The equality of fractal dimension and uncertainty dimension for certain dynamical systems

[MGOY] introduced the uncertainty dimension as a quantative measure for final state sensitivity in a system. In [MGOY] and [P] it was conjectured that the box-counting dimension equals the uncertainty dimension for basin boundaries in typical dynamical systems. In this paper our main result is that the box-counting dimension, the uncertainty dimension and the Hausdorff dimension are all equal for the basin boundaries of one and two dimensional systems, which are uniformly hyperbolic on their basin boundary. When the box-counting dimension of the basin boundary is large, that is, near the dimension of the phase space, this result implies that even a large decrease in the uncertainty of the position of the initial condition yields only a relatively small decrease in the uncertainty of which basin that initial point is in.Research in part supported by AFOSR and by the Department of Energy (Scientific Computing Staff Office of Energy Research)     

Robust dangerous border-collision bifurcations in piecewise smooth systems

Physical and computer experiments involving systems describable by piecewise smooth continuous maps that are nondifferentiable on some surface in phase space exhibit novel types of bifurcations in which an attracting fixed point exists before and after the bifurcation. The striking feature of these bifurcations is that they typically lead to "unbounded behavior" of orbits as a system parameter is slowly varied through its bifurcation value. This new type of border-collision bifurcation is fundamental and robust. A method that prevents such "dangerous border-collision bifurcations" is given. These bifurcations may be found in a variety of experiments including circuits.     

Yttrium aluminate crystals for slabs

The methods of growing YAG:Nd crystals with a flat interface and YAP:Nd crystals with a sharp conical interface are described. The form of the interface was controlled by the He and H₂O content in the reducing atmosphere composed mainly of Ar and H₂ as well as by axial temperature gradient above the melt level. The crystals of 120–180 mm in length were machined to the high-quality slabs.     

EPR spectroscopy of protein microcrystals oriented in a liquid crystalline polymer medium

Correlation of the g-tensor of a paramagnetic active center of a protein with its structure provides a unique experimental information on the electronic structure of the metal site. To address this problem, we made solid films containing metalloprotein (Desulfovibrio gigas cytochrome c(3)) microcrystals. The microcrystals in a liquid crystalline polymer medium (water/hydroxypropylcellulose) were partially aligned by a shear flow. A strong orientation effect of the metalloprotein was observed by EPR spectroscopy and polarizing optical microscopy. The EPR spectra of partially oriented samples were simulated, allowing for molecular orientation distribution function determination. The observed effect results in enhanced sensitivity and resolution of the EPR spectra and provides a new approach towards the correlation of spectroscopic data, obtained by EPR or some other technique, with the three-dimensional structure of a protein or a model compound.     

Optimized pathway selection in intraresidual triple-resonance experiments

An optimized intraresidual pulse sequence element with better sensitivity and suppression of sequential cross peaks is presented. Concatenation of three magnetization transfer delays allows their independent setting, in accordance with the relaxation properties of the individual spins, without concomitantly prolonging the pulse sequence. Additionally, implementations of the scheme to HNCA, HNCACB, and the TROSY based triple-resonance experiments are proposed. The feasibility of the new element was verified by recording HNCA and HNCACB on the small 8.6 kDa protein ubiquitin. The corresponding HNCA-TROSY experiment was tested on a larger protein, the 30.4 kDa Cel6A from the thermophilic soil bacterium Thermobifida fusca at 800 (1)H MHz.     

Intra- and intergroup vocal behavior in resident killer whales, Orcinus orca

Vocal communication within and between groups of individuals has been described extensively in birds and terrestrial mammals, however, little is known about how cetaceans utilize their sounds in their natural environment. Resident killer whales, Orcinus orca, live in highly stable matrilines and exhibit group-specific vocal dialects. Single call types cannot exclusively be associated with particular behaviors and calls are thought to function in group identification and intragroup communication. In the present study call usage of three closely related matrilines of the Northern resident community was compared in various intra- and intergroup contexts. In two out of the three matrilines significant changes in vocal behavior depending both on the presence and identity of accompanying whales were found. Most evidently, family-specific call subtypes, as well as aberrant and variable calls, were emitted at higher rates, whereas "low arousal" call types were used less in the presence of matrilines from different pods, subclans, or clans. Ways in which the observed changes may function both in intra- and intergroup communication.     

The diagnostic accuracy of MRI for the detection of partial- and full-thickness rotator cuff tears in adults

This study assessed the diagnostic test accuracy of magnetic resonance imaging (MRI) in the detection of partial- and full-thickness rotator cuff tears in the adult population. A systematic review was conducted of the following electronic databases: Cochrane Central Register of Controlled Trials, Medline, Embase, CINAHL, AMED, ISI Web of Science, Current Controlled Trials, National Technical Information Service, the National Institute for Health Research Portfolio, the UK National Research Register Archive and WHO International Clinical Trials Registry Platform database and reference lists of articles. All studies assessing the sensitivity and/or specificity of MRI for adult patients with suspected rotator cuff tear where surgical procedures were the reference standard were included in the study. A meta-analysis was performed to calculate pooled sensitivity, specificity, likelihood and diagnostic odds ratio values, and summary receiver operating characteristic plots were constructed. Forty-four studies were included. These included 2751 shoulders in 2710 patients. For partial-thickness rotator cuff tears, the pooled sensitivity and specificity values were 0.80 [95% confidence interval (CI): 0.79-0.84] and 0.95 (95% CI: 0.94-0.97), respectively. For full-thickness tears, the sensitivity and specificity values were 0.91 (95% CI: 0.86-0.94) and 0.97 (95% CI: 0.96-0.98), respectively. While there was no substantial difference in diagnostic test accuracy between MRIs reviewed by general radiologists and those reviewed by musculoskeletal radiologists, higher-field-strength (3.0 T) MRI systems provided the greatest diagnostic test accuracy.     

Electronic transport in graphene nanostructures on SiO2

We report two experiments on graphene nanostructures. The first was performed on a graphene nanoribbon, where the nature of electronic transport was investigated in detail. Electrons or holes are found to localize in pockets of the potential along the ribbon. Transport is governed by the joint action of localization and Coulomb interaction. The temperature-dependence of the conductance shows activated behavior at temperatures above a few Kelvin. The activation energy retraces the edges of Coulomb blockade diamonds found in nonlinear transport. In the second experiment the metallic tip of a low-temperature scanning force microscope was scanned above a graphene quantum dot. In addition to the familiar Coulomb blockade fringes, localized states are detected forming in the constrictions connecting the dot to source and drain.     

Study of Blood Porphyrin Spectral Profile for Diagnosis of Chronic Renal Failure

The progression to end-stage renal failure is independent of the initial pathogenic mechanism. Metabolic acidosis is a common consequence of chronic renal failure that results from inadequate ammonium excretion and decreased tubular bicarbonate reabsorption. Protoporphyrin IX (PpIX) is the immediate metabolic precursor of the heme molecule. The purpose of this study was to evaluate the levels of erythrocytes protoporphyrin IX at an animal model during progressive renal disease. A total of 36 eight-week-old male Wistar rats were divided into six groups: Normal, 4 and 8 weeks after 5/6 nephrectomy (NX). Renal function was evaluated by creatinine clearance and plasma creatinine levels. The autofluorescence of erythrocytes porphyrin of healthy and NX rats was analyzed using fluorescence spectroscopy. Emission spectra were obtained by exciting the samples at 405 nm. Significant differences between normal and NX rats autofluorescence shape occurred in the 600–700 nm spectral region. A correlation was observed between emission band intensity at 635 nm and progression of renal disease.     

Particle shape in thixotropic aluminium and thorium molybdates gels

Summary Electron microscope examination of thixotropic aluminium and thorium molybdate gels shows that one hour after formation they are constituted by short fibrils of small axial ratio. The fibrils of the aluminium molybdate gels, with ageing at room temperature or with boiling, increase in diameter and length; the fibrous shape of the particles is maintained after two and a half years of ageing; all fibrils are crystalline by electron diffraction. The fibrils of the thorium molybdate gels, except in the gels containing hydrochloric acid, change with ageing at room temperature or with boiling, into plates of hexagonal, elliptical or rectangular profile; the fibrils and plates are crystalline and have the same electron diffraction pattern as the fibrils.This work was aided, in part, by grants from Conselho Nacional de Pesquisas and the Rockefeller Foundation.