Transport in the random Kronig-Penney model

The Kronig-Penney model with random Dirac potentials on the lattice \ZM has critical energies at which the Lyapunov exponent vanishes and the density of states has a van Hove singularity. This leads to a non-trivial quantum diffusion even though the spectrum is known to be pure-point

Antidepressant drugs and the response in the placebo group: the real problem lies in our understanding of the issue

In a recent paper, Horder and colleagues (Horder et al., 2010, J Psychopharmacol 25: 1277–1288) have suggested that the mainproblem in the Kirsch analysis is methodological. We argue that the results are similar irrespective of the method used. In our opinion the data suggest that placebo and drug effects are non-additive: antidepressants act independently of depression severity, while the placebo effect is present only in milder cases. While the response in the placebo group is due to unstable ‘noise’ and ‘artefacts’, the medication effect is reliable, valid and stable

Dance training shapes action perception and its neural implementation within the young and older adult brain

How we perceive others in action is shaped by our prior experience. Many factors influence brain responses when observing others in action, including training in a particular physical skill, such as sport or dance, and also general development and aging processes. Here, we investigate how learning a complex motor skill shapes neural and behavioural responses among a dance-naïve sample of 20 young and 19 older adults. Across four days, participants physically rehearsed one set of dance sequences, observed a second set, and a third set remained untrained. Functional MRI was obtained prior to and immediately following training. Participants’ behavioural performance on motor and visual tasks improved across the training period, with younger adults showing steeper performance gains than older adults. At the brain level, both age groups demonstrated decreased sensorimotor cortical engagement after physical training, with younger adults showing more pronounced decreases in inferior parietal activity compared to older adults. Neural decoding results demonstrate that among both age groups, visual and motor regions contain experience-specific representations of new motor learning. By combining behavioural measures of performance with univariate and multivariate measures of brain activity, we can start to build a more complete picture of age-related changes in experience-dependent plasticity

A rigorous approach to the magnetic response in disordered systems

This paper is a part of an ongoing study on the diamagnetic behavior of a 3-dimensional quantum gas of non-interacting charged particles subjected to an external uniform magnetic field together with a random electric potential. We prove the existence of an almost-sure non-random thermodynamic limit for the grand-canonical pressure, magnetization and zero- field orbital magnetic susceptibility. We also give an explicit formulation of these thermodynamic limits. Our results cover a wide class of physically relevant random potentials which model not only crystalline disordered solids, but also amorphous solids.Comment: 35 pages. Revised version. Accepted for publication in RM

Positivity of Lyapunov exponents for a continuous matrix-valued Anderson model

We study a continuous matrix-valued Anderson-type model. Both leading Lyapunov exponents of this model are proved to be positive and distinct for all ernergies in $(2,+\infty)$ except those in a discrete set, which leads to absence of absolutely continuous spectrum in $(2,+\infty)$. This result is an improvement of a previous result with Stolz. The methods, based upon a result by Breuillard and Gelander on dense subgroups in semisimple Lie groups, and a criterion by Goldsheid and Margulis, allow for singular Bernoulli distributions

Extended path-indexing

The performance of a theorem prover crucially depends on the speed of the basic retrieval operations, such as finding terms that are unifiable with (instances of, or more general than) some query term. Among the known indexing methods for term retrieval in deduction systems, Path--Indexing exhibits a good performance in general. However, as Path--Indexing is not a perfect filter, the candidates found by this method have still to be subjected to a unification algorithm in order to detect occur--check failures and indirect clashes. As perfect filters, discrimination trees and abstraction trees thus outperform Path--Indexing in some cases. We present an improved version of Path--Indexing that provides both the query trees and the Path--Index with indirect clash an occur--check information. Thus compared to the standard method we dismiss much more terms as possible candidates

From Poincare to affine invariance: How does the Dirac equation generalize?

A generalization of the Dirac equation to the case of affine symmetry, with SL(4,R) replacing SO(1,3), is considered. A detailed analysis of a Dirac-type Poincare-covariant equation for any spin j is carried out, and the related general interlocking scheme fulfilling all physical requirements is established. Embedding of the corresponding Lorentz fields into infinite-component SL(4,R) fermionic fields, the constraints on the SL(4,R) vector-operator generalizing Dirac's gamma matrices, as well as the minimal coupling to (Metric-)Affine gravity are studied. Finally, a symmetry breaking scenario for SA(4,R) is presented which preserves the Poincare symmetry.Comment: 34 pages, LaTeX2e, 8 figures, revised introduction, typos correcte

In-orbit Vignetting Calibrations of XMM-Newton Telescopes

We describe measurements of the mirror vignetting in the XMM-Newton Observatory made in-orbit, using observations of SNR G21.5-09 and SNR 3C58 with the EPIC imaging cameras. The instrument features that complicate these measurements are briefly described. We show the spatial and energy dependences of measured vignetting, outlining assumptions made in deriving the eventual agreement between simulation and measurement. Alternate methods to confirm these are described, including an assessment of source elongation with off-axis angle, the surface brightness distribution of the diffuse X-ray background, and the consistency of Coma cluster emission at different position angles. A synthesis of these measurements leads to a change in the XMM calibration data base, for the optical axis of two of the three telescopes, by in excess of 1 arcminute. This has a small but measureable effect on the assumed spectral responses of the cameras for on-axis targets.Comment: Accepted by Experimental Astronomy. 26 pages, 18 figure

Inverse Scattering for Gratings and Wave Guides

We consider the problem of unique identification of dielectric coefficients for gratings and sound speeds for wave guides from scattering data. We prove that the "propagating modes" given for all frequencies uniquely determine these coefficients. The gratings may contain conductors as well as dielectrics and the boundaries of the conductors are also determined by the propagating modes.Comment: 12 page