Local reconstruction of low‐rank matrices and subspaces

We study the problem of reconstructing a low‐rank matrix, where the input is an n × m matrix M over a field and the goal is to reconstruct a (near‐optimal) matrix that is low‐rank and close to M under some distance function Δ. Furthermore, the reconstruction must be local, i.e., provides access to any desired entry of by reading only a few entries of the input M (ideally, independent of the matrix dimensions n and m). Our formulation of this problem is inspired by the local reconstruction framework of Saks and Seshadhri (SICOMP, 2010). Our main result is a local reconstruction algorithm for the case where Δ is the normalized Hamming distance (between matrices). Given M that is ‐close to a matrix of rank (together with d and ), this algorithm computes with high probability a rank‐d matrix that is ‐close to M. This is a local algorithm that proceeds in two phases. The preprocessing phase reads only random entries of M, and stores a small data structure. The query phase deterministically outputs a desired entry by reading only the data structure and 2d additional entries of M. We also consider local reconstruction in an easier setting, where the algorithm can read an entire matrix column in a single operation. When Δ is the normalized Hamming distance between vectors, we derive an algorithm that runs in polynomial time by applying our main result for matrix reconstruction. For comparison, when Δ is the truncated Euclidean distance and , we analyze sampling algorithms by using statistical learning tools. A preliminary version of this paper appears appears in ECCC, see: http://eccc.hpi-web.de/report/2015/128/ © 2017 Wiley Periodicals, Inc. Random Struct. Alg., 51, 607–630, 2017     

Phosphonate-anchored monolayers for antibody binding to magnetic nanoparticles

Targeted delivery of magnetic iron oxide nanoparticles (IONPs) to a specific tissue can be achieved by conjugation with particular biological ligands on an appropriately functionalized IONP surface. To take best advantage of the unique magnetic properties of IONPs and to maximize their blood half-life, thin, strongly bonded, functionalized coatings are required. The work reported herein demonstrates the successful application of phosphonate-anchored self-assembled monolayers (SAMs) as ultrathin coatings for such particles. It also describes a new chemical approach to the anchoring of antibodies on the surface of SAM-coated IONPs (using nucleophilic aromatic substitution). This anchoring strategy results in stable, nonhydrolyzable, covalent attachment and allows the reactivity of the particles toward antibody binding to be activated in situ, such that prior to the activation the modified surface is stable for long-term storage. While the SAMs do not have the well-packed crystallinity of other such monolayers, their structure was studied using smooth model substrates based on an iron oxide layer on a double-side polished silicon wafer. In this way, atomic force microscopy, ellipsometry, and contact angle goniometry (tools that could not be applied to the nanoparticles' surfaces) could contribute to the determination of their monomolecular thickness and uniformity. Finally, the successful conjugation of IgG antibodies to the SAM-coated IONPs such that the antibodies retain their biological activity is verified by their complexation to a secondary fluorescent antibody.     

Nonlinear pulse response of p-i-n photodiode caused by the change of the bias voltage

An analytical expression is derived for nonlinear response of a p-i-n photodiode, commonly used in optical communications. Nonlinearity is caused only by the change of bias voltage, in case of pulse light excitation. The response time increases slowly with increasing the incident pulse power as a result of this nonlinearity. It is assumed in calculations that the optical excitation is not so strong to cause space charge redistribution.     

Ozonolysis by microwave discharge of oxygen of naphthalene adsorbed on florisil

Microwave discharge of O₂ produces O(³P) atoms which form O₃ on florisil surface. Reaction with adsorbed naphthalene results in $\text{o}$-formylcinnamaldehydes as the main product.     

On the mechanism of aromatic hydroxylation by O(3P) atoms

It is shown that O(³P) oxidation of aromatic compounds in the liquid phase leading to phenols may involve the intermediacy of triplet diradicals.     

Light-induced charge redistribution in the retinal chromophore is required for initiating the bacteriorhodopsin photocycle

Bacteriorhodopsin's photocycle is initiated by the retinal chromophore light absorption. It has usually been assumed that light primarily isomerizes a retinal double bond which in turn induces protein conformational alterations and biological activity. We have studied several artificial pigments derived from retinal analogues tailored to substantially reduce the light-induced chromophore polarization. The lack of chromophore polarization was reflected in an undetectable second harmonic generation (SHG) signal. It was revealed that these artificial pigments did not exhibit any detectable light-induced photocycle nor light acceleration of the hydroxylamine-bleaching reaction. We suggest that light-induced retinal polarization triggers protein polarization which controls the course of the isomerization reaction by determining the relative efficiency of forward versus back-branching processes.     

Phase Recognition in AlN-Ti System by Energy Dispersive Spectroscopy and Electron Backscatter Diffraction

 The combination of energy dispersive spectroscopy (EDS) and electron backscatter diffraction (EBSD) techniques in scanning electron microscope was employed to characterize the reacted interface between Ti matrix and AlN particles. Due to the high localization of EDS and EBSD, representative measurements of chemical composition and reliable determination of the crystal structure were possible for each phase in the reaction zone with complex morphology. The TiN_1−x (cubic, NaCl type), Ti₃AlN (cubic, perovskite type) and Ti-rich Ti₃ Al (hexagonal, Ni₃Sn type) phases were identified in the reaction zone after annealing at 1100 °C. EDS+EBSD combination is an efficient tool for phase analysis at the interface in reactive multicomponent systems. Received August 21, 1999. Revision November 21, 1999.