Learning distance to subspace for the nearest subspace methods in high-dimensional data classification

The nearest subspace methods (NSM) are a category of classification methods widely applied to classify high-dimensional data. In this paper, we propose to improve the classification performance of NSM through learning tailored distance metrics from samples to class subspaces. The learned distance metric is termed as ‘learned distance to subspace’ (LD2S). Using LD2S in the classification rule of NSM can make the samples closer to their correct class subspaces while farther away from their wrong class subspaces. In this way, the classification task becomes easier and the classification performance of NSM can be improved. The superior classification performance of using LD2S for NSM is demonstrated on three real-world high-dimensional spectral datasets

Travelling waves in hyperbolic chemotaxis equations

Mathematical models of bacterial populations are often written as systems of partial differential equations for the densities of bacteria and concentrations of extracellular (signal) chemicals. This approach has been employed since the seminal work of Keller and Segel in the 1970s [Keller and Segel, J. Theor. Biol., 1971]. The system has been shown to permit travelling wave solutions which correspond to travelling band formation in bacterial colonies, yet only under specific criteria, such as a singularity in the chemotactic sensitivity function as the signal approaches zero. Such a singularity generates infinite macroscopic velocities which are biologically unrealistic. In this paper, we formulate a model that takes into consideration relevant details of the intracellular processes while avoiding the singularity in the chemotactic sensitivity. We prove the global existence of solutions and then show the existence of travelling wave solutions both numerically and analytically

Stem-root flow effect on soil–atmosphere interactions and uncertainty assessments

Abstract. Soil water can rapidly enter deeper layers via vertical redistribution of soil water through the stem–root flow mechanism. This study develops the stem–root flow parameterization scheme and coupled this scheme with the Simplified Simple Biosphere model (SSiB) to analyze its effects on land–atmospheric interactions. The SSiB model was tested in a single column mode using the Lien Hua Chih (LHC) measurements conducted in Taiwan and HAPEX-Mobilhy (HAPEX) measurements in France. The results show that stem–root flow generally caused a decrease in the moisture content at the top soil layer and moistened the deeper soil layers. Such soil moisture redistribution results in significant changes in heat flux exchange between land and atmosphere. In the humid environment at LHC, the stem–root flow effect on transpiration was minimal, and the main influence on energy flux was through reduced soil evaporation that led to higher soil temperature and greater sensible heat flux. In the Mediterranean environment of HAPEX, the stem–root flow significantly affected plant transpiration and soil evaporation, as well as associated changes in canopy and soil temperatures. However, the effect on transpiration could either be positive or negative depending on the relative changes in the moisture content of the top soil vs. deeper soil layers due to stem–root flow and soil moisture diffusion processes

Mathematics from China to Virginia by Way of Singapore

Our article follows from an interesting concurrence of mathematical and educational lines. At least the concurrence seems so to us and we hope that those who read on will agree. The lines or streams are a joint minimester program at St. Catherine’s and St. Christopher‘s Schools, an interest in problem solving, and a Singapore connection. We shall describe the lines first and then describe the mathematics that we found at their intersection

Inclinations and black hole masses of Seyfert 1 galaxies

A tight correlation of black hole mass and central velocity dispersion has been found recently for both active and quiescent galaxies. By applying this correlation, we develop a simple method to derive the inclination angles for a sample of 11 Seyfert 1 galaxies that have both measured central velocity dispersions and black hole masses estimated by reverberation mapping. These angles, with a mean value of 36 degree that agrees well with the result obtained by fitting the iron K$\alpha$ lines of Seyfert 1s observed with ASCA, provide further support to the orientation-dependent unification scheme of AGN. A positive correlation of the inclinations with observed FWHMs of H$\beta$ line and a possible anti-correlation with the nuclear radio-loudness have been found. We conclude that more accurate knowledge on inclinations and broad line region dynamics is needed to improve the black hole mass determination of AGN with the reverberation mapping technique.Comment: 12 pages including 4 figures, accepted for publication in The Astrophysical Journal Letter

A comprehensive numerical study of aerosol-cloud-precipitation interactions in marine stratocumulus

Three-dimensional large-eddy simulations (LES) with detailed bin-resolved microphysics are performed to explore the diurnal variation of marine stratocumulus (MSc) clouds under clean and polluted conditions. The sensitivity of the aerosol-cloud-precipitation interactions to variation of sea surface temperature, free tropospheric humidity, large-scale divergence rate, and wind speed is assessed. The comprehensive set of simulations corroborates previous studies that (1) with moderate/heavy drizzle, an increase in aerosol leads to an increase in cloud thickness; and (2) with non/light drizzle, an increase in aerosol results in a thinner cloud, due to the pronounced effect on entrainment. It is shown that for higher SST, stronger large-scale divergence, drier free troposphere, or lower wind speed, the cloud thins and precipitation decreases. The sign and magnitude of the Twomey effect, droplet dispersion effect, cloud thickness effect, and cloud optical depth susceptibility to aerosol perturbations (i.e., change in cloud optical depth to change in aerosol number concentration) are evaluated by LES experiments and compared with analytical formulations. The Twomey effect emerges as dominant in total cloud optical depth susceptibility to aerosol perturbations. The dispersion effect, that of aerosol perturbations on the cloud droplet size spectrum, is positive (i.e., increase in aerosol leads to spectral narrowing) and accounts for 3% to 10% of the total cloud optical depth susceptibility at nighttime, with greater influence in heavier drizzling clouds. The cloud thickness effect is negative (i.e., increase in aerosol leads to thinner cloud) for non/light drizzling cloud and positive for a moderate/heavy drizzling clouds; the cloud thickness effect contributes 5% to 22% of the nighttime total cloud susceptibility. Overall, the total cloud optical depth susceptibility ranges from ~0.28 to 0.53 at night; an increase in aerosol concentration enhances cloud optical depth, especially with heavier precipitation and in a more pristine environment. During the daytime, the range of magnitude for each effect is more variable owing to cloud thinning and decoupling. The good agreement between LES experiments and analytical formulations suggests that the latter may be useful in evaluations of the total cloud susceptibility. The ratio of the magnitude of the cloud thickness effect to that of the Twomey effect depends on cloud base height and cloud thickness in unperturbed (clean) clouds

Microscopic theory of single-electron tunneling through molecular-assembled metallic nanoparticles

We present a microscopic theory of single-electron tunneling through metallic nanoparticles connected to the electrodes through molecular bridges. It combines the theory of electron transport through molecular junctions with the description of the charging dynamics on the nanoparticles. We apply the theory to study single-electron tunneling through a gold nanoparticle connected to the gold electrodes through two representative benzene-based molecules. We calculate the background charge on the nanoparticle induced by the charge transfer between the nanoparticle and linker molecules, the capacitance and resistance of molecular junction using a first-principles based Non-Equilibrium Green's Function theory. We demonstrate the variety of transport characteristics that can be achieved through ``engineering'' of the metal-molecule interaction.Comment: To appear in Phys. Rev.