Pseudo Approximation Algorithms with Applications to Optimal Motion Planning

We introduce a technique for computing approximate solutions to optimization problems. If $X$ is the set of feasible solutions, the standard goal of approximation algorithms is to compute $x\in X$ that is an $\varepsilon$-approximate solution in the following sense: $$d(x) \leq (1+\varepsilon)\, d(x^*),$$ where $x^* \in X$ is an optimal solution, $d\colon\ X\rightarrow {\Bbb R}_{\geq 0}$ is the optimization function to be minimized, and $\varepsilon>0$ is an input parameter. Our approach is first to devise algorithms that compute pseudo $\varepsilon$-approximate solutions satisfying the bound $$d(x) \leq d(x_R^*) + \varepsilon R,$$ where $R>0$ is a new input parameter. Here $x^*_R$ denotes an optimal solution in the space $X_R$ of $R$-constrained feasible solutions. The parameter $R$ provides a stratification of $X$ in the sense that (1) $X_R \subseteq X_{R}$ for $R < R$ and (2) $X_R = X$ for $R$ sufficiently large. We first describe a highly efficient scheme for converting a pseudo $\varepsilon$-approximation algorithm into a true $\varepsilon$-approximation algorithm. This scheme is useful because pseudo approximation algorithms seem to be easier to construct than $\varepsilon$-approximation algorithms. Another benefit is that our algorithm is automatically precision-sensitive. We apply our technique to two problems in robotics: (A) Euclidean Shortest Path (3ESP), namely the shortest path for a point robot amidst polyhedral obstacles in three dimensions, and (B) $d_1$-optimal motion for a rod moving amidst planar obstacles (1ORM). Previously, no polynomial time $\varepsilon$-approximation algorithm for (B) was known. For (A), our new solution is simpler than previous solutions and has an exponentially smaller complexity in terms of the input precision.     

A new oxolane from Enterobacter cloacae

Enterobacter cloacae is a highly pathogenic Gram-negative proteobacterium which is responsible for a wide array of infections. In the present study, the fermentation culture of E. cloacae has yielded one new oxolane compound, Rimboxo (1) in addition to three known compounds, i.e. Maculosine (2), phenylacetic acid (3) and methyl myristate (4). These compounds were isolated and characterised using extensive chromatographic and spectroscopic methods, and were subjected to cytotoxicity evaluations.     

SR-HARDI: Spatially Regularizing High Angular Resolution Diffusion Imaging

High angular resolution diffusion imaging (HARDI) has recently been of great interest in mapping the orientation of intravoxel crossing fibers, and such orientation information allows one to infer the connectivity patterns prevalent among different brain regions and possible changes in such connectivity over time for various neurodegenerative and neuropsychiatric diseases. The aim of this article is to propose a penalized multiscale adaptive regression model (PMARM) framework to spatially and adaptively infer the orientation distribution function (ODF) of water diffusion in regions with complex fiber configurations. In PMARM, we reformulate the HARDI imaging reconstruction as a weighted regularized least-square regression (WRLSR) problem. Similarity and distance weights are introduced to account for spatial smoothness of HARDI, while preserving the unknown discontinuities (e.g., edges between white matter and gray matter) of HARDI. The L₁ penalty function is introduced to ensure the sparse solutions of ODFs, while a scaled L₁ weighted estimator is calculated to correct the bias introduced by the L₁ penalty at each voxel. In PMARM, we integrate the multiscale adaptive regression models, the propagation-separation method, and Lasso (least absolute shrinkage and selection operator) to adaptively estimate ODFs across voxels. Experimental results indicate that PMARM can reduce the angle detection errors on fiber crossing area and provide more accurate reconstruction than standard voxel-wise methods. Supplementary materials for this article are available online.     

Pharmaceutical metabolite profiling using quadrupole/ion mobility spectrometry/time‐of‐flight mass spectrometry

The use of hybrid quadrupole ion mobility spectrometry time‐of‐flight mass spectrometry (Q/IMS/TOFMS) in the metabolite profiling of leflunomide (LEF) and acetaminophen (APAP) is presented. The IMS drift times (T_d) of the drugs and their metabolites were determined in the IMS/TOFMS experiments and correlated with their exact monoisotopic masses and other in silico generated structural properties, such as connolly molecular area (CMA), connolly solvent‐excluded volume (CSEV), principal moments of inertia along the X, Y and Z Cartesian coordinates (MI‐X, MI‐Y and MI‐Z), inverse mobility and collision cross‐section (CCS). The correlation of T_d with these parameters is presented and discussed. IMS/TOF tandem mass spectrometry experiments (MS² and MS³) were successfully performed on the N‐acetyl‐p‐benzoquinoneimine glutathione (NAPQI‐GSH) adduct derived from the in vitro microsomal metabolism of APAP. As comparison, similar experiments were also performed using hybrid triple quadrupole linear ion trap mass spectrometry (QTRAPMS) and quadrupole time‐of‐flight mass spectrometry (QTOFMS). The abilities to resolve the product ions of the metabolite within the drift tube and fragment the ion mobility resolved product ions in the transfer travelling wave‐enabled stacked ring ion guide (TWIG) demonstrated the potential applicability of the Q/IMS/TOFMS technique in pharmaceutical metabolite profiling. Copyright © 2009 John Wiley & Sons, Ltd.     

Synthesis and Photophysics of Core‐Substituted Naphthalene Diimides: Fluorophores for Single Molecule Applications

The synthesis and photophysics of two new aminopropenyl naphthalene diimide (SANDI) dyes are reported. A general and convenient method for the synthesis of the precursor mono‐, di‐, and tetrabrominated 1,4,5,8‐naphthalene tetracarboxylic dianhydrides is described. The two core‐substituted SANDIs exhibit many of the photophysical properties required for fluorescence labeling applications including high photostability and high fluorescence quantum yields (>0.5) in the visible region of the spectrum. The emission wavelength is sensitive to the number of substituents on the NDI core, and the fluorescence decay times are in the range of ～8–12 ns for both compounds in the solvents investigated. Preliminary fluorescence emission data from single molecules of the compounds embedded in poly(methyl methacrylate) films are also reported and show that single molecules have very low yields of photobleaching, particularly the di‐substituted system. Furthermore, only a small proportion (<10 %) of the single molecules studied display fluorescence intermittencies or “blinks” in their photon trajectory. The compounds appear to be excellent candidates for applications at the single molecule level, for example, as FRET labels.     

Locating hot carrier degradation in asymmetric nDeMOS transistors by gated diode technique

In this paper, hot carrier degradation in asymmetric nDeMOS transistors is investigated. For the first time, we found that the worst hot carrier stress condition is at I_g,max, and not at I_b,max and HE stress conditions. The damage regions in transistors upon various hot carrier stress modes are located by using gated diode technique. It is found that the interface traps generation in the gate/n-type graded drain (NGRD) overlap and spacer oxide regions is the dominant mechanism of hot carrier degradation in asymmetric nDeMOS transistors upon various hot carrier stress modes. Furthermore, the bulk silicon damages locating at the p-well and NGRD regions during hot carrier stress must be taken into account, because they lead to a series of issues, such as the increase in I_off current, the off-state breakdown voltage decrease, and so on.     

Crystal Structure of Dimerized 1,3-Diisopropyl Carbodiimide

Abstract  

A crystal structure of dimerized 1,3-diisopropyl carbodiimide (CDI) has been obtained and its synthesis through a reaction of CDI with aluminum chloride (AlCl₃) has been studied. It possesses space group P2₁/c, with a = 9.352(5), b = 7.956(4), c = 11.405(6) ? and β = 112.465(5)°. It has been observed that this reaction is catalytic with respect to AlCl₃. Kinetic studies of the dimer show that its decomposition into CDI is first order with respect to the dimer. The reactivity of the dimer with metals has been investigated through reactions with methyl lithium and alane. The thermal stability of the dimer has been investigated by thermal gravimetric analysis and differential scanning calorimetry.     

Purification of His-tagged hepatitis B core antigen from unclarified bacterial homogenate using immobilized metal affinity-expanded bed adsorption chromatography

Hepatitis B core antigen (HBcAg) is used as a diagnostic reagent for the detection of hepatitis B virus infection. In this study, immobilized metal affinity-expanded bed adsorption chromatography (IMA-EBAC) was employed to purify N-terminally His-tagged HBcAg from unclarified bacterial homogenate. Streamline Chelating was used as the adsorbent and the batch adsorption experiment showed that the optimal binding pH of His-tagged HBcAg was 8.0 with a binding capacity of 1.8 mg per ml of adsorbent. The optimal elution condition for the elution of His-tagged HBcAg from the adsorbent was at pH 7 in the presence of 500 mM imidazole and 1.5 M NaCl. The IMA-EBAC has successfully recovered 56% of His-tagged HBcAg from the unclarified E. coli homogenate with a purification factor of 3.64. Enzyme-linked immunosorbent assay (ELISA) showed that the antigenicity of the recovered His-tagged HBcAg was not affected throughout the IMA-EBAC purification process and electron microscopy revealed that the protein assembled into virus-like particles (VLP).