Resolution of Born Scattering in Curve Geometries: Aspect-Limited Observations and Excitations

In inverse scattering problems, the most accurate possible imaging results require plane waves impinging from all directions and scattered fields observed in all observation directions around the object. Since this full information is infrequently available in actual applications, this paper is concerned with the mathematical analysis and numerical simulations to estimate the achievable resolution in object reconstruction from the knowledge of the scattered far-field when limited data are available at a single frequency. The investigation focuses on evaluating the Number of Degrees of Freedom (NDF) and the Point Spread Function (PSF), which accounts for reconstructing a point-like unknown and depends on the NDF. The discussion concerns objects belonging to curve geometries, in this case, circumference and square scatterers. In addition, since the exact evaluation of the PSF can only be accomplished numerically, an approximated closed-form evaluation is introduced and compared with the exact one. The approximation accuracy of the PSF is verified by numerical results, at least within its main lobe region, which is the most critical as far as the resolution discussion is concerned. The main result of the analysis is the space variance of the PSF for the considered geometries, showing that the resolution is different over the investigation domain. Finally, two numerical applications of the PSF concept are shown, and their relevance in the presence of noisy data is outlined.

Computation of synthetic seismogram in real earth model by eigen function expansion

The method of eigen function expansion has been used in the present study to compute synthetic or theoretical seismogram in layered elastic half-space of real earth model. Simple dislocation source model has been considered. The transverse (SH) or radial and vertical (P-SV) components of displacement field have been computed as summed modes and compared by using both exact and numerical techniques. The methods used in the study, include exact evaluation by propagator matrix approach using Reflection-Transmission coefficients as well as numerical computations using Runge-Kutta method of order 4. The specialty of the present study is to evaluate approximate displacement field for the earth models with homogeneous and / or inhomogeneous layers. The normalization technique has been used in the study to control the overflow errors. The study has an advantage to get an idea of earth structure or source model by an inverse iterative technique.

Superconformal Line Defects in 3D

We review the recent progress in the study of line defects in three-dimensional Chern–Simons-matter superconformal field theories, notably the ABJM theory. The first part is focused on kinematical defects, supporting a topological sector of the theory. After reviewing the construction of this sector, we concentrate on the evaluation of topological correlators from the partition function of the mass-deformed ABJM theory and provide evidence on the existence of topological quantum mechanics living on the line. In the second part, we consider the dynamical defects realized as latitude BPS Wilson loops for which an exact evaluation is available in terms of a latitude Matrix Model. We discuss the fundamental relation between these operators, the defect superconformal field theory and bulk physical quantities, such as the Bremsstrahlung function. This relation assigns a privileged role to BPS Wilson operators, which become the meeting point for three exact approaches: localization, integrability and conformal bootstrap.

Analysis, Evaluation and Exact Tracking of the Finite Precision Error Generated in Arbitrary Number of Multiplications

In the present paper, a novel approach is introduced for the study, estimation and exact tracking of the finite precision error generated and accumulated during any number of multiplications. It is shown that, as a rule, this operation is very “toxic”, in the sense that it may force the finite precision error accumulation to grow arbitrarily large, under specific conditions that are fully described here. First, an ensemble of definitions of general applicability is given for the rigorous determination of the number of erroneous digits accumulated in any quantity of an arbitrary algorithm. Next, the exact number of erroneous digits produced in a single multiplication is given as a function of the involved operands, together with formulae offering the corresponding probabilities. In case the statistical properties of these operands are known, exact evaluation of the aforementioned probabilities takes place. Subsequently, the statistical properties of the accumulated finite precision error during any number of successive multiplications are explicitly analyzed. A method for exact tracking of this accumulated error is presented, together with associated theorems. Moreover, numerous dedicated experiments are developed and the corresponding results that fully support the theoretical analysis are given. Eventually, a number of important, probable and possible applications is proposed, where all of them are based on the methodology and the results introduced in the present work. The proposed methodology is expandable, so as to tackle the round-off error analysis in all arithmetic operations.

Impact of Hyperbaric Oxygen Therapy on Cognitive Functions: a Systematic Review

Hyperbaric oxygen therapy (HBOT) is a modality of treatment in which patients inhale 100% oxygen inside a hyperbaric chamber pressurised to greater than 1 atmosphere. The aim of this review is to discuss neuropsychological findings in various neurological disorders treated with HBOT and to open new perspectives for therapeutic improvement. A literature search was conducted in the MEDLINE (via PubMed) database from the inception up 10 May 2020. Eligibility criteria included original articles published in English. Case studies were excluded. Full-text articles were obtained from the selected studies and were reviewed on the following inclusion criteria (1) performed cognitive processes assessment (2) performed HBOT with described protocol. Two neuropsychologists independently reviewed titles, abstracts, full texts and extracted data. The initial search retrieved 1024 articles, and a total of 42 studies were finally included after applying inclusion and exclusion criteria. The search yielded controversial results with regard to the efficiency of HBOT in various neurological conditions with cognitive disturbance outcome. To the best of our knowledge this is the first state-of-the art, systematic review in the field. More objective and precise neuropsychological assessment methods are needed to exact evaluation of the efficacy of HBOT for neuropsychological deficits. Future studies should widen the assessment of HBOT effects on different cognitive domains because most of the existing studies have focussed on a single process. Finally, there is a need for further longitudinal studies.

Aspects of Distance Education in Combination with Home Offices

This article discusses the impact of a lockdown caused by the novel coronavirus disease 2019 on the educational process at a selected faculty of a public university in the Czech Republic focused on economic education. The aim was to capture relevant aspects in the context of impacts on the management of the educational process in the organization. The unique situation brought the possibility of analyzing the flexibility of the organization, its ability to adapt. A questionnaire survey was conducted among academics. We found out how they coped with this situation, their technical equipment, support from the faculty, and whether they encountered any problems. The goal of the article was not to bring an exact evaluation of selected questions, but to show the state of the actual situation, to point out possible problems of users, and to link these things with the approach to the management of the organization. Based on the analysis, we bring suggestions and recommendations for improving the process of transition to online learning as well as distance education management and recommendation to support teaching, regardless of the teacher’s workplace. The basic areas and activities that need to be managed were also identified.

Technical Note: Coccygeal vein catheterization for sampling of reproductive tract-derived products from the uterine–ovarian drainage

Blood sample collection from the caudal vena cava at the site of uterine–ovarian drainage provides a more exact evaluation of the concentration and pattern of secretion of uterine or ovarian secreted products for studies of reproductive processes in cyclic and pregnant cattle compared with samples collected from general circulation. This paper describes a thorough and updated procedure for cannulating the coccygeal vein into the caudal vena cava for the collection of serial blood samples at or near the site of uterine–ovarian drainage. Concentrations of progesterone were quantified in cows of different reproductive tract sizes with an active corpus luteum to assess the distance for proper catheter placement compared with circulating concentrations collected from the jugular vein. This procedure has a low risk for side effects, can be used effectively in pregnant animals with no major consequence to the viability of the pregnancy, and provides means for frequent collections up to 12 d.

Computed Tomographic Evaluation of Colonic Diverticulum Complications

Cases of diverticulosis of the colon continue to increase, especially in Western countries. In these countries, two-thirds of the population older than 70 years of age are considered to experience this disease. Medical and surgical treatment for diverticulosis is begun actually for the complications of diverticulitis and lower gastrointestinal hemorrhage. The first evaluation of complicated diverticular disease is based on patient history, physical examination, and laboratory data. But all these exams and data can be inaccurate and are often questionable in the diagnoses of many features of the disease. To describe the position, severity, and presence of complications of a detected diverticulum is crucial to its appropriate treatment. The greater part of the patients have the mild disease and can be successfully cured medically. Only a small number of patients admit with acute diverticulitis and need urgent surgical intervention. Determining these patients early is crucial to morbidity and mortality reduction. Radiologic examination is important for exact evaluation of the extent of the course of the disease over the last three decades. This article aims to chart the place of the computed tomography (CT) imaging procedure in the assessment of acute complicated diverticular disease.