telecommunication devices. In the prototype phase, Nautilus policy is oriented towards a massive employment of external collaborators to reduce the development costs. The crucial problem of this kind of management is the harmonious integration of all the teams involved on the project. This paper describes the integration process of the PC-104 on-board computer with the avionic devices, which are electronic systems characterized by complex communication protocols. Attention is focused on the testing, verification, validation and final translation of the embedded control software into the on-board computer, through techniques derived from the automatic code generation, such as Rapid Prototyping and Hardware-In-the-Loop. Copyright © 2006 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved
Random Time Forward Starting Options
We introduce a natural generalization of the forward-starting options, first
discussed by M. Rubinstein. The main feature of the contract presented here is
that the strike-determination time is not fixed ex-ante, but allowed to be
random, usually related to the occurrence of some event, either of financial
nature or not. We will call these options {\bf Random Time Forward Starting
(RTFS)}. We show that, under an appropriate "martingale preserving" hypothesis,
we can exhibit arbitrage free prices, which can be explicitly computed in many
classical market models, at least under independence between the random time
and the assets' prices. Practical implementations of the pricing methodologies
are also provided. Finally a credit value adjustment formula for these OTC
options is computed for the unilateral counterparty credit risk.Comment: 19 pages, 1 figur
Meanders: Exact Asymptotics
We conjecture that meanders are governed by the gravitational version of a
c=-4 two-dimensional conformal field theory, allowing for exact predictions for
the meander configuration exponent \alpha=\sqrt{29}(\sqrt{29}+\sqrt{5})/12, and
the semi-meander exponent {\bar\alpha}=1+\sqrt{11}(\sqrt{29}+\sqrt{5})/24. This
result follows from an interpretation of meanders as pairs of fully packed
loops on a random surface, described by two c=-2 free fields. The above values
agree with recent numerical estimates. We generalize these results to a score
of meandric numbers with various geometries and arbitrary loop fugacities.Comment: new version with note added in proo
Meanders and the Temperley-Lieb algebra
The statistics of meanders is studied in connection with the Temperley-Lieb
algebra. Each (multi-component) meander corresponds to a pair of reduced
elements of the algebra. The assignment of a weight per connected component
of meander translates into a bilinear form on the algebra, with a Gram matrix
encoding the fine structure of meander numbers. Here, we calculate the
associated Gram determinant as a function of , and make use of the
orthogonalization process to derive alternative expressions for meander numbers
as sums over correlated random walks.Comment: 85p, uuencoded, uses harvmac (l mode) and epsf, 88 figure
Permutation combinatorics of worldsheet moduli space
52 pages, 21 figures52 pages, 21 figures; minor corrections, "On the" dropped from title, matches published version52 pages, 21 figures; minor corrections, "On the" dropped from title, matches published versio
- …