Robust optimal strategies in Markov decision problems

An optimal strategy in a Markov decision problem is robust if it is optimal in every decision problem (not necessarily stationary) that is close to the original problem. We prove that when the state and action spaces are finite, an optimal strategy is robust if and only if it is the unique optimal strategy.     

Analysis of quinocide in unprocessed primaquine diphosphate and primaquine diphosphate tablets using gas chromatography–mass spectrometry with supersonic molecular beams

Malaria is one of the most widespread and deadly diseases on the planet. Every year, about 500 million new cases are diagnosed, and the annual death toll is about 3 million. Primaquine has strong antiparasitic effects against gametocytes and can therefore prevent the spread of the parasite from treated patients to mosquitoes. It is also used in radical cures and prevents relapse. Consequently, primaquine is an often-used drug. In this study the separation of unprocessed primaquine from the contaminant quinocide based on gas chromatography–mass spectrometry with supersonic molecular beam (SMB) is presented and 7.5 mg primaquine diphosphate tablets were analyzed. We present a novel method for fast determination of quinocide which is an isomer of primaquine as the main contaminant in unprocessed primaquine and in its medical form as tablets by gas chromatography–mass spectrometry with SMB (also named supersonic GC–MS). Supersonic GC–MS provides enhanced molecular ion without any ion source related peak tailing plus extended range of compounds amenable for GC–MS analysis. In addition, major isomer mass spectral effects were revealed in the mass spectra of primaquine and quinocide which facilitated the unambiguous identification of quinocide in primaquine tablets. Fast GC–MS analysis is demonstrated with less then 2 min elution time of the drug and its main contaminants.     

Benzobis(imidazolium)-cucurbit[8]uril complexes for binding and sensing aromatic compounds in aqueous solution

The utilities of benzobis(imidazolium) salts (BBIs) as stable and fluorescent components of supramolecular assemblies involving the macrocyclic host, cucurbit[8]uril (CB[8]), are described. CB[8] has the unusual ability to bind tightly and selectively to two different guests in aqueous media, typically methyl viologen (MV) as the first guest, followed by an indole, naphthalene, or catechol-containing second guest. Based on similar size, shape, and charge, tetramethyl benzobis(imidazolium) (MBBI) was identified as a potential alternative to MV that would increase the repertoire of guests for cucurbit[8]uril. Isothermal titration calorimetry (ITC) studies showed that MBBI binds to CB[8] in a 1:1 ratio with an equilibrium association constant (K(a)) value of 5.7×10(5) M(-1), and that the resulting MBBI·CB[8] complex binds to a series of aromatic second guests with K(a) values ranging from 10(3) to 10(5) M(-1). These complexation phenomena were supported by mass spectrometry, which confirmed complex formation, and a series of NMR studies that showed the expected upfield perturbation of aromatic peaks and of the MBBI methyl peaks. Surprisingly, the binding behavior of MBBI is strikingly similar to that of MV, and yet MBBI offers a number of substantial advantages for many applications, including intrinsic fluorescence, high chemical stability, and broad synthetic tunability. Indeed, the intense fluorescence emission of the MBBI·CB[8] complex was quenched upon binding to the second guests, thus demonstrating the utility of MBBI as a component for optical sensing. Building on these favorable properties, the MBBI·CB[8] system was successfully applied to the sequence-selective recognition of peptides as well as the controlled disassembly of polymer aggregates in water. These results broaden the available guests for the cucurbit[n]uril family and demonstrate potentially new applications.     

A systems approach to controlling supramolecular architecture and emergent solution properties via host-guest complexation in water

The assembly behavior of aryl/alkyl imidazolium ionic liquid salts in aqueous solution has been investigated. These salts undergo self-assembly into one-dimensional stacks via hydrophobic and π-π interactions upon increasing concentration, which led to a substantial increase in the solution viscosity in water. Addition of the macrocyclic host molecules cucurbit[n]urils (CB[n]) were found to effectively alter the supramolecular assemblies, as evidenced from the dramatic increase (by CB[7]) and decrease (by CB[8]) in solution viscosity and aggregation size in water, on account of the different binding stoichiometries, 1:1 complexation with CB[7] and 2:1 complexation with CB[8]. Furthermore, the aggregate architectures were controllably modified by competitive guests for the CB[n] hosts. This complex supramolecular systems approach has tremendous implications in the fields of molecular sensor design, nonlinear viscosity modification, and controlled release of target molecules from a defined supramolecular scaffold in water.     

Diameters of Chevalley groups over local rings

Let G be a Chevalley group scheme of rank l. Let ${G_n := G(\mathbb{Z} / p^{n} \mathbb{Z})}$ be the family of finite groups for ${n \in \mathbb{N}}$ and some fixed prime number p >?p ₀. We prove a uniform poly-logarithmic diameter bound of the Cayley graphs of G _n with respect to arbitrary sets of generators. In other words, for any subset S which generates G _n , any element of G _n is a product of C n ^d elements from ${S \cup S^{-1}}$ . Our proof is elementary and effective, in the sense that the constant d and the functions p ₀(l) and C(l, p) are calculated explicitly. Moreover, we give an efficient algorithm for computing a short path between any two vertices in any Cayley graph of the groups G _n .     

Strongly fluorescent, switchable perylene bis(diimide) host-guest complexes with cucurbit[8]uril in water

Supramolecular complexation of perylene bis(diimide) (PDI) dyes with the macrocyclic host cucurbit[8]uril (CB[8]) prevents self-aggregation of the dye molecules and enables their use as highly (photo)chemically stable, strongly-emitting fluorophores in water. The complexes are stimuli-responsive to binders and can be electrochemically cycled, leading to reversible on-off fluorescence switching and access to noncovalent formation of higher-order architectures in water.     

High-order harmonic generation from ions in a capillary discharge

We demonstrate a significant extension of the high-order harmonic cutoff by using a fully-ionized capillary discharge plasma as the generation medium. The preionized plasma dramatically reduces ionization-induced defocusing and energy loss of the driving laser due to ionization. This allows for significantly higher photon energies, up to 150 eV, to be generated from xenon ions, compared with the 70 eV observed previously. We also demonstrate enhancement of the harmonic flux of nearly 2 orders of magnitude at photon energies around 90 eV when the capillary discharge is used to ionize xenon, compared with harmonic generation in a hollow waveguide. The use of a plasma as a medium for high-order harmonic generation shows great promise for extending efficient harmonic generation to much shorter wavelengths using ions.     

Size discrimination in the coordination chemistry of an isoindoline pincer ligand with CdII and ZnII

The reactions of Cd2+ and Zn2+ with the pyridine-arm isoindoline ligand 4'-MeLH = 1,3-bis[2-(4-methylpyridyl)imino]isoindoline produced the series of octahedrally coordinated complexes M(4'-MeL)2, [M(4'-MeLH)2]2+, and [M(4'-MeL)(4'-MeLH)]+. The complexes M(4'-MeL)2 resulted from reactions of the respective metal perchlorates with deprotonated ligand, whereas the complexes [M(4'-MeLH)2](ClO4)2 resulted from reactions with ligand in the absence of added base. The mixed-ligand complexes [M(4'-MeL)(4'-MeLH)]+ were generated in solution by reactions of equimolar quantities of M(4'-MeL)2 and [M(4'-MeLH)2]2+. Whereas [Cd(4'-MeL)(4'-MeLH)]+ is stable in solution, [Zn(4'-MeL)(4'-MeLH)]+ converts to and establishes equilibrium with the tetrahedrally coordinated, trinuclear complex [Zn3(4'-MeL)4]2+. The complexes Cd(4'-MeL)2 (1), Zn(4'-MeL)2 (2), and [Cd(4'-MeL)(4'-MeLH)]ClO4 (5) were characterized by single-crystal X-ray diffraction, with the latter complex being shown to contain 4'-MeLH coordinated as a protonated iminium zwitterionic ligand. The [M(4'-MeLH)2]2+ and [M(4'-MeL)(4'-MeLH)]+ complexes are tautomeric in solution because of the shuttling of the iminium protons between imine N atoms. The rate of prototropic tautomerism in [Cd(4'-MeLH)2]+ was followed by 1H NMR spectroscopy. Over the temperature range 276-312 K, a linear Eyring plot with the activation parameters DeltaG++ = 16.0 +/- 0.1 kcal/mol, DeltaH++ = 2.9 +/- 0.1 kcal/mol, and DeltaS++ = -44.0 +/- 0.3 cal/mol.K was obtained.