The Pólya Sum Process: Limit Theorems for Conditioned Random Fields

Zessin (J. Contemp. Math. Anal. 44(1):36–44, 2009) constructed the so-called Pólya sum process via partial integration technique. This process shares some important properties with the Poisson process such as complete randomness and infinite divisibility. This work discusses H-sufficient statistics for the Pólya sum process as was done for the Poisson process by Nguyen and Zessin (Z. Wahrscheinlichkeitstheor. Verw. Geb. 37(3):191–200, 1976/77).     

Morphological, histological, and ultrastructural characterization of degenerating salivary glands in females of the cattle-tick Rhipicephalus (Boophilus) microplus (CANESTRINI, 1887) (Acari: Ixodidae)

The present study describes the morphology and ultrastructure of the salivary glands of semi-engorged females of the southern cattle-tick Rhipicephalus (Boophilus) microplus. The acini that compose these glands, at that specific feeding stage, show cells featuring degenerative process of the salivary glands, such as: vacuolated cytoplasm, condensed chromatin, fragmented nuclei, and presence of apoptotic bodies. In addition, the presence of microorganisms was detected, with morphology typical of protozoa, inside these organs.     

J-modulation effects in DOSY experiments and their suppression: the Oneshot45 experiment

Diffusion-ordered spectroscopy (DOSY) is a powerful NMR method for identifying compounds in mixtures. DOSY experiments are very demanding of spectral quality; even small deviations from expected behaviour in NMR signals can cause significant distortions in the diffusion domain. This is a particular problem when signals overlap, so it is very important to be able to acquire clean data with as little overlap as possible. DOSY experiments all suffer to a greater or lesser extent from multiplet phase distortions caused by J-modulation, requiring a trade-off between such distortions and gradient pulse width. Multiplet distortions increase spectral overlap and may cause unexpected and misleading apparent diffusion coefficients in DOSY spectra. These effects are described here and a simple and effective remedy, the addition of a 45° purging pulse immediately before the onset of acquisition to remove the unwanted anti-phase terms, is demonstrated. As well as affording significantly cleaner results, the new method allows much longer diffusion-encoding pulses to be used without problems from J-modulation, and hence greatly increases the range of molecular sizes that can be studied for coupled spin systems. The sensitivity loss is negligible and the added phase cycling is modest. The new method is illustrated for a widely-used general purpose DOSY pulse sequence, Oneshot.     

High resolution 13C DOSY: the DEPTSE experiment

High Resolution Diffusion-ordered Spectroscopy (HR-DOSY) is a valuable tool for mixture analysis by NMR. It separates the signals from different components according to their diffusion behavior, and can provide exquisite diffusion resolution when there is no signal overlap. In HR-DOSY experiments on (1)H (by far the most common nucleus used for DOSY) there is frequent signal overlap that confuses interpretation. In contrast, a (13)C spectrum usually has little overlap, and is in this respect a much better option for a DOSY experiment. The low signal-to-noise ratio is a critical limiting factor, but with recent technical advances such as cryogenic probes this problem is now less acute. The most widely-used pulse sequences for (13)C DOSY perform diffusion encoding with (1)H, using a stimulated echo in which half of the signal is lost. This signal loss can be avoided by encoding diffusion with (13)C in a spin echo experiment such as the DEPTSE pulse sequence described here.     

A Series of Analogues to the AT2R Prototype Antagonist C38 Allow Fine Tuning of the Previously Reported Antagonist Binding Mode

We here report on our continued studies of ligands binding to the promising drug target angiotensin II type 2 receptor (AT₂R). Two series of compounds were synthesized and investigated. The first series explored the effects of adding small substituents to the phenyl ring of the known selective nonpeptide AT₂R antagonist C38 , generating small but significant shifts in AT₂R affinity. One compound in the first series was equipotent to C38 and showed similar kinetic solubility, and stability in both human and mouse liver microsomes. The second series was comprised of new bicyclic derivatives, amongst which one ligand exhibited a five-fold improved affinity to AT₂R as compared to C38 . The majority of the compounds in the second series, including the most potent ligand, were inferior to C38 with regard to stability in both human and mouse microsomes. In contrast to our previously reported findings, ligands with shorter carbamate alkyl chains only demonstrated slightly improved stability in microsomes. Based on data presented herein, a more adequate, tentative model of the binding modes of ligand analogues to the prototype AT₂R antagonist C38 is proposed, as deduced from docking redefined by molecular dynamic simulations.     

Utility maximization, risk aversion, and stochastic dominance

Consider an investor trading dynamically to maximize expected utility from terminal wealth. Our aim is to study the dependence between her risk aversion and the distribution of the optimal terminal payoff. Economic intuition suggests that high risk aversion leads to a rather concentrated distribution, whereas lower risk aversion results in a higher average payoff at the expense of a more widespread distribution. Dybvig and Wang (J. Econ. Theory, 2011, to appear) find that this idea can indeed be turned into a rigorous mathematical statement in one-period models. More specifically, they show that lower risk aversion leads to a payoff which is larger in terms of second order stochastic dominance. In the present study, we extend their results to (weakly) complete continuous-time models. We also complement an ad-hoc counterexample of Dybvig and Wang, by showing that these results are “fragile”, in the sense that they fail in essentially any model, if the latter is perturbed on a set of arbitrarily small probability. On the other hand, we establish that they hold for power investors in models with (conditionally) independent increments.     

Cations and Anions of Dibenzo[a,e]pentalene and Reduction of a Dibenzo[a,e]pentalenophane

Dibenzo[a,e]pentalene (DBP) is a non-alternant conjugated hydrocarbon with antiaromatic character and ambipolar electrochemical behavior. Upon both reduction and oxidation, it becomes aromatic. We herein study the chemical oxidation and reduction of a planar DBP derivative and a bent DBP-phane. The molecular structures of its planar dication, cation radical and anion radical in the solid state demonstrate the gained aromaticity through bond length equalization, which is supported by nucleus independent chemical shift-calculations. EPR spectra on the cation radical confirm the spin delocalization over the DBP framework. A similar delocalization was not possible in the reduced bent DBP-phane, which stabilized itself by proton abstraction from a solvent molecule upon reduction. This is the first report on structures of a DBP cation radical and dication in the solid state and of a reduced bent DBP derivative. Our study provides valuable insight into the charged species of DBP for its application as semiconductor.     

Sharp thresholds for nonlinear Hamiltonian cycles in hypergraphs

For positive integers r>?, an r‐uniform hypergraph is called an ?‐cycle if there exists a cyclic ordering of its vertices such that each of its edges consists of r consecutive vertices, and such that every pair of consecutive edges (in the natural ordering of the edges) intersect in precisely ? vertices; such cycles are said to be linear when ?=1, and nonlinear when ?>1. We determine the sharp threshold for nonlinear Hamiltonian cycles and show that for all r>?>1, the threshold for the appearance of a Hamiltonian ?‐cycle in the random r‐uniform hypergraph on n vertices is sharp and given by for an explicitly specified function λ. This resolves several questions raised by Dudek and Frieze in 2011.10     

Not Your Usual Bioisostere: Solid State Study of 3D Interactions in Cubanes

Previous studies by Desiraju and co-workers have implicated the acidic hydrogen atoms of cubane as a support network for hydrogen bonding groups. Herein we report a detailed structural analysis of all currently available 1,4-disubstituted cubane structures with an emphasis on how the cubane scaffold interacts in its solid-state environment. In this regard, the interactions between the cubane hydrogen atoms and acids, ester, halogens, ethynyl, nitrogenous groups, and other cubane scaffolds were cataloged. The goal of this study was to investigate the potential of cubane as a substitute for phenyl. This could be achieved by analyzing all contacts that are directed by the cubane hydrogen atoms in the X-ray crystal structures. As a result, we have established several new cubane interaction profiles, such as the catemer formation seen in esters, the preferences of halogen–hydrogen contacts over direct halogen bonding, and the stabilizing effects caused by the cubane hydrogen atoms interacting with ethynyl groups. These interaction profiles can then be used as a guide for designing cubane bioisosteres of known materials and drugs containing phenyl moieties.