Data compression and prediction in neural networks

We study the relationship between data compression and prediction in single-layer neural networks of limited complexity. Quantifying the intuitive notion of Occam's razor using Rissanen's minimum complexity framework, we investigate the model-selection criterion advocated by this principle. While we find that the criterion works well for large sample sizes (as it must for consistency), the behavior for finite sample sizes is rather complex, depending intricately on the relationship between the complexity of the hypothesis space and the target space. We also show that the limited networks studied perform efficient data compression, even in the error full regime.     

The geometric Weil representation

We construct a geometric analogue of the Weil representation over a finite field. Our construction is principally invariant, not choosing any specific realization. This eliminates most of the unpleasant formulas that appear in the traditional (non-invariant) approaches, and puts in the forefront some delicate geometric phenomena which underlie this representation.     

X-RAY INDUCED VISIBLE LUMINESCENCE OF PORPHYRINS

A concept has been presented whereby X-ray irradiation can be used to induce visible luminescence of chromophores such as porphyrins. The essential aspects of the idea have been demonstrated in a supramolecular assembly consisting of a water-dispersed polystyrene latex with an embedded scintillating compound, 2,5-diphenyloxa-zole, and an externally attached hematoporphyrin. X-ray excitation of the assembly yields an emission spectra typical for hematoporphyrin with fluorescent yields. of up to 3% with respect to 2,5-diphenyloxazole emission. Significant quenching in the presence of dioxygen indicates that singlet oxygen is formed at atmospheric conditions.     

Molecular oxygen and oxidation catalysis by phosphovanadomolybdates

The history of aerobic catalytic oxidation mediated by a subclass of polyoxometalates, the phosphovanadomolybdates of the Keggin structure, [PV(x)Mo(12-x)O40](3+x)-, is described. In the earlier research it was shown that phosphovanadomolybdates catalyze oxydehydrogenation reactions through an electron-transfer oxidation of a substrate by the polyoxometalate that is then reoxidized by oxygen. These aerobic oxidations are selective and synthetically useful in various transformations, notably diene aromatization, phenol dimerization and alcohol oxidation. Oxygen transfer from the polyoxometalate to arenes and alkylarenes was also discussed as a homogeneous analog of a Mars-van Krevelen oxidation. "Second generation" catalysts include binary complexes of the polyoxometalate and a organometallic compound useful, for example, for methane oxidation and nanoparticles stabilized by polyoxometalates effective for aerobic alkene epoxidation.     

Interaction of scanning probes with semiconductor nanocrystals; physical mechanism and basis for near-field optical imaging

We investigate the modification of photoluminescence (PL) from single semiconductor nanocrystal quantum dots (NCs) in the proximity of metal and semiconducting atomic force microscope (AFM) tips. The presence of the tip alters the radiative decay rate of an emitter via interference and opens efficient nonradiative decay channels via energy transfer to the tip material. These effects cause quenching (or enhancement) of the emitter's PL intensity as a function of its distance from the interacting tip. We take advantage of this highly distance-dependent effect to realize a contrast mechanism for high-resolution optical imaging. AFM tips are optimized as energy acceptors by chemical functionalization with InAs NCs to achieve optical resolution down to 30 nm. The presented experimental scheme offers high-resolution optical information while maintaining the benefits of traditional AFM imaging. We directly measure the PL intensity of single NCs as a function of the tip distance. Our results are in good agreement with calculations made by a classical theoretical model describing an oscillating dipole interacting with a planar mirror.     

Palladium nanoparticles stabilized by alkylated polyethyleneimine as aqueous biphasic catalysts for the chemoselective stereocontrolled hydrogenation of alkenes

Palladium nanoparticles were prepared, stabilized, and dispersed in water by alkylated branched polyethyleneimine. The palladium nanoparticles were effective aqueous biphasic catalysts for the chemoselective hydrogenation of alkenes with preferential reduction of less hindered double bonds, such as reduction of 3-methylcyclohexene in the presence of 1-methylcyclohexene and 1-octene in the presence of 2-methyl-2-heptene. [structure: see text].     

Generalized Isotonic Regression

We present a new computational and statistical approach for fitting isotonic models under convex differentiable loss functions through recursive partitioning. Models along the partitioning path are also isotonic and can be viewed as regularized solutions to the problem. Our approach generalizes and subsumes the well-known work of Barlow and Brunk on fitting isotonic regressions subject to specially structured loss functions, and expands the range of loss functions that can be used (e.g., adding Huber loss for robust regression). This is accomplished through an algorithmic adjustment to a recursive partitioning approach recently developed for solving large-scale ?₂-loss isotonic regression problems. We prove that the new algorithm solves the generalized problem while maintaining the favorable computational and statistical properties of the l₂ algorithm. The results are demonstrated on both real and synthetic data in two settings: fitting count data using negative Poisson log-likelihood loss, and fitting robust isotonic regressions using Huber loss. Proofs of theorems and a MATLAB-based software package implementing our algorithm are available in the online supplementary materials.     

Electrochemical Hydroxylation of Arenes Catalyzed by a Keggin Polyoxometalate with a Cobalt(IV) Heteroatom

The sustainable, selective direct hydroxylation of arenes, such as benzene to phenol, is an important research challenge. An electrocatalytic transformation using formic acid to oxidize benzene and its halogenated derivatives to selectively yield aryl formates, which are easily hydrolyzed by water to yield the corresponding phenols, is presented. The formylation reaction occurs on a Pt anode in the presence of [Co^IIIW₁₂O₄₀]^5? as a catalyst and lithium formate as an electrolyte via formation of a formyloxyl radical as the reactive species, which was trapped by a BMPO spin trap and identified by EPR. Hydrogen was formed at the Pt cathode. The sum transformation is ArH+H₂O→ArOH+H₂. Non‐optimized reaction conditions showed a Faradaic efficiency of 75 % and selective formation of the mono‐oxidized product in a 35 % yield. Decomposition of formic acid into CO₂ and H₂ is a side‐reaction.