Meromorphy and topology of localized solutions in the Thomas–MHD model

The one-dimensional MHD system first introduced by J.H. Thomas [Phys. Fluids 11, 1245 (1968)] as a model of the dynamo effect is thoroughly studied in the limit of large magnetic Prandtl number. The focus is on two types of localized solutions involving shocks (antishocks) and hollow (bump) waves. Numerical simulations suggest phenomenological rules concerning their generation, stability and basin of attraction. Their topology, amplitude and thickness are compared favourably with those of the meromorphic travelling waves, which are obtained exactly, and respectively those of asymptotic descriptions involving rational or degenerate elliptic functions. The meromorphy bars the existence of certain configurations, while others are explained by assuming imaginary residues. These explanations are tested using the numerical amplitude and phase of the Fourier transforms as probes of the analyticity properties. Theoretically, the proof of the partial integrability backs up the role ascribed to meromorphy. Practically, predictions are derived for MHD plasmas

Discrete Q- and P-symbols for spin s

Non-orthogonal bases of projectors on coherent states are introduced to expand Hermitean operators acting on the Hilbert space of a spin s. It is shown that the expectation values of a Hermitean operator (A) over cap in a family of (2s + 1)(2) spin-coherent states determine the operator unambiguously. In other words, knowing the Q-symbol of (A) over cap at (2s + 1)(2) points on the unit sphere is already sufficient in order to recover the operator. This provides a straightforward method to reconstruct the mixed state of a spin since its density matrix is explicitly parametrized in terms of expectation values. Furthermore, a discrete P-symbol emerges naturally which is related to a basis dual to the original one

Inverse Covariance Estimation for High-Dimensional Data in Linear Time and Space: Spectral Methods for Riccati and Sparse Models

We propose maximum likelihood estimation for learning Gaussian graphical models with a Gaussian (ell_2^2) prior on the parameters. This is in contrast to the commonly used Laplace (ell_1) prior for encouraging sparseness. We show that our optimization problem leads to a Riccati matrix equation, which has a closed form solution. We propose an efficient algorithm that performs a singular value decomposition of the training data. Our algorithm is O(NT^2)-time and O(NT)-space for N variables and T samples. Our method is tailored to high-dimensional problems (N gg T), in which sparseness promoting methods become intractable. Furthermore, instead of obtaining a single solution for a specific regularization parameter, our algorithm finds the whole solution path. We show that the method has logarithmic sample complexity under the spiked covariance model. We also propose sparsification of the dense solution with provable performance guarantees. We provide techniques for using our learnt models, such as removing unimportant variables, computing likelihoods and conditional distributions. Finally, we show promising results in several gene expressions datasets.Comment: Appears in Proceedings of the Twenty-Ninth Conference on Uncertainty in Artificial Intelligence (UAI2013

High-heeled shoes and musculoskeletal injuries : a narrative systematic review

Funding This research received no specific grant from any funding agency in the public, commercial or not-for-profit sectors.Peer reviewedPublisher PD

Event reconstruction in high resolution Compton telescopes

The development of germanium Compton telescopes for nuclear gamma-ray astrophysics (~0.2-20 MeV) requires new event reconstruction techniques to accurately determine the initial direction and energy of photon events, as well as to consistently reject background events. This paper describes techniques for event reconstruction, accounting for realistic instrument/detector performance and uncertainties. An especially important technique is Compton Kinematic Discrimination, which allows proper interaction ordering and background rejection with high probabilities. The use of these techniques are crucial for the realistic evaluation of the performance and sensitivity of any germanium Compton telescope configuration.Comment: Accepted for publication in A&AS

The development of apologies in the Japanese L2 of adult English native speakers

The present paper focuses on the use of seven apologies strategies in the Japanese of 20 adult, high-intermediate English learners/users of Japanese. Nine of these learners had spent a minimum of two years in Japan. The proportions of apology strategies produced by the two groups of learners in response to 8 situations presented to them in a Discourse Completion Test (DCT) were compared with data obtained from a control group of 14 Japanese L1 participants and a control group of 12 British English L1 participants. In total, 1999 tokens of apology strategies were collected. Statistical analyses and an analysis of lexical items allowed us to describe the learners‟ development and the effect of the stay in Japan

Linear elastic fracture mechanics predicts the propagation distance of frictional slip

When a frictional interface is subject to a localized shear load, it is often (experimentally) observed that local slip events initiate at the stress concentration and propagate over parts of the interface by arresting naturally before reaching the edge. We develop a theoretical model based on linear elastic fracture mechanics to describe the propagation of such precursory slip. The model's prediction of precursor lengths as a function of external load is in good quantitative agreement with laboratory experiments as well as with dynamic simulations, and provides thereby evidence to recognize frictional slip as a fracture phenomenon. We show that predicted precursor lengths depend, within given uncertainty ranges, mainly on the kinetic friction coefficient, and only weakly on other interface and material parameters. By simplifying the fracture mechanics model we also reveal sources for the observed non-linearity in the growth of precursor lengths as a function of the applied force. The discrete nature of precursors as well as the shear tractions caused by frustrated Poisson's expansion are found to be the dominant factors. Finally, we apply our model to a different, symmetric set-up and provide a prediction of the propagation distance of frictional slip for future experiments