The Markov-Dubins Problem with Free Terminal Direction in a Nonpositively Curved Cube Complex

State complexes are nonpositively curved cube complexes that model the state spaces of reconfigurable systems. The problem of determining a strategy for reconfiguring the system from a given initial state to a given goal state is equivalent to that of finding a path between two points in the state complex. The additional requirement that allowable paths must have a prescribed initial direction and minimal turning radius determines a Markov-Dubins problem with free terminal direction (MDPFTD). Given a nonpositively curved, locally finite cube complex X, we consider the set of unit-speed paths which satisfy a certain smoothness condition in addition to the boundary conditions and curvature constraint that define a MDPFTD. We show that this set either contains a path of minimal length, or is empty. We then focus on the case that X is a surface with a nonpositively curved cubical structure. We show that any solution to a MDPFTD in X must consist of finitely many geodesic segments and arcs of constant curvature, and we give an algorithm for determining those solutions to the MDPFTD in X which are CL paths, that is, made up of an arc of constant curvature followed by a geodesic segment. Finally, under the assumption that the 1-skeleton of X is d-regular, we give sufficient conditions for a topological ray in X of constant curvature to be a rose curve or a proper ray

Newton\u27s Method Backpropagation for Complex-Valued Holomorphic Neural Networks: Algebraic and Analytic Properties

The study of Newton\u27s method in complex-valued neural networks (CVNNs) faces many difficulties. In this dissertation, we derive Newton\u27s method backpropagation algorithms for complex-valued holomorphic multilayer perceptrons (MLPs), and we investigate the convergence of the one-step Newton steplength algorithm for the minimization of real-valued complex functions via Newton\u27s method. The problem of singular Hessian matrices provides an obstacle to the use of Newton\u27s method backpropagation to train CVNNs. We approach this problem by developing an adaptive underrelaxation factor algorithm that avoids singularity of the Hessian matrices for the minimization of real-valued complex polynomial functions. To provide experimental support for the use of our algorithms, we perform a comparison of using sigmoidal functions versus their Taylor polynomial approximations as activation functions by using the Newton and pseudo-Newton backpropagation algorithms developed here and the known gradient descent backpropagation algorithm. Our experiments indicate that the Newton\u27s method based algorithms, combined with the use of polynomial activation functions, provide significant improvement in the number of training iterations required over the existing algorithms. We also test our underrelaxation factor algorithm using a small-scale polynomial neuron and a polynomial MLP. Finally, we investigate the application of an algebraic root-finding technique to the case of a polynomial MLP to develop a theoretical framework for the location of initial weight vectors that will guarantee successful training

Tandem Mobility Mass Spectrometry Study of Electrosprayed Tetraheptyl Ammonium Bromide Clusters

Multiply charged electrospray ions from concentrated solutions of Heptyl4N+Br− (designated A+B− hereafter) in formamide are analyzed mass spectrometrically (MS) following mobility selection in ambient air in a differential mobility analyzer (DMA). Most of the sharp mobility peaks seen are identified as (AB)nA+ clusters, with 0 ≤ n ≤ 5. One anomalously abundant and mobile ion is identified as NH4+(AB)4. Six ions in the (AB)n(A+)2 series are also identified, completing and correcting earlier mobility data for singly and doubly charged ions up to masses of almost 9000 Da. The more mobile of two broad humps seen in the mobility spectrum includes m/z values approximately from 2500 up to 12,000 Da. It is formed primarily by multiply charged (AB)n(A+)z clusters with multiple ammonium bromide adducts. Because of overlapping of many peaks of different m/z and charge state z, only a few individual species can be identified by MS alone in this highly congested region. However, the spectral simplification brought about by mobility selection upstream of the MS reveals a series of broad modulations in m/z space, with all ions resolved in the second, third, …sixth modulation being in charge states z = 2, 3, …6, respectively. Extrapolation of this trend beyond the sixth wave fixes the ion charge state (in some cases up to z = 15) and mass (beyond m = 175,000 u). This wavy structure had been previously observed and explained in terms of ion evaporation kinetics from volatile drops, though without mass identification. All observations indicate that the clusters are formed as charged residues, but their charge state is fixed by the Iribarne-Thomson ion evaporation mechanism. Consequently, the measured curve of cluster diameter versus z yields the two parameters governing ion evaporation kinetics. Clusters with z > 1 and electrical mobility Z > 0.495 cm2/V/s are metastable and evaporate a singly charged cluster, probably (AB)2A+, between the DMA and the MS. Plotting the electrical mobilities Z of the clusters in the form (z/Z)1/2 versus m1/3 (both proportional to cluster diameter) collapse the data for all cluster sizes and charge states into one single straight line for Z below 0.495 cm2/V/s. This linear relation reveals a uniform apparent cluster density of 0.935 g/cm3 and an effective hard-sphere diameter of the air molecules of 0.44 nm. An anomalous mobility increase is observed at diameters below 3 nm

Lagrangian Statistics and Temporal Intermittency in a Shell Model of Turbulence

We study the statistics of single particle Lagrangian velocity in a shell model of turbulence. We show that the small scale velocity fluctuations are intermittent, with scaling exponents connected to the Eulerian structure function scaling exponents. The observed reduced scaling range is interpreted as a manifestation of the intermediate dissipative range, as it disappears in a Gaussian model of turbulence.Comment: 4 pages, 5 figure

Rapid Patient-Side Evaluation of Endothelial Glycocalyx Thickness in Healthy Sedated Cats Using GlycoCheck (R) Software

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Fresh Activity in Old Systems: Radio AGN in Fossil Groups of Galaxies

We present the first systematic 1.4 GHz Very Large Array radio continuum survey of fossil galaxy group candidates. These are virialized systems believed to have assembled over a gigayear in the past through the merging of galaxy group members into a single, isolated, massive elliptical galaxy and featuring an extended hot X-ray halo. We use new photometric and spectroscopic data from SDSS Data Release 7 to determine that three of the candidates are clearly not fossil groups. Of the remaining 30 candidates, 67% contain a radio-loud (L_1.4GHz > 10^23 W Hz^-1) active galactic nucleus (AGN) at the center of their dominant elliptical galaxy. We find a weak correlation between the radio luminosity of the AGN and the X-ray luminosity of the halo suggesting that the AGN contributes to energy deposition into the intragroup medium. We only find a correlation between the radio and optical luminosity of the central elliptical galaxy when we include X-ray selected, elliptically dominated non-fossil groups, indicating a weak relationship between AGN strength and the mass assembly history of the groups. The dominant elliptical galaxy of fossil groups is on average roughly an order of magnitude more luminous than normal group elliptical galaxies in optical, X-ray, and radio luminosities and our findings are consistent with previous results that the radio-loud fraction in elliptical galaxies is linked to the stellar mass of a population. The current level of activity in fossil groups suggests that AGN fueling continues long after the last major merger. We discuss several possibilities for fueling the AGN at the present epoch.Comment: Accepted for publication in A