Search results for "numeri"
showing 10 items of 2138 documents
Average Performance Analysis of the Stochastic Gradient Method for Online PCA
2019
International audience; This paper studies the complexity of the stochastic gradient algorithm for PCA when the data are observed in a streaming setting. We also propose an online approach for selecting the learning rate. Simulation experiments confirm the practical relevance of the plain stochastic gradient approach and that drastic improvements can be achieved by learning the learning rate.
Cholesky decomposition techniques in electronic structure theory
2011
We review recently developed methods to efficiently utilize the Cholesky decomposition technique in electronic structure calculations. The review starts with a brief introduction to the basics of the Cholesky decomposition technique. Subsequently, examples of applications of the technique to ab inito procedures are presented. The technique is demonstrated to be a special type of a resolution-of-identity or density-fitting scheme. This is followed by explicit examples of the Cholesky techniques used in orbital localization, computation of the exchange contribution to the Fock matrix, in MP2, gradient calculations, and so-called method specific Cholesky decomposition. Subsequently, examples o…
A computer method for estimating volumes and surface areas of complex structures consisting of overlapping spheres
1992
A PASCAL program which calculates volumes and surface areas of structures consisting of overlapping spheres is designed. The calculation is done by modelling the structure in the memory of a computer and then scanning the memory bit- or bytewise. A brief discussion of the error is presented, and an example for testing the algorithm is provided.
How does serendipity affect diversity in recommender systems? A serendipity-oriented greedy algorithm
2018
Most recommender systems suggest items that are popular among all users and similar to items a user usually consumes. As a result, the user receives recommendations that she/he is already familiar with or would find anyway, leading to low satisfaction. To overcome this problem, a recommender system should suggest novel, relevant and unexpected i.e., serendipitous items. In this paper, we propose a serendipity-oriented, reranking algorithm called a serendipity-oriented greedy (SOG) algorithm, which improves serendipity of recommendations through feature diversification and helps overcome the overspecialization problem. To evaluate our algorithm, we employed the only publicly available datase…
Cryptanalysis of Knapsack Cipher Using Ant Colony Optimization
2018
Ant Colony Optimization is a search metaheuristic inspired by the behavior of real ant colonies and shown their effectiveness, robustness to solve a wide variety of complex problems. In this paper, we present a novel Ant Colony Optimization (ACO) based attack for cryptanalysis of knapsack cipher algorithm. A Cipher-text only attack is used to discover the plaintext from the cipher-text. Moreover, our approach allows us to break knapsack cryptosystem in a minimum search space when compared with other techniques. Experimental results prove that ACO can be used as an effective tool to attack knapsack cipher.
Highlighting numerical insights of an efficient SPH method
2018
Abstract In this paper we focus on two sources of enhancement in accuracy and computational demanding in approximating a function and its derivatives by means of the Smoothed Particle Hydrodynamics method. The approximating power of the standard method is perceived to be poor and improvements can be gained making use of the Taylor series expansion of the kernel approximation of the function and its derivatives. The modified formulation is appealing providing more accurate results of the function and its derivatives simultaneously without changing the kernel function adopted in the computation. The request for greater accuracy needs kernel function derivatives with order up to the desidered …
An abstract inf-sup problem inspired by limit analysis in perfect plasticity and related applications
2021
This paper is concerned with an abstract inf-sup problem generated by a bilinear Lagrangian and convex constraints. We study the conditions that guarantee no gap between the inf-sup and related sup-inf problems. The key assumption introduced in the paper generalizes the well-known Babuška–Brezzi condition. It is based on an inf-sup condition defined for convex cones in function spaces. We also apply a regularization method convenient for solving the inf-sup problem and derive a computable majorant of the critical (inf-sup) value, which can be used in a posteriori error analysis of numerical results. Results obtained for the abstract problem are applied to continuum mechanics. In particular…
A Meshfree Solver for the MEG Forward Problem
2015
Noninvasive estimation of brain activity via magnetoencephalography (MEG) involves an inverse problem whose solution requires an accurate and fast forward solver. To this end, we propose the Method of Fundamental Solutions (MFS) as a meshfree alternative to the Boundary Element Method (BEM). The solution of the MEG forward problem is obtained, via the Method of Particular Solutions (MPS), by numerically solving a boundary value problem for the electric scalar potential, derived from the quasi-stationary approximation of Maxwell’s equations. The magnetic field is then computed by the Biot-Savart law. Numerical experiments have been carried out in a realistic single-shell head geometry. The p…
A multi-domain approach for smoothed particle hydrodynamics simulations of highly complex flows
2018
Abstract An efficient and accurate method is proposed to solve the incompressible flow momentum and continuity equations in computational domains partitioned into subdomains in the framework of the smoothed particle hydrodynamics method. The procedure does not require any overlap of the subdomains, which would result in the increase of the computational effort. Perfectly matching solutions are obtained at the surfaces separating neighboring blocks. The block interfaces can be both planar and curved surfaces allowing to easily decompose even geometrically complex domains. The smoothing length of the kernel function is maintained constant in each subdomain, while changing between blocks where…
Fake Nodes approximation for Magnetic Particle Imaging
2020
Accurately reconstructing functions with discontinuities is the key tool in many bio-imaging applications as, for instance, in Magnetic Particle Imaging (MPI). In this paper, we apply a method for scattered data interpolation, named mapped bases or Fake Nodes approach, which incorporates discontinuities via a suitable mapping function. This technique naturally mitigates the Gibbs phenomenon, as numerical evidence for reconstructing MPI images confirms.