Time-dependent angularly averaged inverse transport

This paper concerns the reconstruction of the absorption and scattering parameters in a time-dependent linear transport equation from knowledge of angularly averaged measurements performed at the boundary of a domain of interest. We show that the absorption coefficient and the spatial component of the scattering coefficient are uniquely determined by such measurements. We obtain stability results on the reconstruction of the absorption and scattering parameters with respect to the measured albedo operator. The stability results are obtained by a precise decomposition of the measurements into components with different singular behavior in the time domain

Corrector theory for MsFEM and HMM in random media

We analyze the random fluctuations of several multi-scale algorithms such as the multi-scale finite element method (MsFEM) and the finite element heterogeneous multiscale method (HMM), that have been developed to solve partial differential equations with highly heterogeneous coefficients. Such multi-scale algorithms are often shown to correctly capture the homogenization limit when the highly oscillatory random medium is stationary and ergodic. This paper is concerned with the random fluctuations of the solution about the deterministic homogenization limit. We consider the simplified setting of the one dimensional elliptic equation, where the theory of random fluctuations is well understood. We develop a fluctuation theory for the multi-scale algorithms in the presence of random environments with short-range and long-range correlations. What we find is that the computationally more expensive method MsFEM captures the random fluctuations both for short-range and long-range oscillations in the medium. The less expensive method HMM correctly captures the fluctuations for long-range oscillations and strongly amplifies their size in media with short-range oscillations. We present a modified scheme with an intermediate computational cost that captures the random fluctuations in all cases.Comment: 41 page

Interaction between two Fuzzy Spheres

We have calculated interactions between two fuzzy spheres in 3 dimension. It depends on the distance r between the spheres and the radii rho_1, rho_2. There is no force between the spheres when they are far from each other (long distance case). We have also studied the interaction for r=0 case. We find that an attractive force exists between two fuzzy sphere surfaces.Comment: Latex file, 13 page

Insular Carcinoma of Thyroid Presenting as a Giant Skull Lesion: A Dilemma in Treatment.

Thyroid surgeons are becoming increasingly more aware of a histologically distinct subset of thyroid carcinoma whose classification falls between well-differentiated and anaplastic carcinomas with respect to both cell differentiation and clinical behavior. This subtype of tumors has been categorized as poorly differentiated or insular carcinoma, based on its characteristic cell groupings. Although the differentiation of insular carcinoma from other thyroid carcinomas has important prognostic and therapeutic significance, relatively little about insular carcinoma has been published in the otolaryngology literature. In this article, we discuss a case of insular carcinoma of thyroid presenting with concurrent distant metastasis to skull, lung, ribs, and inguinal region with review of the literature. We conclude that insular thyroid carcinoma warrants aggressive management with total thyroidectomy and excision of accessible giant lesion followed by radioactive iodine ablation of any remaining thyroid tissue

Inverse Transport Theory of Photoacoustics

We consider the reconstruction of optical parameters in a domain of interest from photoacoustic data. Photoacoustic tomography (PAT) radiates high frequency electromagnetic waves into the domain and measures acoustic signals emitted by the resulting thermal expansion. Acoustic signals are then used to construct the deposited thermal energy map. The latter depends on the constitutive optical parameters in a nontrivial manner. In this paper, we develop and use an inverse transport theory with internal measurements to extract information on the optical coefficients from knowledge of the deposited thermal energy map. We consider the multi-measurement setting in which many electromagnetic radiation patterns are used to probe the domain of interest. By developing an expansion of the measurement operator into singular components, we show that the spatial variations of the intrinsic attenuation and the scattering coefficients may be reconstructed. We also reconstruct coefficients describing anisotropic scattering of photons, such as the anisotropy coefficient $g(x)$ in a Henyey-Greenstein phase function model. Finally, we derive stability estimates for the reconstructions

Evaluation of Naked Barley Landraces for Agro-morphological Traits

Naked barley (Hordeum vulgare var. nudum L.) is a traditional, culturally important, climate-resilient winter cereal crop of Nepal. Evaluation of the naked barely genotypes for yield and disease is fundamental for their efficient utilization in plant breeding schemes and effective conservation programs. Therefore, to identify high yielding and yellow rust resistant landraces of naked barley for hilly and mountainous agro-ecosystem, twenty naked barley landraces collected from different locations of Nepal, were evaluated in randomized complete block design (RCBD) with three replications during winter season of 2016 and 2017 at Khumaltar, Lalitpur, Nepal. Combined analysis of variances revealed that NGRC04902 (3.46 t/ha), NGRC00886 (3.28 t/ha), NGRC02309 (3.21 t/ha) and NGRC06026 (3.10 t/ha) were the high yielding landraces and statistically at par with the released variety 'Solu Uwa' (3.15 t/ha). The landraces namely NGRC00837 (ACI Value: 1.86) was found resistant to yellow rust diseases. Landraces NGRC06034 (131.7 days) and NGRC02363 (130.8 days) were found early maturing and NGRC02306 (94.36 cm) was found dwarf landraces among tested genotypes. These landraces having higher yield and better resistance to yellow rust need to be deployed to farmers' field to diversify the varietal options and used in resistant breeding program to improve the productivity of naked barley for Nepalese farmers

The Cop Number of the One-Cop-Moves Game on Planar Graphs

Cops and robbers is a vertex-pursuit game played on graphs. In the classical cops-and-robbers game, a set of cops and a robber occupy the vertices of the graph and move alternately along the graph's edges with perfect information about each other's positions. If a cop eventually occupies the same vertex as the robber, then the cops win; the robber wins if she can indefinitely evade capture. Aigner and Frommer established that in every connected planar graph, three cops are sufficient to capture a single robber. In this paper, we consider a recently studied variant of the cops-and-robbers game, alternately called the one-active-cop game, one-cop-moves game or the lazy-cops-and-robbers game, where at most one cop can move during any round. We show that Aigner and Frommer's result does not generalise to this game variant by constructing a connected planar graph on which a robber can indefinitely evade three cops in the one-cop-moves game. This answers a question recently raised by Sullivan, Townsend and Werzanski.Comment: 32 page

Inverse Diffusion Theory of Photoacoustics

This paper analyzes the reconstruction of diffusion and absorption parameters in an elliptic equation from knowledge of internal data. In the application of photo-acoustics, the internal data are the amount of thermal energy deposited by high frequency radiation propagating inside a domain of interest. These data are obtained by solving an inverse wave equation, which is well-studied in the literature. We show that knowledge of two internal data based on well-chosen boundary conditions uniquely determines two constitutive parameters in diffusion and Schroedinger equations. Stability of the reconstruction is guaranteed under additional geometric constraints of strict convexity. No geometric constraints are necessary when $2n$ internal data for well-chosen boundary conditions are available, where $n$ is spatial dimension. The set of well-chosen boundary conditions is characterized in terms of appropriate complex geometrical optics (CGO) solutions.Comment: 24 page