Approximate solutions to large nonsymmetric differential Riccati problems with applications to transport theory

In the present paper, we consider large scale nonsymmetric differential matrix Riccati equations with low rank right hand sides. These matrix equations appear in many applications such as control theory, transport theory, applied probability and others. We show how to apply Krylov-type methods such as the extended block Arnoldi algorithm to get low rank approximate solutions. The initial problem is projected onto small subspaces to get low dimensional nonsymmetric differential equations that are solved using the exponential approximation or via other integration schemes such as Backward Differentiation Formula (BDF) or Rosenbrok method. We also show how these technique could be easily used to solve some problems from the well known transport equation. Some numerical experiments are given to illustrate the application of the proposed methods to large-scale problem

Recovery of an embedded obstacle and the surrounding medium for Maxwell's system

In this paper, we are concerned with the inverse electromagnetic scattering problem of recovering a complex scatterer by the corresponding electric far-field data. The complex scatterer consists of an inhomogeneous medium and a possibly embedded perfectly electric conducting (PEC) obstacle. The far-field data are collected corresponding to incident plane waves with a fixed incident direction and a fixed polarisation, but frequencies from an open interval. It is shown that the embedded obstacle can be uniquely recovered by the aforementioned far-field data, independent of the surrounding medium. Furthermore, if the surrounding medium is piecewise homogeneous, then the medium can be recovered as well. Those unique recovery results are new to the literature. Our argument is based on low-frequency expansions of the electromagnetic fields and certain harmonic analysis techniques.Comment: 15 page

Gear Fault Data

Time domain gear fault vibration data (DataForClassification_TimeDomain)<div>and</div><div>Gear fault data after angle-frequency domain synchronous analysis (DataForClassification_Stage0)</div><div><br></div><div><div>Number of gear fault types=9={'healthy','missing','crack','spall','chip5a','chip4a','chip3a','chip2a','chip1a'}</div><div>Number of samples per type=104</div><div>Number of total samples=9x104=903</div><div>The data are collected in sequence, the first 104 samples are healthy, 105th ~208th samples are missing, and etc. </div></div

Salt bridge distribution of lipid-free apo A-I MD model.

<p>The backbone of apo A-I is presented by ribbons and colored by residue index from red (N-terminus) to blue (C-terminus). Inter-helix salt bridges (listed on the right) are presented with atomic bond. Acidic amino acids are colored by yellow and basic amino acids are colored by green.</p

DataSheet2_A new type of simulated partial gravity apparatus for rats based on a pully-spring system.pdf

The return to the Moon and the landing on Mars has emphasized the need for greater attention to the effects of partial gravity on human health. Here, we sought to devise a new type of simulated partial gravity apparatus that could more efficiently and accurately provide a partial gravity environment for rat hindlimbs. The new apparatus uses a pulley system and tail suspension to create the simulated partial gravity of the rat’s hind limbs by varying the weight in a balance container attached to the pulley system. An experiment was designed to verify the reliability and stability of the new apparatus. In this experiment, 25 seven-week-old male Wistar Hannover rats were randomly divided into five groups (n = 5 per group): hindlimb full weight-bearing control (1G), sham (1G), and the simulated gravity groups including Mars (3/8G), Moon (1/6G), and interplanetary space (microgravity: µG). The levels of partial gravity experienced by rat hindlimbs in the Mars and Moon groups were provided by a novel simulated partial gravity device. Changes in bone parameters [overall bone mineral density (BMD), trabecular BMD, cortical BMD, cortical bone thickness, minimum moment of area (MMA), and polar moment of area (PMA)] were evaluated using computed tomography in all rats at the proximal, middle, and distal regions of femur and tibia. Reduced gravity led to decreases in bone parameters (overall BMD, trabecular BMD, cortical BMD, MMA, and PMA) in the simulated gravity groups, mainly in distal femur and proximal tibia. The proximal tibia, MMA, and PMA findings indicated greater weakness in the µG group than in the Mars group. The sham group design also excluded the decrease in lower limb bone parameters caused by the suspension attachment of the rat’s tail. The new simulated partial gravity apparatus can provide a continuous and stable level of partial gravity. It offers a reliable and valuable model for studying the effects of extraterrestrial gravity environments on humans.</p

Structural comparison of the four lipid-free models.

<p>A) The X-ray model. B) The CCL/MS model. C) The MD model. D) The CMD model. The left panels show the initial structure of each protein while the right panels show structures after simulation. All proteins are represented in ribbons using Chimera. The region of residues 195 to 217 in the CMD model is indicated by purple.</p

Secondary structure comparisons of experimental lipid-free models and the MD results.

<p>The central line represents the residue index. Rectangles along the line represent α-helices. Rectangles with half width represent β-strands. Secondary structures of all models are measured by VMD using a uniform standard. Experimental results are showing on top and structures after MD simulations are show below).</p

Alternative conformation of local structure in the MD model.

<p>A) The variable position of H5 and H6. The backbone of apo A-I C-terminus is presented in ribbons. Structures were aligned by backbone of residue 170 to 185. B) The changeable center angle in H2. The backbone of apo A-I is presented in ribbons. Structures were aligned by the backbone of residues 51 to 62. The ribbon is colored by index from red to blue. C) Surface hydrophobicity representation of MD model (only helix 1 and 2 are displayed). Hydrophobic surface is represented in orange, while hydrophilic surface is represented in blue. D) RMSDs of multiple simulations with the MD model. RMSDs of all protein atoms were measured over the entire trajectory of over seven simulations of the MD model (MD1 to MD7 indicate seven simulations, respectively).</p

The distribution of neighboring Lys pairs in different lipid-free apo A-I models and their consistency to the CCL/MS experiment.

<p>The relative distance of Cβ in Lys residues in the output structure of the simulation is measured by VMD. Hollow circles indicate experimental CCL/MS data (Davison et al [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0120233#pone.0120233.ref040" target="_blank">40</a>]). The cut-off distance between two Cβ in Lys residues chosen for the calculation was 20 Å. Gray circles present the experimental data from CCL/MS method. The X and Y axes of the plot indicate the residue number of apo A-I (1–243). The cross linking data is shown through Lys pairs with a CCL link distance of 20 Å (grey circles), and compared to the CCL/MS, MD, and CMD PDB models (red plus signs). Circles with a red plus sign mean the generated model Lys distance agrees with the CCL experimental data, consequently a circle without a plus sign means the CCL data did not match the model.</p

Luciferase activity analysis of the recombinant plasmids constructed by g. -963C>A and g. -781A>G in HEK293 cells.

<p>The value of each construct is the mean SEM for three independent experiments, each of which was performed in triplicate. <i>P</i> values are from a <i>t</i>-test (two-tailed). **<i>P<</i> 0.01.</p