The Eikonal Equation in Flat Space: Null Surfaces and Their Singularities I

The level surfaces of solutions to the eikonal equation define null or characteristic surfaces. In this note we study, in Minkowski space, properties of these surfaces. In particular we are interested both in the singularities of these ``surfaces'' (which can in general self-intersect and be only piece-wise smooth) and in the decomposition of the null surfaces into a one parameter family of two-dimensional wavefronts which can also have self-intersections and singularities. We first review a beautiful method for constructing the general solution to the flat-space eikonal equation; it allows for solutions either from arbitrary Cauchy data or for time independent (stationary) solutions of the form S=t-S_{0}(x,y,z). We then apply this method to obtain global, asymptotically spherical, null surfaces that are associated with shearing ("bad") two-dimensional cuts of null infinity; the surfaces are defined from the normal rays to the cut. This is followed by a study of the caustics and singularities of these surfaces and those of their associated wavefronts. We then treat the same set of issues from an alternative point of view, namely from Arnold's theory of generating families. This treatment allows one to deal (parametrically) with the regions of self-intersection and non-smoothness of the null surfaces, regions which are difficult to treat otherwise. Finally we generalize the analysis of the singularities to families of solutions of the eikonal equation.Comment: 33 pages, figures not included, accepted for publication in JM

Performance of a Low Noise Front-end ASIC for Si/CdTe Detectors in Compton Gamma-ray Telescope

Compton telescopes based on semiconductor technologies are being developed to explore the gamma-ray universe in an energy band 0.1--20 MeV, which is not well covered by the present or near-future gamma-ray telescopes. The key feature of such Compton telescopes is the high energy resolution that is crucial for high angular resolution and high background rejection capability. The energy resolution around 1 keV is required to approach physical limit of the angular resolution due to Doppler broadening. We have developed a low noise front-end ASIC (Application-Specific Integrated Circuit), VA32TA, to realize this goal for the readout of Double-sided Silicon Strip Detector (DSSD) and Cadmium Telluride (CdTe) pixel detector which are essential elements of the semiconductor Compton telescope. We report on the design and test results of the VA32TA. We have reached an energy resolution of 1.3 keV (FWHM) for 60 keV and 122 keV at 0 degree C with a DSSD and 1.7 keV (FWHM) with a CdTe detector.Comment: 6 pages, 7 figures, IEEE style file, to appear in IEEE Trans. Nucl. Sc

The age of data-driven proteomics : how machine learning enables novel workflows

A lot of energy in the field of proteomics is dedicated to the application of challenging experimental workflows, which include metaproteomics, proteogenomics, data independent acquisition (DIA), non-specific proteolysis, immunopeptidomics, and open modification searches. These workflows are all challenging because of ambiguity in the identification stage; they either expand the search space and thus increase the ambiguity of identifications, or, in the case of DIA, they generate data that is inherently more ambiguous. In this context, machine learning-based predictive models are now generating considerable excitement in the field of proteomics because these predictive models hold great potential to drastically reduce the ambiguity in the identification process of the above-mentioned workflows. Indeed, the field has already produced classical machine learning and deep learning models to predict almost every aspect of a liquid chromatography-mass spectrometry (LC-MS) experiment. Yet despite all the excitement, thorough integration of predictive models in these challenging LC-MS workflows is still limited, and further improvements to the modeling and validation procedures can still be made. In this viewpoint we therefore point out highly promising recent machine learning developments in proteomics, alongside some of the remaining challenges

Comparação do teor de minerais em vinhos do Vale do Submédio São Francisco, Brasil.

Neste trabalho teve-se como objetivo analisar 28 minerais por espectrometria de emissão ótica com plasma acoplado indutivamente (ICP-OES) em 48 amostras de vinhos provenientes de três vinícolas desta região

Thermostatistics of overdamped motion of interacting particles

We show through a nonlinear Fokker-Planck formalism, and confirm by molecular dynamics simulations, that the overdamped motion of interacting particles at T=0, where T is the temperature of a thermal bath connected to the system, can be directly associated with Tsallis thermostatistics. For sufficiently high values of T, the distribution of particles becomes Gaussian, so that the classical Boltzmann-Gibbs behavior is recovered. For intermediate temperatures of the thermal bath, the system displays a mixed behavior that follows a novel type of thermostatistics, where the entropy is given by a linear combination of Tsallis and Boltzmann-Gibbs entropies.Comment: 4 pages, 2 figure

The phase portrait of a matter bounce in Horava-Lifshitz cosmology

The occurrence of a bounce in FRW cosmology requires modifications of general relativity. An example of such a modification is the recently proposed Horava-Lifshitz theory of gravity, which includes a ``dark radiation'' term with a negative coefficient in the analog of the Friedmann equation. This paper describes a phase space analysis of models of this sort with the aim of determining to what extent bouncing solutions can occur. A simplification, valid in the relevant region, allows a reduction of the dimension of phase space so that visualization in three dimensions is possible. It is found that a bounce is possible, but not generic in models under consideration. Apart from previously known bouncing solutions some new ones are also described. Other interesting solutions found include ones which describe a novel sort of oscillating universes.Comment: 14 pages, 8 figure