Search results for "Tensor"
showing 10 items of 550 documents
Monte Carlo simulation of micelle formation in block copolymer solutions
1998
Short block copolymers in selective solvents (bad for A-block, good for B-block) are modeled by flexible bead-spring chains, where beads interact with short range Morse potentials of variable strength. It is shown that already very short chains (N A = N B = 2) exhibit a rather well-defined critical micelle concentration (cmc). The mass distribution of the micelles and their gyration tensor components as well as their internal structure are studied. It is shown that the relaxation time increases exponentially with the strength E AA of the attractive energy between the A-monomers, and thus frozen-in micelles of medium size are obtained when E AA is chosen too large. Our results are compared t…
Low-Rank Tucker-2 Model for Multi-Subject fMRI Data Decomposition with Spatial Sparsity Constraint
2022
Tucker decomposition can provide an intuitive summary to understand brain function by decomposing multi-subject fMRI data into a core tensor and multiple factor matrices, and was mostly used to extract functional connectivity patterns across time/subjects using orthogonality constraints. However, these algorithms are unsuitable for extracting common spatial and temporal patterns across subjects due to distinct characteristics such as high-level noise. Motivated by a successful application of Tucker decomposition to image denoising and the intrinsic sparsity of spatial activations in fMRI, we propose a low-rank Tucker-2 model with spatial sparsity constraint to analyze multi-subject fMRI dat…
The Rank of Trifocal Grassmann Tensors
2019
Grassmann tensors arise from classical problems of scene reconstruction in computer vision. Trifocal Grassmann tensors, related to three projections from a projective space of dimension k onto view-spaces of varying dimensions are studied in this work. A canonical form for the combined projection matrices is obtained. When the centers of projections satisfy a natural generality assumption, such canonical form gives a closed formula for the rank of the trifocal Grassmann tensors. The same approach is also applied to the case of two projections, confirming a previous result obtained with different methods in [6]. The rank of sequences of tensors converging to tensors associated with degenerat…
Markovian Connection, Curvature and Weitzenböck Formula on Riemannian Path Spaces
2001
Abstract We shall consider on a Riemannian path space P m o ( M ) the Cruzeiro–Malliavin's Markovian connection. The Laplace operator will be defined as the divergence of the gradient. We shall compute explicitly the associated curvature tensor. A Weitzenbock formula will be established. To this end, we shall introduce an “inner product” between the tangent processes and simple vector fields.
Graded metrics adapted to splittings
1997
Homogeneous graded metrics over split ℤ2-graded manifolds whose Levi-Civita connection is adapted to a given splitting, in the sense recently introduced by Koszul, are completely described. A subclass of such is singled out by the vanishing of certain components of the graded curvature tensor, a condition that plays a role similar to the closedness of a graded symplectic form in graded symplectic geometry: It amounts to determining a graded metric by the data {g, ω, Δ′}, whereg is a metric tensor onM, ω 0 is a fibered nondegenerate skewsymmetric bilinear form on the Batchelor bundleE → M, and Δ′ is a connection onE satisfying Δ′ω = 0. Odd metrics are also studied under the same criterion an…
xloops - Automated Feynman diagram calculation
1998
The program package xloops, a general, model independent tool for the calculation of high energy processes up to the two-loop level, is introduced. xloops calculates massive one- and two-loop Feynman diagrams in the standard model and related theories both analytically and numerically. A user-friendly Xwindows frontend is part of the package. xloops relies on the application of parallel space techniques. The treatment of tensor structure and the separation of divergences in analytic expressions is described in this scheme. All analytic calculations are performed with Maple. We describe the mathematical methods and computer algebra techniques xloops uses and give a brief introduction how to …
Module categories of finite Hopf algebroids, and self-duality
2017
International audience; We characterize the module categories of suitably finite Hopf algebroids (more precisely, $X_R$-bialgebras in the sense of Takeuchi (1977) that are Hopf and finite in the sense of a work by the author (2000)) as those $k$-linear abelian monoidal categories that are module categories of some algebra, and admit dual objects for "sufficiently many" of their objects. Then we proceed to show that in many situations the Hopf algebroid can be chosen to be self-dual, in a sense to be made precise. This generalizes a result of Pfeiffer for pivotal fusion categories and the weak Hopf algebras associated to them.
Architettura e argenteria in Sicilia: alcune considerazioni
2008
Il rapporto tra argenteria e architettura, in Sicilia come in molti altri centri d'Europa, appare intrecciato e problematico e investe una serie di aspetti non omogenei. La continuità o la trasmigrazione professionale è del resto un fenomeno che coinvolge ulteriori circuiti artistici: dalla pittura alla scultura, dall'incisione all'ebanisteria.
Grounding concepts as emerging clusters in multiple conceptual spaces
2018
A novel framework for symbol grounding in artificial agents is presented, which relies on the key idea that concepts "emerge" implicitly at the perceptual level as clusters of points with similar features forming homogeneous regions in multiple perceptual Conceptual Spaces (pCS). Such spaces describe percepts such as color, texture, shape, and position that in turn are the properties of the objects populating the agent's environment. Objects are represented in a suitable object Conceptual Space where all their features are composed together again using clustering in pCSs. Symbols will be learned from such a tensor space. A detailed description of both the framework and its theoretical found…
La sfera d’oro di Palazzo Abatellis e gli ostensori con smalti, gemme, coralli del Barocco siciliano
2018
Si analizza la raffinata produzione di opere di oreficeria siciliana del XVII secolo, tra cui i preziosi ostensori con coralli, smalti e gemme eseguiti da abili maestri, come don Camillo Barbavara e i fratelli Montalbano, e ci si sofferma sull'utilizzo degli smalti ad imitazione delle pietre preziose, come confermano ulteriormente inediti documenti Itanalyzes the fine production of Sicilian goldsmith's works of the seventeenth century, including the precious ostensories with corals, enamels and gems made by skilled masters, suchas Don Camillo Barbavara and the Montalbano brothers, and it focuses on the use of enamels in imitation of precious stones, as further confirmed by unpublished docum…