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

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

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

Dynamics of parametric fluctuations induced by quasiparticle tunneling in superconducting flux qubits

We present experiments on the dynamics of a two-state parametric fluctuator in a superconducting flux qubit. In spectroscopic measurements, the fluctuator manifests itself as a doublet line. When the qubit is excited in resonance with one of the two doublet lines, the correlation of readout results exhibits an exponential time decay which provides a measure of the fluctuator transition rate. The rate increases with temperature in the interval 40 to 158 mK. Based on the magnitude of the transition rate and the doublet line splitting we conclude that the fluctuation is induced by quasiparticle tunneling. These results demonstrate the importance of considering quasiparticles as a source of decoherence in flux qubits.Comment: 12 pages, including supplementary informatio

Radiation- and Phonon-Bottleneck-Induced Tunneling in the Fe8 Single-Molecule Magnet

We measure magnetization changes in a single crystal of the single-molecule magnet Fe8 when exposed to intense, short (<20 $\mu$s) pulses of microwave radiation resonant with the m = 10 to 9 transition. We find that radiation induces a phonon bottleneck in the system with a time scale of ~5 $\mu$s. The phonon bottleneck, in turn, drives the spin dynamics, allowing observation of thermally assisted resonant tunneling between spin states at the 100-ns time scale. Detailed numerical simulations quantitatively reproduce the data and yield a spin-phonon relaxation time of T1 ~ 40 ns.Comment: 6 RevTeX pages, including 4 EPS figures, version accepted for publicatio

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

Inversion formulas for the broken-ray Radon transform

We consider the inverse problem of the broken ray transform (sometimes also referred to as the V-line transform). Explicit image reconstruction formulas are derived and tested numerically. The obtained formulas are generalizations of the filtered backprojection formula of the conventional Radon transform. The advantages of the broken ray transform include the possibility to reconstruct the absorption and the scattering coefficients of the medium simultaneously and the possibility to utilize scattered radiation which, in the case of the conventional X-ray tomography, is typically discarded.Comment: To be submitted to Inverse Problem

Agrobiodiversity and Its Conservation in Nepal

Nepal is a part of the world\u27s biodiversity hotspot and ranks the 49th in the world for biodiversity. Agrobiodiversity and its conservation status were studied through literature review, field survey, key informant survey and focus group discussion. Results of field implementation of some good practices and action research were also documented. Among 24,300 total species in the country, 28% are agricultural genetic resources (AGRs), termed as agrobiodiversity. Agrobiodiversity has six components (crops, forages, livestock, aquatic, insects and microorganisms) and four sub-components (domesticated, semi-domesticated, wild relatives and wild edible) in Nepal. Agrobiodiversity on each component exists at agroecosystem, species, variety/breed/biotype/race/strain, genotype and allele levels, within an altitude range from 60 to 5,000 masl. There are 12 agroecosystems supporting 1026 species under crop component, 510 under forage, 35 under livestock, 250 under the aquatic animal, 17 under aquatic plant, 3,500 under insect and 800 under microorganism. An estimated loss of agrobiodiversity is 40%, however, farmers have reported up to 100% loss of AGRs in some areas for a particular species. Conservation of agrobiodiversity has been initiated since 1986. Four strategies namely ex-situ, on-farm, in-situ and breeding have been adopted for conservation and sustainable utilization of AGRs. Eighty good practices including process, methods and actions for managing agrobiodiversity have been in practice and these practices come under five conservation components (sensitization, method and approach, accelerator, value and enabling environment). Within the country, 18,765 accessions of AGRs have been conserved in different kinds of banks. A total of 24,683 accessions of Nepalese crops, forages and microbes have been conserved in different International and foreign genebanks. Some collections are conserved as safety duplication and safety backup in different CGIARs\u27 banks and World Seed Vault, Korea. Two global databases (GENESYS and EURISCO) have maintained 19,200 Nepalese accessions. Geographical Information System, Climate Analog Tool and biotechnological tools have been applied for better managing AGRs. Many stakeholders need to further concentrate on the conservation and utilization of AGRs. Global marketing of some native AGRs is necessary for sustaining agriculture and attracting young generations as well as conserving them through use