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Register a new userThe Tensorial Connections
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Authors
Luca Fabbri
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In a series of recent papers, we have introduced an object that was constructed on the connection but which was proven to be a tensor: this object, thus called tensorial connection, has been defined and some of its properties have been given. In the present paper, we intend to present all the results found so far, complementing them with some new ones, in a systematic and organic manner.
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The analysis of correlations between fluctuations of alpha- and beta-decay rates for different radio-active elements is carried out. These fluctuations exceed significantly errors of measurements in many cases. They have the periodical character and reveal definite spatial directions. We suggest that the observed fluctuations are caused by the unique physical reason connected with the global anisotropy of physical space and by the new force.
We describe a tensorial generalization of the Navier slip boundary condition and illustrate its use in solving for flows around anisotropic textured surfaces. Tensorial slip can be derived from molecular or microstructural theories or simply postulated as an constitutive relation, subject to certain general constraints on the interfacial mobility. The power of the tensor formalism is to capture complicated effects of surface anisotropy, while preserving a simple fluid domain. This is demonstrated by exact solutions for laminar shear flow and pressure-driven flow between parallel plates of arbitrary and different textures. From such solutions, the effects of rotating a texture follow from simple matrix algebra. Our results may be useful to extracting local slip tensors from global measurements, such as the permeability of a textured channel or the force required to move a patterned surface, in experiments or simulations.
Casting neural networks in generative frameworks is a highly sought-after endeavor these days. Contemporary methods, such as Generative Adversarial Networks, capture some of the generative capabilities, but not all. In particular, they lack the ability of tractable marginalization, and thus are not suitable for many tasks. Other methods, based on arithmetic circuits and sum-product networks, do allow tractable marginalization, but their performance is challenged by the need to learn the structure of a circuit. Building on the tractability of arithmetic circuits, we leverage concepts from tensor analysis, and derive a family of generative models we call Tensorial Mixture Models (TMMs). TMMs assume a simple convolutional network structure, and in addition, lend themselves to theoretical analyses that allow comprehensive understanding of the relation between their structure and their expressive properties. We thus obtain a generative model that is tractable on one hand, and on the other hand, allows effective representation of rich distributions in an easily controlled manner. These two capabilities are brought together in the task of classification under missing data, where TMMs deliver state of the art accuracies with seamless implementation and design.
We have analyzed the electron anti-neutrino scattering off electrons and the electron anti-neutrino-nuclei coherent scattering in order to obtain constraints on tensorial couplings. We have studied the formalism of non-standard interactions (NSI), as well as the case of Unparticle physics. For our analysis we have focused on the recent TEXONO collaboration results and we have obtained current constraints to possible electron anti-neutrino-electron tensorial couplings in both new physics formalisms. The possibility of measuring for the first time electron anti-neutrino-nucleus coherent scattering and its potential to further constrain electron anti-neutrino-quark tensorial couplings is also discussed.
Within the lowest-order relativistic approximation ($sim v^2/c^2$) and to first order in $m_e/M$, the tensorial form of the relativistic corrections of the nuclear recoil Hamiltonian is derived, opening interesting perspectives for calculating isotope shifts in the multiconfiguration Dirac-Hartree-Fock framework. Their calculation is illustrated for selected Li-, B- and C-like ions. The present work underlines the fact that the relativistic corrections to the nuclear recoil are definitively necessary for getting reliable isotope shift values.
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