Descent properties of hermitian Witt groups in inseparable extensions

Let k be a field of characteristic ≠ 2, A be a central simple algebra with involution σ over k and W(A, σ) be the associated Witt group of hermitian forms. We prove that for all purely inseparable extensions L of k, the canonical map $${r_{L/k}: W(A, \sigma) \longrightarrow W(A_L, \sigma_L)}$$ is an isomorphis

Cogex: A semantically and contextually enriched logic prover for question answering

AbstractThis paper presents the architecture and functionality of a logic prover designed for question answering. The approach transforms questions and answer passages into logic representations based on syntactic, semantic and contextual information. World knowledge supplements the linguistic, ontological, and temporal axioms supplied to the prover which renders a deep understanding of the relationship between the question and answer text. The trace of the proofs provides a basis for generating human comprehensible answer justifications. The results show that the prover boosts the performance of the Question Answering system on TREC 2004 questions by 12%

A Heuristic Computational Model of Basic Cellular Processes and Oxygenation during Spheroid-Dependent Biofabrication

An emerging approach in biofabrication is the creation of 3D tissue constructs through scaffold-free, cell spheroid-only methods. The basic mechanism in this technology is spheroid fusion, which is driven by the minimization of energy, the same biophysical mechanism that governs spheroid formation. However, other factors such as oxygen and metabolite accessibility within spheroids impact on spheroid properties and their ability to form larger-scale structures. The goal of our work is to develop a simulation platform eventually capable of predicting the conditions that minimize metabolism-related cell loss within spheroids. To describe the behavior and dynamic properties of the cells in response to their neighbors and to transient nutrient concentration fields, we developed a hybrid discrete-continuous heuristic model, combining a cellular Potts-type approach with field equations applied to a randomly populated spheroid cross-section of prescribed cell-type constituency. This model allows for the description of: (i) cellular adhesiveness and motility; (ii) interactions with concentration fields, including diffusivity and oxygen consumption; and (iii) concentration-dependent, stochastic cell dynamics, driven by metabolite-dependent cell death. Our model readily captured the basic steps of spheroid-based biofabrication (as specifically dedicated to scaffold-free bioprinting), including intra-spheroid cell sorting (both in 2D and 3D implementations), spheroid defect closure, and inter-spheroid fusion. Moreover, we found that when hypoxia occurring at the core of the spheroid was set to trigger cell death, this was amplified upon spheroid fusion, but could be mitigated by external oxygen supplementation. In conclusion, optimization and further development of scaffold-free bioprinting techniques could benefit from our computational model which is able to simultaneously account for both cellular dynamics and metabolism in constructs obtained by scaffold-free biofabrication

Descent properties of hermitian Witt groups in inseparable extensions

Let k be a field of characteristic ≠2, A be a central simple algebra with involution σ over k and W(A,σ) be the associated Witt group of hermitian forms. We prove that for all purely inseparable extensions L of k, the canonical map rL/k:W(A,σ)⟶W(AL,σL) is an isomorphism

Sesquilinear forms over rings with involution

Many classical results concerning quadratic forms have been extended to Hermitian forms over algebras with involution. However, not much is known in the case of sesquilinear forms without any symmetry property. The present paper will establish a Witt cancellation result, an analogue of Springer's theorem, as well as some local-global and finiteness results in this context. (C) 2013 Elsevier B.V. All rights reserved

Metal-assisted etching of silicon molds for electroforming

Ordered arrays of high-aspect-ratio micro/nanostructures in semiconductors stirred a huge scientific interest due to their unique one-dimensional physical morphology and the associated electrical, mechanical, chemical, optoelectronic, and thermal properties. Metal-assisted chemical etching enables fabrication of such high aspect ratio Si nanostructures with controlled diameter, shape, length, and packing density, but suffers from structure deformation and shape inconsistency due to uncontrolled migration of noble metal structures during etching. Hereby the authors prove that a Ti adhesion layer helps in stabilizing gold structures, preventing their migration on the wafer surface while not impeding the etching. Based on this finding, the authors demonstrate that the method can be used to fabricate linear Fresnel zone plates

Laplace inversions applied to multi–component T 2 – T 2 exchange experiments

Two-dimensional (2D) T2-T2 molecular exchange NMR experiments with a period of magnetization storage between the two T2 relaxation encoding periods are presented. The two-dimensional time map was inverted using a fast Laplace algorithm to obtain the T2–T2 exchange map. T2–MZ(store)–T2 2D 1H NMR spectra recorded at high and low homogeneous magnetic fields of water and oil in sand, air bubbles in water and foams, exchange of liquid / foam and liquid / saturated vapours of chloroform are presented. Uni– and bi–directional exchange was observed for bubbles in water, superficial liquid shell, and foam