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Earthquake Occurrence provides the reader with a review of algorithms applicable for modeling seismicity, such as short-term earthquake clustering and pseudo-periodic long-term behavior of major earthquakes.The concept of the likelihood ratio of a set of observations under different hypotheses is applied for comparison among various models.

Aim of the present study was to compare different methods, viz., Sheather's sugar flotation (SSF), Ziehl-Neelsen (ZN), Kinyoun's acid-fast method (KAF), safranin-methylene blue staining (SMB), and negative staining techniques such as nigrosin staining, light green staining, and malachite green staining for the detection of Cryptosporidium spp. oocysts in bovines. A total of 455 fecal samples from bovines were collected from private, government farms and from the clinical cases presented to Department of Medicine, Veterinary College, Bengaluru. They were subjected for SSF, ZN, KAF, SMB and negative staining methods. Out of 455 animal fecal samples screened 5.71% were found positive for Cryptosporidium spp. oocysts. The species were identified as Cryptosporidium parvum in calves and Cryptosporidium andersoni in adults based on the morphological characterization and micrometry of the oocysts. Of all the techniques, fecal flotation with sheather's was found to be more specific and sensitive method for the detection of Cryptosporidium spp. oocysts. Among the conventional staining methods, the SMB gives better differentiation between oocysts and yeast. Among the three negative staining methods, malachite green was found sensitive over the other methods.

In this paper, we introduce novel methods for computing middle surfaces between various 3D data sets such as point clouds and/or discrete surfaces. Traditionally the middle surface is obtained by detecting singularities in computed distance function such as ridges, triple junctions, etc. It requires to compute second order differential characteristics, and also some kinds of heuristics must be applied. Opposite to that, we determine the middle surface just from computing the distance function itself which is a fast and simple approach. We present and compare the results of the fast sweeping method, the vector distance transform algorithm, the fast marching method, and the Dijkstra-Pythagoras method in finding the middle surface between 3D data sets.

The travel time computation of microseismic waves in different directions (particularly, the diagonal direction) in three-dimensional space has been found to be inaccurate, which seriously affects the localization accuracy of three-dimensional microseismic sources. In order to solve this problem, this research study developed a method of calculating the P-wave travel time based on a 3D high-order fast marching method (3D_H_FMM). This study focused on designing a high-order finite-difference operator in order to realize the accurate calculation of the P-wave travel time in three-dimensional space. The method was validated using homogeneous velocity models and inhomogeneous layered media velocity models of different scales. The results showed that the overall mean absolute error (MAE) of the two homogenous models using 3D_H_FMM had been reduced by 88.335%, and 90.593% compared with the traditional 3D_FMM. On that basis, the three-dimensional localization of microseismic sources was carried out using a particle swarm optimization algorithm. The developed 3D_H_FMM was used to calculate the travel time, then to conduct the localization of the microseismic source in inhomogeneous models. The mean error of the localization results of the different positions in the three-dimensional space was determined to be 1.901 m, and the localization accuracy was found to be superior to that of the traditional 3D_FMM method (mean absolute localization error: 3.447 m) with the small-scaled inhomogeneous model.

Fast Marching and Fast Sweeping are the two most commonly used methods for solving the eikonal equation. Each of these methods performs best on a different set of problems. Fast Sweeping, for example, will outperform Fast Marching on problems where the characteristics are largely straight lines. Fast Marching, on the other hand, is usually more efficient than Fast Sweeping on problems where characteristics frequently change their directions and on domains with complicated geometry. In this paper we explore the possibility of combining the best features of both approaches by using Marching on a coarser scale and sweeping on a finer scale. We present three new hybrid methods based on this idea and illustrate their properties in several numerical examples with continuous and piecewise-constant speed functions in R^2.

The use of local single-pass methods (like, e.g., the fast marching method) has become popular in the solution of some Hamilton--Jacobi equations. The prototype of these equations is the eikonal equation, for which the methods can be applied saving CPU time and possibly memory allocation. Then some questions naturally arise: Can local single-pass methods solve any Hamilton--Jacobi equation? If not, where should the limit be set? This paper tries to answer these questions. In order to give a complete picture, we present an overview of some fast methods available in the literature and briefly analyze their main features. We also introduce some numerical tools and provide several numerical tests which are intended to exhibit the limitations of the methods. We show that the construction of a local single-pass method for general Hamilton--Jacobi equations is very hard, if not impossible. Nevertheless, some special classes of problems can actually be solved, making local single-pass methods very useful from a practical point of view. [PUBLICATION ABSTRACT]

In this paper, we develop a fast linearized virtual element method (VEM) for the approximation of the nonlinear time-fractional diffusion equations on polygonal meshes. The L 1-scheme with graded meshes is used to deal with the non-smooth system, the Newton linearized method is adopted to handle the nonlinear term and VEM is employed to discrete the spatial variable. Then the error splitting approach is used to prove the unconditional optimal error estimate of the fully discrete linearized L1-VEM scheme. In order to reduce the storage and computational cost caused by the nonlocality of the Caputo fractional operator, a fast memory-saving L1-VEM is developed. It is proved that the difference between the solution of the L1-VEM and the fast L1-VEM can be made arbitrarily small and is independently of the sizes of the time and/or space grids. Finally, numerical results are implemented to verify the theoretical results.

This paper illustrates the development of a recursive QR technique for the analysis of transient events, such as disruptions or scenario evolution, in fusion devices with three-dimensional conducting structures using an integral eddy current formulation. An integral formulation involves the solution, at each time step, of a large full linear system. For this reason, a direct solution is impractical in terms of time and memory consumption. Moreover, typical fusion devices show a symmetric/periodic structure. This can be properly exploited when the plasma and other sources possess the same symmetry/periodicity of the structure. Indeed, in this case, the computation can be reduced to only a single sector of the overall structure. In this work the periodicity and the symmetries are merged in the recursive QR technique, exhibiting a huge decrease in the computational cost. Finally, the proposed technique is applied to a realistic large-scale problem related to the International Thermonuclear Experimental Reactor (ITER).

This paper introduces a new directional multilevel algorithm for solving $N$-body or $N$-point problems with highly oscillatory kernels. These systems often result from the boundary integral formulations of scattering problems and are difficult due to the oscillatory nature of the kernel and the non-uniformity of the particle distribution. We address the problem by first proving that the interaction between a ball of radius $r$ and a well-separated region has an approximate low rank representation, as long as the well-separated region belongs to a cone with a spanning angle of $O(1/r)$ and is at a distance which is at least $O(r^2)$ away from from the ball. We then propose an efficient and accurate procedure which utilizes random sampling to generate such a separated, low rank representation. Based on the resulting representations, our new algorithm organizes the high frequency far field computation by a multidirectional and multiscale strategy to achieve maximum efficiency. The algorithm performs well on a large group of highly oscillatory kernels. Our algorithm is proved to have $O(N\\log N)$ computational complexity for any given accuracy when the points are sampled from a two dimensional surface. We also provide numerical results to demonstrate these properties.

We consider global efficiency of algorithms for minimizing a sum of a convex function and a composition of a Lipschitz convex function with a smooth map. The basic algorithm we rely on is the prox-linear method, which in each iteration solves a regularized subproblem formed by linearizing the smooth map. When the subproblems are solved exactly, the method has efficiency O(ε-2), akin to gradient descent for smooth minimization. We show that when the subproblems can only be solved by first-order methods, a simple combination of smoothing, the prox-linear method, and a fast-gradient scheme yields an algorithm with complexity O~(ε-3). We round off the paper with an inertial prox-linear method that automatically accelerates in presence of convexity.