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.

The role of London forces in defining noncentrosymmetric order of high dipole moment–high hyperpolarizability chromophores in electrically poled polymeric thin films

Graphs of second harmonic generation coefficients and electro-optic coefficients (measured by ellipsometry, attenuated total reflection, and two-slit interference modulation) as a function of chromophore number density (chromophore loading) are experimentally observed to exhibit maxima for polymers containing chromophores characterized by large dipole moments and polarizabilities. Modified London theory is used to demonstrated that this behavior can be attributed to the competition of chromophore-applied electric field and chromophore–chromophore electrostatic interactions. The comparison of theoretical and experimental data explains why the promise of exceptional macroscopic second-order optical nonlinearity predicted for organic materials has not been realized and suggests routes for circumventing current limitations to large optical nonlinearity. The results also suggest extensions of measurement and theoretical methods to achieve an improved understanding of intermolecular interactions in condensed phase materials including materials prepared by sequential synthesis and block copolymer methods.

A fast, high resolution, second-order central scheme for incompressible flows

A high resolution, second-order central difference method for incompressible flows is presented. The method is based on a recent second-order extension of the classic Lax–Friedrichs scheme introduced for hyperbolic conservation laws (Nessyahu H. & Tadmor E. (1990) J. Comp. Physics. 87, 408-463; Jiang G.-S. & Tadmor E. (1996) UCLA CAM Report 96-36, SIAM J. Sci. Comput., in press) and augmented by a new discrete Hodge projection. The projection is exact, yet the discrete Laplacian operator retains a compact stencil. The scheme is fast, easy to implement, and readily generalizable. Its performance was tested on the standard periodic double shear-layer problem; no spurious vorticity patterns appear when the flow is underresolved. A short discussion of numerical boundary conditions is also given, along with a numerical example.

A genome-wide search for chromosomal loci linked to mental health wellness in relatives at high risk for bipolar affective disorder among the Old Order Amish

Bipolar affective disorder (BPAD; manic-depressive illness) is characterized by episodes of mania and/or hypomania interspersed with periods of depression. Compelling evidence supports a significant genetic component in the susceptibility to develop BPAD. To date, however, linkage studies have attempted only to identify chromosomal loci that cause or increase the risk of developing BPAD. To determine whether there could be protective alleles that prevent or reduce the risk of developing BPAD, similar to what is observed in other genetic disorders, we used mental health wellness (absence of any psychiatric disorder) as the phenotype in our genome-wide linkage scan of several large multigeneration Old Order Amish pedigrees exhibiting an extremely high incidence of BPAD. We have found strong evidence for a locus on chromosome 4p at D4S2949 (maximum genehunter-plus nonparametric linkage score = 4.05, P = 5.22 × 10−4; sibpal Pempirical value <3 × 10−5) and suggestive evidence for a locus on chromosome 4q at D4S397 (maximum genehunter-plus nonparametric linkage score = 3.29, P = 2.57 × 10−3; sibpal Pempirical value <1 × 10−3) that are linked to mental health wellness. These findings are consistent with the hypothesis that certain alleles could prevent or modify the clinical manifestations of BPAD and perhaps other related affective disorders.

Bond orientational order, molecular motion, and free energy of high-density DNA mesophases.

By equilibrating condensed DNA arrays against reservoirs of known osmotic stress and examining them with several structural probes, it has been possible to achieve a detailed thermodynamic and structural characterization of the change between two distinct regions on the liquid-crystalline phase diagram: (i) a higher density hexagonally packed region with long-range bond orientational order in the plane perpendicular to the average molecular direction and (ii) a lower density cholesteric region with fluid-like positional order. X-ray scattering on highly ordered DNA arrays at high density and with the helical axis oriented parallel to the incoming beam showed a sixfold azimuthal modulation of the first-order diffraction peak that reflects the macroscopic bond-orientational order. Transition to the less-dense cholesteric phase through osmotically controlled swelling shows the loss of this bond orientational order, which had been expected from the change in optical birefringence patterns and which is consistent with a rapid onset of molecular positional disorder. This change in order was previously inferred from intermolecular force measurements and is now confirmed by 31P NMR. Controlled reversible swelling and compaction under osmotic stress, spanning a range of densities between approximately 120 mg/ml to approximately 600 mg/ml, allow measurement of the free-energy changes throughout each phase and at the phase transition, essential information for theories of liquid-crystalline states.

Mixed spermatogenic germ cell nuclear extracts exhibit high base excision repair activity

Spermatogenic cells exhibit a lower spontaneous mutation frequency than somatic tissues in a lacI transgene and many base excision repair (BER) genes display the highest observed level of expression in the testis. In this study, uracil-DNA glycosylase-initiated BER activity was measured in nuclear extracts prepared from tissues obtained from each of three mouse strains. Extracts from mixed spermatogenic germ cells displayed the greatest activity followed by liver then brain for all three strains, and the activity for a given tissue was consistent among the three strains. Levels of various BER proteins were examined by western blot analyses and found to be consistent with activity levels. Nuclear extracts prepared from purified Sertoli cells, a somatic component of the seminiferous epithelium, exhibited significantly lower activity than mixed spermatogenic cell-type nuclear extracts, thereby suggesting that the high BER activity observed in mixed germ cell nuclear extracts was not a characteristic of all testicular cell types. Nuclear extracts from thymocytes and small intestines were assayed to assess activity in a mitotically active cell type and tissue. Overall, the order of tissues/cells exhibiting the greatest to lowest activity was mixed germ cells > Sertoli cells > thymocytes > small intestine > liver > brain.

Partial molar volume, surface area, and hydration changes for equilibrium unfolding and formation of aggregation transition state: High-pressure and cosolute studies on recombinant human IFN-γ

The equilibrium dissociation of recombinant human IFN-γ was monitored as a function of pressure and sucrose concentration. The partial molar volume change for dissociation was −209 ± 13 ml/mol of dimer. The specific molar surface area change for dissociation was 12.7 ± 1.6 nm2/molecule of dimer. The first-order aggregation rate of recombinant human IFN-γ in 0.45 M guanidine hydrochloride was studied as a function of sucrose concentration and pressure. Aggregation proceeded through a transition-state species, N*. Sucrose reduced aggregation rate by shifting the equilibrium between native state (N) and N* toward the more compact N. Pressure increased aggregation rate through increased solvation of the protein, which exposes more surface area, thus shifting the equilibrium away from N toward N*. The changes in partial molar volume and specific molar surface area between the N* and N were −41 ± 9 ml/mol of dimer and 3.5 ± 0.2 nm2/molecule, respectively. Thus, the structural change required for the formation of the transition state for aggregation is small relative to the difference between N and the dissociated state. Changes in waters of hydration were estimated from both specific molar surface area and partial molar volume data. From partial molar volume data, estimates were 25 and 128 mol H2O/mol dimer for formation of the aggregation transition state and for dissociation, respectively. From surface area data, estimates were 27 and 98 mol H2O/mol dimer. Osmotic stress theory yielded values ≈4-fold larger for both transitions.

Kinetics of photo-induced electron transfer from high-potential iron-sulfur protein to the photosynthetic reaction center of the purple phototroph Rhodoferax fermentans.

The kinetics of photo-induced electrontransfer from high-potential iron-sulfur protein (HiPIP) to the photosynthetic reaction center (RC) of the purple phototroph Rhodoferarfermentans were studied. The rapid photooxidation of heme c-556 belonging to RC is followed, in the presence of HiPIP, by a slower reduction having a second-order rate constant of 4.8 x 10(7) M(-1) x s(-1). The limiting value of kobs at high HiPIP concentration is 95 s(-1). The amplitude of this slow process decreases with increasing HiPIP concentration. The amplitude of a faster phase, observed at 556 and 425 nm and involving heme c-556 reduction, increases proportionately. The rate constant of this fast phase, determined at 425 and 556 nm, is approximately 3 x 10(5) s(-1). This value is not dependent on HiPIP concentration, indicating that it is related to a first-order process. These observations are interpreted as evidence for the formation of a HiPIP-RC complex prior to the excitation flash, having a dissociation constant of -2.5 microM. The fast phase is absent at high ionic strength, indicating that the complex involves mainly electrostatic interactions. The ionic strength dependence of kobs for the slow phase yields a second-order rate constant at infinite ionic strength of 5.4 x 10(6) M(-1) x s(-1) and an electrostatic interaction energy of -2.1 kcal/mol (1 cal = 4.184 J). We conclude that Rhodoferar fermentans HiPIP is a very effective electron donor to the photosynthetic RC.

Mechanisms underlying the sensitivity of songbird forebrain neurons to temporal order.

Neurons in the songbird forebrain area HVc (hyperstriatum ventrale pars caudale or high vocal center) are sensitive to the temporal structure of the bird's own song and are capable of integrating auditory information over a period of several hundred milliseconds. Extracellular studies have shown that the responses of some HVc neurons depend on the combination and temporal order of syllables from the bird's own song, but little is known about the mechanisms underlying these response properties. To investigate these mechanisms, we recorded intracellular responses to a set of auditory stimuli designed to assess the degree of dependence of the responses on temporal context. This report provides evidence that HVc neurons encode information about temporal structure by using a variety of mechanisms including syllable-specific inhibition, excitatory postsynaptic potentials with a range of different time courses, and burst-firing nonlinearity. The data suggest that the sensitivity of HVc neurons to temporal combinations of syllables results from the interactions of several cells and does not arise in a single step from afferent inputs alone.