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 $q_{t}$ and $q_{xxx}$ have the same sign (KdVI) or two boundary conditions if $q_{t}$ and $q_{xxx}$ 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 $\{q(x,0),q(0,t) \}$ and $\{q(x,0),q(0,t),q_{x}(0,t) \}$ are given for the KdVI and KdVII equations, respectively, then one must construct the unknown boundary values $\{q_{x}(0,t),q_{xx}(0,t) \}$ and $\{q_{xx}(0,t) \}$, respectively. We show that this can be achieved without solving for $q(x,t)$ 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 $\Phi^{(t)}(t,k)$, where $\Phi^{(t)}$ satisifies the $t$-part of the associated Lax pair evaluated at $x=0$. Indeed, by employing a Gelfand--Levitan--Marchenko triangular representation for $\Phi^{(t)}$, 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 $\Phi^{(t)}$. 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 $\omega$ is a massive one-particle Hamiltonian acting on $\ch$ and $V$ is a Wick polynomial \Wick(w) for a kernel $w$ satisfying some decay properties at infinity. We describe the essential spectrum of $H$, 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 $H$. As a consequence $H$ 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