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.

Radical SAM, a novel protein superfamily linking unresolved steps in familiar biosynthetic pathways with radical mechanisms: functional characterization using new analysis and information visualization methods

A novel protein superfamily with over 600 members was discovered by iterative profile searches and analyzed with powerful bioinformatics and information visualization methods. Evidence exists that these proteins generate a radical species by reductive cleavage of S-adenosylmethionine (SAM) through an unusual Fe-S center. The superfamily (named here Radical SAM) provides evidence that radical-based catalysis is important in a number of previously well- studied but unresolved biochemical pathways and reflects an ancient conserved mechanistic approach to difficult chemistries. Radical SAM proteins catalyze diverse reactions, including unusual methylations, isomerization, sulfur insertion, ring formation, anaerobic oxidation and protein radical formation. They function in DNA precursor, vitamin, cofactor, antibiotic and herbicide biosynthesis and in biodegradation pathways. One eukaryotic member is interferon-inducible and is considered a candidate drug target for osteoporosis; another is observed to bind the neuronal Cdk5 activator protein. Five defining members not previously recognized as homologs are lysine 2,3-aminomutase, biotin synthase, lipoic acid synthase and the activating enzymes for pyruvate formate-lyase and anaerobic ribonucleotide reductase. Two functional predictions for unknown proteins are made based on integrating other data types such as motif, domain, operon and biochemical pathway into an organized view of similarity relationships.

Extremely sensitive, background-free gene detection using binary probes and beta replicase.

We have developed a specific and sensitive nucleic acid amplification assay that is suitable for routine gene detection. The assay is based on a novel molecular genetic strategy in which two different RNA probes are hybridized to adjacent positions on a target nucleic acid and then ligated to form an amplifiable reporter RNA. The reporter RNA is then replicated up to a hundred billion-fold in a 30-min isothermal reaction that signals the presence of the target. The assay can detect fewer than 100 nucleic acid molecules; it provides quantitative results over a wide range of target concentrations and it employs a universal format that can detect any infectious agent.