Inverse problem by Cauchy data on arbitrary subboundary for system of elliptic equations

We consider an inverse problem of determining coefficient matrices in an $N$-system of second-order elliptic equations in a bounded two dimensional domain by a set of Cauchy data on arbitrary subboundary. The main result of the article is as follows: If two systems of elliptic operators generate the same set of partial Cauchy data on an arbitrary subboundary, then the coefficient matrices of the first-order and zero-order terms satisfy the prescribed system of first-order partial differential equations. The main result implies the uniqueness of any two coefficient matrices provided that the one remaining matrix among the three coefficient matrices is known

Local Analysis of Inverse Problems: H\"{o}lder Stability and Iterative Reconstruction

We consider a class of inverse problems defined by a nonlinear map from parameter or model functions to the data. We assume that solutions exist. The space of model functions is a Banach space which is smooth and uniformly convex; however, the data space can be an arbitrary Banach space. We study sequences of parameter functions generated by a nonlinear Landweber iteration and conditions under which these strongly converge, locally, to the solutions within an appropriate distance. We express the conditions for convergence in terms of H\"{o}lder stability of the inverse maps, which ties naturally to the analysis of inverse problems

Effect of the photoperiod on the glutamate level in the suprachiasmatic nucleus of pregnant and non-pregnant rabbits

[EN] Microdialysis sampling was used to measure the glutamate level (GLU) contained in the suprachiasmatic nucleus (SCN) in 10 pregnant and 10 non-pregnant, subjected to either a 16:8 h light-dark cycle or a 12 h advanced photoperiod. Results revealed that GLU levels were significantly greater in samples taken for 2 h (15 min intervals), ¿60, ¿45 and ¿30 min before parturition (P<0.009, P<0.04, P<0.02), and +45 and +60 min after birth (P<0.009, P<0.05) respectively, in pregnant rabbits subjects to a 16:8 LD photoperiod (with light from 6:00-22:00 h). Parturition in these animals occurred at day 31 of gestation. Pregnant rabbits exposed to 12 h advanced photoperiod showed lower GLU levels in the SCN, and a longer gestation period and parturition process. In non-pregnant rabbits the GLU levels in the SCN were also significantly higher (P<0.009, in all samples) in comparison with rabbits subjected to the 12 h shifted photoperiod. It is possible that the photoperiod may have influenced GLU levels, and consequently, the length of gestation, the number of young and the time of birth. However, further studies involving new biotechnologies and a greater number of animals are needed to confirm these results.Reyes-Guerrero, G.; Vázquez-García, M.; Calderón-Guzmán, D.; Donatti-Albarrán, O.; Guevara-Guzmán, R. (2008). Effect of the photoperiod on the glutamate level in the suprachiasmatic nucleus of pregnant and non-pregnant rabbits. World Rabbit Science. 16(3). doi:10.4995/wrs.2008.62316

Stride: a flexible software platform for high-performance ultrasound computed tomography

BACKGROUND AND OBJECTIVE: Advanced ultrasound computed tomography techniques like full-waveform inversion are mathematically complex and orders of magnitude more computationally expensive than conventional ultrasound imaging methods. This computational and algorithmic complexity, and a lack of open-source libraries in this field, represent a barrier preventing the generalised adoption of these techniques, slowing the pace of research, and hindering reproducibility. Consequently, we have developed Stride, an open-source Python library for the solution of large-scale ultrasound tomography problems. METHODS: On one hand, Stride provides high-level interfaces and tools for expressing the types of optimisation problems encountered in medical ultrasound tomography. On the other, these high-level abstractions seamlessly integrate with high-performance wave-equation solvers and with scalable parallelisation routines. The wave-equation solvers are generated automatically using Devito, a domain-specific language, and the parallelisation routines are provided through the custom actor-based library Mosaic. RESULTS: We demonstrate the modelling accuracy achieved by our wave-equation solvers through a comparison (1) with analytical solutions for a homogeneous medium, and (2) with state-of-the-art modelling software applied to a high-contrast, complex skull section. Additionally, we show through a series of examples how Stride can handle realistic numerical and experimental tomographic problems, in 2D and 3D, and how it can scale robustly from a local multi-processing environment to a multi-node high-performance cluster. CONCLUSIONS: Stride enables researchers to rapidly and intuitively develop new imaging algorithms and to explore novel physics without sacrificing performance and scalability. This will lead to faster scientific progress in this field and will significantly ease clinical translation

Extended WKB method, resonances and supersymmetric radial barriers

Semiclassical approximations are implemented in the calculation of position and width of low energy resonances for radial barriers. The numerical integrations are delimited by t/T<<8, with t the period of a classical particle in the barrier trap and T the resonance lifetime. These energies are used in the construction of `haired' short range potentials as the supersymmetric partners of a given radial barrier. The new potentials could be useful in the study of the transient phenomena which give rise to the Moshinsky's diffraction in time.Comment: 12 pages, 4 figures, 3 table

Correlación existente entre los tipos de fibras musculares, el ph y la capacidad de retención de agua de la carne en el cerdo chato murciano.

Mediante análisis de correlación se valora la influencia que los tipos de fibras I, IIA y IIX tienen sobre el pH y la capacidad de retención de agua en el músculo longísimo lumbar del cerdo “Chato Murciano”. Los resultados demuestran que los tipos de fibras no influyen sobre el pH a los 45’, pero sí durante la caída del mismo a las 24 h del sacrificio. Por otra parte, nuestros resultados indican que la capacidad de retención de agua está relacionada negativamente con el tamaño de las fibras tipo IIA

Evaluación de los tipos de fibras musculares en cerdos de raza chato murciano criados en sistema intensivo

Mediante técnicas histoquímicas y de análisis de imagen se estudian las características de los distintos tipos de fibras que integran el músculo longísimo lumbar del cerdo “Chato Murciano” criado mediante sistema intensivo. Asimismo, se estima y valora la presencia de fibras anómalas. Los resultados obtenidos demuestran la presencia de al menos tres tipos principales de fibras, catalogadas como tipos I, IIA y IIX. Los datos morfométricos revelan la existencia de alto porcentaje (79%) y gran tamaño de las fibras IIX (glucolíticas). Un 50 % de los animales analizados presentó fibras gigantes aunque en porcentajes muy escasos (<1%)

Importance of tissue sampling, laboratory methods, and patient characteristics for detection of Pneumocystis in autopsied lungs of non-immunosuppressed individuals

To understand the epidemiological significance of Pneumocystis detection in a lung tissue sample of non-immunosuppressed individuals, we examined sampling procedures, laboratory methodology, and patient characteristics of autopsy series reported in the literature. Number of tissue specimens, DNA-extraction procedures, age and underlying diagnosis highly influence yield and are critical to understand yield differences of Pneumocystis among reports of pulmonary colonization in immunocompetent individuals.publishersversionpublishe

Inverse problem for wave equation with sources and observations on disjoint sets

We consider an inverse problem for a hyperbolic partial differential equation on a compact Riemannian manifold. Assuming that $\Gamma_1$ and $\Gamma_2$ are two disjoint open subsets of the boundary of the manifold we define the restricted Dirichlet-to-Neumann operator $\Lambda_{\Gamma_1,\Gamma_2}$. This operator corresponds the boundary measurements when we have smooth sources supported on $\Gamma_1$ and the fields produced by these sources are observed on $\Gamma_2$. We show that when $\Gamma_1$ and $\Gamma_2$ are disjoint but their closures intersect at least at one point, then the restricted Dirichlet-to-Neumann operator $\Lambda_{\Gamma_1,\Gamma_2}$ determines the Riemannian manifold and the metric on it up to an isometry. In the Euclidian space, the result yields that an anisotropic wave speed inside a compact body is determined, up to a natural coordinate transformations, by measurements on the boundary of the body even when wave sources are kept away from receivers. Moreover, we show that if we have three arbitrary non-empty open subsets $\Gamma_1,\Gamma_2$, and $\Gamma_3$ of the boundary, then the restricted Dirichlet-to-Neumann operators $\Lambda_{\Gamma_j,\Gamma_k}$ for $1\leq j<k\leq 3$ determine the Riemannian manifold to an isometry. Similar result is proven also for the finite-time boundary measurements when the hyperbolic equation satisfies an exact controllability condition