Search results for " Algebra"
showing 10 items of 2082 documents
Efficient analysis of cubic junction of rectangular waveguides using admittance-matrix representation
2000
In the paper an efficient and accurate method, based on the multimode-admittance-matrix representation and the theory of cavities, is proposed for the analysis of a six-port ‘cubic’ junction composed of the orthogonal intersection of three rectangular waveguides. Very simple closed-form analytical expressions are explicitly detailed for all matrix elements of this basic key building block. More general waveguide multiport junctions, composed of a central cubic junction with arbitrarily shaped waveguide access ports, are also studied using a segmentation procedure. To validate the theory, numerical results are first discussed for a standard rectangular waveguide six-port cross junction. Fina…
Worst Case Analysis of Non-local Games
2013
Non-local games are studied in quantum information because they provide a simple way for proving the difference between the classical world and the quantum world. A non-local game is a cooperative game played by 2 or more players against a referee. The players cannot communicate but may share common random bits or a common quantum state. A referee sends an input x i to the i th player who then responds by sending an answer a i to the referee. The players win if the answers a i satisfy a condition that may depend on the inputs x i .
Advantage of Quantum Strategies in Random Symmetric XOR Games
2013
Non-local games are known as a simple but useful model which is widely used for displaying nonlocal properties of quantum mechanics. In this paper we concentrate on a simple subset of non-local games: multiplayer XOR games with 1-bit inputs and 1-bit outputs which are symmetric w.r.t. permutations of players.
Understanding star-fundamental algebras
2021
Star-fundamental algebras are special finite dimensional algebras with involution ∗ * over an algebraically closed field of characteristic zero defined in terms of multialternating ∗ * -polynomials. We prove that the upper-block matrix algebras with involution introduced in Di Vincenzo and La Scala [J. Algebra 317 (2007), pp. 642–657] are star-fundamental. Moreover, any finite dimensional algebra with involution contains a subalgebra mapping homomorphically onto one of such algebras. We also give a characterization of star-fundamental algebras through the representation theory of the symmetric group.
Automatic construction of test sets: Theoretical approach
2005
We consider the problem of automatic construction of complete test set (CTS) from program text. The completeness criterion adopted is C1, i.e., it is necessary to execute all feasible branches of program at least once on the tests of CTS. A simple programming language is introduced with the property that the values used in conditional statements are not arithmetically deformed. For this language the CTS problem is proved to be algorithmically solvable and CTS construction algorithm is obtained. Some generalizations of this language containing counters, stacks or arrays are considered where the CTS problem remains solvable. In conclusion the applications of the obtained results to CTS constr…
Integrated dimensional and drive-train design optimization of a light-weight anthropomorphic arm
2012
An approach to minimize the mass of robotic manipulators is developed by integrated dimensional and drive-train optimization. The method addresses the influences of dimensions and characteristics of drive-trains in the design optimization. Constraints are formulated on the basis of kinematic performance and dynamic requirements, whereas the main objective is to minimize the total mass. Case studies are included to demonstrate the application of the optimization method in the design of assistive robots.
Kernel manifold alignment for domain adaptation
2016
The wealth of sensory data coming from different modalities has opened numerous opportu- nities for data analysis. The data are of increasing volume, complexity and dimensionality, thus calling for new methodological innovations towards multimodal data processing. How- ever, multimodal architectures must rely on models able to adapt to changes in the data dis- tribution. Differences in the density functions can be due to changes in acquisition conditions (pose, illumination), sensors characteristics (number of channels, resolution) or different views (e.g. street level vs. aerial views of a same building). We call these different acquisition modes domains, and refer to the adaptation proble…
Topology of synaptic connectivity constrains neuronal stimulus representation, predicting two complementary coding strategies
2022
In motor-related brain regions, movement intention has been successfully decoded from in-vivo spike train by isolating a lower-dimension manifold that the high-dimensional spiking activity is constrained to. The mechanism enforcing this constraint remains unclear, although it has been hypothesized to be implemented by the connectivity of the sampled neurons. We test this idea and explore the interactions between local synaptic connectivity and its ability to encode information in a lower dimensional manifold through simulations of a detailed microcircuit model with realistic sources of noise. We confirm that even in isolation such a model can encode the identity of different stimuli in a lo…
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…
Non-Model Based Method for an Automation of 3D Acquisition and Post-Processing
2008
Most of the automation for 3D acquisition concerns objects with simple shape, like mechanical parts. For cultural heritage artefacts, the process is more complex, and it doesn't exist general solution nowadays. This paper presents a method to generate a complete 3D model of cultural heritage artefacts. In a first step, MVC is used to solve the view planning problem. Then, holes remaining in 3D model are detected, and their features are calculated to finish acquisition. Different post-processing are applied on each view to increase quality of the 3D model. This procedure has been tested with simulated scanner, before being implemented on a motion system with five degrees of freedom.