Beam combination of a radial laser array: Flat-topped beam

An analytical expression of a radial laser array for flat-topped beam is derived based on the generalized Collins formula. The intensity distribution of the resulting beam focused by a lens at the focus plane, for phase-locked and nonphase-locked cases, is studied numerically. The effect of the Fresnel number and normalized radius on intensity distribution for phase-locked and nonphase-locked cases is also presented. It is found that intensity distribution for nonphase-locked case is much less sensible to the Fresnel number and normalized radius than that of phase-locked case. (C) 2008 Elsevier Ltd. All rights reserved.

Structural Integrity of the Contralesional Hemisphere Predicts Cognitive Impairment in Ischemic Stroke at Three Months

After stroke, white matter integrity can be affected both locally and distally to the primary lesion location. It has been shown that tract disruption in mirror's regions of the contralateral hemisphere is associated with degree of functional impairment. Fourteen patients suffering right hemispheric focal stroke (S) and eighteen healthy controls (HC) underwent Diffusion Weighted Imaging (DWI) and neuropsychological assessment. The stroke patient group was divided into poor (SP; n = 8) and good (SG; n = 6) cognitive recovery groups according to their cognitive improvement from the acute phase (72 hours after stroke) to the subacute phase (3 months post-stroke). Whole-brain DWI data analysis was performed by computing Diffusion Tensor Imaging (DTI) followed by Tract Based Spatial Statistics (TBSS). Assessment of effects was obtained computing the correlation of the projections on TBSS skeleton of Fractional Anisotropy (FA) and Radial Diffusivity (RD) with cognitive test results. Significant decrease of FA was found only in right brain anatomical areas for the S group when compared to the HC group. Analyzed separately, stroke patients with poor cognitive recovery showed additional significant FA decrease in several left hemisphere regions; whereas SG patients showed significant decrease only in the left genu of corpus callosum when compared to the HC. For the SG group, whole brain analysis revealed significant correlation between the performance in the Semantic Fluency test and the FA in the right hemisphere as well as between the performance in the Grooved Pegboard Test (GPT) and theTrail Making Test-part A and the FA in the left hemisphere. For the SP group, correlation analysis revealed significant correlation between the performance in the GPT and the FA in the right hemisphere.

Effect of environmental conditions on the distribution of Pacific mackerel (Scomber japonicus) larvae in the California Current system

We modeled the probability of capturing Pacif ic mackerel (Scomber japonicus) larvae as a function of environmental variables for the Southern California Bight (SCB) most years from 1951 through 2008 and Mexican waters offshore of Baja California from 1951 through 1984. The model exhibited acceptable fit, as indicated by the area under a receiver-operating-characteristic curve of 0.80 but was inconsistent with the zero catches that occurred frequently in the 2000s. Two types of spawners overlapped spatially within the survey area: those that exhibited peak spawning during April in the SCB at about 15.5°C and a smaller group that exhibited peak spawning in August near Punta Eugenia, Mexico, at 20°C or greater. The SCB generally had greater zooplankton than Mexican waters but less appropriate (lower) geostrophic f lows. Mexican waters generally exhibited greater predicted habitat quality than the SCB in cold years. Predicted quality of the habitat in the SCB was greater from the 1980s to 2008 than in the earlier years of the survey primarily because temperatures and geostrophic flows were more appropriate for larvae. However, stock size the previous year had a larger effect on predictions than any environmental variable, indicating that larval Pacific mackerel did not fully occupy the suitable habitat during most years.

Temporal and spatial distribution and abundance of flathead sole (Hippoglossoides elassodon) eggs and larvae in the western Gulf of Alaska

Data from ichthyoplankton surveys conducted in 1972 and from 1977 to 1999 (no data were collected in 1980) by the Alaska Fisheries Science Center (NOAA, NMFS) in the western Gulf of Alaska were used to examine the timing of spawning, geographic distribution and abundance, and the vertical distribution of eggs and larvae of flathead sole (Hippoglossoides elassodon). In the western Gulf of Alaska, flathead sole spawning began in early April and peaked from early to mid-May on the continental shelf. It progressed in a southwesterly direction along the Alaska Peninsula where three main areas of flathead sole spawning were indentified: near the Kenai Peninsula, in Shelikof Strait, and between the Shumagin Islands and Unimak Island. Flathead sole eggs are pelagic, and their depth distribution may be a function of their developmental stage. Data from MOCNESS tows indicated that eggs sink near time of hatching and the larvae rise to the surface to feed. The geographic distribution of larvae followed a pattern similar to the distribution of eggs, only it shifted about one month later. Larval abundance peaked from early to mid-June in the southern portion of Shelikof Strait. Biological and environmental factors may help to retain flathead sole larvae on the continental shelf near their juvenile nursery areas.

Distribution theory and fundamental solutions of differential operators

The objective of this dissertation is to study the theory of distributions and some of its applications. Certain concepts which we would include in the theory of distributions nowadays have been widely used in several fields of mathematics and physics. It was Dirac who first introduced the delta function as we know it, in an attempt to keep a convenient notation in his works in quantum mechanics. Their work contributed to open a new path in mathematics, as new objects, similar to functions but not of their same nature, were being used systematically. Distributions are believed to have been first formally introduced by the Soviet mathematician Sergei Sobolev and by Laurent Schwartz. The aim of this project is to show how distribution theory can be used to obtain what we call fundamental solutions of partial differential equations.

Structure-function analysis of USP1: insights into the role of Ser313 phosphorylation site and the effect of cancer-associated mutations on autocleavage

Background: In complex with its cofactor UAF1, the USP1 deubiquitinase plays an important role in cellular processes related to cancer, including the response to DNA damage. The USP1/UAF1 complex is emerging as a novel target in cancer therapy, but several aspects of its function and regulation remain to be further clarified. These include the role of the serine 313 phosphorylation site, the relative contribution of different USP1 sequence motifs to UAF1 binding, and the potential effect of cancer-associated mutations on USP1 regulation by autocleavage. Methods: We have generated a large set of USP1 structural variants, including a catalytically inactive form (C90S), non-phosphorylatable (S313A) and phosphomimetic (S313D) mutants, deletion mutants lacking potential UAF1 binding sites, a mutant (GG/AA) unable to undergo autocleavage at the well-characterized G670/G671 diglycine motif, and four USP1 mutants identified in tumor samples that cluster around this cleavage site (G667A, L669P, K673T and A676T). Using cell-based assays, we have determined the ability of these mutants to bind UAF1, to reverse DNA damage-induced monoubiquitination of PCNA, and to undergo autocleavage. Results: A non-phosphorylatable S313A mutant of USP1 retained the ability to bind UAF1 and to reverse PCNA ubiquitination in cell-based assays. Regardless of the presence of a phosphomimetic S313D mutation, deletion of USP1 fragment 420-520 disrupted UAF1 binding, as determined using a nuclear relocation assay. The UAF1 binding site in a second UAF1-interacting DUB, USP46, was mapped to a region homologous to USP1(420-520). Regarding USP1 autocleavage, co-expression of the C90S and GG/AA mutants did not result in cleavage, while the cancer-associated mutation L669P was found to reduce cleavage efficiency. Conclusions: USP1 phosphorylation at S313 is not critical for PCNA deubiquitination, neither for binding to UAF1 in a cellular environment. In this context, USP1 amino acid motif 420-520 is necessary and sufficient for UAF1 binding. This motif, and a homologous amino acid segment that mediates USP46 binding to UAF1, map to the Fingers sub-domain of these DUBs. On the other hand, our results support the view that USP1 autocleavage may occur in cis, and can be altered by a cancer-associated mutation.

Response probability distribution of built-up vibro-acoustic systems

The vibro-acoustic response of built-up structures, consisting of stiff components with low modal density and flexible components with high modal density, is sensitive to small imperfections in the flexible components. In this paper, the uncertainty of the response is considered by modeling the low modal density master system as deterministic and the high modal density subsystems in a nonparametric stochastic way, i.e., carrying a diffuse wave field, and by subsequently computing the response probability density function. The master system's mean squared response amplitude follows a singular noncentral complex Wishart distribution conditional on the subsystem energies. For a single degree of freedom, this is equivalent to a chi-square or an exponential distribution, depending on the loading conditions. The subsystem energies follow approximately a chi-square distribution when their relative variance is smaller than unity. The results are validated by application to plate structures, and good agreement with Monte Carlo simulations is found. © 2012 Acoustical Society of America.

Long range exhaustion-a mathematical model for the axisymmetric air flow of a local exhaust ventilation hood assisted by a turbulent radial jet

Abstract-Mathematical modelling techniques are used to predict the axisymmetric air flow pattern developed by a state-of-the-art Banged exhaust hood which is reinforced by a turbulent radial jet flow. The high Reynolds number modelling techniques adopted allow the complexity of determining the hood's air Bow to be reduced and provide a means of identifying and assessing the various parameters that control the air Bow. The mathematical model is formulated in terms of the Stokes steam function, ψ, and the governing equations of fluid motion are solved using finite-difference techniques. The injection flow of the exhaust hood is modelled as a turbulent radial jet and the entrained Bow is assumed to be an inviscid potential flow. Comparisons made between contours of constant air speed and centre-line air speeds deduced from the model and all the available experimental data show good agreement over a wide range of typical operating conditions. | Mathematical modelling techniques are used to predict the axisymmetric air flow pattern developed by a state-of-the-art flanged exhaust hood which is reinforced by a turbulent radial jet flow. The high Reynolds number modelling techniques adopted allow the complexity of determining the hood's air flow to be reduced and provide a means of identifying and assessing the various parameters that control the air flow. The mathematical model is formulated in terms of the Stokes steam function, Ψ, and the governing equations of fluid motion are solved using finite-difference techniques. The injection flow of the exhaust hood is modelled as a turbulent radial jet and the entrained flow is assumed to be an inviscid potential flow. Comparisons made between contours of constant air speed and centre-line air speeds deduced from the model and all the available experimental data show good agreement over a wide range of typical operating conditions.

On the applicability of the lognormal distribution in random dynamical systems

This paper is concerned with the probability density function of the energy of a random dynamical system subjected to harmonic excitation. It is shown that if the natural frequencies and mode shapes of the system conform to the Gaussian Orthogonal Ensemble, then under common types of loading the distribution of the energy of the response is approximately lognormal, providing the modal overlap factor is high (typically greater than two). In contrast, it is shown that the response of a system with Poisson natural frequencies is not approximately lognormal. Numerical simulations are conducted on a plate system to validate the theoretical findings and good agreement is obtained. Simulations are also conducted on a system made from two plates connected with rotational springs to demonstrate that the theoretical findings can be extended to a built-up system. The work provides a theoretical justification of the commonly used empirical practice of assuming that the energy response of a random system is lognormal.