The Hausdorff dimension of graphs of Weierstrass functions

The Weierstrass nowhere differentiable function, and functions constructed from similar infinite series, have been studied often as examples of functions whose graph is a fractal. Though there is a simple formula for the Hausdorff dimension of the graph which is widely accepted, it has not been rigorously proved to hold. We prove that if arbitrary phases are included in each term of the summation for the Weierstrass function, the Hausdorff dimension of the graph of the function has the conjectured value for almost every sequence of phases. The argument extends to a much wider class of Weierstrass-like functions.

     

DefibViz: A Visualization Tool for the Assessment of Electrode Parameters on Transthoracic Defibrillation Thresholds

DefibViz is a software application developed for defibrillation simulation and visualization. It exploits both surface techniques and methods for the interactive exploration of volumetric datasets for the analysis of transthoracic defibrillation simulation results. DefibViz has a graphical user interface for the specification of the shape, size, position, and applied voltage of a defibrillator's electrodes. An option is provided for using 3D slice plane widgets, which operate on the volumetric datasets, such that the distribution of the voltage gradient induced by an electric shock can be visually inspected in various tissues throughout the myocardium and torso. One goal of DefibViz is to enhance understanding of how electrode parameters relate to the change of the voltage gradient distribution throughout the heart, which may help lead to optimal defibrillator design. DefibViz is significant, in that, it is built by using an open-source graphics and visualization framework providing a platform for subsequent modifiability and extensibility. Moreover, it integrates simulation and visualization techniques, which previously required the running of several independent software executables, into an enhanced, seamless, and comprehensive software application.     

Temperature and modulation characteristics of resonant-cavitylight-emitting diodes

Resonant-cavity light-emitting diodes (RCLED) are novel, high-efficiency light-emitting diodes which employ optical microcavities. These diodes have higher intensities and higher spectral purity as compared to conventional LEDs. Analytical formulas are derived for the enhancement of the spontaneous emission along the optical axis of the cavity. The design rules for high-efficiency operation of RCLEDs are established. The temperature dependence of the emission intensity is analyzed in the range 20-80° and it is described by an exponential dependence with a characteristic temperature of 112 K. The modulation characteristics of RCLEDs exhibit 3 dB frequencies of 580 MHz. Eye diagrams at transmission rates of 622 Mb/s are wide open indicating the suitability of RCLEDs for high-speed data transmission     

Comparisons of NMR spectral quality and success in crystallization demonstrate that NMR and X-ray crystallography are complementary methods for small protein structure determination

X-ray crystallography and NMR spectroscopy provide the only sources of experimental data from which protein structures can be analyzed at high or even atomic resolution. The degree to which these methods complement each other as sources of structural knowledge is a matter of debate; it is often proposed that small proteins yielding high quality, readily analyzed NMR spectra are a subset of those that readily yield strongly diffracting crystals. We have examined the correlation between NMR spectral quality and success in structure determination by X-ray crystallography for 159 prokaryotic and eukaryotic proteins, prescreened to avoid proteins providing polydisperse and/or aggregated samples. This study demonstrates that, across this protein sample set, the quality of a protein's [15N-1H]-heteronuclear correlation (HSQC) spectrum recorded under conditions generally suitable for 3D structure determination by NMR, a key predictor of the ability to determine a structure by NMR, is not correlated with successful crystallization and structure determination by X-ray crystallography. These results, together with similar results of an independent study presented in the accompanying paper (Yee, et al., J. Am. Chem. Soc., accompanying paper), demonstrate that X-ray crystallography and NMR often provide complementary sources of structural data and that both methods are required in order to optimize success for as many targets as possible in large-scale structural proteomics efforts.     

Iodine(V) reagents in organic synthesis. Part 3. New routes to heterocyclic compounds via o-iodoxybenzoic acid-mediated cyclizations: generality, scope, and mechanism

The discovery and development of the o-iodoxybenzoic acid (IBX) reaction with certain unsaturated N-aryl amides (anilides) to form heterocycles are described. The application of the method to the synthesis of delta-lactams, cyclic urethanes, hydroxy amines, and amino sugars among other important building blocks and intermediates is detailed. In addition to the generality and scope of this cyclization reaction, this article describes a number of mechanistic investigations suggesting a single electron transfer from the anilide functionality to IBX and implicating a radical-based mechanism for the reaction.     

Serum protein immunogenicity: implications for liver xenografting

The objectives of this study were threefold: (i) assess immunogenicity of donor plasma proteins following hepatic xenotransplantation, (ii) identify potential immunogens, and (iii) consider the implications of antibody formation against these plasma proteins in xenograft survival. We studied liver and heart xenografts in a concordant combination, hamster to rat. All grafts were examined at necropsy for evidence of rat immunoglobulin G (IgG) deposition. Cardiac xenografts were placed in recipients who had, or had not, been sensitized with hamster serum. Hepatic xenografts were placed in naive recipients to see if antibodies to hamster serum proteins could be eluted from the rejecting organ. Sera of immunized rats were examined for the presence of anti-hamster antibodies by immunoelectrophoresis and by Western blotting following sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) separation of hamster serum. Antibodies in sera of immunized rats were compared with those eluted from rejecting livers. Candidate antigens were identified by tandem mass spectrometry, sequence analysis, and reference to protein databases. Results showed that sera of immunized rats recognized a minimum of four different antigens in hamster serum by immunoelectrophoresis, and a minimum of seven by the more sensitive SDS-PAGE Western blot. IgG eluted from rejecting livers bound three of seven candidate antigens recognized by sera of the immunized animals. Sequence analysis searches revealed proteinase inhibitors in each of the three SDS-PAGE bands common to the above samples. All of these candidate proteinase inhibitor immunogens share a common catabolic fate, uptake via the lipoprotein-related protein (LRP/alpha 2-macroglobulin receptor (CD91). Sensitization to hamster serum proteins hastened cardiac xenograft rejection in 30-50% of recipients (depending on sensitization protocol). Vascular deposition of rat IgG occurred in all rejecting xenografts. Antibody binding to proteinase inhibitors could disturb their functional activity and contribute to the pathogenesis of delayed xenograft rejection.