Kinematic geometry of mass-triangles and reduction of Schrödinger’s equation of three-body systems to partial differential equations solely defined on triangular parameters

Schrödinger’s equation of a three-body system is a linear partial differential equation (PDE) defined on the 9-dimensional configuration space, ℝ9, naturally equipped with Jacobi’s kinematic metric and with translational and rotational symmetries. The natural invariance of Schrödinger’s equation with respect to the translational symmetry enables us to reduce the configuration space to that of a 6-dimensional one, while that of the rotational symmetry provides the quantum mechanical version of angular momentum conservation. However, the problem of maximizing the use of rotational invariance so as to enable us to reduce Schrödinger’s equation to corresponding PDEs solely defined on triangular parameters—i.e., at the level of ℝ6/SO(3)—has never been adequately treated. This article describes the results on the orbital geometry and the harmonic analysis of (SO(3),ℝ6) which enable us to obtain such a reduction of Schrödinger’s equation of three-body systems to PDEs solely defined on triangular parameters.

Two-component kinase-like activity of nm23 correlates with its motility-suppressing activity

Nm23 genes, which encode nucleoside diphosphate kinases, have been implicated in suppressing tumor metastasis. The motility of human breast carcinoma cells can be suppressed by transfection with wild-type nm23-H1, but not by transfections with two nm23-H1 mutants, nm23-H1S12OG and nm23-H1P96S. Here we report that nm23-H1 can transfer a phosphate from its catalytic histidine to aspartate or glutamate residues on 43-kDa membrane proteins. One of the 43-kDa membrane proteins was not phosphorylated by either nm23-H1P96S or nm23-H1S120G, and another was phosphorylated much more slowly by nm23-H1P96S and by nm23-H1S120G than by wild-type nm23-H1. Nm23-H1 also can transfer phosphate from its catalytic histidine to histidines on ATP-citrate lyase and succinic thiokinase. The rates of phosphorylation of ATP-citrate lyase by nm23-H1S120G and nm23-H1P96S were similar to that by wild-type nm23-H1. The rate of phosphorylation of succinic thiokinase by nm23-H1S120 was similar to that by wild-type nm23-H1, and the rate of phosphorylation of succinic thiokinase by nm23-H1P96S was about half that by wild-type nm23-H1. Thus, the transfer of phosphate from nm23-H1 to aspartates or glutamates on other proteins appears to correlate better with the suppression of motility than does the transfer to histidines.

One ring or two? Determination of ring number in carotenoids by lycopene ɛ-cyclases

Carotenoids in the photosynthetic membranes of plants typically contain two β-rings (e.g., β-carotene and zeaxanthin) or one ɛ- and one β-ring (e.g., lutein). Carotenoids with two ɛ-rings are uncommon. We reported earlier that the Arabidopsis thaliana lycopene ɛ-cyclase (LCYe) adds one ɛ-ring to the symmetrical linear substrate lycopene, whereas the structurally related lycopene β-cyclase (LCYb) adds two β-rings. Here we describe a cDNA encoding LCYe in romaine lettuce (Lactuca sativa var. romaine), one of the few plant species known to accumulate substantial quantities of a carotenoid with two ɛ-rings: lactucaxanthin. The product of the lettuce cDNA, similar in sequence to the Arabidopsis LCYe (77% amino acid identity), efficiently converted lycopene into the bicyclic ɛ-carotene in a heterologous Escherichia coli system. Regions of the lettuce and Arabidopsis ɛ-cyclases involved in the determination of ring number were mapped by analysis of chimeric ɛ-cyclases constructed by using an inverse PCR approach. A single amino acid was found to act as a molecular switch: lettuce LCYe mutant H457L added only one ɛ-ring to lycopene, whereas the complementary Arabidopsis LCYe mutant, L448H, added two ɛ-rings. An R residue in this position also yields a bi-ɛ-cyclase for both the lettuce and Arabidopsis enzymes. Construction and analysis of chimera of related enzymes with differing catalytic activities provide an informative approach that may be of particular utility for studying membrane-associated enzymes that cannot easily be crystallized or modeled to existing crystal structures.

The optimal measure of allelic association

Allelic association between pairs of loci is derived in terms of the association probability ρ as a function of recombination θ, effective population size N, linear systematic pressure v, and time t, predicting both ρrt, the decrease of association from founders and ρct, the increase by genetic drift, with ρt = ρrt + ρct. These results conform to the Malecot equation, with time replaced by distance on the genetic map, or on the physical map if recombination in the region is uniform. Earlier evidence suggested that ρ is less sensitive to variations in marker allele frequencies than alternative metrics for which there is no probability theory. This robustness is confirmed for six alternatives in eight samples. In none of these 48 tests was the residual variance as small as for ρ. Overall, efficiency was less than 80% for all alternatives, and less than 30% for two of them. Efficiency of alternatives did not increase when information was estimated simultaneously. The swept radius within which substantial values of ρ are conserved lies between 385 and 893 kb, but deviation of parameters between measures is enormously significant. The large effort now being devoted to allelic association has little value unless the ρ metric with the strongest theoretical basis and least sensitivity to marker allele frequencies is used for mapping of marker association and localization of disease loci.

Vaccinia virus DNA replication: two hundred base pairs of telomeric sequence confer optimal replication efficiency on minichromosome templates.

Vaccinia virus is a complex DNA virus that exhibits significant genetic and physical autonomy from the host cell. Most if not all of the functions involved in replication and transcription of the 192-kb genome are virally encoded. Although significant progress has been made in identifying trans-acting factors involved in DNA synthesis, the mechanism of genome replication has remained poorly understood. The genome is a linear duplex with covalently closed hairpin termini, and it has been presumed that sequences and/or structures within these termini are important for the initiation of genome replication. In this report we describe the construction of minichromosomes containing a central plasmid insert flanked by hairpin termini derived from the viral genome and their use as replication templates. When replication of these minichromosomes was compared with a control substrate containing synthetic hairpin termini, specificity for viral telomeres was apparent. Inclusion of > or = 200 bp from the viral telomere was sufficient to confer optimal replication efficiency, whereas 65-bp telomeres were not effective. Chimeric 200-bp telomeres containing the 65-bp terminal element and 135 bp of ectopic sequence also failed to confer efficient replication, providing additional evidence that telomere function is sequence-specific. Replication of these exogenous templates was dependent upon the viral replication machinery, was temporally coincident with viral replication, and generated covalently closed minichromosome products. These data provide compelling evidence for specificity in template recognition and utilization in vaccinia virus-infected cells.

Operator binding by lambda repressor heterodimers with one or two N-terminal arms.

The first 6 amino acids (NH2-Ser1-Thr2-Lys3-Lys4-Lys5-Pro6) of bacteriophage lambda cI repressor form a flexible arm that wraps around the operator DNA. Homodimeric lambda repressor has two arms. To determine whether both arms are necessary or only one arm is sufficient for operator binding, we constructed heterodimeric repressors with two, one, or no arms by fusing the DNA binding domain of lambda repressor to leucine zippers from Fos and Jun. Although only one arm is visible in the cocrystal structure of the N-domain-operator complex, our results indicate that both arms are required for optimal operator binding and normal site discrimination.

Comparison between clinical results of two diffractive multifocal lenses with the same platform but different additions

PURPOSE: To evaluate visual results with two multifocal diffractive lenses designed with the same platform but with different additions. SETTING: Grupo Innova Ocular clinics. METHODS: A total of 50 eyes from 50 patients were included. Group 1 (n = 25) was implanted with the TECNIS® 1 ZLB +3.25 and group 2 (n = 25) with the TECNIS® 1 ZKB +2.75. Patients were assessed at 24 hours, 1 week and 1 month postoperatively. At surgical discharge, corrected (CDVA) and uncorrected distance visual acuity (UCDVA), near visual acuity (VA) at 25, 40 and 80 cm, visual quality and the defocus curve were measured. RESULTS: Changes in sphere and spherical equivalent were statistically significant (p<0.01) in both groups at 1 week and 1 month compared to preoperative values. In group 1, UCDVA logMAR at 1 month was 0.06 ± 0.02. In group 2, UCDVA at 1 month was 0.03 ± 0.03. In near vision, the TECNIS® 1 ZLB group obtained a VA logMAR of 0.35 ± 0.02 at 25 cm, 0.13 ± 0.02 at 40 cm and 0.27 ± 0.02 at 80 cm, while in the TECNIS® 1 ZKB group, the values were 0.38  ± 0.03, 0.14 ± 0.03 and 0.23 ± 0.06, respectively. No statistically significant differences were found either when results for visual quality were compared. CONCLUSION: Both the TECNIS® 1 ZLB and TECNIS® 1 ZKB are excellent options for obtaining good distance and near vision, in addition to providing good intermediate vision, especially at distances such as those required for working with computers.

Numerical resolution of Emden's equation using Adomian polynomials

Purpose: In this paper the authors aim to show the advantages of using the decomposition method introduced by Adomian to solve Emden's equation, a classical non‐linear equation that appears in the study of the thermal behaviour of a spherical cloud and of the gravitational potential of a polytropic fluid at hydrostatic equilibrium. Design/methodology/approach: In their work, the authors first review Emden's equation and its possible solutions using the Frobenius and power series methods; then, Adomian polynomials are introduced. Afterwards, Emden's equation is solved using Adomian's decomposition method and, finally, they conclude with a comparison of the solution given by Adomian's method with the solution obtained by the other methods, for certain cases where the exact solution is known. Findings: Solving Emden's equation for n in the interval [0, 5] is very interesting for several scientific applications, such as astronomy. However, the exact solution is known only for n=0, n=1 and n=5. The experiments show that Adomian's method achieves an approximate solution which overlaps with the exact solution when n=0, and that coincides with the Taylor expansion of the exact solutions for n=1 and n=5. As a result, the authors obtained quite satisfactory results from their proposal. Originality/value: The main classical methods for obtaining approximate solutions of Emden's equation have serious computational drawbacks. The authors make a new, efficient numerical implementation for solving this equation, constructing iteratively the Adomian polynomials, which leads to a solution of Emden's equation that extends the range of variation of parameter n compared to the solutions given by both the Frobenius and the power series methods.

Comparative analysis of the visual performance and aberrometric outcomes with a new hybrid and two silicone hydrogel multifocal contact lenses: a pilot study

Background: The aim was to evaluate the visual performance achieved with a new multifocal hybrid contact lens and to compare it with that obtained with two other currently available multifocal soft contact lenses. Methods: This pilot prospective comparative study comprised a total of 16 presbyopic eyes of eight patients ranging in age from 43 to 58 years. All patients were fitted with three different models of multifocal contact lens: Duette multifocal (SynergEyes), Air Optix AQUA multifocal (Alcon) and Biofinity multifocal (CooperVision). Fittings were performed randomly in each patient according to a random number sequence, with a wash-out period between fittings of seven days. At two weeks post-fitting, visual, photopic contrast sensitivity and ocular aberrometry were evaluated. Results: No statistically significant differences were found in distance and near visual acuity achieved with the three different types of multifocal contact lens (p ≥ 0.05). Likewise, no significant differences between lenses were found in the monocular and binocular defocus curve (p ≥ 0.10). Concerning contrast sensitivity, better monocular contrast sensitivities for 6, 12 and 18 cycles per degree were found with the Duette and Air Optix multifocal compared to Biofinity (p = 0.02). Binocularly, differences between lenses were not significant (p ≥ 0.27). Furthermore, trefoil aberration was significantly higher with Biofinity multifocal (p < 0.01) and Air Optix (p = 0.01) multifocal compared to Duette. Conclusions: The Duette multifocal hybrid contact lens seems to provide similar visual quality outcomes in presbyopic patients with low corneal astigmatism, when compared with other soft multifocal contact lenses. This preliminary result should be confirmed in studies with larger samples.

Dynamic, convex, and robust optimization with Bayesian learning for response-guided dosing

Thesis (Ph.D.)--University of Washington, 2016-08

A new analytical solution for water table fluctuations in coastal aquifers with sloping beaches

The Boussinesq equation appears as the zeroth-order term in the shallow water flow expansion of the non-linear equation describing the flow of fluid in an unconfined aquifer. One-dimensional models based on the Boussinesq equation have been used to analyse tide-induced water table fluctuations in coastal aquifers. Previous analytical solutions for a sloping beach are based on the perturbation parameter, epsilon(N) = alphaepsilon cot beta (in which beta is the beach slope, alpha is the amplitude parameter and epsilon is the shallow water parameter) and are limited to tan(-1) (alphaepsilon) much less than beta less than or equal to pi/2. In this paper, a new higher-order solution to the non-linear boundary value problem is derived. The results demonstrate the significant influence of the higher-order components and beach slope on the water table fluctuations. The relative difference between the linear solution and the present solution increases as 6 and a increase, and reaches 7% of the linear solution. (C) 2003 Elsevier Ltd. All rights reserved.

Comparative proteomic analysis of GS-NSO murine myeloma cell lines with varying recombinant monoclonal antibody production rate

We have employed an inverse engineering strategy based on quantitative proteome analysis to identify changes in intracellular protein abundance that correlate with increased specific recombinant monoclonal antibody production (qMab) by engineered murine myeloma (NSO) cells. Four homogeneous NSO cell lines differing in qMab were isolated from a pool of primary transfectants. The proteome of each stably transfected cell line was analyzed at mid-exponential growth phase by two-dimensional gel electrophoresis (2D-PAGE) and individual protein spot volume data derived from digitized gel images were compared statistically. To identify changes in protein abundance associated with qMab clatasets were screened for proteins that exhibited either a linear correlation with cell line qMab or a conserved change in abundance specific only to the cell line with highest qMab. Several proteins with altered abundance were identified by mass spectrometry. Proteins exhibiting a significant increase in abundance with increasing qMab included molecular chaperones known to interact directly with nascent immunoglobulins during their folding and assembly (e.g., BiP, endoplasmin, protein disulfide isomerase). 2D-PAGE analysis showed that in all cell lines Mab light chain was more abundant than heavy chain, indicating that this is a likely prerequisite for efficient Mab production. In summary, these data reveal both the adaptive responses and molecular mechanisms enabling mammalian cells in culture to achieve high-level recombinant monoclonal antibody production. (C) 2004 Wiley Periodicals, Inc.

Conditional production of superpositions of coherent states with inefficient photon detection

It is shown that a linear superposition of two macroscopically distinguishable optical coherent states can be generated using a single photon source and simple all-optical operations. Weak squeezing on a single photon, beam mixing with an auxiliary coherent state, and photon detecting with imperfect threshold detectors are enough to generate a coherent state superposition in a free propagating optical field with a large coherent amplitude (alpha>2) and high fidelity (F>0.99). In contrast to all previous schemes to generate such a state, our scheme does not need photon number resolving measurements nor Kerr-type nonlinear interactions. Furthermore, it is robust to detection inefficiency and exhibits some resilience to photon production inefficiency.

Constriction flows of monodisperse linear entangled polymers: Multiscale modeling and flow visualization

We explore both the rheology and complex flow behavior of monodisperse polymer melts. Adequate quantities of monodisperse polymer were synthesized in order that both the materials rheology and microprocessing behavior could be established. In parallel, we employ a molecular theory for the polymer rheology that is suitable for comparison with experimental rheometric data and numerical simulation for microprocessing flows. The model is capable of matching both shear and extensional data with minimal parameter fitting. Experimental data for the processing behavior of monodisperse polymers are presented for the first time as flow birefringence and pressure difference data obtained using a Multipass Rheometer with an 11:1 constriction entry and exit flow. Matching of experimental processing data was obtained using the constitutive equation with the Lagrangian numerical solver, FLOWSOLVE. The results show the direct coupling between molecular constitutive response and macroscopic processing behavior, and differentiate flow effects that arise separately from orientation and stretch. (c) 2005 The Society of Rheology.

A new repair-replace strategy for items sold with a two-dimensional warranty

For repairable items, the manufacturer has the option to either repair or replace a failed item that is returned under warranty. In this paper, we look at a new warranty servicing strategy for items sold with two-dimensional warranty where the failed item is replaced by a new one when it fails for the first time in a specified region of the warranty and all other failures are repaired minimally. The region is characterised by two parameters and we derive the optimal values for these to minimise the total expected warranty servicing cost. We compare the results with other repair-replace strategies reported in the literature. (C) 2003 Elsevier Ltd. All rights reserved.