High-dimensional simplexes for supermetric search

In a metric space, triangle inequality implies that, for any three objects, a triangle with edge lengths corresponding to their pairwise distances can be formed. The n-point property is a generalisation of this where, for any (n+1) objects in the space, there exists an n-dimensional simplex whose edge lengths correspond to the distances among the objects. In general, metric spaces do not have this property; however in 1953, Blumenthal showed that any semi-metric space which is isometrically embeddable in a Hilbert space also has the n-point property. We have previously called such spaces supermetric spaces, and have shown that many metric spaces are also supermetric, including Euclidean, Cosine, Jensen-Shannon and Triangular spaces of any dimension. Here we show how such simplexes can be constructed from only their edge lengths, and we show how the geometry of the simplexes can be used to determine lower and upper bounds on unknown distances within the original space. By increasing the number of dimensions, these bounds converge to the true distance. Finally we show that for any Hilbert-embeddable space, it is possible to construct Euclidean spaces of arbitrary dimensions, from which these lower and upper bounds of the original space can be determined. These spaces may be much cheaper to query than the original. For similarity search, the engineering tradeoffs are good: we show significant reductions in data size and metric cost with little loss of accuracy, leading to a significant overall improvement in exact search performance

Algebras generated by two bounded holomorphic functions

We study the closure in the Hardy space or the disk algebra of algebras generated by two bounded functions, of which one is a finite Blaschke product. We give necessary and sufficient conditions for density or finite codimension of such algebras. The conditions are expressed in terms of the inner part of a function which is explicitly derived from each pair of generators. Our results are based on identifying z-invariant subspaces included in the closure of the algebra. Versions of these results for the case of the disk algebra are given.Comment: 22 pages ; a number of minor mistakes have been corrected, and some points clarified. Conditionally accepted by Journal d'Analyse Mathematiqu

Progress Report to the Department Committee on Graduate Study and Research

Progress Report to the Department Committee on Graduate Study and Research on a Trouble-Location Scheme for a Digital Electronic Computer

Spatially resolved XMM-Newton analysis and a model of the nonthermal emission of MSH 15-52

We present an X-ray analysis and a model of the nonthermal emission of the pulsar wind nebula (PWN) MSH15-52. We analyzed XMM-Newton data to obtain the spatially resolved spectral parameters around the pulsar PSRB1509-58. A steepening of the fitted power-law spectra and decrease in the surface brightness is observed with increasing distance from the pulsar. In the second part of this paper, we introduce a model for the nonthermal emission, based on assuming the ideal magnetohydrodynamic limit. This model is used to constrain the parameters of the termination shock and the bulk velocity of the leptons in the PWN. Our model is able to reproduce the spatial variation of the X-ray spectra. The parameter ranges that we found agree well with the parameter estimates found by other authors with different approaches. In the last part of this paper, we calculate the inverse Compton emission from our model and compare it to the emission detected with the H.E.S.S. telescope system. Our model is able to reproduce the flux level observed with H.E.S.S., but not the spectral shape of the observed TeV {\gamma}-ray emission.Comment: Accepted for publication in A&A, 9 pages, 15 figure

A simple analytical model for dark matter halo structure and adiabatic contraction

A simple analytical model for describing inner parts of dark matter halo is considered. It is assumed that dark matter density is power-law. The model deals with dark matter distribution function in phase space of adiabatic invariants (radial action and angular momentum). Two variants are considered for the angular part of the distribution function: narrow and broad distribution. The model allows to describe explicitly the process of adiabatic contraction of halo due to change of gravitational potential caused by condensation of baryonic matter in the centre. The modification of dark matter density in the centre is calculated, and is it shown that the standard algorithm of adiabatic contraction calculation overestimates the compressed halo density, especially in the case of strong radial anisotropy.Comment: 5 pages, 3 figures. v3 - major improvements, another halo model introduced, discussion extende

Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides

All-optical signal processing is envisioned as an approach to dramatically decrease power consumption and speed up performance of next-generation optical telecommunications networks. Nonlinear optical effects, such as four-wave mixing (FWM) and parametric gain, have long been explored to realize all-optical functions in glass fibers. An alternative approach is to employ nanoscale engineering of silicon waveguides to enhance the optical nonlinearities by up to five orders of magnitude, enabling integrated chip-scale all-optical signal processing. Previously, strong two-photon absorption (TPA) of the telecom-band pump has been a fundamental and unavoidable obstacle, limiting parametric gain to values on the order of a few dB. Here we demonstrate a silicon nanophotonic optical parametric amplifier exhibiting gain as large as 25.4 dB, by operating the pump in the mid-IR near one-half the band-gap energy (E~0.55eV, lambda~2200nm), at which parasitic TPA-related absorption vanishes. This gain is high enough to compensate all insertion losses, resulting in 13 dB net off-chip amplification. Furthermore, dispersion engineering dramatically increases the gain bandwidth to more than 220 nm, all realized using an ultra-compact 4 mm silicon chip. Beyond its significant relevance to all-optical signal processing, the broadband parametric gain also facilitates the simultaneous generation of multiple on-chip mid-IR sources through cascaded FWM, covering a 500 nm spectral range. Together, these results provide a foundation for the construction of silicon-based room-temperature mid-IR light sources including tunable chip-scale parametric oscillators, optical frequency combs, and supercontinuum generators

Prolonged podocyte depletion in larval zebrafish resembles mammalian focal and segmental glomerulosclerosis

Focal and segmental glomerulosclerosis (FSGS) is a histological pattern frequently found in patients with nephrotic syndrome that often progress to end-stage kidney disease. The initial step in development of this histologically defined entity is injury and ultimately depletion of podocytes, highly arborized interdigitating cells on the glomerular capillaries with important function for the glomerular filtration barrier. Since there are still no causal therapeutic options, animal models are needed to develop new treatment strategies. Here, we present an FSGS-like model in zebrafish larvae, an eligible vertebrate model for kidney research. In a transgenic zebrafish strain, podocytes were depleted, and the glomerular response was investigated by histological and morphometrical analysis combined with immunofluorescence staining and ultrastructural analysis by transmission electron microscopy. By intravenous injection of fluorescent high-molecular weight dextran, we confirmed leakage of the size selective filtration barrier. Additionally, we observed severe podocyte foot process effacement of remaining podocytes, activation of proximal tubule-like parietal epithelial cells identified by ultrastructural cytomorphology, and expression of proximal tubule markers. These activated cells deposited extracellular matrix on the glomerular tuft which are all hallmarks of FSGS. Our findings indicate that glomerular response to podocyte depletion in larval zebrafish resembles human FSGS in several important characteristics. Therefore, this model will help to investigate the disease development and the effects of potential drugs in a living organism

The impact of baryonic physics on the shape and radial alignment of substructures in cosmological dark matter haloes

We use two simulations performed within the Constrained Local UniversE Simulation (CLUES) project to study both the shape and radial alignment of (the dark matter component of) subhaloes; one of the simulations is a dark matter only model while the other run includes all the relevant gas physics and star formation recipes. We find that the involvement of gas physics does not have a statistically significant effect on either property -- at least not for the most massive subhaloes considered in this study. However, we observe in both simulations including and excluding gasdynamics a (pronounced) evolution of the dark matter shapes of subhaloes as well as of the radial alignment signal since infall time. Further, this evolution is different when positioned in the central and outer regions of the host halo today; while subhaloes tend to become more aspherical in the central 50% of their host's virial radius, the radial alignment weakens in the central regime while strengthening in the outer parts. We confirm that this is due to tidal torquing and the fact that subhaloes at pericentre move too fast for the alignment signal to respond.Comment: 10 pages, 8 figures, 2 tables, accepted for publication in MNRAS, replaced with proof-corrected version (minor typos

Constrained simulations of the Local Group: on the radial distribution of substructures

We examine the properties of satellites found in high resolution simulations of the local group. We use constrained simulations designed to reproduce the main dynamical features that characterize the local neighborhood, i.e. within tens of Mpc around the Local Group (LG). Specifically, a LG-like object is found located within the 'correct' dynamical environment and consisting of three main objects which are associated with the Milky Way, M31 and M33. By running two simulations of this LG from identical initial conditions - one with and one without baryons modeled hydrodynamically - we can quantify the effect of gas physics on the $z=0$ population of subhaloes in an environment similar to our own. We find that above a certain mass cut, $M_{\rm sub} > 2\times10^{8}h^{-1} M_{\odot}$ subhaloes in hydrodynamic simulations are more radially concentrated than those in simulations with out gas. This is caused by the collapse of baryons into stars that typically sit in the central regions of subhaloes, making them denser. The increased central density of such a subhalo, results in less mass loss due to tidal stripping than the same subhalo simulated with only dark matter. The increased mass in hydrodynamic subhaloes with respect to dark matter ones, causes dynamical friction to be more effective, dragging the subhalo towards the centre of the host. This results in these subhaloes being effectively more radially concentrated then their dark matter counterparts.Comment: 12 pages, 9 figure