Empirical minimization

We investigate the behavior of the empirical minimization algorithm using various methods. We first analyze it by comparing the empirical, random, structure and the original one on the class, either in an additive sense, via the uniform law of large numbers, or in a multiplicative sense, using isomorphic coordinate projections. We then show that a direct analysis of the empirical minimization algorithm yields a significantly better bound, and that the estimates we obtain are essentially sharp. The method of proof we use is based on Talagrand's concentration inequality for empirical processes. Research partially supported by NSF under award DMS-0434393. Research partially supported by the Australian Research Council Discovery Porject DP0343616.     

Synthesis and characteristics of microspheres of polystyrene derivatives

Two sytrene derivatives formylstyrene and styrene sulfonylcholoride, were synthesized. Polymeric microspheres in diameters ranging from 0.1 to 2 μm were synthesized by polymerization of chlormoethylstyrene, formylstyrene, and styrene sulfonylcholoride in organic solvents, in the presence of appropriate surfactants. The kinetics of microsphere formation were studied. The molecular weight distribution of the products was determined by gel permeation chromatography. Conditions for binding various amino ligands to the microspheres were also established.     

The synthesis and characterization of thiol-based aryl diazonium modified glassy carbon electrode for the voltammetric determination of low levels of Hg(II)

Electrochemical determination of Hg(II) in aquatic solutions on bare and modified glassy carbon electrode (GCE) is reported. Optimizing the parameters used for a bare GCE, such as the electrolyte solution, the potential and time of deposition, resulted in linear response over a large range of Hg(II) concentrations (4–160 ppb) using linear sweep anodic stripping voltammetry. Modification of the electrode with 4,4′-disulfanediyldibenzenediazonium (DSBD) yielded a lowest detection limit of 1 ppb. Two procedures for DSBD synthesis are described for the first time, and the product was characterized by microanalysis, FTIR and ¹H-NMR. The electrochemical attachment of DSBD to the electrode was studied and compared with the electrochemical behaviour of DSBD analogous molecules, i.e. 4-aminophenyl disulfide, p-aminothiophenol and phenyl disulfide.     

The Proalgebraic Completion of Rigid Groups

A finitely generated group is called representation rigid (briefly, rigid) if for every n, has only finitely many classes of simple representations in dimension n. Examples include higher rank S-arithmetic groups. By Margulis super rigidity, the latter have a stronger property: they are representation super rigid; i.e., their proalgebraic completion is finite dimensional. We construct examples of nonlinear rigid groups which are not super rigid, and which exhibit every possible type of infinite dimensionality. Whether linear representation rigid groups are super rigid remains an open question.     

Observation of a quantized hall resistivity in the presence of mesoscopic fluctuations

We present an experimental study of mesoscopic, two-dimensional electronic systems at high magnetic fields. Our samples, prepared from a low-mobility InGaAs/InAlAs wafer, exhibit reproducible, sample specific, resistance fluctuations. Focusing on the lowest Landau level, we find that, while the diagonal resistivity displays strong fluctuations, the Hall resistivity is free of fluctuations and remains quantized at its nu=1 value, h/e(2). This is true also in the insulating phase that terminates the quantum Hall series. These results extend the validity of the semicircle law of conductivity in the quantum Hall effect to the mesoscopic regime.     

Parallel magnetic field induced transition in transport in the dilute two-dimensional hole system in GaAs

A magnetic field applied parallel to the two-dimensional hole system in the GaAs/AlGaAs heterostructure, which is metallic in the absence of an external magnetic field, can drive the system into insulating at a finite field through a well-defined transition. The value of resistivity at the transition is found to depend strongly on density.     

Embedding with a Lipschitz function

We investigate a new notion of embedding of subsets of {?1,1}ⁿ in a given normed space, in a way which preserves the structure of the given set as a class of functions on {1, …, n}. This notion is an extension of the margin parameter often used in Nonparametric Statistics. Our main result is that even when considering “small” subsets of {?1, 1}ⁿ, the vast majority of such sets do not embed in a better way than the entire cube in any normed space that satisfies a minor structural assumption. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005     

Angular dependence of the magnetic-field driven superconductor-insulator transition in thin films of amorphous indium-oxide

A significant anisotropy of the magnetic-field driven superconductor-insulator transition is observed in thin films of amorphous indium-oxide. The anisotropy is largest for more disordered films which have a lower transition field. At higher magnetic fields the anisotropy reduces and even changes sign beyond a sample specific and temperature independent magnetic field value. The data are consistent with the existence of more than one mechanism affecting transport at high magnetic fields.