Search results for " representation"
showing 10 items of 811 documents
Generalised Deformations, Koszul Resolutions, Moyal Products
1998
We generalise Gerstenhaber's theory of deformations, by dropping the assumption that the deformation parameter should commute with the elements of the original algebra. We give the associated cohomology and construct a Koszul resolution for the polynomial algebra [Formula: see text] in the "homogeneous" case. We then develop examples in the case of [Formula: see text] and find some Moyal-like products of a new type. Finally, we show that, for any field K, matrix algebras with coefficients in K and finite degree extensions of K are rigid, as in the commutative case.
Hartmanis-Stearns Conjecture on Real Time and Transcendence
2012
Hartmanis-Stearns conjecture asserts that any number whose decimal expansion can be computed by a multitape Turing machine is either rational or transcendental. After half a century of active research by computer scientists and mathematicians the problem is still open but much more interesting than in 1965.
Star representations of E(2)
1990
We give a complete and explicit realization of the unitary irreducible representations of the universal covering group G of E(2), the Euclidean group in two dimensions, by deformation of the algebra of functions on the dual g* of the Lie algebra of G. We define an adapted Fourier transform for G which gives a natural description of the harmonic analysis of G.
Angular Pseudomomentum Theory for the Generalized Nonlinear Schr\"{o}dinger Equation in Discrete Rotational Symmetry Media
2009
We develop a complete mathematical theory for the symmetrical solutions of the generalized nonlinear Schr\"odinger equation based on the new concept of angular pseudomomentum. We consider the symmetric solitons of a generalized nonlinear Schr\"odinger equation with a nonlinearity depending on the modulus of the field. We provide a rigorous proof of a set of mathematical results justifying that these solitons can be classified according to the irreducible representations of a discrete group. Then we extend this theory to non-stationary solutions and study the relationship between angular momentum and pseudomomentum. We illustrate these theoretical results with numerical examples. Finally, we…
El proyecto mapa escolar de Valencia: Análisis de la zonificación educativa de la ciudad de Valencia
2018
The research project Mapa Escolar de Valencia (School Map of Valencia) was born out of an agreement between the City Council and the University of Valencia in order to carry out an investigation of the compulsory education system of the city and propose, if necessary, modifications to the current school zoning. The project is structured in several research areas. An analysis of the specialized scientific literature and public policies concerning education and schooling has been done, and it is currently analysing the evolution of quantitative and qualitative data on compulsory schooling in Valencia, its school zoning, the representations of education and the school climate in the city schoo…
Sturmian words and overexponential codimension growth
2018
Abstract Let A be a non necessarily associative algebra over a field of characteristic zero satisfying a non-trivial polynomial identity. If A is a finite dimensional algebra or an associative algebra, it is known that the sequence c n ( A ) , n = 1 , 2 , … , of codimensions of A is exponentially bounded. If A is an infinite dimensional non associative algebra such sequence can have overexponential growth. Such phenomenon is present also in the case of Lie or Jordan algebras. In all known examples the smallest overexponential growth of c n ( A ) is ( n ! ) 1 2 . Here we construct a family of algebras whose codimension sequence grows like ( n ! ) α , for any real number α with 0 α 1 .
Investigating the Impact of Radiation-Induced Soft Errors on the Reliability of Approximate Computing Systems
2020
International audience; Approximate Computing (AxC) is a well-known paradigm able to reduce the computational and power overheads of a multitude of applications, at the cost of a decreased accuracy. Convolutional Neural Networks (CNNs) have proven to be particularly suited for AxC because of their inherent resilience to errors. However, the implementation of AxC techniques may affect the intrinsic resilience of the application to errors induced by Single Events in a harsh environment. This work introduces an experimental study of the impact of neutron irradiation on approximate computing techniques applied on the data representation of a CNN.
From Historical Silk Fabrics to Their Interactive Virtual Representation and 3D Printing
2020
The documentation, dissemination, and enhancement of Cultural Heritage is of great relevance. To that end, technological tools and interactive solutions (e.g., 3D models) have become increasingly popular. Historical silk fabrics are nearly flat objects, very fragile and with complex internal geometries, related to different weaving techniques and types of yarns. These characteristics make it difficult to properly document them, at the yarn level, with current technologies. In this paper, we bring a new methodology to virtually represent such heritage and produce 3D printouts, also making it highly interactive through the tool Virtual Loom. Our work involves sustainability from different per…
Artificial intelligence techniques for cancer treatment planning
1988
An artificial intelligence system, NEWCHEM, for the development of new oncology therapies is described. This system takes into account the most recent advances in molecular and cellular biology and in cell-drug interaction, and aims to guide experimentation in the design of new optimal protocols. Further work is being carried out, aimed to embody in the system all the basic knowledge of biology, physiopathology and pharmacology, to reason qualitatively from first principles so as to be able to suggest cancer therapies.
An associative link from geometric to symbolic representations in artificial vision
1991
Recent approaches to modelling the reference of internal symbolic representations of intelligent systems suggest to consider a computational level of a subsymbolic kind. In this paper the integration between symbolic and subsymbolic processing is approached in the framework of the research work currently carried on by the authors in the field of artificial vision. An associative mapping mechanism is defined in order to relate the constructs of the symbolic representation to a geometric model of the observed scene.