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.

A fast marching level set method for monotonically advancing fronts.

A fast marching level set method is presented for monotonically advancing fronts, which leads to an extremely fast scheme for solving the Eikonal equation. Level set methods are numerical techniques for computing the position of propagating fronts. They rely on an initial value partial differential equation for a propagating level set function and use techniques borrowed from hyperbolic conservation laws. Topological changes, corner and cusp development, and accurate determination of geometric properties such as curvature and normal direction are naturally obtained in this setting. This paper describes a particular case of such methods for interfaces whose speed depends only on local position. The technique works by coupling work on entropy conditions for interface motion, the theory of viscosity solutions for Hamilton-Jacobi equations, and fast adaptive narrow band level set methods. The technique is applicable to a variety of problems, including shape-from-shading problems, lithographic development calculations in microchip manufacturing, and arrival time problems in control theory.

A model-based approach for assessing in vivo combination therapy interactions

We present an approach for evaluating the efficacy of combination antitumor agent schedules that accounts for order and timing of drug administration. Our model-based approach compares in vivo tumor volume data over a time course and offers a quantitative definition for additivity of drug effects, relative to which synergism and antagonism are interpreted. We begin by fitting data from individual mice receiving at most one drug to a differential equation tumor growth/drug effect model and combine individual parameter estimates to obtain population statistics. Using two null hypotheses: (i) combination therapy is consistent with additivity or (ii) combination therapy is equivalent to treating with the more effective single agent alone, we compute predicted tumor growth trajectories and their distribution for combination treated animals. We illustrate this approach by comparing entire observed and expected tumor volume trajectories for a data set in which HER-2/neu-overexpressing MCF-7 human breast cancer xenografts are treated with a humanized, anti-HER-2 monoclonal antibody (rhuMAb HER-2), doxorubicin, or one of five proposed combination therapy schedules.

On the controllability of distributed systems

To “control” a system is to make it behave (hopefully) according to our “wishes,” in a way compatible with safety and ethics, at the least possible cost. The systems considered here are distributed—i.e., governed (modeled) by partial differential equations (PDEs) of evolution. Our “wish” is to drive the system in a given time, by an adequate choice of the controls, from a given initial state to a final given state, which is the target. If this can be achieved (respectively, if we can reach any “neighborhood” of the target) the system, with the controls at our disposal, is exactly (respectively, approximately) controllable. A very general (and fuzzy) idea is that the more a system is “unstable” (chaotic, turbulent) the “simplest,” or the “cheapest,” it is to achieve exact or approximate controllability. When the PDEs are the Navier–Stokes equations, it leads to conjectures, which are presented and explained. Recent results, reported in this expository paper, essentially prove the conjectures in two space dimensions. In three space dimensions, a large number of new questions arise, some new results support (without proving) the conjectures, such as generic controllability and cases of decrease of cost of control when the instability increases. Short comments are made on models arising in climatology, thermoelasticity, non-Newtonian fluids, and molecular chemistry. The Introduction of the paper and the first part of all sections are not technical. Many open questions are mentioned in the text.

“Coarse” stability and bifurcation analysis using time-steppers: A reaction-diffusion example

Evolutionary, pattern forming partial differential equations (PDEs) are often derived as limiting descriptions of microscopic, kinetic theory-based models of molecular processes (e.g., reaction and diffusion). The PDE dynamic behavior can be probed through direct simulation (time integration) or, more systematically, through stability/bifurcation calculations; time-stepper-based approaches, like the Recursive Projection Method [Shroff, G. M. & Keller, H. B. (1993) SIAM J. Numer. Anal. 30, 1099–1120] provide an attractive framework for the latter. We demonstrate an adaptation of this approach that allows for a direct, effective (“coarse”) bifurcation analysis of microscopic, kinetic-based models; this is illustrated through a comparative study of the FitzHugh-Nagumo PDE and of a corresponding Lattice–Boltzmann model.

Use of differential display analysis to assess the effect of human cytomegalovirus infection on the accumulation of cellular RNAs: Induction of interferon-responsive RNAs

We used differential display analysis to identify mRNAs that accumulate to enhanced levels in human cytomegalovirus-infected cells as compared with mock-infected cells. RNAs were compared at 8 hr after infection of primary human fibroblasts. Fifty-seven partial cDNA clones were isolated, representing about 26 differentially expressed mRNAs. Eleven of the mRNAs were virus-coded, and 15 were of cellular origin. Six of the partial cDNA sequences have not been reported previously. All of the cellular mRNAs identified in the screen are induced by interferon α. The induction in virus-infected cells, however, does not involve the action of interferon or other small signaling molecules. Neutralizing antibodies that block virus infection also block the induction. These RNAs accumulate after infection with virus that has been inactivated by treatment with UV light, indicating that the inducer is present in virions. We conclude that human cytomegalovirus induces interferon-responsive mRNAs.

Differential Control of Xanthophylls and Light-Induced Stress Proteins, as Opposed to Light-Harvesting Chlorophyll a/b Proteins, during Photosynthetic Acclimation of Barley Leaves to Light Irradiance

Barley (Hordeum vulgare L.) plants were grown at different photon flux densities ranging from 100 to 1800 μmol m−2 s−1 in air and/or in atmospheres with reduced levels of O2 and CO2. Low O2 and CO2 partial pressures allowed plants to grow under high photosystem II (PSII) excitation pressure, estimated in vivo by chlorophyll fluorescence measurements, at moderate photon flux densities. The xanthophyll-cycle pigments, the early light-inducible proteins, and their mRNA accumulated with increasing PSII excitation pressure irrespective of the way high excitation pressure was obtained (high-light irradiance or decreased CO2 and O2 availability). These findings indicate that the reduction state of electron transport chain components could be involved in light sensing for the regulation of nuclear-encoded chloroplast gene expression. In contrast, no correlation was found between the reduction state of PSII and various indicators of the PSII light-harvesting system, such as the chlorophyll a-to-b ratio, the abundance of the major pigment-protein complex of PSII (LHCII), the mRNA level of LHCII, the light-saturation curve of O2 evolution, and the induced chlorophyll-fluorescence rise. We conclude that the chlorophyll antenna size of PSII is not governed by the redox state of PSII in higher plants and, consequently, regulation of early light-inducible protein synthesis is different from that of LHCII.

Differential recognition of the type I interferon receptor by interferons tau and alpha is responsible for their disparate cytotoxicities.

Interferon tau (IFN tau), originally identified as a pregnancy recognition hormone, is a type I interferon that is related to the various IFN alpha species (IFN alpha s). Ovine IFN tau has antiviral activity similar to that of human IFN alpha A on the Madin-Darby bovine kidney (MDBK) cell line and is equally effective in inhibiting cell proliferation. In this study, IFN tau was found to differ from IFN alpha A in that is was > 30-fold less toxic to MDBK cells at high concentrations. Excess IFN tau did not block the cytotoxicity of IFN alpha A on MDBK cells, suggesting that these two type I IFNs recognize the type I IFN receptor differently on these cells. In direct binding studies, 125I-IFN tau had a Kd of 3.90 x 10(-10) M for receptor on MDBK cells, whereas that of 125I-IFN alpha A was 4.45 x 10(-11) M. Consistent with the higher binding affinity, IFN alpha A was severalfold more effective than IFN tau in competitive binding against 125I-IFN tau to receptor on MDBK cells. Paradoxically, the two IFNs had similar specific antiviral activities on MDBK cells. However, maximal IFN antiviral activity required only fractional occupancy of receptors, whereas toxicity was associated with maximal receptor occupancy. Hence, IFN alpha A, with the higher binding affinity, was more toxic than IFN tau. The IFNs were similar in inducing the specific phosphorylation of the type I receptor-associated tyrosine kinase Tyk2, and the transcription factors Stat1 alpha and Stat2, suggesting that phosphorylation of these signal transduction proteins is not involved in the cellular toxicity associated with type I IFNs. Experiments using synthetic peptides suggest that differences in the interaction at the N terminal of IFN tau and IFN alpha with the type I receptor complex contribute significantly to differences in high-affinity equilibrium binding of these molecules. It is postulated that such a differential recognition of the receptor is responsible for the similar antiviral but different cytotoxic effects of these IFNs. Moreover, these data imply that receptors are "spare'' with respect to certain biological properties, and we speculate that IFNs may induce a concentration-dependent selective association of receptor subunits.