Solution of the pulse width modulation problem using orthogonal polynomials and Korteweg-de Vries equations

The mathematical underpinning of the pulse width modulation (PWM) technique lies in the attempt to represent “accurately” harmonic waveforms using only square forms of a fixed height. The accuracy can be measured using many norms, but the quality of the approximation of the analog signal (a harmonic form) by a digital one (simple pulses of a fixed high voltage level) requires the elimination of high order harmonics in the error term. The most important practical problem is in “accurate” reproduction of sine-wave using the same number of pulses as the number of high harmonics eliminated. We describe in this paper a complete solution of the PWM problem using Padé approximations, orthogonal polynomials, and solitons. The main result of the paper is the characterization of discrete pulses answering the general PWM problem in terms of the manifold of all rational solutions to Korteweg-de Vries equations.

Blind separation of auditory event-related brain responses into independent components

Averaged event-related potential (ERP) data recorded from the human scalp reveal electroencephalographic (EEG) activity that is reliably time-locked and phase-locked to experimental events. We report here the application of a method based on information theory that decomposes one or more ERPs recorded at multiple scalp sensors into a sum of components with fixed scalp distributions and sparsely activated, maximally independent time courses. Independent component analysis (ICA) decomposes ERP data into a number of components equal to the number of sensors. The derived components have distinct but not necessarily orthogonal scalp projections. Unlike dipole-fitting methods, the algorithm does not model the locations of their generators in the head. Unlike methods that remove second-order correlations, such as principal component analysis (PCA), ICA also minimizes higher-order dependencies. Applied to detected—and undetected—target ERPs from an auditory vigilance experiment, the algorithm derived ten components that decomposed each of the major response peaks into one or more ICA components with relatively simple scalp distributions. Three of these components were active only when the subject detected the targets, three other components only when the target went undetected, and one in both cases. Three additional components accounted for the steady-state brain response to a 39-Hz background click train. Major features of the decomposition proved robust across sessions and changes in sensor number and placement. This method of ERP analysis can be used to compare responses from multiple stimuli, task conditions, and subject states.

Segment-specific pattern of sympathetic preganglionic projections in the chicken embryo spinal cord is altered by retinoids

Sympathetic preganglionic neurons exhibit segment-specific projections. Preganglionic neurons located in rostral spinal segments project rostrally within the sympathetic chain, those located in caudal spinal segments project caudally, and those in midthoracic segments project either rostrally or caudally in segmentally graded proportions. Moreover, rostrally and caudally projecting preganglionic neurons are skewed toward the rostral and caudal regions, respectively, of each midthoracic segment. The mechanisms that establish these segment-specific projections are unknown. Here we show that experimental manipulation of retinoid signaling in the chicken embryo alters the segment-specific pattern of sympathetic preganglionic projections and that this effect is mediated by the somitic mesoderm. Application of exogenous retinoic acid to a single rostral thoracic somite decreases the number of rostrally projecting preganglionic neurons at that level. Conversely, disrupting endogenous synthesis of retinoic acid in a single caudal thoracic somite increases the number of rostrally projecting preganglionic neurons at that level. The number of caudally projecting neurons does not change in either case, indicating that the effect is specific for rostrally projecting preganglionic neurons. These results indicate that the sizes of the rostrally and caudally projecting populations may be independently regulated by different factors. Opposing gradients of such factors along the longitudinal axis of the thoracic region of the embryo could be sufficient, in combination, to determine the segment-specific identity of preganglionic projections.

The effects of health changes on projections of health service needs for the elderly population of the United States

The 1982–1994 National Long-Term Care Surveys indicate an accelerating decline in disability among the U.S. elderly population, suggesting that a 1.5% annual decline in chronic disability for elderly persons is achievable. Furthermore, many risk factors for chronic diseases show improvements, many linked to education, from 1910 to the present. Projections indicate the proportion of persons aged 85–89 with less than 8 years of education will decline from 65% in 1980 to 15% in 2015. Health and socioeconomic status trends are not directly represented in Medicare Trust Fund and Social Security Administration beneficiary projections. Thus, they may have different economic implications from projections directly accounting for health trends. A 1.5% annual disability decline keeps the support ratio (ratio of economically active persons aged 20–64 to the number of chronically disabled persons aged 65+) above its 1994 value, 22:1, when the Hospital Insurance Trust Fund was in fiscal balance, to 2070. With no changes in disability, projections indicate a support ratio in 2070 of 8:1—63% below a cash flow balance.

Double-level “orthogonal” dynamic combinatorial libraries on transition metal template

Dynamic combinatorial libraries are mixtures of compounds that exist in a dynamic equilibrium and can be driven to compositional self adaptation via selective binding of a specific assembly of certain components to a molecular target. We present here an extension of this initial concept to dynamic libraries that consists of two levels, the first formed by the coordination of terpyridine-based ligands to the transition metal template, and the second, by the imine formation with the aldehyde substituents on the terpyridine moieties. Dialdehyde 7 has been synthesized, converted into a variety of ligands, oxime ethers L11–L33 and acyl hydrazones L44–L77, and subsequently into corresponding cobalt complexes. A typical complex, Co(L22)22+ is shown to engage in rapid exchange with a competing ligand L11 and with another complex, Co(L22)22+ in 30% acetonitrile/water at pH 7.0 and 25°C. The exchange in the corresponding Co(III) complexes is shown to be much slower. Imine exchange in the acyl hydrazone complexes (L44–L77) is strongly controlled by pH and temperature. The two types of exchange, ligand and imine, can thus be used as independent equilibrium processes controlled by different types of external intervention, i.e., via oxidation/reduction of the metal template and/or change in the pH/temperature of the medium. The resulting double-level dynamic libraries are therefore named orthogonal, in similarity with the orthogonal protecting groups in organic synthesis. Sample libraries of this type have been synthesized and showed the complete expected set of components in electrospray ionization MS.

Orthogonal combinatorial mutagenesis: a codon-level combinatorial mutagenesis method useful for low multiplicity and amino acid-scanning protocols

We describe here a method to generate combinatorial libraries of oligonucleotides mutated at the codon-level, with control of the mutagenesis rate so as to create predictable binomial distributions of mutants. The method allows enrichment of the libraries with single, double or larger multiplicity of amino acid replacements by appropriate choice of the mutagenesis rate, depending on the concentration of synthetic precursors. The method makes use of two sets of deoxynucleoside-phosphoramidites bearing orthogonal protecting groups [4,4′-dimethoxytrityl (DMT) and 9-fluorenylmethoxycarbonyl (Fmoc)] in the 5′ hydroxyl. These phosphoramidites are divergently combined during automated synthesis in such a way that wild-type codons are assembled with commercial DMT-deoxynucleoside-methyl-phosphoramidites while mutant codons are assembled with Fmoc-deoxynucleoside-methyl-phosphoramidites in an NNG/C fashion in a single synthesis column. This method is easily automated and suitable for low mutagenesis rates and large windows, such as those required for directed evolution and alanine scanning. Through the assembly of three oligonucleotide libraries at different mutagenesis rates, followed by cloning at the polylinker region of plasmid pUC18 and sequencing of 129 clones, we concluded that the method performs essentially as intended.

GABAergic feedforward projections from the inferior colliculus to the medial geniculate body.

A novel and robust projection from gamma-aminobutyric acid-containing (GABAergic) inferior colliculus neurons to the media] geniculate body (MGB) was discovered in the cat using axoplasmic transport methods combined with immunocytochemistry. This input travels with the classical inferior colliculus projection to the MGB, and it is a direct ascending GABAergic pathway to the sensory thalamus that may be inhibitory. This bilateral projection constitutes 10-30% of the neurons in the auditory tectothalamic system. Studies by others have shown that comparable input to the corresponding thalamic visual or somesthetic nuclei is absent. This suggests that monosynaptic inhibition or disinhibition is a prominent feature in the MGB and that differences in neural circuitry distinguish it from its thalamic visual and somesthetic counterparts.

Local densities orthogonal to beta-sheet amide planes: patterns of packing in globular proteins.

We have investigated the efficiency of packing by calculating intramolecular packing density above and below peptide planes of internal beta-pleated sheet residues in five globular proteins. The orientation of interest was chosen to allow study of regions that are approximately perpendicular to the faces of beta-pleated sheets. In these locations, nonbonded van der Waals packing interactions predominate over hydrogen bonding and solvent interactions. We observed considerable variability in packing densities within these regions, confirming that the interior packing of a protein does not result in uniform occupation of the available space. Patterns of fluctuation in packing density suggest that the regular backbone-to-backbone network of hydrogen bonds is not likely to be interrupted to maximize van der Waals interactions. However, high-density packing tends to occur toward the ends of beta-structure strands where hydrogen bonds are more likely to involve nonpolar side-chain groups or solvent molecules. These features result in internal protein folding with a central low-density core surrounded by a higher-density subsurface shell, consistent with our previous calculations regarding overall protein packing density.

Peptide synthesis using unprotected peptides through orthogonal coupling methods.

We describe an approach to the synthesis of peptides from segments bearing no protecting groups through an orthogonal coupling method to capture the acyl segment as a thioester that then undergoes an intramolecular acyl transfer to the amine component with formation of a peptide bond. Two orthogonal coupling methods to give the covalent ester intermediate were achieved by either a thiol-thioester exchange mediated by a trialkylphosphine and an alkylthiol or a thioesterification by C alpha-thiocarboxylic acid reacting with a beta-bromo amino acid. With this approach, unprotected segments ranging from 4 to 37 residues were coupled to aqueous solution to give free peptides up to 54 residues long with high efficiency.