Search results for " Algebra"
showing 10 items of 2082 documents
Identifying the characteristics of China’s maritime trading partners on the basis of bilateral shipping connectivity: a cluster analysis
2021
China is ranked as the number one maritime connected country in the world. This study attempts to analyse the characteristics of its 155 maritime trading partners. Five components of maritime conne...
Discrete Structure Shakedown Design Ices ’95, Hawai, July 30 – August 3, 1995
1995
The minimum volume shakedown design problem was already approached by several authors with studies devoted to discrete structures (see e.g. [1]–[5]) and to continuous structures (see e.g. [6]). Except some very simple structural typologies, also the optimal shakedown design problem formulations for continuous structures need to be discretized in the application stage. In any case, the relevant optimal shakedown design problem for discrete (or discretized) structures is formulated in terms of design variables as well as behavioural variables, and consists in the search for the/a minimum volume design among all feasible designs (i.e. able to shakedown). Due to its strong non-linearity, the la…
GAPP Compiler for Hardware Accelerated Geometric Algebra Computing
2016
Because of the high numeric complexity of Geometric Algebra, its use in engineering applications relies heavily on tools for ecient implementations. In this article, we introduce a new quality of Geometric Algebra Computing solutions based on a new compiler for Geometric Algebra Parallelism Programs (GAPP). These programs are already optimized in a sense that only the really needed computations are left. The GAPP compiler is able to generate two output formats leading to advanced hardware accelerated Geometric Algebra Computing. On one hand, there is the direct generation of HSAIL code, in order to more eciently support the solutions of the broad range of heterogeneous computing architectur…
Topological Hopf Algebras, Quantum Groups and Deformation Quantization
2019
After a presentation of the context and a brief reminder of deformation quantization, we indicate how the introduction of natural topological vector space topologi es on Hopf algebras associated with Poisson Lie groups, Lie bialgebras and their doubles explains their dualities a nd provides a comprehensive framework. Relations with deformation quantization and applications to the deformation quantization of symmetric spaces are described.
Gradings on matrices
2008
Semisupervised nonlinear feature extraction for image classification
2012
Feature extraction is of paramount importance for an accurate classification of remote sensing images. Techniques based on data transformations are widely used in this context. However, linear feature extraction algorithms, such as the principal component analysis and partial least squares, can address this problem in a suboptimal way because the data relations are often nonlinear. Kernel methods may alleviate this problem only when the structure of the data manifold is properly captured. However, this is difficult to achieve when small-size training sets are available. In these cases, exploiting the information contained in unlabeled samples together with the available training data can si…
Kernel-Based Inference of Functions Over Graphs
2018
Abstract The study of networks has witnessed an explosive growth over the past decades with several ground-breaking methods introduced. A particularly interesting—and prevalent in several fields of study—problem is that of inferring a function defined over the nodes of a network. This work presents a versatile kernel-based framework for tackling this inference problem that naturally subsumes and generalizes the reconstruction approaches put forth recently for the signal processing by the community studying graphs. Both the static and the dynamic settings are considered along with effective modeling approaches for addressing real-world problems. The analytical discussion herein is complement…
Model selection based product kernel learning for regression on graphs
2013
The choice of a suitable graph kernel is intrinsically hard and often cannot be made in an informed manner for a given dataset. Methods for multiple kernel learning offer a possible remedy, as they combine and weight kernels on the basis of a labeled training set of molecules to define a new kernel. Whereas most methods for multiple kernel learning focus on learning convex linear combinations of kernels, we propose to combine kernels in products, which theoretically enables higher expressiveness. In experiments on ten publicly available chemical QSAR datasets we show that product kernel learning is on no dataset significantly worse than any of the competing kernel methods and on average the…
Arc crossing minimization in graphs with GRASP
2001
Graphs are commonly used to represent information in many fields of science and engineering. Automatic drawing tools generate comprehensible graphs from data, taking into account a variety of properties, enabling users to see important relationships in the data. The goal of limiting the number of arc crossings is a well-admitted criterion for a good drawing. In this paper, we present a Greedy Randomized Adaptive Search Procedure (GRASP) for the problem of minimizing arc crossings in graphs. Computational experiments with 200 graphs with up to 350 vertices are presented to assess the merit of the method. We show that simple heuristics are very fast but result in inferior solutions, while hig…