Syntheses,homeomorphic and configurational isomerizations,and structures of macrocyclic aliphatic dibridgehead diphosphines; molecules that turn themselves inside out

The diphosphine complexes cis- or trans- PtCl₂(P((CH₂)_n)₃P ) (n = b/12, c/14, d/16, e/18) are demetalated by MC X nucleophiles to give the title compounds (P((CH₂)_n)₃)P (3b–e, 91–71%). These “empty cages” react with PdCl₂ or PtCl₂ sources to afford trans- MCl₂(P((CH₂)_n)₃P ). Low temperature ³¹P NMR spectra of 3b and c show two rapidly equilibrating species (3b, 86 : 14; 3c, 97 : 3), assigned based upon computational data to in,in (major) and out,out isomers. These interconvert by homeomorphic isomerizations, akin to turning articles of clothing inside out (3b/c: ΔH^‡ 7.3/8.2 kcal mol⁻¹, ΔS^‡ −19.4/−11.8 eu, minor to major). At 150 °C, 3b, c, e epimerize to (60–51) : (40–49) mixtures of (in,in/out,out) : in,out isomers, which are separated via the bis(borane) adducts 3b, c, e·2BH₃. The configurational stabilities of in,out-3b, c, e preclude phosphorus inversion in the interconversion of in,in and out,out isomers. Low temperature ³¹P NMR spectra of in,out-3b, c reveal degenerate in,out/out,in homeomorphic isomerizations (ΔG^‡_Tc 12.1, 8.5 kcal mol⁻¹). When (in,in/out,out)-3b, c, e are crystallized, out,out isomers are obtained, despite the preference for in,in isomers in solution. The lattice structures are analyzed, and the D₃ symmetry of out,out-3c enables a particularly favorable packing motif. Similarly, (in,in/out,out)-3c, e·2BH₃ crystallize in out,out conformations, the former with a cycloalkane solvent guest inside.

It’s not a magic trick. Molecules can turn themselves inside out, just like articles of clothing or other familiar household objects. This behavior is demonstrated for the title compounds through a combination of synthesis, rate, and NMR studies.     

High throughput screening for neurodegeneration and complex disease phenotypes

High throughput screening (HTS) for complex diseases is challenging. This stems from the fact that complex phenotypes are difficult to adapt to rapid, high throughput assays. We describe the recent development of high throughput and high-content screens (HCS) for neurodegenerative diseases, with a focus on inherited neurodegenerative disorders, such as Huntington's disease. We describe, among others, HTS assays based on protein aggregation, neuronal death, caspase activation and mutant protein clearance. Furthermore, we describe high-content screens that are being used to prioritize hits identified in such HTS assays. These assays and screening approaches should accelerate drug discovery for neurodegenerative disorders and guide the development of screening approaches for other complex disease phenotypes.     

On the integration of data and mathematical modeling languages

This paper examines ways in which the addition of data modeling features can enhance the capabilities of mathematical modeling languages. It demonstrates how such integration is achieved as an application of the embedded languages technique proposed by Bhargava and Kimbrough [4]. Decision-making, and decision support systems, require the representation and manipulation of both data and mathematical models. Several data modeling languages as well as several mathematical modeling languages exist, but they have different sets of these capabilities. We motivate with a detailed example the need for the integration of these capabilities. We describe the benefits that might result, and claim that this could lead to a significant improvement in the functionality of model management systems. Then we present our approach for the integration of these languages, and specify how the claimed benefits can be realized.The author's work on this paper was performed in conjunction with research funded by the Naval Postgraduate School.     

Pricing under quality of service uncertainty: Market segmentation via statistical QoS guarantees

This article examines how performance-contingent pricing schemes with long-term statistical performance guarantees can be applied to many IT services. We study two forms of performance-contingent pricing, with rebate proportional to failure rate and fixed rebate for below-threshold performance. We show that threshold-performance contingency pricing can increase both profits and fairness (customers who receive higher benefits pay higher effective price) relative to standard pricing. But an even better solution is to offer a menu of performance guarantees: this can increase the firm’s profit and segment the market. Only service providers whose performance level is sufficiently better than the industry standard can benefit from this pricing mechanism.     

Practical synthesis of chiral 9,9'-spirobixanthene-1,1'-diol

A concise four-step synthesis of 9,9'-spirobixanthene-1,1'-diol is reported, featuring a practical preparation at large scale without the use of column chromatography purification. Co-crystallization with N-benzylcinchonidinium chloride and N-benzylquininium chloride rendered the optically pure product in both enantiomers.     

Aryl trihydroxyborates: easily isolated discrete species convenient for direct application in coupling reactions

A conceptually and practically simple alternative approach to the use of arylboron species as the organometallic component in cross-coupling processes is described whereby trihydroxyborate salts are isolated and directly employed. The protocol derives practical benefit from the ease and convenience of the isolation and subsequent use of the discrete borate salts, eliminates the need for additional base, and aids the use of correct reaction stoichiometry.     

The Conjugacy Class Number k(G): A Different Perspective

For a finite group G, let m(G) denote the least positive integer such that the union of any m(G) distinct nontrivial conjugacy classes of G together with the identity of G is a subgroup of G. We prove that m(G) = k(G) ?1 for all m(G) ≥2.     

Applications of Hybrid Monte Carlo to Bayesian Generalized Linear Models: Quasicomplete Separation and Neural Networks

Abstract

The “leapfrog” hybrid Monte Carlo algorithm is a simple and effective MCMC method for fitting Bayesian generalized linear models with canonical link. The algorithm leads to large trajectories over the posterior and a rapidly mixing Markov chain, having superior performance over conventional methods in difficult problems like logistic regression with quasicomplete separation. This method offers a very attractive solution to this common problem, providing a method for identifying datasets that are quasicomplete separated, and for identifying the covariates that are at the root of the problem. The method is also quite successful in fitting generalized linear models in which the link function is extended to include a feedforward neural network. With a large number of hidden units, however, or when the dataset becomes large, the computations required in calculating the gradient in each trajectory can become very demanding. In this case, it is best to mix the algorithm with multivariate random walk Metropolis—Hastings. However, this entails very little additional programming work.     

Design of a highly sensitive photonic crystal waveguide platform for refractive index based biosensing

In this paper, a photonic crystal waveguide platform on silicon-on-insulator substrate is proposed in order to realize a highly sensitive refractive index based biosensor. Following the design, the analysis of the sensor structure are made by using the three dimensional Finite Difference Time Domain method. The principle of sensing is based on the change in refractive index, which in turn changes the output spectrum of the waveguide. Results show that the sensitivity of the sensor depends mainly on the geometrical properties of the defect region of the photonic crystal structure. The phenomenon is verified for various samples having refractive index ranging from 1 (air) to 1.57 (Bovine serum albumin). Further, the structure is compared with few other conventional photonic crystal waveguide designs to analyze the sensing performance. The estimated value of sensitivity of the sensor is found to be 260 nm/RIU with a detection limit of 0.001 RIU. This high sensitivity can enhance the performance of low-concentration analytes detection.     

Fixed point results for mappings satisfying (ψ φ)-weakly contractive condition in ordered partial metric spaces

In [18], Matthews introduced a new class of metric spaces, that is, the concept of partial metric spaces, or equivalently, weightable quasi-metrics, are investigated to generalize metric spaces (X, d), to develop and to introduce a new fixed point theory. In partial metric spaces, the self-distance for any point need not be equal to zero. In this paper, we study some results for single map satisfying (ψ,φ)-weakly contractive condition in partial metric spaces endowed with partial order. An example is given to support the useability of our results.