Search results for " computational"
showing 10 items of 661 documents
A Tight Lower Bound on Certificate Complexity in Terms of Block Sensitivity and Sensitivity
2014
Sensitivity, certificate complexity and block sensitivity are widely used Boolean function complexity measures. A longstanding open problem, proposed by Nisan and Szegedy, is whether sensitivity and block sensitivity are polynomially related. Motivated by the constructions of functions which achieve the largest known separations, we study the relation between 1-certificate complexity and 0-sensitivity and 0-block sensitivity. Previously the best known lower bound was $C_1(f)\geq \frac{bs_0(f)}{2 s_0(f)}$, achieved by Kenyon and Kutin. We improve this to $C_1(f)\geq \frac{3 bs_0(f)}{2 s_0(f)}$. While this improvement is only by a constant factor, this is quite important, as it precludes achi…
Introduction to the GiNaC Framework for Symbolic Computation within the C++ Programming Language
2002
AbstractThe traditional split into a low level language and a high level language in the design of computer algebra systems may become obsolete with the advent of more versatile computer languages. We describe GiNaC, a special-purpose system that deliberately denies the need for such a distinction. It is entirely written in C++and the user can interact with it directly in that language. It was designed to provide efficient handling of multivariate polynomials, algebras and special functions that are needed for loop calculations in theoretical quantum field theory. It also bears some potential to become a more general purpose symbolic package.
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.
Approximate 3-Dimensional Electrical Impedance Imaging
2001
We discuss a new approach to three-dimensional electrical impedance imaging based on a reduction of the information to be demanded from a reconstruction algorithm. Images are obtained from a single measurement by suitably simplifying the geometry of the measuring chamber and by restricting the nature of the object to be imaged and the information required from the image. In particular we seek to establish the existence or non-existence of a single object (or a small number of objects) in a homogeneous background and the location of the former in the (x,y)-plane defined by the measuring electrodes. Given in addition the conductivity of the object rough estimates of its position along the z-a…
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 …
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…
Non-equilibrium Markov state modeling of periodically driven biomolecules
2019
Molecular dynamics simulations allow to study the structure and dynamics of single biomolecules in microscopic detail. However, many processes occur on time scales beyond the reach of fully atomistic simulations and require coarse-grained multiscale models. While systematic approaches to construct such models have become available, these typically rely on microscopic dynamics that obey detailed balance. In vivo, however, biomolecules are constantly driven away from equilibrium in order to perform specific functions and thus break detailed balance. Here we introduce a method to construct Markov state models for systems that are driven through periodically changing one (or several) external p…
Nonnegative Tensor Train Decompositions for Multi-domain Feature Extraction and Clustering
2016
Tensor train (TT) is one of the modern tensor decomposition models for low-rank approximation of high-order tensors. For nonnegative multiway array data analysis, we propose a nonnegative TT (NTT) decomposition algorithm for the NTT model and a hybrid model called the NTT-Tucker model. By employing the hierarchical alternating least squares approach, each fiber vector of core tensors is optimized efficiently at each iteration. We compared the performances of the proposed method with a standard nonnegative Tucker decomposition (NTD) algorithm by using benchmark data sets including event-related potential data and facial image data in multi-domain feature extraction and clustering tasks. It i…
On the application of the generalized means to construct multiresolution schemes satisfying certain inequalities proving stability
2021
Multiresolution representations of data are known to be powerful tools in data analysis and processing, and they are particularly interesting for data compression. In order to obtain a proper definition of the edges, a good option is to use nonlinear reconstructions. These nonlinear reconstruction are the heart of the prediction processes which appear in the definition of the nonlinear subdivision and multiresolution schemes. We define and study some nonlinear reconstructions based on the use of nonlinear means, more in concrete the so-called Generalized means. These means have two interesting properties that will allow us to get associated reconstruction operators adapted to the presence o…
Boolean Networks: A Primer
2021
Abstract Autism Spectrum Disorders (ASDs) stand out as a relevant example where omics-data approaches have been extensively and successfully employed. For instance, an outstanding outcome of the Autism Genome Project relies in the identification of biomarkers and the mapping of biological processes potentially implicated in ASDs’ pathogenesis. Several of these mapped processes are related to molecular and cellular events (e.g., synaptogenesis and synapse function, axon growth and guidance, etc.) that are required for the development of a correct neuronal connectivity. Interestingly, these data are consistent with results of brain imaging studies of some patients. Despite these remarkable pr…