963 research outputs found
Comparing Mean Field and Euclidean Matching Problems
Combinatorial optimization is a fertile testing ground for statistical
physics methods developed in the context of disordered systems, allowing one to
confront theoretical mean field predictions with actual properties of finite
dimensional systems. Our focus here is on minimum matching problems, because
they are computationally tractable while both frustrated and disordered. We
first study a mean field model taking the link lengths between points to be
independent random variables. For this model we find perfect agreement with the
results of a replica calculation. Then we study the case where the points to be
matched are placed at random in a d-dimensional Euclidean space. Using the mean
field model as an approximation to the Euclidean case, we show numerically that
the mean field predictions are very accurate even at low dimension, and that
the error due to the approximation is O(1/d^2). Furthermore, it is possible to
improve upon this approximation by including the effects of Euclidean
correlations among k link lengths. Using k=3 (3-link correlations such as the
triangle inequality), the resulting errors in the energy density are already
less than 0.5% at d>=2. However, we argue that the Euclidean model's 1/d series
expansion is beyond all orders in k of the expansion in k-link correlations.Comment: 11 pages, 1 figur
Analysis of Genetic Changes in Single-Variety Ryegrass Swards
Ryegrass varieties are synthetics, with a wide within-variety genetic variance for most traits. Ryegrass swards are likely to experience genetic changes with seasons and years because of plant death, asymmetric vegetative reproduction or plant recruitment through reproduction or seed immigration. These changes may be related to or induce changes in agronomic traits, such as biomass production or dry matter composition. The present research was undertaken to measure genetic changes in swards obtained from sowings of a single variety of ryegrass. These changes were evaluated using both neutral molecular markers and morphological traits. The present paper deals with the molecular markers
The random link approximation for the Euclidean traveling salesman problem
The traveling salesman problem (TSP) consists of finding the length of the
shortest closed tour visiting N ``cities''. We consider the Euclidean TSP where
the cities are distributed randomly and independently in a d-dimensional unit
hypercube. Working with periodic boundary conditions and inspired by a
remarkable universality in the kth nearest neighbor distribution, we find for
the average optimum tour length = beta_E(d) N^{1-1/d} [1+O(1/N)] with
beta_E(2) = 0.7120 +- 0.0002 and beta_E(3) = 0.6979 +- 0.0002. We then derive
analytical predictions for these quantities using the random link
approximation, where the lengths between cities are taken as independent random
variables. From the ``cavity'' equations developed by Krauth, Mezard and
Parisi, we calculate the associated random link values beta_RL(d). For d=1,2,3,
numerical results show that the random link approximation is a good one, with a
discrepancy of less than 2.1% between beta_E(d) and beta_RL(d). For large d, we
argue that the approximation is exact up to O(1/d^2) and give a conjecture for
beta_E(d), in terms of a power series in 1/d, specifying both leading and
subleading coefficients.Comment: 29 pages, 6 figures; formatting and typos correcte
The Generalized Dirichlet to Neumann map for the KdV equation on the half-line
For the two versions of the KdV equation on the positive half-line an
initial-boundary value problem is well posed if one prescribes an initial
condition plus either one boundary condition if and have the
same sign (KdVI) or two boundary conditions if and have
opposite sign (KdVII). Constructing the generalized Dirichlet to Neumann map
for the above problems means characterizing the unknown boundary values in
terms of the given initial and boundary conditions. For example, if
and are given for the KdVI
and KdVII equations, respectively, then one must construct the unknown boundary
values and , respectively. We
show that this can be achieved without solving for by analysing a
certain ``global relation'' which couples the given initial and boundary
conditions with the unknown boundary values, as well as with the function
, where satisifies the -part of the associated
Lax pair evaluated at . Indeed, by employing a Gelfand--Levitan--Marchenko
triangular representation for , the global relation can be solved
\emph{explicitly} for the unknown boundary values in terms of the given initial
and boundary conditions and the function . This yields the unknown
boundary values in terms of a nonlinear Volterra integral equation.Comment: 21 pages, 3 figure
Spectral and scattering theory for some abstract QFT Hamiltonians
We introduce an abstract class of bosonic QFT Hamiltonians and study their
spectral and scattering theories. These Hamiltonians are of the form
H=\d\G(\omega)+ V acting on the bosonic Fock space \G(\ch), where
is a massive one-particle Hamiltonian acting on and is a Wick
polynomial \Wick(w) for a kernel satisfying some decay properties at
infinity. We describe the essential spectrum of , prove a Mourre estimate
outside a set of thresholds and prove the existence of asymptotic fields. Our
main result is the {\em asymptotic completeness} of the scattering theory,
which means that the CCR representations given by the asymptotic fields are of
Fock type, with the asymptotic vacua equal to the bound states of . As a
consequence is unitarily equivalent to a collection of second quantized
Hamiltonians
Szeg\"o kernel asymptotics and Morse inequalities on CR manifolds
We consider an abstract compact orientable Cauchy-Riemann manifold endowed
with a Cauchy-Riemann complex line bundle. We assume that the manifold
satisfies condition Y(q) everywhere. In this paper we obtain a scaling
upper-bound for the Szeg\"o kernel on (0, q)-forms with values in the high
tensor powers of the line bundle. This gives after integration weak Morse
inequalities, analogues of the holomorphic Morse inequalities of Demailly. By a
refined spectral analysis we obtain also strong Morse inequalities which we
apply to the embedding of some convex-concave manifolds.Comment: 40 pages, the constants in Theorems 1.1-1.8 have been modified by a
multiplicative constant 1/2 ; v.2 is a final updat
"Diseño Ambientalmente Consciente (DAC). Hacia una arquitectura sustentable para el hombre y la sociedad": innovación pedagógica implementada en la Cátedra Arquitectura II UPB
Se presenta una experiencia de innovación pedagógica implementada en la cátedra Arquitectura II – UP “B”, referida a la introducción del Diseño Ambientalmente Consciente en la resolución de problemas de diseño en el Taller de Arquitectura. Se analizan los resultados obtenidos y sus implicancias, en diferentes dimensiones de interés en la práctica docente universitaria, contrastadas con encuestas realizadas a los alumnos de la asignatura. La sistematización y valoración de las actividades desarrolladas permite califi car la experiencia como muy satisfactoria, no solo desde el punto de vista disciplinar, sino también por propiciar una actitud crítica y refl exiva frente al desafío de la Arquitectura Sustentable
IL-1 beta and TNF alpha Promote Monocyte Viability through the Induction of GM-CSF Expression by Rheumatoid Arthritis Synovial Fibroblasts
Background. Macrophages and synovial fibroblasts (SF) are two major cells implicated in the pathogenesis of rheumatoid arthritis (RA). SF could be a source of cytokines and growth factors driving macrophages survival and activation. Here, we studied the effect of SF on monocyte viability and phenotype. Methods. SF were isolated from synovial tissue of RA patients and CD14+ cells were isolated from peripheral blood of healthy donors. SF conditioned media were collected after 24 hours of culture with or without stimulation with TNFα or IL-1β. Macrophages polarisation was studied by flow cytometry. Results. Conditioned medium from SF significantly increased monocytes viability by 60% compared to CD14+ cells cultured in medium alone . This effect was enhanced using conditioned media from IL-1β and TNFα stimulated SF. GM-CSF but not M-CSF nor IL34 blocking antibodies was able to significantly decrease monocyte viability by 30% when added to the conditioned media from IL-1β and TNFα stimulated SF . Finally, monocyte cultured in presence of SF conditioned media did not exhibit a specific M1 or M2 phenotype. Conclusion. Overall, rheumatoid arthritis synovial fibroblasts stimulated with proinflammatory cytokines (IL-1β and TNFα) promote monocyte viability via GM-CSF but do not induce a specific macrophage polarization
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