Inference in complex biological systems with Gaussian processes and parallel tempering

Parameter inference in mathematical models of complex biological systems, expressed as coupled ordinary differential equations (ODEs), is a challenging problem. These depend on kinetic parameters, which cannot all be measured and have to be ascertained a different way. However, the computational costs associated with repeatedly solving the ODEs are often staggering, making many techniques impractical. Therefore, aimed at reducing this cost, new concepts using gradient matching have been proposed. This paper combines current adaptive gradient matching approaches, using Gaussian processes, with a parallel tempering scheme, in order to compare 2 different paradigms using the same nonlinear regression method. We use 2 ODE systems to assess our technique, showing an improvement over the recent method in Calderhead et al. (2008)

Thematic mapper data quality and performance assessment in renewable resource/agricultural remote sensing

A "quick look" investigation of the initial LANDSAT-4, thematic mapper (TM) scene received from Goddard Space Flight Center was performed to gain early insight into the characteristics of TM data. The initial scene, containing only the first four bands of the seven bands recorded by the TM, was acquired over the Detroit, Michigan, area on July 20, 1982. It yielded abundant information for scientific investigation. A wide variety of studies were conducted to assess all aspects of TM data. They ranged from manual analyses of image products to detect obvious optical, electronic, or mechanical defects to detailed machine analyses of the digital data content for evaluation of spectral separability of vegetative/nonvegetative classes. These studies were applied to several segments extracted from the full scene. No attempt was made to perform end-to-end statistical evaluations. However, the output of these studies do identify a degree of positive performance from the TM and its potential for advancing state-of-the-art crop inventory and condition assessment technology

Spatially partitioned embedded Runge-Kutta Methods

We study spatially partitioned embedded Runge–Kutta (SPERK) schemes for partial differential equations (PDEs), in which each of the component schemes is applied over a different part of the spatial domain. Such methods may be convenient for problems in which the smoothness of the solution or the magnitudes of the PDE coefficients vary strongly in space. We focus on embedded partitioned methods as they offer greater efficiency and avoid the order reduction that may occur in non-embedded schemes. We demonstrate that the lack of conservation in partitioned schemes can lead to non-physical effects and propose conservative additive schemes based on partitioning the fluxes rather than the ordinary differential equations. A variety of SPERK schemes are presented, including an embedded pair suitable for the time evolution of fifth-order weighted non-oscillatory (WENO) spatial discretizations. Numerical experiments are provided to support the theory

AC impedance study of degradation of porous nickel battery electrodes

AC impedance spectra of porous nickel battery electrodes were recorded periodically during charge/discharge cycling in concentrated KOH solution at various temperatures. A transmission line model (TLM) was adopted to represent the impedance of the porous electrodes, and various model parameters were adjusted in a curve fitting routine to reproduce the experimental impedances. Degradation processes were deduced from changes in model parameters with electrode cycling time. In developing the TLM, impedance spectra of planar (nonporous) electrodes were used to represent the pore wall and backing plate interfacial impedances. These data were measured over a range of potentials and temperatures, and an equivalent circuit model was adopted to represent the planar electrode data. Cyclic voltammetry was used to study the characteristics of the oxygen evolution reaction on planar nickel electrodes during charging, since oxygen evolution can affect battery electrode charging efficiency and ultimately electrode cycle life if the overpotential for oxygen evolution is sufficiently low

Effective order strong stability preserving Runge–Kutta methods

We apply the concept of effective order to strong stability preserving (SSP) explicit Runge–Kutta methods. Relative to classical Runge–Kutta methods, effective order methods are designed to satisfy a relaxed set of order conditions, but yield higher order accuracy when composed with special starting and stopping methods. The relaxed order conditions allow for greater freedom in the design of effective order methods. We show that this allows the construction of four-stage SSP methods with effective order four (such methods cannot have classical order four). However, we also prove that effective order five methods—like classical order five methods—require the use of non-positive weights and so cannot be SSP. By numerical optimization, we construct explicit SSP Runge–Kutta methods up to effective order four and establish the optimality of many of them. Numerical experiments demonstrate the validity of these methods in practice

Renormalised four-point coupling constant in the three-dimensional O(N) model with N=0

We simulate self-avoiding walks on a cubic lattice and determine the second virial coefficient for walks of different lengths. This allows us to determine the critical value of the renormalized four-point coupling constant in the three-dimensional N-vector universality class for N=0. We obtain g* = 1.4005(5), where g is normalized so that the three-dimensional field-theoretical beta-function behaves as \beta(g) = - g + g^2 for small g. As a byproduct, we also obtain precise estimates of the interpenetration ratio Psi*, Psi* = 0.24685(11), and of the exponent \nu, \nu = 0.5876(2).Comment: 16 page

The Caliphate

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Improved position measurement of nano electromechanical systems using cross correlations

We consider position measurements using the cross-correlated output of two tunnel junction position detectors. Using a fully quantum treatment, we calculate the equation of motion for the density matrix of the coupled detector-detector-mechanical oscillator system. After discussing the presence of a bound on the peak-to-background ratio in a position measurement using a single detector, we show how one can use detector cross correlations to overcome this bound. We analyze two different possible experimental realizations of the cross correlation measurement and show that in both cases the maximum cross-correlated output is obtained when using twin detectors and applying equal bias to each tunnel junction. Furthermore, we show how the double-detector setup can be exploited to drastically reduce the added displacement noise of the oscillator.Comment: 9 pages, 1 figure; v2: new Sec.

Screw instability of the magnetic field connecting a rotating black hole with its surrounding disk

Screw instability of the magnetic field connecting a rotating black hole (BH) with its surrounding disk is discussed based on the model of the coexistence of the Blandford-Znajek (BZ) process and the magnetic coupling (MC) process (CEBZMC). A criterion for the screw instability with the state of CEBZMC is derived based on the calculations of the poloidal and toroidal components of the magnetic field on the disk. It is shown by the criterion that the screw instability will occur, if the BH spin and the power-law index for the variation of the magnetic field on the disk are greater than some critical values. It turns out that the instability occurs outside some critical radii on the disk. It is argued that the state of CEBZMC always accompanies the screw instability. In addtition, we show that the screw instability contributes only a small fraction of magnetic extraction of energy from a rotating BH.Comment: 18 pages, 13 figures; Accepted by Ap

Group 13 Decamethylmetallocenium Cations

Salts containing the decamethylmetallocenium cations, [( C5Me5) M-2](+) ( or Cp*M-2(+)) of the group 13 "metals" B, Al and Ga have been prepared using a variety of synthetic routes. Precursor molecules of the type Cp*2MX ( X = Cl, Br, Me) exhibit structural features that vary significantly depending on the size and electronegativity of the central atom. While salt metathesis, halide abstraction and methanide abstraction methods represent viable routes for the preparation of salts of Cp*B-2(+) and Cp*Al-2(+), acidolysis of a Cp* group from Cp*Ga-3 is the most reliable method for the synthesis of the analogous gallium cation. Gallocenium cations are less stable than either of the lighter congeneric cations since they prove to be susceptible to decomposition reactions involving the "back-transfer" of ligands from the counter anion. Density functional theory (DFT) calculations revealed that, whereas Cp*Ga-2(+) is predicted to adopt a molecular structure more similar to that of Cp*B-2(+), the electronic structure of the gallium cation bears a greater resemblance to that of Cp*Al-2(+).Chemistr