Bayesian estimation in a multidimensional diffusion model with high frequency data

We consider nonparametric Bayesian inference in a multidimensional diffusion model with reflecting boundary conditions based on discrete high-frequency observations. We prove a general posterior contraction rate theorem in $L^2$-loss, which is applied to Gaussian priors. The resulting posteriors, as well as their posterior means, are shown to converge to the ground truth at the minimax optimal rate over H\"older smoothness classes in any dimension. Of independent interest and as part of our proofs, we show that certain frequentist penalized least squares estimators are also minimax optimal.Comment: 56 pages, 1 figur

Can only flavor-nonsinglet H dibaryons be stable against strong decays?

Using the QCD sum rule approach, we show that the flavor-nonsinglet $H$ dibaryon states with J$^{\pi} = 1^+$, J$^{\pi} = 0^+$, I=1 (27plet) are nearly degenerate with the J$^{\pi} = 0^+$, I=0 singlet $H_0$ dibaryon, which has been predicted to be stable against strong decay, but has not been observed. Our calculation, which does not require an instanton correction, suggests that the $H_0$ is slightly heavier than these flavor-nonsinglet $H$s over a wide range of the parameter space. If the singlet $H_0$ mass lies above the $\Lambda \Lambda$ threshold (2231~MeV), then the strong interaction breakup to $\Lambda \Lambda$ would produce a very broad resonance in the $\Lambda \Lambda$ invariant mass spectrum which would be very difficult to observe. On the other hand, if these flavor-nonsinglet J=0 and 1 $H$ dibaryons are also above the $\Lambda \Lambda$ threshold, but below the $\Xi^0n$ breakup threshold (2254 MeV), then because the direct, strong interaction decay to the $\Lambda \Lambda$ channel is forbidden, these flavor-nonsinglet states might be more amenable to experimental observation. The present results allow a possible reconciliation between the reported observation of $\Lambda \Lambda$ hypernuclei, which argue against a stable $H_0$, and the possible existence of $H$ dibaryons in general.Comment: 10 pages, 2 figure

Insensitivity of the elastic proton-nucleus reaction to the neutron radius of 208Pb

The sensitivity--or rather insensitivity--of the elastic proton-nucleus reaction to the neutron radius of 208Pb is investigated using a non-relativistic impulse-approximation approach. The energy region (Tlab=500 MeV and Tlab=800 MeV) is selected so that the impulse approximation may be safely assumed. Therefore, only free nucleon-nucleon scattering data are used as input for the optical potential. Further, the optical potential includes proton and neutron ground-state densities that are generated from accurately-calibrated models. Even so, these models yield a wide range of values (from 0.13 fm to 0.28 fm) for the poorly known neutron skin thickness in 208Pb. An excellent description of the experimental cross section is obtained with all neutron densities. We have invoked analytic insights developed within the eikonal approximation to understand the insensitivity of the differential cross section to the various neutron densities. As the diffractive oscillations of the cross sections are controlled by the matter radius of the nucleus, the large spread in the neutron skin among the various models gets diluted into a mere 1.5% difference in the matter radius. This renders ineffective the elastic reaction as a precision tool for the measurement of neutron radii.Comment: 17 pages with 5 figure

Predicting Runoff Risks By Digital Soil Mapping

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Digital soil mapping (DSM) permits continuous mapping soil types and properties through raster formats considering variation within soil class, in contrast to the traditional mapping that only considers spatial variation of soils at the boundaries of delineated polygons. The objective of this study was to compare the performance of SoLIM (Soil Land Inference Model) for two sets of environmental variables on digital mapping of saturated hydraulic conductivity and solum depth (A + B horizons) and to apply the best model on runoff risk evaluation. The study was done in the Posses watershed, MG, Brazil, and SoLIM was applied for the following sets of co-variables: 1) terrain attributes (AT): slope, plan curvature, elevation and topographic wetness index. 2) Geomorphons and terrain attributes (GEOM): slope, plan curvature, elevation and topographic wetness index combined with geomorphons. The most precise methodology was applied to predict runoff areas risk through the Wetness Index based on contribution area, solum depth, and saturated hydraulic conductivity. GEOM was the best set of co-variables for both properties, so this was the DSM model used to predict the runoff risk. The runoff risk showed that the critical months are from November to March. The new way to classify the landscape to use on DSM was demonstrated to be an efficient tool with which to model process that occurs on watersheds and can be used to forecast the runoff risk.40Brazilian Coordination for the Improvement of Higher Education Personnel - CAPESBrazilian National Council for Scientific and Technological Development - CNPq [471522/2012-0, 201987/2012-0, 305010/2013-1]Minas Gerais State Research Foundation - FAPEMIG [CAG-APQ-01423-11, CAG-PPM-00422-13]Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq

Dynamic simulation and modeling of gripper for applications in autonomous drone catcher

With advancing technology allowing for drones to become more efficient and evasive in their flight paths, researchers are looking for ways to solve the question of how can these drone be caught midair? Drawing inspiration from nature, the Biomimetics and Dexterous Manipulation Laboratory has developed a method of catching drone’s midair with an in-house designed and manufactured drone utilizing mechanisms from natures design. In implementing this drone design, simulations were needed to gain a better understanding of how the drone catcher would work as well as what data could be collected from a simulated collision. The 3D modeling software Solidworks was utilized to run a realistic simulation on the movement and motion of the main drone catching gripper. In running the simulations on the gripper collisions, it was found that this software was not capable of running high speed collisions at such a high rate of speed. In order for accurate simulations to be run, numerous calculations were needed to be evaluated in the span of a few thousandths of a second. This processing power could not be run on relatively powerful computers and the simulation was run at a slower, micro-gravity emulating, rate of speed. The resulting simulation gave a better understanding of how the drone catching device could capture objects midair, as well as how the mechanism worked within an instance of a collision.Oklahoma Louis Stokes Alliance for Minority Participation ProgramStanford University. Summer Undergraduate Research FellowshipSkydioMechanical Engineerin

Relativistic anisotropic charged fluid spheres with varying cosmological constant

Static spherically symmetric anisotropic source has been studied for the Einstein-Maxwell field equations assuming the erstwhile cosmological constant $\Lambda$ to be a space-variable scalar, viz., $\Lambda = \Lambda(r)$. Two cases have been examined out of which one reduces to isotropic sphere. The solutions thus obtained are shown to be electromagnetic in origin as a particular case. It is also shown that the generally used pure charge condition, viz., $\rho + p_r = 0$ is not always required for constructing electromagnetic mass models.Comment: 15 pages, 3 eps figure

Mid-infrared imaging of the massive young star AFGL 2591: Probing the circumstellar environment of an outflow source

Most, if not all, stars are now believed to produce energetic outflows during their formation. Yet, almost 20 years after the discovery of bipolar outflows from young stars, the origins of this violent phenomenon are not well understood. One of the difficulties of probing the outflow process, particularly in the case of massive embedded stars, is a deficit of high spatial resolution observations. Here, we present sub-arcsecond-resolution mid-infrared images of one massive young stellar object, AFGL 2591, and its immediate surroundings. Our images, at 11.7, 12.5 and 18.0 microns, reveal a knot of emission ~6'' SW of the star, which may be evidence for a recent ejection event or an embedded companion star. This knot is roughly coincident with a previously seen near-infrared reflection nebula and a radio source, and lies within the known large-scale CO outflow. We also find a new faint NW source which may be another embedded lower-luminosity star. The IRAS mid-infrared spectrum of AFGL 2591 shows a large silicate absorption feature at 10 microns, implying that the primary source is surrounded by an optically thick dusty envelope. We discuss the interrelationship of these phenomena and suggest that mid-infrared imaging and spectroscopy provide powerful tools for probing massive star birth.Comment: 14 pages, 3 PostScript figures, accepted for publication in The Astrophysical Journal Letter

Species composition of shoreline wolf spider communities vary with salinity, but their diets vary with wrack inflow

Wolf spiders are typically the most common group of arthropod predators on both lake and marine shorelines because of the high prey availability in these habitats. However, shores are also harsh environments due to flooding and, in proximity to marine waters, to toxic salinity levels. Here, we describe the spider community, prey availabilities, and spider diets between shoreline sites with different salinities, albeit with comparatively small differences (5‰ vs. 7‰). Despite the small environmental differences, spider communities between lower and higher saline sites showed an almost complete species turnover. At the same time, differences in prey availability or spider gut contents did not match changes in spider species composition but rather changed with habitat characteristics within a region, where spiders collected at sites with thick wrack beds had a different diet than sites with little wrack. These data suggest that shifts in spider communities are due to habitat characteristics other than prey availabilities, and the most likely candidate restricting species in high salinity would be saline sensitivity. At the same time, species absence from low-saline habitats remains unresolved.Peer reviewe

Computational complexity of reconstruction and isomorphism testing for designs and line graphs

Graphs with high symmetry or regularity are the main source for experimentally hard instances of the notoriously difficult graph isomorphism problem. In this paper, we study the computational complexity of isomorphism testing for line graphs of $t$-$(v,k,\lambda)$ designs. For this class of highly regular graphs, we obtain a worst-case running time of $O(v^{\log v + O(1)})$ for bounded parameters $t,k,\lambda$. In a first step, our approach makes use of the Babai--Luks algorithm to compute canonical forms of $t$-designs. In a second step, we show that $t$-designs can be reconstructed from their line graphs in polynomial-time. The first is algebraic in nature, the second purely combinatorial. For both, profound structural knowledge in design theory is required. Our results extend earlier complexity results about isomorphism testing of graphs generated from Steiner triple systems and block designs.Comment: 12 pages; to appear in: "Journal of Combinatorial Theory, Series A