Discrete Hamilton-Jacobi Theory

We develop a discrete analogue of Hamilton-Jacobi theory in the framework of discrete Hamiltonian mechanics. The resulting discrete Hamilton-Jacobi equation is discrete only in time. We describe a discrete analogue of Jacobi's solution and also prove a discrete version of the geometric Hamilton-Jacobi theorem. The theory applied to discrete linear Hamiltonian systems yields the discrete Riccati equation as a special case of the discrete Hamilton-Jacobi equation. We also apply the theory to discrete optimal control problems, and recover some well-known results, such as the Bellman equation (discrete-time HJB equation) of dynamic programming and its relation to the costate variable in the Pontryagin maximum principle. This relationship between the discrete Hamilton-Jacobi equation and Bellman equation is exploited to derive a generalized form of the Bellman equation that has controls at internal stages.Comment: 26 pages, 2 figure

Nonparametric Transient Classification using Adaptive Wavelets

Classifying transients based on multi band light curves is a challenging but crucial problem in the era of GAIA and LSST since the sheer volume of transients will make spectroscopic classification unfeasible. Here we present a nonparametric classifier that uses the transient's light curve measurements to predict its class given training data. It implements two novel components: the first is the use of the BAGIDIS wavelet methodology - a characterization of functional data using hierarchical wavelet coefficients. The second novelty is the introduction of a ranked probability classifier on the wavelet coefficients that handles both the heteroscedasticity of the data in addition to the potential non-representativity of the training set. The ranked classifier is simple and quick to implement while a major advantage of the BAGIDIS wavelets is that they are translation invariant, hence they do not need the light curves to be aligned to extract features. Further, BAGIDIS is nonparametric so it can be used for blind searches for new objects. We demonstrate the effectiveness of our ranked wavelet classifier against the well-tested Supernova Photometric Classification Challenge dataset in which the challenge is to correctly classify light curves as Type Ia or non-Ia supernovae. We train our ranked probability classifier on the spectroscopically-confirmed subsample (which is not representative) and show that it gives good results for all supernova with observed light curve timespans greater than 100 days (roughly 55% of the dataset). For such data, we obtain a Ia efficiency of 80.5% and a purity of 82.4% yielding a highly competitive score of 0.49 whilst implementing a truly "model-blind" approach to supernova classification. Consequently this approach may be particularly suitable for the classification of astronomical transients in the era of large synoptic sky surveys.Comment: 14 pages, 8 figures. Published in MNRA

A further study of Jimsphere wind profiles as related to space vehicle design and operations

Statistical characteristics of wind profiles from Jimsphere balloon sensors for space vehicle desig

Contributions from Dilatonic Strings to the Flat Behaviour of the Rotational Curves in Galaxies

We analyse the flat behaviour of the rotational curves in some galaxies in the framework of a dilatonic, current-carrying string. We determine the expression of the tangential velocity of test objects following a stable circular equatorial orbit in this spacetime.Comment: This version to be published in the Int. Journal of Modern Phys.

Differential coupling of G protein alpha subunits to seven-helix receptors expressed in Xenopus oocytes

Xenopus oocytes were used to examine the coupling of the serotonin 1c (5HT1c) and thyrotropin-releasing hormone (TRH) receptors to both endogenous and heterologously expressed G protein alpha subunits. Expression of either G protein-coupled receptor resulted in agonist- induced, Ca(2+)-activated Cl- currents that were measured using a two- electrode voltage clamp. 5HT-induced Cl- currents were reduced 80% by incubating the injected oocytes with pertussis toxin (PTX) and inhibited 50-65% by injection of antisense oligonucleotides to the PTX- sensitive Go alpha subunit. TRH-induced Cl- currents were reduced only 20% by PTX treatment but were inhibited 60% by injection of antisense oligonucleotides to the PTX-insensitive Gq alpha subunit. Injection of antisense oligonucleotides to a novel Xenopus phospholipase C-beta inhibited the 5HT1c (and Go)-induced Cl- current with little effect on the TRH (and Gq)-induced current. These results suggest that receptor- activated Go and Gq interact with different effectors, most likely different isoforms of phospholipase C-beta. Co-expression of each receptor with seven different mammalian G protein alpha subunit cRNAs (Goa, Gob, Gq, G11, Gs, Golf, and Gt) was also examined. Co-expression of either receptor with the first four of these G alpha subunits resulted in a maximum 4-6-fold increase in Cl- currents; the increase depended on the amount of G alpha subunit cRNA injected. This increase was blocked by PTX for G alpha oa and G alpha ob co-expression but not for G alpha q or G alpha 11 co-expression. Co-expression of either receptor with Gs, Golf, or Gt had no effect on Ca(2+)-activated Cl- currents; furthermore, co-expression with Gs or Golf also failed to reveal 5HT- or TRH-induced changes in adenylyl cyclase as assessed by activation of the cystic fibrosis transmembrane conductance regulator Cl- channel. These results indicate that in oocytes, the 5HT1c and TRH receptors do the following: 1) preferentially couple to PTX-sensitive (Go) and PTX-insensitive (Gq) G proteins and that these G proteins act on different effectors, 2) couple within the same cell type to several different heterologously expressed G protein alpha subunits to activate the oocyte's endogenous Cl- current, and 3) fail to couple to G protein alpha subunits that activate cAMP or phosphodiesterase

Types and correlates of school non-attendance in students with autism spectrum disorders

School non-attendance in autism spectrum disorders (ASD) has received very little attention to date. The study aimed to provide a comprehensive description of school non-attendance in students with ASD. Through an online survey, parents of 486 children (mean age 11 years) reported on school attendance over one month, and reasons for instances of non-attendance. On average, students missed five days of school of a possible 23 days. Persistent non-attendance (absent on 10%+ of available sessions) occurred among 43% of students. School non-attendance was associated with child older age, not living in a two-parent household, parental unemployment and, especially, attending a mainstream school. School refusal accounted for 43% of non-attendance. School exclusion and school withdrawal each accounted for 9% of absences. Truancy was almost non-existent. Non-problematic absenteeism (mostly related to medical appointments and illness) accounted for 32% of absences. Non-problematic absenteeism was more likely among those with intellectual disability, school refusal was more likely among older students, and school exclusion was more likely among students from single-parent, unemployed, and well educated households. Findings suggest school non-attendance in ASD is a significant issue, and that it is important to capture detail about attendance patterns and reasons for school non-attendance

Chromium boron surfaced nickel-iron base alloys

Chromium boron diffusion coatings on nickel iron alloys uniquely provide them with improvement in high cycle fatigue strength (up to 30%) and erosion resistance (up to 15 times), compared to uncoated alloy. The diffused chromium layer extends in two essential concentration zones to a total depth of about 40.times.10.sup.-6 m, while the succeeding boron layer is limited to 50-90% of the depth of the richest Cr layer nearest the surface. Both coatings are applied using conventional pack diffusion processes

A Brane model with two asymptotic regions

Some brane models rely on a generalization of the Melvin magnetic universe including a complex scalar field among the sources. We argue that the geometric interpretation of Kip.S.Thorne of this geometry restricts the kind of potential a complex scalar field can display to keep the same asymptotic behavior. While a finite energy is not obtained for a Mexican hat potential in this interpretation, this is the case for a potential displaying a broken phase and an unbroken one. We use for technical simplicity and illustrative purposes an ad hoc potential which however shares some features with those obtained in some supergravity models. We construct a sixth dimensional cylindrically symmetric solution which has two asymptotic regions: the Melvin-like metric on one side and a flat space displaying a conical singularity on the other. The causal structure of the configuration is discussed. Unfortunately, gravity is not localized on the brane.Comment: 9 pages revtex, 4 figures,version to appear in PR

Energy Distribution in Melvin's Magnetic Universe

We use the energy-momentum complexes of Landau and Lifshitz and Papapetrou to obtain the energy distribution in Melvin's magnetic universe. For this space-time we find that these definitions of energy give the same and convincing results. The energy distribution obtained here is the same as we obtained earlier for the same space-time using the energy-momentum complex of Einstein. These results uphold the usefulness of the energy-momentum complexes.Comment: 8 pages, RevTex, no figure

On multidimensional analogs of Melvin's solution for classical series of Lie algebras

A multidimensional generalization of Melvin's solution for an arbitrary simple Lie algebra $\cal G$ is presented. The gravitational model contains n 2-forms and $l \geq n$ scalar fields, wheren is the rank of $\cal G$. The solution is governed by a set of n functions obeying n ordinary differential equations with certain boundary conditions. It was conjectured earlier that these functions should be polynomials (the so-called fluxbrane polynomials). A program (in Maple) for calculating of these polynomials for classical series of Lie algebras is suggested (see Appendix). The polynomials corresponding to the Lie algebra D_4 are obtained. It is conjectured that the polynomials for A_n-, B_n- and C_n-series may be obtained from polynomials for D_{n+1}-series by using certain reduction formulas.Comment: 6 pages, based on a report at RUSGRAV-13 (23-28 June, 2008, PFUR, Moscow