Clustering a large number of compounds. 3. The limits of classification

Clustering is normally used to group items that are similar. In this application of obtaining a diverse sample from the 230,000 compounds in the National Cancer Institute Repository, we cluster to select compounds that are different from the rest, to optimize screening for new leads. With these constraints, our approach yielded many singleton clusters. We can interpret these results as evidence for a limit to classification, contrary to the customary view of chemistry as a study of classes of compounds.     

Hopping conduction in disordered carbon nanotubes

We report electrical transport measurements on individual disordered multiwalled carbon nanotubes, grown catalytically in a nanoporous anodic aluminum oxide template. In both as-grown and annealed types of nanotubes, the low-field conductance shows an exp[−(T₀/T)^1/2] dependence on temperature T, suggesting that hopping conduction is the dominant transport mechanism, albeit with different disorder-related coefficients T₀. The electric field dependence of low-temperature conductance behaves as exp[−(ξ₀/ξ)^1/2] at high electric field ξ at sufficiently low T. Finally, both annealed and unannealed nanotubes exhibit weak positive magnetoresistance at . Comparison with theory indicates that our data are best explained by Coulomb-gap variable-range hopping conduction and permits the extraction of disorder-dependent localization length and dielectric constant.     

On a Characterization of Idempotent Distributions on Discrete Fields and on the Field of <Emphasis Type="Italic">p</Emphasis>-Adic Numbers

We prove the following theorem. Let X be a discrete field, and \(\xi \) and \(\eta \) be independent identically distributed random variables with values in X and distribution \(\mu \). The random variables \(S=\xi +\eta \) and \(D=(\xi -\eta )^2\) are independent if and only if \(\mu \) is an idempotent distribution. A similar result is also proved in the case when \(\xi \) and \(\eta \) are independent identically distributed random variables with values in the field of p-adic numbers \({\mathbf {Q}}_p\), where \(p>2\), assuming that the distribution \(\mu \) has a continuous density.     

Communication: stabilization of radical anions with weakly bound electron in condensed media: a case study of diacetonyl radical anion

The radical anion resulting from electron capture by diacetonyl molecule has been characterized by EPR and optical absorption spectroscopy in glassy ether matrices at 77 K. In non-polar alkane glasses this species was not observed under the same conditions, which confirms the crucial role of matrix interactions in stabilizing this species. Calculations at the MP2 level show the vertical detachment energy to increase gradually from roughly zero for a bare anion to ～1 eV for the complex involving six ether molecules.     

Extending Pummerer reaction chemistry: studies in the palau'amine synthesis area

Exploratory oxidative cyclization studies on cyclopentanelated and cyclohexenelated oroidin derivatives utilized Pummerer chemistry to generate pentacyclic structures related to the palau'amine family of sponge metabolites. Stereochemical issues were paramount, and appropriate choice of annelated ring size led to formation of the pentacyclic framework with complete diastereoselectivity for all of the core bonds.     

Nonlocal Geometric Expansion of Convex Planar Curves

We consider a class of nonlocal geometric equations for expanding curves in the plane, arising in the study of evolutions governed by Monge-Kantorovich mass transfer. We construct convex solutions, given convex initial data. In order to obtain such solutions, we develop a new version of Perron's method. We give applications to the problem of characterizing fast/slow diffusion limits.