On boosting kernel regression

In this paper we propose a simple multistep regression smoother which is constructed in an iterative manner, by learning the Nadaraya-Watson estimator with L-2 boosting. We find, in both theoretical analysis and simulation experiments, that the bias converges exponentially fast. and the variance diverges exponentially slow. The first boosting step is analysed in more detail, giving asymptotic expressions as functions of the smoothing parameter, and relationships with previous work are explored. Practical performance is illustrated by both simulated and real data

Kernel density classification and boosting: an L2 sub analysis

Kernel density estimation is a commonly used approach to classification. However, most of the theoretical results for kernel methods apply to estimation per se and not necessarily to classification. In this paper we show that when estimating the difference between two densities, the optimal smoothing parameters are increasing functions of the sample size of the complementary group, and we provide a small simluation study which examines the relative performance of kernel density methods when the final goal is classification. A relative newcomer to the classification portfolio is “boosting”, and this paper proposes an algorithm for boosting kernel density classifiers. We note that boosting is closely linked to a previously proposed method of bias reduction in kernel density estimation and indicate how it will enjoy similar properties for classification. We show that boosting kernel classifiers reduces the bias whilst only slightly increasing the variance, with an overall reduction in error. Numerical examples and simulations are used to illustrate the findings, and we also suggest further areas of research

Free boundary problems for Tumor Growth: a Viscosity solutions approach

The mathematical modeling of tumor growth leads to singular stiff pressure law limits for porous medium equations with a source term. Such asymptotic problems give rise to free boundaries, which, in the absence of active motion, are generalized Hele-Shaw flows. In this note we use viscosity solutions methods to study limits for porous medium-type equations with active motion. We prove the uniform convergence of the density under fairly general assumptions on the initial data, thus improving existing results. We also obtain some additional information/regularity about the propagating interfaces, which, in view of the discontinuities, can nucleate and, thus, change topological type. The main tool is the construction of local, smooth, radial solutions which serve as barriers for the existence and uniqueness results as well as to quantify the speed of propagation of the free boundary propagation

Quantum Measurement and the Aharonov-Bohm Effect with Superposed Magnetic Fluxes

We consider the magnetic flux in a quantum mechanical superposition of two values and find that the Aharonov-Bohm effect interference pattern contains information about the nature of the superposition, allowing information about the state of the flux to be extracted without disturbance. The information is obtained without transfer of energy or momentum and by accumulated nonlocal interactions of the vector potential $\vec{A}$ with many charged particles forming the interference pattern, rather than with a single particle. We suggest an experimental test using already experimentally realized superposed currents in a superconducting ring and discuss broader implications.Comment: 6 pages, 4 figures; Changes from version 3: corrected typo (not present in versions 1 and 2) in Eq. 8; Changes from version 2: shortened abstract; added refs and material in Section IV. The final publication is available at: http://link.springer.com/article/10.1007/s11128-013-0652-

Are rotating strange quark stars good sources of gravitational waves?

We study the viscosity driven (Jacobi-like) bar mode instability of rapidly rotating strange stars in general relativity. A triaxial, "bar shaped" compact star could be an efficient source of continuous wave gravitational radiation in the frequency range of the forthcoming interferometric detectors. We locate the secular instability point along several constant baryon mass sequences of uniformly rotating strange stars described by the MIT bag model. Contrary to neutron stars, strange stars with T/|W| (the ratio of the rotational kinetic energy to the absolute value of the gravitational potential energy) much lower than the corresponding value for the mass-shed limit can be secularly unstable to bar mode formation if shear viscosity is high enough to damp out any deviation from uniform rotation. The instability develops for a broad range of gravitational masses and rotational frequencies of strange quark stars. It imposes strong constraints on the lower limit of the frequency at the innermost stable circular orbit around rapidly rotating strange stars. The above results are robust for all linear self-bound equations of state assuming the growth time of the instability is faster than the damping timescale. We discuss astrophysical scenarios where triaxial instabilities (r-mode and viscosity driven instability) could be relevant in strange stars described by the standard MIT bag model of normal quark matter. Taking into account actual values of viscosities in strange quark matter and neglecting the magnetic field we show that Jacobi-like instability cannot develop in any astrophysicaly interesting temperature windows. The main result is that strange quark stars described by the MIT bag model can be accelerated to very high frequency in Low Mass X-ray binaries if the strange quark mass is ~ 200 MeV or higher.Comment: 15 pages, 10 figures, to appear in Astronomy and Astrophysic

Computing Volume Bounds of Inclusions by EIT Measurements

The size estimates approach for Electrical Impedance Tomography (EIT) allows for estimating the size (area or volume) of an unknown inclusion in an electrical conductor by means of one pair of boundary measurements of voltage and current. In this paper we show by numerical simulations how to obtain such bounds for practical application of the method. The computations are carried out both in a 2D and a 3D setting.Comment: 20 pages with figure

A stochastic model for internal HIV dynamics

In this paper we analyse a stochastic model representing HIV internal virus dynamics. The stochasticity in the model is introduced by parameter perturbation which is a standard technique in stochastic population modelling. We show that the model established in this paper possesses non-negative solutions as this is essential in any population dynamics model. We also carry out analysis on the asymptotic behaviour of the model. We approximate one of the variables by a mean reverting process and nd out the mean and variance of this process. Numerical simulations conclude the paper

Secular spin-down of the AMP XTE J1751-305

Context. Of the 13 known accreting millisecond pulsars, only a few showed more than one outburst during the RXTE era. XTE J1751-305 showed, after the main outburst in 2002, other three dim outbursts. We report on the timing analysis of the latest one, occurred on October 8, 2009 and serendipitously observed from its very beginning by RXTE. Aims. The detection of the pulsation during more than one outburst permits to obtain a better constraint of the orbital parameters and their evolution as well as to track the secular spin frequency evolution of the source. Methods. Using the RXTE data of the last outburst of the AMP XTE J1751-305, we performed a timing analysis to improve the orbital parameters. Because of the low statistics, we used an epoch folding search technique on the whole data set to improve the local estimate of the time of ascending node passage. Results. Using this new orbital solution we epoch folded data obtaining three pulse phase delays on a time span of 1.2 days, that we fitted using a constant spin frequency model. Comparing this barycentric spin frequency with that of the 2002 outburst, we obtained a secular spin frequency derivative of -0.55(12) x 10^{-14} Hz s^{-1}. In the hypothesis that the secular spin-down is due to a rotating magneto-dipole emission, consistently with what is assumed for radio pulsars, we estimate the pulsar's magnetic dipole value. We derive an estimate of the magnetic field strength at the polar cap of B_{PC} = 4.0(4) x 10^8 Gauss, for a neutron star mass of 1.4M\odot, assuming the Friedman Pandharipande Skyrme equation of state.Comment: 7 pages, 4 figures, accepted for publication on A&