A Numerical Framework For Nonlinear Peridynamics On Two-dimensional Manifolds Based On Implicit P-(Ec)k Schemes

In this manuscript, an original numerical procedure for the nonlinear peridynamics on arbitrarily--shaped two-dimensional (2D) closed manifolds is proposed. When dealing with non parameterized 2D manifolds at the discrete scale, the problem of computing geodesic distances between two non-adjacent points arise. Here, a routing procedure is implemented for computing geodesic distances by re-interpreting the triangular computational mesh as a non-oriented graph; thus returning a suitable and general method. Moreover, the time integration of the peridynamics equation is demanded to a P-(EC)$^k$ formulation of the implicit $\beta$-Newmark scheme. The convergence of the overall proposed procedure is questioned and rigorously proved. Its abilities and limitations are analyzed by simulating the evolution of a two-dimensional sphere. The performed numerical investigations are mainly motivated by the issues related to the insurgence of singularities in the evolution problem. The obtained results return an interesting picture of the role played by the nonlocal character of the integrodifferential equation in the intricate processes leading to the spontaneous formation of singularities in real materials

A NOTE ON ESTIMATES OF DIAGONAL ELEMENTS OF THE INVERSE OF DIAGONALLY DOMINANT TRIDIAGONAL MATRICES

ABSTRACT. In this note we show how to improve some recent upper and lower bounds for the elements of the inverse of diagonally dominant tridiagonal matrices. In particular, a technique described by [R. Peluso, and T. Politi, Some improvements on two-sided bounds on the inverse of diagonally dominant tridiagonal matrices, Lin. Alg. Appl. Vol. 330 (2001) 1-14], is used to obtain better bounds for the diagonal elements. Key words and phrases: Tridiagonal matrices, Bounds of entries of the inverse. 2000 Mathematics Subject Classification. 65F50, 15A39. 1

“A Fortran90 routine for the solution of orthogonal differential problems”

In this paper we describe a Fortran90 routine for the numerical integration of orthogonal differential systems based on the Cayley transform methods. Three different implementations of the methods are given: with restart, with restart at each step and in composed form. Numerical tests will show the performances of the solver for the solution of orthogonal test problems, of orthogonal rectangular problems and for the calculation of Lyapunov exponents in the linear and nonlinear cases, and finally for solving inverse eigenvalue problem for Toeplitz matrices. The results obtained using Cayley methods are compared with those given by Fortran90 version of Munthe-Kaas methods, which have been coded in a similar way

8th Workshop SDS2014 STRUCTURAL DYNAMICAL SYSTEM: Computational Aspects

The main aim of this workshop is to put together researchers of different areas, in particular Mathematics and Engineering, to give them the opportunity of discussing, in a friendly atmosphere, recent developments in computational and theoretical methods for Dynamical Systems and their applications

Combined Color Semantics and Deep Learning for the Automatic Detection of Dolphin Dorsal Fins

Photo-identification is a widely used non-invasive technique in biological studies for understanding if a specimen has been seen multiple times only relying on specific unique visual characteristics. This information is essential to infer knowledge about the spatial distribution, site fidelity, abundance or habitat use of a species. Today there is a large demand for algorithms that can help domain experts in the analysis of large image datasets. For this reason, it is straightforward that the problem of identify and crop the relevant portion of an image is not negligible in any photo-identification pipeline. This paper approaches the problem of automatically cropping cetaceans images with a hybrid technique based on domain analysis and deep learning. Domain knowledge is applied for proposing relevant regions with the aim of highlighting the dorsal fins, then a binary classification of fin vs. no-fin is performed by a convolutional neural network. Results obtained on real images demonstrate the feasibility of the proposed approach in the automated process of large datasets of Risso’s dolphins photos, enabling its use on more complex large scale studies. Moreover, the results of this study suggest to extend this methodology to biological investigations of different species