Search results for " computational"
showing 10 items of 661 documents
On Shimura subvarieties of the Prym locus
2018
We show that families of Pryms of abelian Galois covers of $\mathbb{P}^1$ in $A_{g-1}$ (resp. $A_g$) do not give rise to high dimensional Shimura subvareties.
Toward a Collective Agenda on AI for Earth Science Data Analysis
2021
In the last years we have witnessed the fields of geosciences and remote sensing and artificial intelligence to become closer. Thanks to both the massive availability of observational data, improved simulations, and algorithmic advances, these disciplines have found common objectives and challenges to advance the modeling and understanding of the Earth system. Despite such great opportunities, we also observed a worrying tendency to remain in disciplinary comfort zones applying recent advances from artificial intelligence on well resolved remote sensing problems. Here we take a position on research directions where we think the interface between these fields will have the most impact and be…
Efficient Analysis and Synthesis Using a New Factorization of the Gabor Frame Matrix
2018
In this paper, we consider the case in which one needs to carry out Gabor analysis and synthesis on large signals using a short support analysis window and its corresponding, possibly longer canonical dual window, respectively. In this asymmetric context, we propose a novel factorization of the Gabor frame operator that exploits its strong and well-known structure and leads to a computational cost for synthesis, which is comparable to the one needed for short support analysis. The proposed factorization applies to any Gabor system with very mild conditions and leads to a potentially promising alternative to current synthesis algorithms in the case of short analysis windows whose support is …
Multidomain spectral method for the Gauss hypergeometric function
2018
International audience; We present a multidomain spectral approach for Fuchsian ordinary differential equations in the particular case of the hypergeometric equation. Our hybrid approach uses Frobenius’ method and Moebius transformations in the vicinity of each of the singular points of the hypergeometric equation, which leads to a natural decomposition of the real axis into domains. In each domain, solutions to the hypergeometric equation are constructed via the well-conditioned ultraspherical spectral method. The solutions are matched at the domain boundaries to lead to a solution which is analytic on the whole compactified real line R∪∞, except for the singular points and cuts of the Rie…
Quantum counter automata
2011
The question of whether quantum real-time one-counter automata (rtQ1CAs) can outperform their probabilistic counterparts has been open for more than a decade. We provide an affirmative answer to this question, by demonstrating a non-context-free language that can be recognized with perfect soundness by a rtQ1CA. This is the first demonstration of the superiority of a quantum model to the corresponding classical one in the real-time case with an error bound less than 1. We also introduce a generalization of the rtQ1CA, the quantum one-way one-counter automaton (1Q1CA), and show that they too are superior to the corresponding family of probabilistic machines. For this purpose, we provide gene…
Bill2d - a software package for classical two-dimensional Hamiltonian systems
2015
Abstract We present Bill2d , a modern and efficient C++ package for classical simulations of two-dimensional Hamiltonian systems. Bill2d can be used for various billiard and diffusion problems with one or more charged particles with interactions, different external potentials, an external magnetic field, periodic and open boundaries, etc. The software package can also calculate many key quantities in complex systems such as Poincare sections, survival probabilities, and diffusion coefficients. While aiming at a large class of applicable systems, the code also strives for ease-of-use, efficiency, and modularity for the implementation of additional features. The package comes along with a use…
The Dynamical Kernel Scheduler - Part 1
2015
Emerging processor architectures such as GPUs and Intel MICs provide a huge performance potential for high performance computing. However developing software using these hardware accelerators introduces additional challenges for the developer such as exposing additional parallelism, dealing with different hardware designs and using multiple development frameworks in order to use devices from different vendors. The Dynamic Kernel Scheduler (DKS) is being developed in order to provide a software layer between host application and different hardware accelerators. DKS handles the communication between the host and device, schedules task execution, and provides a library of built-in algorithms. …
First Experiences on an Accurate SPH Method on GPUs
2017
It is well known that the standard formulation of the Smoothed Particle Hydrodynamics is usually poor when scattered data distribution is considered or when the approximation near the boundary occurs. Moreover, the method is computational demanding when a high number of data sites and evaluation points are employed. In this paper an enhanced version of the method is proposed improving the accuracy and the efficiency by using a HPC environment. Our implementation exploits the processing power of GPUs for the basic computational kernel resolution. The performance gain demonstrates the method to be accurate and suitable to deal with large sets of data.
Performance potential for simulating spin models on GPU
2012
Graphics processing units (GPUs) are recently being used to an increasing degree for general computational purposes. This development is motivated by their theoretical peak performance, which significantly exceeds that of broadly available CPUs. For practical purposes, however, it is far from clear how much of this theoretical performance can be realized in actual scientific applications. As is discussed here for the case of studying classical spin models of statistical mechanics by Monte Carlo simulations, only an explicit tailoring of the involved algorithms to the specific architecture under consideration allows to harvest the computational power of GPU systems. A number of examples, ran…
Separatrix reconstruction to identify tipping points in an eco-epidemiological model
2018
Many ecological systems exhibit tipping points such that they suddenly shift from one state to another. These shifts can be devastating from an ecological point of view, and additionally have severe implications for the socio-economic system. They can be caused by overcritical perturbations of the state variables such as external shocks, disease emergence, or species removal. It is therefore important to be able to quantify the tipping points. Here we present a study of the tipping points by considering the basins of attraction of the stable equilibrium points. We address the question of finding the tipping points that lie on the separatrix surface, which partitions the space of system traj…