Neural Network Methods for Boundary Value Problems Defined in Arbitrarily Shaped Domains

Partial differential equations (PDEs) with Dirichlet boundary conditions defined on boundaries with simple geometry have been succesfuly treated using sigmoidal multilayer perceptrons in previous works. This article deals with the case of complex boundary geometry, where the boundary is determined by a number of points that belong to it and are closely located, so as to offer a reasonable representation. Two networks are employed: a multilayer perceptron and a radial basis function network. The later is used to account for the satisfaction of the boundary conditions. The method has been successfuly tested on two-dimensional and three-dimensional PDEs and has yielded accurate solutions

Synthesis and photolytic evaluation of a nitroindoline-caged glycine with a side chain of high negative charge for use in neuroscience

A photolabile precursor of the neuroinhibitory amino acid glycine has been synthesised with two phosphate groups attached to the indoline nucleus at a 4-alkoxy substituent. In common with the photochemical properties of other 1-acyl-7-nitroindolines, this releases glycine on a sub-is time scale upon irradiation with near-UV light. The synthetic route previously developed for the preparation of the GABA analogue required some modifications because of the greater hydrolytic sensitivity of the glycine compound. The phosphorylation method used here could be beneficial to the synthesis of other nitroindoline-caged amino acids, especially the related caged GABA derivative. Glycine released by laser photolysis on spinal cord neurons generated fast-rising responses and the pharmacological properties of the reagent are such that it is useful for physiological experiments

An alternative characterization of MAR in shared parameter models for incomplete longitudinal data and its utili

Dropout is a common complication in longitudinal studies, especially since the distinction between missing not at random (MNAR) and missing at random (MAR) dropout is intractable. Consequently, one starts with an analysis that is valid under MAR and then performs a sensitivity analysis by considering MNAR departures from it. To this end, specific classes of joint models, such as pattern-mixture models (PMMs) and selection models (SeMs), have been proposed. On the contrary, shared-parameter models (SPMs) have received less attention, possibly because they do not embody a characterization of MAR. A few approaches to achieve MAR in SPMs exist, but are difficult to implement in existing software. In this article, we focus on SPMs for incomplete longitudinal and time-to-dropout data and propose an alternative characterization of MAR by exploiting the conditional independence assumption, under which outcome and missingness are independent given a set of random effects. By doing so, the censoring distribution can be utilized to cover a wide range of assumptions for the missing data mechanism on the subject-specific level. This approach offers substantial advantages over its counterparts and can be easily implemented in existing software. More specifically, it offers flexibility over the assumption for the missing data generating mechanism that governs dropout by allowing subject-specific perturbations of the censoring distribution, whereas in PMMs and SeMs dropout is considered MNAR strictly

Noise induced state transitions, intermittency and universality in the noisy Kuramoto-Sivashinsky equation

We analyze the effect of pure additive noise on the long-time dynamics of the noisy Kuramoto-Sivashinsky (KS) equation in a regime close to the instability onset. We show that when the noise is highly degenerate, in the sense that it acts only on the first stable mode, the solution of the KS equation undergoes several transitions between different states, including a critical on-off intermittent state that is eventually stabilized as the noise strength is increased. Such noise-induced transitions can be completely characterized through critical exponents, obtaining that both the KS and the noisy Burgers equation belong to the same universality class. The results of our numerical investigations are explained rigorously using multiscale techniques.Comment: 4 pages, 4 figure

A qq-anaolg of the sixth Painlev\'e equation

A $q$-difference analog of the sixth Painlev\'e equation is presented. It arises as the condition for preserving the connection matrix of linear $q$-difference equations, in close analogy with the monodromy preserving deformation of linear differential equations. The continuous limit and special solutions in terms of $q$-hypergeometric functions are also discussed.Comment: 8 pages, LaTeX file (Two misprints corrected

Selective Reflection Spectroscopy on the UV Third Resonance Line of Cs : Simultaneous Probing of a van der Waals Atom-Surface Interaction Sensitive to Far IR Couplings and of Interatomic Collisions

We report on the analysis of FM selective reflection experiments on the 6S1/2->8P3/2 transition of Cs at 388 nm, and on the measurement of the surface van der Waals interaction exerted by a sapphire interface on Cs(8P3/2). Various improvements in the systematic fitting of the experiments have permitted to supersede the major difficulty of a severe overlap of the hyperfine components, originating on the one hand in a relatively small natural structure, and on the other hand on a large pressure broadening imposed by the high atomic density needed for the observation of selective reflection on a weak transition. The strength of the van der Waals surface interaction is evaluated to be 73$\pm$10 kHz.$\mu$m3. An evaluation of the pressure shift of the transition is also provided as a by-product of the measurement. We finally discuss the significance of an apparent disagreement between the experimental measurement of the surface interaction, and the theoretical value calculated for an electromagnetic vacuum at a null temperature. The possible influence of the thermal excitation of the surface is evoked, because, the dominant contributions to the vW interaction for Cs(8P3/2) lie in the far infrared range.Comment: submitted to Laser Physics - issue in the memory of Herbert Walther

Infinitely many symmetries and conservation laws for quad-graph equations via the Gardner method

The application of the Gardner method for generation of conservation laws to all the ABS equations is considered. It is shown that all the necessary information for the application of the Gardner method, namely B\"acklund transformations and initial conservation laws, follow from the multidimensional consistency of ABS equations. We also apply the Gardner method to an asymmetric equation which is not included in the ABS classification. An analog of the Gardner method for generation of symmetries is developed and applied to discrete KdV. It can also be applied to all the other ABS equations

Controlling spatiotemporal chaos in active dissipative-dispersive nonlinear systems

We present a new methodology for the stabilization and control of infinite-dimensional dynamical systems exhibiting low-dimensional spatiotemporal chaos. We show that with an appropriate choice of time-dependent controls we are able to stabilize and/or control all stable or unstable solutions, including steady solutions, traveling waves (single and multipulse ones/bound states) and spatiotemporal chaos. We exemplify our methodology with the generalized Kuramoto-Sivashinsky equation, a paradigmatic model of spatiotemporal chaos, which is known to exhibit a rich spectrum of wave forms and wave transitions and a rich variety of spatiotemporal structures

The development of planar Gunn diodes for the realisation of MMIC oscillators

This review presents the development of planar Gunn diodes over the last few years for the implementation of millimetre-wave sources. The fabrication procedure incorporates electron beam lithography and the oscillation frequency is determined by the anode-to-cathode distance. The evolution of the material design for the maximisation of the maximum frequency of oscillation and the enhancement of the generated power is presented in this paper. The recent implementation of a planar Gunn diode with a high-electron mobility transistor on the same substrate is also described in this work

High-Spatial-Resolution Monitoring of Strong Magnetic Field using Rb vapor Nanometric-Thin Cell

We have implemented the so-called $\lambda$-Zeeman technique (LZT) to investigate individual hyperfine transitions between Zeeman sublevels of the Rb atoms in a strong external magnetic field $B$ in the range of $2500 - 5000$ G (recently it was established that LZT is very convenient for the range of $10 - 2500$ G). Atoms are confined in a nanometric thin cell (NTC) with the thickness $L = \lambda$, where $\lambda$ is the resonant wavelength 794 nm for Rb $D_1$ line. Narrow velocity selective optical pumping (VSOP) resonances in the transmission spectrum of the NTC are split into several components in a magnetic field with the frequency positions and transition probabilities depending on the $B$-field. Possible applications are described, such as magnetometers with nanometric local spatial resolution and tunable atomic frequency references.Comment: 12 page