696 research outputs found
Counting Integer flows in Networks
This paper discusses new analytic algorithms and software for the enumeration
of all integer flows inside a network. Concrete applications abound in graph
theory \cite{Jaeger}, representation theory \cite{kirillov}, and statistics
\cite{persi}. Our methods clearly surpass traditional exhaustive enumeration
and other algorithms and can even yield formulas when the input data contains
some parameters. These methods are based on the study of rational functions
with poles on arrangements of hyperplanes
Sharp error terms for return time statistics under mixing conditions
We describe the statistics of repetition times of a string of symbols in a
stochastic process. Denote by T(A) the time elapsed until the process spells
the finite string A and by S(A) the number of consecutive repetitions of A. We
prove that, if the length of the string grows unbondedly, (1) the distribution
of T(A), when the process starts with A, is well aproximated by a certain
mixture of the point measure at the origin and an exponential law, and (2) S(A)
is approximately geometrically distributed. We provide sharp error terms for
each of these approximations. The errors we obtain are point-wise and allow to
get also approximations for all the moments of T(A) and S(A). To obtain (1) we
assume that the process is phi-mixing while to obtain (2) we assume the
convergence of certain contidional probabilities
Joint inversion of teleseismic and GOCE gravity data: application to the Himalayas
Our knowledge and understanding of the 3-D lithospheric structure of the Himalayas and the Tibetan Plateau is still challenging although numerous geophysical studies have been performed in the region. The GOCE satellite mission has the ambitious goal of mapping Earth's gravity field with unprecedented precision (i.e. an accuracy of 1-2 mGal for a spatial resolution of 100 km) to observe the lithosphere and upper-mantle structure. Consequently, it gives new insights in the lithospheric structure beneath the Himalayas and the Tibetan Plateau. Indeed, the GOCE gravity data now allow us to develop a new strategy for joint gravimetry-seismology inversion. Combined with teleseismic data over a large region in a joint inversion scheme, they will lead to lithospheric velocity-density models constrained in two complementary ways. We apply this joint inversion scheme to the Hi-CLIMB (Himalayan-Tibetan Continental Lithosphere during Mountain Building) seismological network which was deployed in South Tibet and the Himalayas for a 3-yr period. The large size of the network, the high quality of the seismological data and the new GOCE gravity data set allow us to image the entire lithosphere of this active area in an innovative way. We image 3-D low velocity and density structures in the middle crust that fit the location of discontinuous low S-velocity zones revealed by receiver functions in previous geophysical studies. In the deeper parts of our velocity model we image a positive anomaly interpreted to be the heterogenous Indian lithosphere vertically descending beneath the centre of the Tibetan Platea
Polarimetry of an Intermediate-age Open Cluster: NGC 5617
We present polarimetric observations in the UBVRI bands of 72 stars located
in the direction of the medium age open cluster NGC 5617. Our intention is to
use polarimetry as a tool membership identification, by building on previous
investigations intended mainly to determine the cluster's general
characteristics rather than provide membership suitable for studies such as
stellar content and metallicity, as well as study the characteristics of the
dust lying between the Sun and the cluster. The obsevations were carried out
using the five-channel photopolarimeter of the Torino Astronomical Observatory
attached to the 2.15m telescope at the Complejo Astron\'omico El Leoncito
(CASLEO; Argentina. We are able to add 32 stars to the list of members of NGC
5617, and review the situation for others listed in the literature. In
particular, we find that five blue straggler stars in the region of the cluster
are located behind the same dust as the member stars are and we confirm the
membership of two red giants. The proposed polarimetric memberships are
compared with those derived by photometric and kinematical methods, with
excellent results. Among the observed stars, we identify 10 with intrinsic
polarization in their light. NGC 5617 can be polarimetrically characterized
with and . The spread in polarization
values for the stars observed in the direction of the cluster seems to be
caused by the uneven distribution of dust in front of the cluster's face.
Finally, we find that in the direction of the cluster, the interstellar medium
is apparently free of dust, from the Sun's position up to the
Carina-Sagittarius arm, where NGC 5617 seems to be located at its farthest
border
Optical polarization observations in the Scorpius region: NGC 6124
We have obtained optical multicolour (UBVRI) linear polarimetric data for 46
of the brightest stars in the area of the open cluster NGC 6124 in order to
investigate the properties of the interstellar medium (ISM) that lies along the
line of sight toward the cluster. Our data yield a mean polarization efficiency
of 0.62, i.e., a value lower than the polarization produced
by the ISM with normal efficiency for an average color excess of
as that found for NGC 6124. Besides, the polarization shows an orientation of
.1 which is not parallel to the Galactic Disk,an effect
that we think may be caused by the Lupus Cloud. Our analysis also indicates
that the observed visual extinction in NGC 6124 is caused by the presence of
three different absorption sheets located between the Sun and NGC 6124. The
values of the internal dispersion of the polarization ()
and of the colour excess ( mag) for the members of NGC
6124 seem to be compatible with the presence of an intra-cluster dust
component. Only six stars exhibit some evidence of intrinsic polarization.Our
work also shows that polarimetry provides an excellent tool to distinguish
between member and non-member stars of a cluster
Invariants of solvable rigid Lie algebras up to dimension 8
The invariants of all complex solvable rigid Lie algebras up to dimension
eight are computed. Moreover we show, for rank one solvable algebras, some
criteria to deduce to non-existence of non-trivial invariants or the existence
of fundamental sets of invariants formed by rational functions of the Casimir
invariants of the associated nilradical.Comment: 16 pages, 7 table
On the athermal character of structural phase transitions
The significance of thermal fluctuations on nucleation in structural
first-order phase transitions has been examined. The prototype case of
martensitic transitions has been experimentally investigated by means of
acoustic emission techniques. We propose a model based on the mean
first-passage time to account for the experimental observations. Our study
provides a unified framework to establish the conditions for isothermal and
athermal transitions to be observed.Comment: 5 pages, 4 figures, accepted in Phys. Rev. Let
Equivariant volumes of non-compact quotients and instanton counting
Motivated by Nekrasov's instanton counting, we discuss a method for
calculating equivariant volumes of non-compact quotients in symplectic and
hyper-K\"ahler geometry by means of the Jeffrey-Kirwan residue-formula of
non-abelian localization. In order to overcome the non-compactness, we use
varying symplectic cuts to reduce the problem to a compact setting, and study
what happens in the limit that recovers the original problem. We implement this
method for the ADHM construction of the moduli spaces of framed Yang-Mills
instantons on and rederive the formulas for the equivariant volumes
obtained earlier by Nekrasov-Shadchin, expressing these volumes as iterated
residues of a single rational function.Comment: 34 pages, 2 figures; minor typos corrected, to appear in Comm. Math.
Phy
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