Critical sets of nonlinear Sturm-Liouville operators of Ambrosetti-Prodi type

The critical set C of the operator F:H^2_D([0,pi]) -> L^2([0,pi]) defined by F(u)=-u''+f(u) is studied. Here X:=H^2_D([0,pi]) stands for the set of functions that satisfy the Dirichlet boundary conditions and whose derivatives are in L^2([0,pi]). For generic nonlinearities f, C=\cup C_k decomposes into manifolds of codimension 1 in X. If f''0, the set C_j is shown to be non-empty if, and only if, -j^2 (the j-th eigenvalue of u -> u'') is in the range of f'. The critical components C_k are (topological) hyperplanes.Comment: 6 pages, no figure

The fast sampling algorithm for Lie-Trotter products

A fast algorithm for path sampling in path integral Monte Carlo simulations is proposed. The algorithm utilizes the Levy-Ciesielski implementation of Lie-Trotter products to achieve a mathematically proven computational cost of n*log_2(n) with the number of time slices n, despite the fact that each path variable is updated separately, for reasons of optimality. In this respect, we demonstrate that updating a group of random variables simultaneously results in loss of efficiency.Comment: 4 pages, 1 figure; fast rejection from Phys. Rev. Letts; transfered to PRE as a Rapid Communication. Eq. 6 to 10 contained some inconsistencies that have been repaired in the present version; A sample code implementing the algorithm for LJ clusters is available from the author upon reques

A flux-ratio anomaly in the CO spectral line emission from gravitationally-lensed quasar MG J0414+0534

We present an analysis of archival observations with the Atacama Large (sub-)Millimetre Array (ALMA) of the gravitationally lensed quasar MG J0414+0534, which show four compact images of the quasar and an Einstein ring from the dust associated with the quasar host galaxy. We confirm that the flux-ratio anomalies observed in the mid-infrared and radio persists into the sub-mm for the continuum images of the quasar. We report the detection of CO (11-10) spectral line emission, which traces a region of compact gas around the quasar nucleus. This line emission also shows evidence of a flux-ratio anomaly between the merging lensed images that is consistent with those observed at other wavelengths, suggesting high-excitation CO can also provide a useful probe of substructures that is unaffected by microlensing or dust extinction. However, we do not detect the candidate dusty dwarf galaxy that was previously reported with this dataset, which we conclude is due to a noise artefact. Thus, the cause of the flux-ratio anomaly between the merging lensed images is still unknown. The composite compact and diffuse emission in this system suggest lensed quasar-starbursts will make excellent targets for detecting dark sub-haloes and testing models for dark matter.Comment: Accepted as MNRAS Lette

Volatility and dividend risk in perpetual American options

American options are financial instruments that can be exercised at any time before expiration. In this paper we study the problem of pricing this kind of derivatives within a framework in which some of the properties --volatility and dividend policy-- of the underlaying stock can change at a random instant of time, but in such a way that we can forecast their final values. Under this assumption we can model actual market conditions because some of the most relevant facts that may potentially affect a firm will entail sharp predictable effects. We will analyse the consequences of this potential risk on perpetual American derivatives, a topic connected with a wide class of recurrent problems in physics: holders of American options must look for the fair price and the optimal exercise strategy at once, a typical question of free absorbing boundaries. We present explicit solutions to the most common contract specifications and derive analytical expressions concerning the mean and higher moments of the exercise time.Comment: 21 pages, 5 figures, iopart, submitted for publication; deep revision, two new appendice

Persistence of Randomly Coupled Fluctuating Interfaces

We study the persistence properties in a simple model of two coupled interfaces characterized by heights h_1 and h_2 respectively, each growing over a d-dimensional substrate. The first interface evolves independently of the second and can correspond to any generic growing interface, e.g., of the Edwards-Wilkinson or of the Kardar-Parisi-Zhang variety. The evolution of h_2, however, is coupled to h_1 via a quenched random velocity field. In the limit d\to 0, our model reduces to the Matheron-de Marsily model in two dimensions. For d=1, our model describes a Rouse polymer chain in two dimensions advected by a transverse velocity field. We show analytically that after a long waiting time t_0\to \infty, the stochastic process h_2, at a fixed point in space but as a function of time, becomes a fractional Brownian motion with a Hurst exponent, H_2=1-\beta_1/2, where \beta_1 is the growth exponent characterizing the first interface. The associated persistence exponent is shown to be \theta_s^2=1-H_2=\beta_1/2. These analytical results are verified by numerical simulations.Comment: 15 pages, 3 .eps figures include

Resting on transport trailer reduces Salmonella at harvest

A potential intervention strategy to reduce the prevalence of Salmonella enterica at harvest was evaluated, which consisted of resting pigs prior to harvest on their transport vehicle, instead of in the abattoir holding pen. Individual fecal samples were collected at the farm and at the abattoir (n= 120 pigs), where half of the pigs were unloaded, and moved to a holding pen, whereas the other half stayed in the transport trailer

Salmonella enterica prevalence and serotype distribution in swine at slaughter

The objective of this cross-sectional study was to analyze data available from multiple studies conducted by our research team estimating the prevalence of S. enterica, and the serotype d1stribution in swine at slaughter, based on different sample types A total of 1,110 pigs from three large capacity abattoirs located in the Midwestern U S. were individually sampled at slaughter. Individually paired samples collected mcluded. cecal contents and ileocecal lymph nodes. Samples were collected on multiple occasions in all three abattoirs, transported to the laboratory, and processed for the isolation and identification of S. enterica. The overall prevalence of S. enterica, based on cecal contents, mesentenc lymph nodes, and any of the samples (i.e., cecal contents and/or mesenteric lymph nodes) was 54.7%, 27.9%, and 62.6%, respectively. There was a Significant difference (P\u3c0.05) between prevalence estimates based on cecal contents and mesenteric lymph node samples in all three abattoirs, and overall. A variety of S. enterica serotypes was isolated m all abattoirs The average number of serotypes isolated per group was 3.48. This study confirms that the S. entenca prevalence at slaughter in swine is high, requiring attention due to the associated risk of contamination of the abattoir environment. Moreover, our results demonstrate the common occurrence of a high diversity of serotypes in swine at slaughter. This study also shows that both cecal contents and mesenteric lymph nodes should be considered for a better estimate of S. enterica prevalence at slaughter

Salmonella prevalence in first pull versus close out market pigs

Identifying potential risk factors to direct intervention strategies is fundamental to reduce the risk of pork contamination with Salmonella. This study was designed to compare the Salmonella prevalence in the first group of pigs selected for slaughter (uFirst pull ) versus the last group of pigs selected for slaughter ( Close out ) from typical commercial finishing barns containing 800 - 1,000 animals. Nine finishing barns from two production sites were included in the study {4 paired samplings from site A, and 5 paired samplings from site B). Each paired sampling consisted in matched groups of pigs from the same barn as the first pair and the close out with a 4-week interval between groups. From each group, individual fecal samples (n = 45) and meat samples (n = 50) were collected, on-farm and at slaughter, respectively. In the laboratory, fecal samples were selectively enriched, and analyzed for the presence of Salmonella by a commercially available antigen-capture ELISA. Meat samples were kept frozen, and thawed for processing. The resulting liquid ( meat juice ) was collected and analyzed for the presence of antibodies against Salmonella by a commercially available ELISA. All lots of pigs housed in the finishing barns studied were Salmonella-positive, based on sampling from first pull and close out . In 7/9 (77.8%) of the studied barns, an increase in Salmonella prevalence was observed, based on both bacteriologic and serologic analysis. Overall, there was an increase of 9.3% (P\u3c0.05) in bacteriologic prevalence, and 25.1% (P\u3c0.05) in serologic prevalence from first pull to close out groups. This study demonstrates that a significant increase of Salmonella prevalence occurs between the first and the last group of pigs from a finishing barn shipped to slaughter. In conclusion, close out groups of finishing pigs constitute a higher risk for Salmonella contamination of pork products

2-D constrained Navier-Stokes equation and intermediate asymptotics

We introduce a modified version of the two-dimensional Navier-Stokes equation, preserving energy and momentum of inertia, which is motivated by the occurrence of different dissipation time scales and related to the gradient flow structure of the 2-D Navier-Stokes equation. The hope is to understand intermediate asymptotics. The analysis we present here is purely formal. A rigorous study of this equation will be done in a forthcoming paper

The Casimir Effect for Parallel Plates Revisited

The Casimir effect for a massless scalar field with Dirichlet and periodic boundary conditions (b.c.) on infinite parallel plates is revisited in the local quantum field theory (lqft) framework introduced by B.Kay. The model displays a number of more realistic features than the ones he treated. In addition to local observables, as the energy density, we propose to consider intensive variables, such as the energy per unit area $\epsilon$, as fundamental observables. Adopting this view, lqft rejects Dirichlet (the same result may be proved for Neumann or mixed) b.c., and accepts periodic b.c.: in the former case $\epsilon$ diverges, in the latter it is finite, as is shown by an expression for the local energy density obtained from lqft through the use of the Poisson summation formula. Another way to see this uses methods from the Euler summation formula: in the proof of regularization independence of the energy per unit area, a regularization-dependent surface term arises upon use of Dirichlet b.c. but not periodic b.c.. For the conformally invariant scalar quantum field, this surface term is absent, due to the condition of zero trace of the energy momentum tensor, as remarked by B.De Witt. The latter property does not hold in tha application to the dark energy problem in Cosmology, in which we argue that periodic b.c. might play a distinguished role.Comment: 25 pages, no figures, late