Optical wavelength filtering by diffraction from a surface relief

We present an analytical solution to the problem of finding a diffractive surface relief that generates a specific optical amplitude and phase spectral reflection in a particular direction. We show that any discrete finite impulse response filter can be generated to within a multiplicative constant at nonzero frequencies. We propose an implementation of such a filter that works in the visible and the near infrared, based on a two-dimensional array of dual-state tiltable mirrors. A 1024 x 1024 array results in a 1024-tap filter with 10-bit quantization of the impulse response. The applications of such a device include spectroscopy and wavelength-division multiplex switching.     

MtsslWizard: In Silico Spin-Labeling and Generation of Distance Distributions in PyMOL

MtsslWizard is a computer program, which operates as a plugin for the PyMOL molecular graphics system. MtsslWizard estimates distances between spin labels on proteins quickly with user-configurable options through a simple graphical interface. In default mode, the program searches for ensembles of possible MTSSL conformations that do not clash with a static model of the protein. Once conformations are assigned, distance distributions between two or more ensembles are calculated, displayed, and can be exported to other software. The program’s use is evaluated in a number of challenging test cases and its strengths and weaknesses evaluated. The benefits of the program are its accuracy and simplicity.     

Sequences of orthogonal Laurent polynomials,bi-orthogonality and quadrature formulas on the unit circle

In this paper, the construction of orthogonal bases in the space of Laurent polynomials on the unit circle is considered. As an application, a connection with the so-called bi-orthogonal systems of trigonometric polynomials is established and quadrature formulas on the unit circle based on Laurent polynomials are studied.     

Model building in chemistry,a unified approach

The generation, confirmation and reduction of models is discussed. The latent-variable approach is extended so as to encompass the possibility of interaction (nonadditivity) between variables. Various congruence coefficients and association measures are used in the model building process: (i) to examine models for general factors; (ii) to reveal marker variables, i.e., variables that are insensitive to all but one chemical process or phenomenon; and (iii) to examine latent-variable models for nonadditivity. Marker variables, carrying the same information as the latent variables in a model, represent the link between the latent-variable and multiple regression approaches to model building. Thus, in principle, any multiple linear regression model is obtainable from corresponding higher-order latent-variable models. By combining the marker approach as used for model reduction with various simple techniques for data transformation, several classes of chemical and physical models are shown to correspond to subsets of the more general latent-variable model.     

EPR‐Based Approach for the Localization of Paramagnetic Metal Ions in Biomolecules

Metal ions play an important role in the catalysis and folding of proteins and oligonucleotides. Their localization within the three‐dimensional fold of such biomolecules is therefore an important goal in understanding structure–function relationships. A trilateration approach for the localization of metal ions by means of long‐range distance measurements based on electron paramagnetic resonance (EPR) is introduced. The approach is tested on the Cu²⁺ center of azurin, and factors affecting the precision of the method are discussed.     

Relaxation oscillations in spruce–budworm interactions

We review and complement the study of the mathematical properties of the predator–prey dynamical system for spruce–budworm interactions studied in Ludwig et al. [D. Ludwig, D. Jones, C.S. Holling, Qualitative analysis of insect outbreak systems: the spruce budworm and forest, Journal of Animal Ecology 47 (1978), 315–332]. We use the singular perturbation method to identify parameter regimes which permit relaxation oscillations. The leading order contribution to the period of these oscillations is computed by means of this method and compared with the outcome of direct numerical simulations.     

Rotation-vibration coupling effects in the nucleus Si

Faessler and Greiner's rotation-vibration coupling theory allows us to interprete the low-energy part of the excitation spectrum of ²⁹Si, as well as to see that the l = 2 j-effect and the non-stripping type angular distributions observed in the ²⁸Si(d,p)²⁹Si reaction are interrelated phenomena.