Fine Tuning of Chlorophyll Spectra by Protein‐Induced Ring Deformation

The ability to tune the light‐absorption properties of chlorophylls by their protein environment is the key to the robustness and high efficiency of photosynthetic light‐harvesting proteins. Unfortunately, the intricacy of the natural complexes makes it very difficult to identify and isolate specific protein–pigment interactions that underlie the spectral‐tuning mechanisms. Herein we identify and demonstrate the tuning mechanism of chlorophyll spectra in type II water‐soluble chlorophyll binding proteins from Brassicaceae (WSCPs). By comparing the molecular structures of two natural WSCPs we correlate a shift in the chlorophyll red absorption band with deformation of its tetrapyrrole macrocycle that is induced by changing the position of a nearby tryptophan residue. We show by a set of reciprocal point mutations that this change accounts for up to 2/3 of the observed spectral shift between the two natural variants.     

Mathematical Modelling and Computer Simulation of Linear Polymer Degradation: Simple Scissions

Summary: Degradation of a polymer in a reactor by the degrading agent(s) follows a distinct pattern, primarily influenced by structural integrity and reactor environment. This distinct pattern is recorded in the changes in the evolved molecular weight distribution (MWD) or polymer chain length distribution (PCLD) curve characteristics from the initial intact state. Modern size exclusion chromatography (SEC) is the best laboratory‐based method that can clearly provide these plots in the form of chromatogram; however, detailed molecular information is not available. The nature of molecular destruction can be well‐characterised if the distinct MWD shift patterns can be simulated to fingerprint the different chain scission dynamics. This is investigated by our current research using the power of computer simulation techniques to gain insight into the polymer ageing processes. One such technique for studying simple decay processes is presented here, and the results are compared with experimental findings. The concept of a binary tree scission model is introduced to show chain rupture as a sequence of probabilistic events and as a non‐linear function of time. Two new mathematical algorithms, an iterative Monte Carlo structured probability scheme and a semi‐iterative algebraic exact statistical formulation method, are investigated to implement this model and simulate the evolution of resultant temporal MW distribution. The latter, an innovative approach to mathematical modelling, has the potential to generate a statistically perfect instant MWD decay curve. A statistical comparison of the product yield is presented from the data obtained using a wide variety of simulated scission regimes to determine the sources of variability.

Simulated MWD lateral shift for percent cut scission model showing deviation from the initial MWD (red) over degradation time zones T_j(0 ≥ j ≤ 9) with bimodal and curve broadening effect due to accumulation of varied percent cut range 5–30%.     

Heegaard splittings of twisted torus knots

Little is known on the classification of Heegaard splittings for hyperbolic 3-manifolds. Although Kobayashi gave a complete classification of Heegaard splittings for the exteriors of 2-bridge knots, our knowledge of other classes is extremely limited. In particular, there are very few hyperbolic manifolds that are known to have a unique minimal genus splitting. Here we demonstrate that an infinite class of hyperbolic knot exteriors, namely exteriors of certain “twisted torus knots” originally studied by Morimoto, Sakuma and Yokota, have a unique minimal genus Heegaard splitting of genus two. We also conjecture that these manifolds possess irreducible yet weakly reducible splittings of genus three. There are no known examples of such Heegaard splittings.     

Directed DNA metallization

Genes of interest can be selectively metallized via the incorporation of modified triphosphates. These triphosphates bear functions that can be further derivatized with aldehyde groups via the use of click chemistry. Treatment of the aldehyde-labeled gene mixture with the Tollens reagent, followed by a development process, results in the selective metallization of the gene of interest in the presence of natural DNA strands.     

Miniature array postdetection-encoded MRI

A method for performing nuclear magnetic resonance (NMR) measurements simultaneously from more than a single radiofrequency (RF) coil is presented. The method employs the detection of magnetic resonance signals in an array of detectors, where each detector is responsible for detecting a unique frequency bandwidth or a magnetic resonance signal from a unique location in a region in a primary, substantially homogeneous, static magnetic field. The detectors may be separated logically into groups, whereby all the detectors in a given group are essentially RF-decoupled from each other to substantially eliminate cross-talk by switching circuits or by being placed from each other sufficiently remotely. Sampling of detected signals from detectors in this array is done simultaneously over groups of noninteracting detectors. The detected signals from all detectors in a given group are simultaneously transmitted to a single preamplifier, thus increasing significantly the signal-to-noise ratio (SNR) in that preamplifier. Prior to transmitting each detected NMR signal of each detector to the preamplifier, each detected signal is separately and uniquely encoded electronically. This provides a method whereby the signal of each detector is uniquely encoded. Accumulating all these encoded signals, which were simultaneously received in a number of RF detectors into a single amplifier, results in the total signal having a high SNR ratio. This total amplified signal is later decoded into each detector's original signal by a decoding circuitry. Conventional magnetic resonance imaging (MRI) techniques may be thereafter applied to obtain an image. Or else, conventional NMR techniques may be thereafter applied to obtain an improved SNR from a sample, using a single preamplifier with a multitude of detectors. Applying this method to a large number of miniature and closely packed RF detectors placed in an array-like configuration results in an MRI technique with a very fast acquisition time, an increased SNR and a high spatial resolution equivalent to the number of detectors per unit of length. Deblurring and decoupling algorithms allow for images from layers as deep as 6 mm to be acquired.     

Spatial beam properties of combined lasers' delivery fibers

The superiority of parabolic-index fibers over step-index fibers in delivering high-beam-quality light out of incoherently combined lasers is demonstrated numerically and experimentally. By utilizing the tapered fused bundle-combining approach and connecting it with delivery fiber, we point to an efficient, rugged, all-glass, integrated, and nearly brightness-preserving device that is capable of transmitting high-quality output beams.     

Perfect imaging through a disordered waveguide lattice

It is experimentally demonstrated that perfect imaging is possible in disordered wave guiding media, provided that the disorder is off-diagonal, i.e., that only the spacing varies randomly between the otherwise identical lattice sites. On-diagonal disorder or Kerr nonlinearity destroys the imaging.     

Asymptotic centers and best compact approximation of operators intoC(K)

The existence of best compact approximations for all bounded linear operators fromX intoC(K) is related to the behavior of asymptotic centers inX ^*. IfK is just one convergent sequence, the condition is that everyω ^*-convergent sequence inX ^* will have an asymptotic center. We first study this property, solving some open problems in the theory of asymptotic centers. IfK is more “complex,” the asymptotic centers should behave “continuously.” We use this observation to construct operators fromC[0,1] intoC(ω ²) and from ?₁ intoL ₁ without best compact approximation. We also construct spacesX ₁,X ₂, isomorphic to a Hilbert space, and operatorsT ₁,∶X ₁→C(ω ²),T ₂∶?₁→X ₂ without best compact approximations.     

Automated antenna positioning algorithms for wireless fixed-access networks

This article addresses a real-life problem - obtaining communication links between multiple base station sites, by positioning a minimal set of fixed-access relay antenna sites on a given terrain. Reducing the number of relay antenna sites is considered critical due to substantial installation and maintenance costs. Despite the significant cost saved by eliminating even a single antenna site, an inefficient manual approach is employed due to the computational complexity of the problem. From the theoretical point of view we show that this problem is not only NP hard, but also does not have a constant approximation. In this paper we suggest several alternative automated heuristics, relying on terrain preprocessing to find educated potential points for positioning relay stations. A large-scale computer-based experiment consisting of approximately 7,000 different scenarios was conducted. The quality of alternative solutions was compared by isolating and displaying factors that were found to affect the standard deviation of the solutions supplied by the tested heuristics. The results of the simulation based experiments show that the saving potential increases when more base stations are needed to be interconnected. The designs of a human expert were compared to the automatically generated solutions for a small subset of the experiment scenarios. Our studies indicate that for small networks (e.g., connecting up to ten base stations), the results obtained by human experts are adequate although they rarely exceed the quality of automated alternatives. However, the process of obtaining these results in comparison to automated heuristics is longer. In addition, when more base station sites need to be interconnected, the human approach is easily outperformed by our heuristics, both in terms of better results (fewer antennas) and in significant shorter calculation times.