Multivariate Liouville distributions

A random vector (X₁, …, X_n), with positive components, has a Liouville distribution if its joint probability density function is of the formf(x₁ + … + x_n)x₁^a₁.1 … x_n^a_n.1 with thea_i all positive. Examples of these are the Dirichlet and inverted Dirichlet distributions. In this paper, a comprehensive treatment of the Liouville distributions is provided. The results pertain to stochastic representations, transformation properties, complete neutrality, marginal and conditional distributions, regression functions, and total positivity and reverse rule properties. Further, these topics are utilized in various characterizations of the Dirichlet and inverted Dirichlet distributions. Matrix analogs of the Liouville distributions are also treated, and many of the results obtained in the vector setting are extended appropriately.     

Optimization of Biocompatibility for a Hydrophilic Biological Molecule Encapsulation System

Despite considerable advances in recent years, challenges in delivery and storage of biological drugs persist and may delay or prohibit their clinical application. Though nanoparticle-based approaches for small molecule drug encapsulation are mature, encapsulation of proteins remains problematic due to destabilization of the protein. Reverse micelles composed of decylmonoacyl glycerol (10MAG) and lauryldimethylamino-N-oxide (LDAO) in low-viscosity alkanes have been shown to preserve the structure and stability of a wide range of biological macromolecules. Here, we present a first step on developing this system as a future platform for storage and delivery of biological drugs by replacing the non-biocompatible alkane solvent with solvents currently used in small molecule delivery systems. Using a novel screening approach, we performed a comprehensive evaluation of the 10MAG/LDAO system using two preparation methods across seven biocompatible solvents with analysis of toxicity and encapsulation efficiency for each solvent. By using an inexpensive hydrophilic small molecule to test a wide range of conditions, we identify optimal solvent properties for further development. We validate the predictions from this screen with preliminary protein encapsulation tests. The insight provided lays the foundation for further development of this system toward long-term room-temperature storage of biologics or toward water-in-oil-in-water biologic delivery systems.     

Application of the Suzuki reaction to the asymmetric desymmetrisation of 1,2- and 1,3-disubstituted bulky cobalt metallocenes

Reaction of (η⁵-cyclopentadienyl)(η⁴-tetraphenylcyclobutadiene)cobalt with Hg(OAc)₂ (2.3 equiv) in 1:1 MeOH/CH₂Cl₂ followed by the addition of LiCl resulted in the formation of (η⁵-1,2-dichloromercuricyclopentadienyl)(η⁴-tetraphenylcyclobutadiene)cobalt (33%) and its 1,3-isomer (6%). Following conversion into their corresponding diiodides these compounds were desymmetrised by Suzuki reactions with ArB(OH)₂ employing [(R)-BINAP]PdCl₂, with the highest ee of 24% being obtained for (η⁵-1-iodo-3-(2-methoxyphenyl)cyclopentadienyl)(η⁴-tetraphenylcyclobutadiene)cobalt.     

Pattern recognition and massively distributed computing

A feature of Peter Kollman's research was his exploitation of the latest computational techniques to devise novel applications of the free energy perturbation method. He would certainly have seized upon the opportunities offered by massively distributed computing. Here we describe the use of over a million personal computers to perform virtual screening of 3.5 billion druglike molecules against protein targets by pharmacophore pattern matching, together with other applications of pattern recognition such as docking ligands without any a priori knowledge about the binding site location.     

Estimate of the cosmological bispectrum from the MAXIMA-1 cosmic microwave background map

We use the measurement of the cosmic microwave background taken during the MAXIMA-1 flight to estimate the bispectrum of cosmological perturbations. We propose an estimator for the bispectrum that is appropriate in the flat sky approximation, apply it to the MAXIMA-1 data, and evaluate errors using bootstrap methods. We compare the estimated value with what would be expected if the sky signal were Gaussian and find that it is indeed consistent, with a chi(2) per degree of freedom of approximately unity. This measurement places constraints on models of inflation.     

Different auditory filter bandwidth estimates based on profile analysis, notched noise, and hybrid tasks

Auditory filter bandwidths were estimated in three experiments. The first experiment was a profile-analysis experiment. The stimuli were composed of sinusoidal components ranging in frequency from 200 to 5000 Hz. The standard stimulus was the sum of equal-amplitude tones, and the signal stimulus had a power spectrum that varied up-down ... up-down. The number of components ranged from four to 60. Interval-by-interval level randomization prevented the change in level of a single component from reliably indicating the change from standard to signal. The second experiment was a notched-noise experiment in which the 1000-Hz tone to be detected was added to a noise with a notch arithmetically centered at 1000 Hz. Detection thresholds were estimated both in the presence of and in the absence of level randomization. In the third, hybrid, experiment a 1000-Hz tone was to be detected, and the masker was composed of equal-amplitude sinusoidal components ranging in frequency from 200 to 5000 Hz. For this experiment, thresholds were estimated both in the presence and absence of level variation. For both the notched-noise and hybrid experiments, only modest effects of level randomization were obtained. A variant of Durlach et al.'s channel model ["Towards a model for discrimination of broadband signals," J. Acoust. Soc. Am. 80, 63-72 (1986)] was used to estimate auditory filter bandwidths for all three experiments. When a two-parameter roex(p,r) filter weighting function was used to fit the data, bandwidth estimates were approximately two to three times as large for the two detection tasks than for the profile-analysis task.     

Structural changes within the plastic phase of diamantane

Structural changes within the pre-melting plastic phase of diamantane have been revealed from high-temperature X-ray powder diffraction data. A gradual transition to a more disordered state is suggested, and hexagonal symmetry ($\text{a = 14.1}\text{A}\text{?}\text{, c = 11.0}\text{A}\text{?}$) for the plastic phase is firmly established.     

Photoionisation cross-section calculations for satellite processes: Relaxed Hartree—Fock theory with application to helium n = 2 lines

The calculation of photoionisation cross-sections for atomic diagram and satellite transitions in a relaxed-orbital Hartree—Fock framework within the dipole approximation is considered, with specific numerical application to the helium system. The length, velocity and acceleration forms of the dipole operator are investigated. A reformulation of the dipole-operator expression is required for conjugate shake-up processes to ensure that the ratio of the various dipole forms is independent of photon energy at the Hartree—Fock level. The most suitable treatment produces cross-sections of accuracy comparable to experimental precision for the diagram transition at photon energies down to threshold, and for satellite transitions down to 15 eV above threshold. On the basis of the present findings, electron correlation contributions other than relaxation effects may not be as important as previously thought in contributing to satellite intensities in singly ionised systems, except in the threshold region.     

Determination of pharmaceutical compounds in skin by imaging matrix-assisted laser desorption/ionisation mass spectrometry

Matrix-assisted laser desorption/ionisation (MALDI) quadrupole time-of-flight mass spectrometry (Q-TOFMS) has been used to detect and image the distribution of a xenobiotic substance in skin. Porcine epidermal tissue was treated with 'Nizoral', a medicated shampoo containing ketoconazole (+/-)-1-acetyl-4-[p-[[(2R,4S)-2-(2,4-dichlorophenyl)-2-(imidazol-1-ylmethyl)-1,3-dioxolan-4-yl]methoxy]phenyl]piperazine) as active ingredient. Following incubation for 1 h at 37 degrees C all excess formulation was washed from the surface. A cross-section of the drug-treated tissue was then blotted onto a cellulose membrane, precoated in matrix (alpha-cyano-4-hydroxycinnamic acid (CHCA)), by airspray deposition. In separate experiments the tissue surface was treated with Nizoral within a triangular former, and subsequently blotted onto a matrix-coated membrane. Sample membranes were then mounted into the recess of specialised MALDI targets with adhesive tape. All samples were analysed by MALDI-TOFMS using an Applied Biosystem 'Q-star Pulsar i' hybrid Q-TOF mass spectrometer fitted with an orthagonal MALDI ion source and imaging software. Detection of the protonated molecule was readily achievable by this technique. Treatment of the tissue within a template gave rise to images depicting the expected distribution of the drug, demonstrating that this technique is capable of producing spatially useful data. Ion images demonstrating the permeation of the applied compound into the skin were achieved by imaging a cross-sectional imprint of treated tissue. A calibration graph for the determination of ketoconazole was prepared using the sodium adduct of the matrix ion as an internal standard. This enabled construction of a quantitative profile of drug in skin. Conventional haematoxylin and eosin staining and microscopy methods were employed to obtain a histological image of the porcine epidermal tissue. Superimposing the mass spectrometric and histological images appeared to indicate drug permeation into the dermal tissue layer.