Continuity of the spectra for families of magnetic operators on Z^d

For families of magnetic self-adjoint operators on ${\mathbb Z}^d$ whose symbols and magnetic fields depend continuously on a parameter $\epsilon$, it is shown that the main spectral properties of these operators also vary continuously with respect to $\epsilon$. The proof is based on an algebraic setting involving twisted crossed product C*-algebras.Comment: 13 page

Long-wavelength limit of gyrokinetics in a turbulent tokamak and its intrinsic ambipolarity

Recently, the electrostatic gyrokinetic Hamiltonian and change of coordinates have been computed to order $\epsilon^2$ in general magnetic geometry. Here $\epsilon$ is the gyrokinetic expansion parameter, the gyroradius over the macroscopic scale length. Starting from these results, the long-wavelength limit of the gyrokinetic Fokker-Planck and quasineutrality equations is taken for tokamak geometry. Employing the set of equations derived in the present article, it is possible to calculate the long-wavelength components of the distribution functions and of the poloidal electric field to order $\epsilon^2$. These higher-order pieces contain both neoclassical and turbulent contributions, and constitute one of the necessary ingredients (the other is given by the short-wavelength components up to second order) that will eventually enter a complete model for the radial transport of toroidal angular momentum in a tokamak in the low flow ordering. Finally, we provide an explicit and detailed proof that the system consisting of second-order gyrokinetic Fokker-Planck and quasineutrality equations leaves the long-wavelength radial electric field undetermined; that is, the turbulent tokamak is intrinsically ambipolar.Comment: 70 pages. Typos in equations (63), (90), (91), (92) and (129) correcte

Non-hermitian approach to decaying ultracold bosonic systems

A paradigm model of modern atom optics is studied, strongly interacting ultracold bosons in an optical lattice. This many-body system can be artificially opened in a controlled manner by modern experimental techniques. We present results based on a non-hermitian effective Hamiltonian whose quantum spectrum is analyzed. The direct access to the spectrum of the metastable many-body system allows us to easily identify relatively stable quantum states, corresponding to previously predicted solitonic many-body structures

Stellarator bootstrap current and plasma flow velocity at low collisionality

The bootstrap current and flow velocity of a low-collisionality stellarator plasma are calculated. As far as possible, the analysis is carried out in a uniform way across all low-collisionality regimes in general stellarator geometry, assuming only that the confinement is good enough that the plasma is approximately in local thermodynamic equilibrium. It is found that conventional expressions for the ion flow speed and bootstrap current in the low-collisionality limit are accurate only in the $1/\nu$-collisionality regime and need to be modified in the $\sqrt{\nu}$-regime. The correction due to finite collisionality is also discussed and is found to scale as $\nu^{2/5}$

What memory binding functions is the hippocampus responsible for?

The role of the hippocampus in binding information in working memory (WM) is little understood. When complex experiences comprise associations between different pieces of information such as objects and locations (relational binding), the function of the hippocampus is required to hold them in WM (Mitchell et al., 2000; 2006; Piekema, 2006). However, recent evidence suggests that if the to-be-associated information leads to the formation of integrated objects such as coloured shapes (conjunctive binding), the hippocampus is less involved in holding temporary representations of these complex events in WM (Baddeley et al., 2010; Piekema, 2006). We investigated the relational and conjunctive binding hypotheses of the hippocampal functions in a patient with right hippocampal damage. The patient and controls were asked to study visual arrays of stimuli which consisted of shape-colour relations (shape-colour pairs) or shape-colour conjunctions (coloured shapes). After the study array, they were presented with a new screen consisting of one set of shapes (line drawings) and one set of colours. They were asked to reconstruct the bindings by selecting the shapes and their corresponding colours. As compared to healthy controls, the patient was impaired in holding relations of shapes and colours in WM whereas he could retain the conjunctions similarly to controls. These results lend support to the role of the hippocampus in supporting memory for inter-item associations but not memory for conjunctions of features which define objects' identity

Quantitative Stability and Optimality Conditions in Convex Semi-Infinite and Infinite Programming

This paper concerns parameterized convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional Banach (resp. finite-dimensional) spaces and that are indexed by an arbitrary fixed set T . Parameter perturbations on the right-hand side of the inequalities are measurable and bounded, and thus the natural parameter space is $l_{\infty}(T)$. Based on advanced variational analysis, we derive a precise formula for computing the exact Lipschitzian bound of the feasible solution map, which involves only the system data, and then show that this exact bound agrees with the coderivative norm of the aforementioned mapping. On one hand, in this way we extend to the convex setting the results of [4] developed in the linear framework under the boundedness assumption on the system coefficients. On the other hand, in the case when the decision space is reflexive, we succeed to remove this boundedness assumption in the general convex case, establishing therefore results new even for linear infinite and semi-infinite systems. The last part of the paper provides verifiable necessary optimality conditions for infinite and semi-infinite programs with convex inequality constraints and general nonsmooth and nonconvex objectives. In this way we extend the corresponding results of [5] obtained for programs with linear infinite inequality constraints

Short-term memory binding in mild cognitive impairment

We showed that short-term memory (STM) binding is sensitive to sporadic and familial Alzheimer's disease (AD) but is not affected by healthy ageing, chronic depression in the elderly or other forms of dementia. STM binding deficits were also observed in individuals with a genetic susceptibility for AD in the preclinical stages. Hence, we aim to investigate longitudinally individuals with Mild Cognitive Impairment (MCI) using STM binding tasks. Here we report on preliminary cross-sectional results. A comprehensive neuropsychological test battery and a visual STM task were given to 21 MCI patients and 20 controls. The STM task required participants to recognise changes across two consecutive arrays presenting either single features (colour or shape) or feature bindings. The MCI group performed significantly poorer than controls on standard tests of memory, attention and on the binding condition of the STM task, but not on single feature conditions. Performance on the binding task and on standard memory tests did not correlate. Eight MCI patients clearly performed outwith the range of normality in the binding task. However, they did not significantly differ from the other 13 MCI patients in disease severity or demographic and neuropsychological variables. Six patients with binding impairments showed a multiple domain profile whereas ten patients with a preserved binding function showed an amnesic profile [Chi-square = 5.45, p = 0.020]. These results suggest that (1) the binding task is assessing a function different from other memory tests and that (2) STM binding may be differentially impaired in MCI subgroups