Variable Metric Random Pursuit

We consider unconstrained randomized optimization of smooth convex objective functions in the gradient-free setting. We analyze Random Pursuit (RP) algorithms with fixed (F-RP) and variable metric (V-RP). The algorithms only use zeroth-order information about the objective function and compute an approximate solution by repeated optimization over randomly chosen one-dimensional subspaces. The distribution of search directions is dictated by the chosen metric. Variable Metric RP uses novel variants of a randomized zeroth-order Hessian approximation scheme recently introduced by Leventhal and Lewis (D. Leventhal and A. S. Lewis., Optimization 60(3), 329--245, 2011). We here present (i) a refined analysis of the expected single step progress of RP algorithms and their global convergence on (strictly) convex functions and (ii) novel convergence bounds for V-RP on strongly convex functions. We also quantify how well the employed metric needs to match the local geometry of the function in order for the RP algorithms to converge with the best possible rate. Our theoretical results are accompanied by numerical experiments, comparing V-RP with the derivative-free schemes CMA-ES, Implicit Filtering, Nelder-Mead, NEWUOA, Pattern-Search and Nesterov's gradient-free algorithms.Comment: 42 pages, 6 figures, 15 tables, submitted to journal, Version 3: majorly revised second part, i.e. Section 5 and Appendi

In Defence of Modest Doxasticism About Delusions

Here I reply to the main points raised by the commentators on the arguments put forward in my Delusions and Other Irrational Beliefs (OUP, 2009). My response is aimed at defending a modest doxastic account of clinical delusions, and is articulated in three sections. First, I consider the view that delusions are in-between perceptual and doxastic states, defended by Jacob Hohwy and Vivek Rajan, and the view that delusions are failed attempts at believing or not-quite-beliefs, proposed by Eric Schwitzgebel and Maura Tumulty. Then, I address the relationship between the doxastic account of delusions and the role, nature, and prospects of folk psychology, which is discussed by Dominic Murphy, Keith Frankish, and Maura Tumulty in their contributions. In the final remarks, I turn to the continuity thesis and suggest that, although there are important differences between clinical delusions and non-pathological beliefs, these differences cannot be characterised satisfactorily in epistemic terms. \u

Effect of initial spin polarization on spin dephasing and electron g factor in a high-mobility two-dimensional electron system

We have investigated the spin dynamics of a high-mobility two-dimensional electron system (2DES) in a GaAs--Al$_{0.3}$Ga$_{0.7}$As single quantum well by time-resolved Faraday rotation (TRFR) in dependence on the initial degree of spin polarization, $P$, of the 2DES. From $P\sim 0$ to $P\sim 30$ %, we observe an increase of the spin dephasing time, $T_2^\ast$, by an order of magnitude, from about 20 ps to 200 ps, in good agreement with theoretical predictions by Weng and Wu [Phys. Rev. B {\bf 68}, 075312 (2003)]. Furthermore, by applying an external magnetic field in the Voigt configuration, also the electron $g$ factor is found to decrease for increasing $P$. Fully microscopic calculations, by numerically solving the kinetic spin Bloch equations considering the D'yakonov-Perel' and the Bir-Aronov-Pikus mechanisms, reproduce the most salient features of the experiments, {\em i.e}., a dramatic decrease of spin dephasing and a moderate decrease of the electron $g$ factor with increasing $P$. We show that both results are determined dominantly by the Hartree-Fock contribution of the Coulomb interaction.Comment: 4 pages, 4 figures, to be published in PR

Flat Spacetime Vacuum in Loop Quantum Gravity

We construct a state in the loop quantum gravity theory with zero cosmological constant, which should correspond to the flat spacetime vacuum solution. This is done by defining the loop transform coefficients of a flat connection wavefunction in the holomorphic representation which satisfies all the constraints of quantum General Relativity and it is peaked around the flat space triads. The loop transform coefficients are defined as spin foam state sum invariants of the spin networks embedded in the spatial manifold for the SU(2) quantum group. We also obtain an expression for the vacuum wavefunction in the triad represntation, by defining the corresponding spin networks functional integrals as SU(2) quantum group state sums.Comment: 20 pages, 6 figure

Acceleration Schemes for Ab-Initio Molecular Dynamics and Electronic Structure Calculations

We study the convergence and the stability of fictitious dynamical methods for electrons. First, we show that a particular damped second-order dynamics has a much faster rate of convergence to the ground-state than first-order steepest descent algorithms while retaining their numerical cost per time step. Our damped dynamics has efficiency comparable to that of conjugate gradient methods in typical electronic minimization problems. Then, we analyse the factors that limit the size of the integration time step in approaches based on plane-wave expansions. The maximum allowed time step is dictated by the highest frequency components of the fictitious electronic dynamics. These can result either from the large wavevector components of the kinetic energy or from the small wavevector components of the Coulomb potential giving rise to the so called {\it charge sloshing} problem. We show how to eliminate large wavevector instabilities by adopting a preconditioning scheme that is implemented here for the first-time in the context of Car-Parrinello ab-initio molecular dynamics simulations of the ionic motion. We also show how to solve the charge-sloshing problem when this is present. We substantiate our theoretical analysis with numerical tests on a number of different silicon and carbon systems having both insulating and metallic character.Comment: RevTex, 9 figures available upon request, to appear in Phys. Rev.

Detection of large magneto-anisotropy of electron spin dephasing in a high-mobility two-dimensional electron system in a [001][001] GaAs/AlGaAs quantum well

In time-resolved Faraday rotation experiments we have detected an inplane anisotropy of the electron spin-dephasing time (SDT) in an $n$--modulation-doped GaAs/Al$_{0.3}$Ga$_{0.7}$As single quantum well. The SDT was measured with magnetic fields of $B\le 1$ T, applied in the $[110]$ and $[1\bar{1}0]$ inplane crystal directions of the GaAs quantum well. For fields along $[1\bar{1}0]$, we have found an up to a factor of about 2 larger SDT than in the perpendicular direction. Fully microscopic calculations, by numerically solving the kinetic spin Bloch equations considering the D'yakonov-Perel' and the Bir-Aronov-Pikus mechanisms, reproduce the experimental findings quantitatively. This quantitative analysis of the data allowed us to determine the relative strengths of Rashba and Dresselhaus terms in our sample. Moreover, we could estimate the SDT for spins aligned in the $[110]$ {\em inplane} direction to be on the order of several nanoseconds, which is up to two orders of magnitude larger than that in the perpendicular {\em inplane} direction.Comment: 4 pages, 4 figures, to be published in PR

FAD binding, cobinamide binding and active site communication in the corrin reductase (CobR)

Adenosylcobalamin, the coenzyme form of vitamin B12, is one Nature's most complex coenzyme whose de novo biogenesis proceeds along either an anaerobic or aerobic metabolic pathway. The aerobic synthesis involves reduction of the centrally chelated cobalt metal ion of the corrin ring from Co(II) to Co(I) before adenosylation can take place. A corrin reductase (CobR) enzyme has been identified as the likely agent to catalyse this reduction of the metal ion. Herein, we reveal how Brucella melitensis CobR binds its coenzyme FAD (flavin dinucleotide) and we also show that the enzyme can bind a corrin substrate consistent with its role in reduction of the cobalt of the corrin ring. Stopped-flow kinetics and EPR reveal a mechanistic asymmetry in CobR dimer that provides a potential link between the two electron reduction by NADH to the single electron reduction of Co(II) to Co(I)

Intranasal oxytocin reduces provoked symptoms in female patients with posttraumatic stress disorder despite exerting sympathomimetic and positive chronotropic effects in a randomized controlled trial

Background: Posttraumatic stress disorder (PTSD) is a severe psychiatric disease accompanied by neuroendocrine changes such as adrenergic overdrive and hence an elevated cardiovascular morbidity. Current pharmacotherapeutic options for PTSD are less than suboptimal, necessitating the development of PTSD-specific drugs. Although the neuropeptide oxytocin has been repeatedly suggested to be effective in PTSD treatment, there are, to our knowledge, only three studies that have assessed its efficacy on the intensity of PTSD symptoms in PTSD patients - among them one symptom provocation study in male veterans. Methods: To evaluate for the first time how oxytocin influences the intensity of provoked PTSD symptoms and, furthermore, cardiac control in female PTSD patients, we assessed their psychic and cardiac response to trauma-script exposure with and without oxytocin pretreatment in a double-blind randomized placebo-controlled study. We used a within-subject design to study 35 female PTSD patients who received oxytocin and placebo in a 2-week interval. Furthermore, we performed a small pilot study to get an idea of the relation of the stress-modulated endogenous oxytocin levels and heart rate - we correlated oxytocin serum levels with the heart rate of 10 healthy individuals before and after exposure to the Trier Social Stress Test (TSST). Results: Intranasal oxytocin treatment was followed by a reduction of provoked total PTSD symptoms, in particular of avoidance, and by an elevation in baseline and maximum heart rate together with a drop in the pre-ejection period, a marker for sympathetic cardiac control. Furthermore, we found a positive correlation between endogenous oxytocin levels and heart rate both before and after TSST challenge in healthy control subjects. Conclusions: This study provides the first evidence that oxytocin treatment reduces the intensity of provoked PTSD symptoms in female PTSD patients. The small size of both samples and the heterogeneity of the patient sample restrict the generalizability of our findings. Future studies have to explore the gender dependency and the tolerability of the oxytocin- mediated increase in heart rate

Dynamic Structure Factor of Liquid and Amorphous Ge From Ab Initio Simulations

We calculate the dynamic structure factor S(k,omega) of liquid Ge (l-Ge) at temperature T = 1250 K, and of amorphous Ge (a-Ge) at T = 300 K, using ab initio molecular dynamics. The electronic energy is computed using density-functional theory, primarily in the generalized gradient approximation, together with a plane wave representation of the wave functions and ultra-soft pseudopotentials. We use a 64-atom cell with periodic boundary conditions, and calculate averages over runs of up to 16 ps. The calculated liquid S(k,omega) agrees qualitatively with that obtained by Hosokawa et al, using inelastic X-ray scattering. In a-Ge, we find that the calculated S(k,omega) is in qualitative agreement with that obtained experimentally by Maley et al. Our results suggest that the ab initio approach is sufficient to allow approximate calculations of S(k,omega) in both liquid and amorphous materials.Comment: 31 pages and 8 figures. Accepted for Phys. Rev.