Invariant imbedding and perturbation techniques applied to diffuse reflection from spherical shells

Invariant imbedding and perturbation techniques applied to diffuse reflection from spherical shell

Estimation of internal source distributions using external field measurements in radiative transfer

Intensity of emergent radiation for finite homogeneous slab which absorbs radiation and scatters it isotropicall

Numerical estimation of derivatives with an application to radiative transfer in spherical shells

Numerical estimation of derivatives with application to radiative transfer in spherical shell

The invariant imbedding equation for the dissipation function of a homogeneous finite slab

Differential-integral equation for dissipation function and derivation of conservation relationship connecting reflection, transmission and dissipation functions of finite sla

Computational results for diffuse transmission and reflection for homogenous finite slabs with isotropic scattering

Diffuse reflection and transmission coefficients computed for radiative transfer in homogeneous slabs of finite thickness with isotropic scatterin

Geometric Approach to Pontryagin's Maximum Principle

Since the second half of the 20th century, Pontryagin's Maximum Principle has been widely discussed and used as a method to solve optimal control problems in medicine, robotics, finance, engineering, astronomy. Here, we focus on the proof and on the understanding of this Principle, using as much geometric ideas and geometric tools as possible. This approach provides a better and clearer understanding of the Principle and, in particular, of the role of the abnormal extremals. These extremals are interesting because they do not depend on the cost function, but only on the control system. Moreover, they were discarded as solutions until the nineties, when examples of strict abnormal optimal curves were found. In order to give a detailed exposition of the proof, the paper is mostly self\textendash{}contained, which forces us to consider different areas in mathematics such as algebra, analysis, geometry.Comment: Final version. Minors changes have been made. 56 page

Nonlocal Automated Comparative Static Analysis

This paper reviews work on the development of a program Nasa for the automated comparative static analysis of parameterized nonlinear systems over parameter intervals. Nasa incorporates a fast and efficient algorithm Feed for the automatic evaluation of higher-order partial derivatives, as well as an adaptive homotopy continuation algorithm for obtaining all required initial conditions. Applications are envisioned for fields such as economics where models tend to be complex and closed-form solutions are difficult to obtain

Defending the genome from the enemy within:mechanisms of retrotransposon suppression in the mouse germline

The viability of any species requires that the genome is kept stable as it is transmitted from generation to generation by the germ cells. One of the challenges to transgenerational genome stability is the potential mutagenic activity of transposable genetic elements, particularly retrotransposons. There are many different types of retrotransposon in mammalian genomes, and these target different points in germline development to amplify and integrate into new genomic locations. Germ cells, and their pluripotent developmental precursors, have evolved a variety of genome defence mechanisms that suppress retrotransposon activity and maintain genome stability across the generations. Here, we review recent advances in understanding how retrotransposon activity is suppressed in the mammalian germline, how genes involved in germline genome defence mechanisms are regulated, and the consequences of mutating these genome defence genes for the developing germline

Liquid 4He: contributions to first principles theory of quantized vortices, thermohydrodynamic properties, and the lambda transition

Liquid 4He has been studied extensively for almost a century, but there are still a number of outstanding weak or missing links in our comprehension of it. This paper reviews some of the principal paths taken in previous research and then proceeds to fill gaps and create an integrated picture with more complete understanding through first principles treatment of a realistic model that starts with a microscopic, atomistic description of the liquid. Newly derived results for vortex cores and thermohydrodynamic properties for a two-fluid model are used to show that interacting quantized vortices may produce a lambda anomaly in specific heat near the superfluid transition where flow properties change. The nature of the order in the superfluid state is explained. Experimental support for new calculations is exhibited, and a unique specific heat experiment is proposed to test predictions of the theory. Relevance of the theory to modern research in cosmology, astrophysics, and Bose-Einstein condensates is discussed.Comment: 155 pages, 28 figure

A Drosophila Model of ALS: Human ALS-Associated Mutation in VAP33A Suggests a Dominant Negative Mechanism

ALS8 is caused by a dominant mutation in an evolutionarily conserved protein, VAPB (vesicle-associated membrane protein (VAMP)-associated membrane protein B)/ALS8). We have established a fly model of ALS8 using the corresponding mutation in Drosophila VAPB (dVAP33A) and examined the effects of this mutation on VAP function using genetic and morphological analyses. By simultaneously assessing the effects of VAPwt and VAPP58S on synaptic morphology and structure, we demonstrate that the phenotypes produced by neuronal expression of VAPP58S resemble VAP loss of function mutants and are opposite those of VAP overexpression, suggesting that VAPP58S may function as a dominant negative. This is brought about by aggregation of VAPP58S and recruitment of wild type VAP into these aggregates. Importantly, we also demonstrate that the ALS8 mutation in dVAP33A interferes with BMP signaling pathways at the neuromuscular junction, identifying a new mechanism underlying pathogenesis of ALS8. Furthermore, we show that mutant dVAP33A can serve as a powerful tool to identify genetic modifiers of VAPB. This new fly model of ALS, with its robust pathological phenotypes, should for the first time allow the power of unbiased screens in Drosophila to be applied to study of motor neuron diseases