On bounds for the mode and median of the generalized hyperbolic and related distributions

Except for certain parameter values, a closed form formula for the mode of the generalized hyperbolic (GH) distribution is not available. In this paper, we exploit results from the literature on modified Bessel functions and their ratios to obtain simple but tight two-sided inequalities for the mode of the GH distribution for general parameter values. As a special case, we deduce tight two-sided inequalities for the mode of the variance-gamma (VG) distribution, and through a similar approach we also obtain tight two-sided inequalities for the mode of the McKay Type I distribution. The analogous problem for the median is more challenging, but we conjecture some monotonicity results for the median of the VG and McKay Type I distributions, from we which we conjecture some tight two-sided inequalities for their medians. Numerical experiments support these conjectures and also lead us to a conjectured tight lower bound for the median of the GH distribution.     

Anatomical and functional MR imaging in the macaque monkey using a vertical large-bore 7 Tesla setup

Functional magnetic resonance imaging (MRI) in the nonhuman primate promises to provide a much desired link between brain research in humans and the large body of systems neuroscience work in animals. We present here a novel high field, large-bore, vertical MR system (7 T/60 cm, 300 MHz), which was optimized for neuroscientific research in macaque monkeys. A strong magnetic field was applied to increase sensitivity and spatial resolution for both MRI and spectroscopy. Anatomical imaging with voxel sizes as small as 75×150×300 μm³ and with high contrast-to-noise ratios permitted the visualization of the characteristic lamination of some neocortical areas, e.g., Baillarger lines. Relaxation times were determined for different structures: at 7 T, T1 was 2.01/1.84/1.54 s in GM/GM-V1/WM, T2 was 59.1/54.4 ms in GM/WM and T2* was 29 ms. At 4.7 T, T1 was 25% shorter, T2 and T2* 18% longer compared to 7T. Spatiotemporally resolved blood-oxygen-level-dependent (BOLD) signal changes yielded robust activations and deactivations (negative BOLD), with average amplitudes of 4.1% and −2.4%, respectively. Finally, the first high-resolution (500 μm in-plane) images of cerebral blood flow in the anesthetized monkey are presented. On functional activation we observed flow increases of up to 38% (59 to 81 ml/100 g/min) in the primary visual cortex, V1. Compared to BOLD maps, functional CBF maps were found to be localized entirely within the gray matter, providing unequivocal evidence for high spatial specificity. The exquisite sensitivity of the system and the increased specificity of the hemodynamic signals promise further insights into the relationship of the latter to the underlying physiological activity.     

Static and Dynamic Quenching of Tryptophan Fluorescence in Various Proteins by a Chromium (III) Complex

The interaction of a chromium (III) complex, (R,R)-N,N′-Bis(3,5-di-tert-butylsalicylidene)-1,2-cyclohexane-diaminochromium (III), with human serum albumin, bovine serum albumin, lysozyme, and free tryptophan was studied using steady-state fluorescence spectroscopy. Dynamic and static quenching constants were calculated using Stern-Volmer kinetics. The complex bound more tightly to the serum albumins than to lysozyme or free tryptophan, but only one binding site was determined in all systems. The interaction was also determined to be thermodynamically favorable, and the binding constants were on the order of 10³–10⁶. The fluorescence quenching was static in nature with Forster distances in the 1.8–2.0 nm range.     

Constructive equivalence relations on computable probability measures

A central object of study in the field of algorithmic randomness are notions of randomness for sequences, i.e., infinite sequences of zeros and ones. These notions are usually defined with respect to the uniform measure on the set of all sequences, but extend canonically to other computable probability measures. This way each notion of randomness induces an equivalence relation on the computable probability measures where two measures are equivalent if they have the same set of random sequences.In what follows, we study the equivalence relations induced by Martin-Löf randomness, computable randomness, Schnorr randomness and Kurtz randomness, together with the relations of equivalence and consistency from probability theory. We show that all these relations coincide when restricted to the class of computable strongly positive generalized Bernoulli measures. For the case of arbitrary computable measures, we obtain a complete and somewhat surprising picture of the implications between these relations that hold in general.     

Comparison of an instrumental and modified Kjeldahl technique for determination of nitrogen in niobium and tantalum alloys

Results obtained for the determination of nitrogen in two tantalum alloys and six niobium alloys by modified Kjeldahl and Leco TC-30 nitrogen—oxygen determinator are compared. In the 5–25 ppm range, for tantalum alloys, the relative standard deviation was 3–9% by the Kjeldahl procedure and 9–11% by the instrumental technique. In the range 30–80 ppm, for niobium alloys, the relative standard deviation was 2–8% by the Kjeldahl procedure and 5–7% by the instrumental technique.     

Current transport along grain boundaries in d-wave superconductors

The use of a classic phase retrieval algorithm has been previously used to determine the local critical current J_c(x) along the length of grain boundary Josephson junctions that can be characterized using a standard s-wave model. The phase retrieval approach has been modified for use with d-wave dominated superconductors to allow for negative local currents along the boundary. In general solutions to the 1-D phase problem are not unique, however in the present work special constraints are employed experimentally to ensure uniqueness. The various current distribution solutions and their possible uniqueness are explored. The solutions are consistent with most existing d-wave Josephson junction boundary models and can be used to understand the basic current distribution along 45° YaBa₂Cu₃O_7−x grain boundary junctions as well as providing a means for mapping the location of self-generated flux cores.     

Ultrahigh-gain bulk solid-state stimulated Brillouin scattering phase-conjugation material

We report what is believed to be the first observation of phase conjugation by stimulated Brillouin scattering (SBS) in TeO2 single crystal. The observed very low threshold for phase-conjugate mirror (PCM) formation, high PCM reflectivities in this initial experiment, and commercial availability of material hold promise for a host of practical applications in the near future. The resultant steady-state gain parameter, approximately 100 cm/GW, is to our knowledge the largest ever reported for any SBS material.     

Structure of peptide solutions: A light scattering and numerical study

We investigated the interactions between protein molecules in solution, in particular for low salt concentrations and thus strong electrostatic interactions where a treatment based on the second virial coefficient is not sufficient. Static and dynamic light scattering experiments on solutions containing the peptide human calcitonin (hCT) were combined with calculations based on the Ornstein-Zernike equation with the hypernetted chain (HNC) closure and computer simulations within the primitive electrolyte model. The simulation illustrates the distribution of proteins in solution and the formation of (transient) protein aggregates. It furthermore allows us to predict the physical stability of hCT solutions in dependence of ionic strength, pH and hCT concentration.Received: 26 December 2003, Published online: 25 March 2004PACS: 87.15.Nn Properties of solutions; aggregation and crystallization of macromolecules - 61.20.Qg Structure of associated liquids: electrolytes, molten salts, etc. - 87.14.Ee ProteinsV. Lobaskin: Present address: Max-Planck-Institut für Polymerforschung, 55128 Mainz, Germany     

Completion of Countably Seminormed Spaces

Let E be a vector space with a topology generated by countably many increasing seminorms p1 p2 ...and let _{p i} be the completion of E/ker (pi) with respect to pi. If pi are norms compatible in a certain sense, it is known that E is a complete space if and only if E=_{i=1 p i} . In this paper we give a similar characterization of complete spaces in a general case when pi are seminorms, without any additional assumptions. Our characterization coincides with the known one if pi are compatible norms.