Comparison of Gaussian process modeling software

Gaussian process fitting, or kriging, is often used to create a model from a set of data. Many available software packages do this, but we show that very different results can be obtained from different packages even when using the same data and model. We describe the parameterization, features, and optimization used by eight different fitting packages that run on four different platforms. We then compare these eight packages using various data functions and data sets, revealing that there are stark differences between the packages. In addition to comparing the prediction accuracy, the predictive variance--which is important for evaluating precision of predictions and is often used in stopping criteria--is also evaluated

Comprehensive theory of the relative phase in atom-field interactions

We explore the role played by the quantum relative phase in a well-known model of atom-field interaction, namely, the Dicke model. We introduce an appropriate polar decomposition of the atom-field relative amplitudes that leads to a truly Hermitian relative-phase operator, whose eigenstates correctly describe the phase properties, as we demonstrate by studying the positive operator-valued measure derived from it. We find the probability distribution for this relative phase and, by resorting to a numerical procedure, we study its time evolution.Comment: 20 pages, 4 figures, submitted to Phys. Rev.

On the relationship between pump chirp and single-photon chirp in spontaneous parametric downconversion

We study the chronocyclic character, i.e. the joint temporal and spectral properties, of the single-photon constituents of photon pairs generated by spontaneous parametric down conversion. In particular we study how single photon properties, including purity and single-photon chirp, depend on photon pair properties, including the type of signal-idler spectral and correlations and the level of pump chirp.Comment: 13 pages, 6 figure

CXCL12-induced neurotoxicity critically depends on NMDA receptor-gated and L-type Ca2+ channels upstream of p38 MAPK.

BackgroundThe chemokine receptor CXCR4 (CD184) and its natural ligand CXCL12 contribute to many physiological processes, including decisions about cell death and survival in the central nervous system. In addition, CXCR4 is a co-receptor for human immunodeficiency virus (HIV)-1 and mediates the neurotoxicity of the viral envelope protein gp120. However, we previously observed that CXCL12 also causes toxicity in cerebrocortical neurons but the cellular mechanism remained incompletely defined.MethodsPrimary neuronal-glial cerebrocortical cell cultures from rat were exposed to a neurotoxicity-inducing CXCL12 concentration for different times and the activity of the stress-associated mitogen-activated protein kinase p38 (p38 MAPK) was assessed using an in vitro kinase assay. Neurotoxicity of CXCL12 and cellular localization of p38 MAPK was analyzed by immunofluorescence microscopy. Pharmacological inhibition of NMDA-type glutamate receptor-gated ion channels (NMDAR) of L-type Ca2+ channels was employed during 12- and 24-h exposure to neurotoxic amounts of CXCL12 to study the effects on active p38 MAPK and neuronal survival by Western blotting and microscopy, respectively. Neurotoxicity of CXCL12 was also assessed during pharmacological inhibition of p38 MAPK.ResultsHere, we show that a neurotoxic amount of CXCL12 triggers a significant increase of endogenous p38 MAPK activity in cerebrocortical cells. Immunofluorescence and Western blotting experiments with mixed neuronal-glial and neuron-depleted glial cerebrocortical cells revealed that the majority of active/phosphorylated p38 MAPK was located in neurons. Blockade of NMDAR-gated ion channels or L-type Ca2+ channels both abrogated an increase of active p38 MAPK and toxicity of CXCL12 in cerebrocortical neurons. Inhibition of L-type Ca2+ channels with nimodipine kept the active kinase at levels not significantly different from baseline while blocking NMDAR with MK-801 strongly reduced phosphorylated p38 MAPK below baseline. Finally, we confirmed that directly blocking p38 MAPK also abrogated neurotoxicity of CXCL12.ConclusionsOur findings link CXCL12-induced neuronal death to the regulation of NMDAR-gated ion channels and L-type Ca2+ channels upstream of p38 MAPK activation

Continuous Time Random Walks in periodic systems: fluid limit and fractional differential equations on the circle

In this article, the continuous time random walk on the circle is studied. We derive the corresponding generalized master equation and discuss the effects of topology, especially important when Levy flights are allowed. Then, we work out the fluid limit equation, formulated in terms of the periodic version of the fractional Riemann-Liouville operators, for which we provide explicit expressions. Finally, we compute the propagator in some simple cases. The analysis presented herein should be relevant when investigating anomalous transport phenomena in systems with periodic dimensions.Comment: 14 pages, 1 figure. References added. Published versio

High-Tc bolometers with silicon-nitride spiderwebsuspension for far-infrared detection

High-Tc GdBa2Cu3O7-δ (GBCO) superconducting transition edge bolometers with operating temperatures near 90 K have been made with both closed silicon-nitride membranes and patterned silicon-nitride (SiN) spiderweb-like suspension structures. As a substrate silicon-on-nitride (SON) wafers are used which are made by fusion bonding of a silicon wafer to a silicon wafer with a silicon-nitride top layer. The resulting monocrystalline silicon top layer on the silicon-nitride membranes enables the epitaxial growth of GBCO. By patterning the silicon-nitride the thermal conductance G is reduced from about 20 to 3 μW/K. The noise of both types of bolometers is dominated by the intrinsic noise from phonon fluctuations in the thermal conductance G. The optical efficiency in the far infrared is about 75% due to a goldblack absorption layer. The noise equivalent power NEP for FIR detection is 1.8 pW/√Hz, and the detectivity D* is 5.4×1010 cm √Hz/W. Time constants are 0.1 and 0.6 s, for the closed membrane and the spiderweb like bolometers respectively. The effective time constant can be reduced with about a factor 3 by using voltage bias. Further reduction necessarily results in an increase of the NEP due to the 1/f noise of the superconductor

Spontaneous formation of optically induced surface relief gratings

A model based on Fick's law of diffusion as a phenomenological description of the molecular motion, and on the coupled mode theory, is developped to describe single-beam surface relief grating formation in azopolymers thin films. It allows to explain the mechanism of spontaneous patterning, and self-organization. It allows also to compute the surface relief profile and its evolution in time with good agreement with experiments

Current profiles and AC losses of a superconducting strip with elliptic cross-section in perpendicular magnetic field

The case of a hard type II superconductor in the form of strip with elliptic cross-section when placed in transverse magnetic field is studied. We approach the problem in two steps, both based on the critical-state model. First we calculate numerically the penetrated current profiles that ensure complete shielding in the interior, without assuming an a priori form for the profiles. In the second step we introduce an analytical approximation that asumes that the current profiles are ellipses. Expressions linking the sample magnetization to the applied field are derived covering the whole range of applied fields. The theoretical predictions are tested by the comparison with experimental data for the imaginary part of AC susceptibility.Comment: 12 pages; 3 figure

Exponential splitting of bound states in a waveguide with a pair of distant windows

We consider Laplacian in a straight planar strip with Dirichlet boundary which has two Neumann ``windows'' of the same length the centers of which are $2l$ apart, and study the asymptotic behaviour of the discrete spectrum as $l\to\infty$. It is shown that there are pairs of eigenvalues around each isolated eigenvalue of a single-window strip and their distances vanish exponentially in the limit $l\to\infty$. We derive an asymptotic expansion also in the case where a single window gives rise to a threshold resonance which the presence of the other window turns into a single isolated eigenvalue