Dimension improvement in Dhar's refutation of the Eden conjecture

We consider the Eden model on the d-dimensional hypercubical unoriented lattice, for large d. Initially, every lattice point is healthy, except the origin which is infected. Then, each infected lattice point contaminates any of its neighbours with rate 1. The Eden model is equivalent to first passage percolation, with exponential passage times on edges. The Eden conjecture states that the limit shape of the Eden model is a Euclidean ball. By pushing the computations of Dhar [5] a little further with modern computers and efficient implementation we obtain improved bounds for the speed of infection. This shows that the Eden conjecture does not hold in dimension superior to 22 (the lowest known dimension was 35).     

Classification of live, untethered zooplankton from observations of multiple-angle acoustic scatter

A broadband, multiple-angle acoustic array was used to classify millimeter to centimeter sized live zooplankton in a laboratory tank. Reflections in the frequency range from 1.5 to 2.5 MHz were recorded from untethered 1-4 mm calanoid copepods and 8-12 mm mysids over an angular range of 0 degrees -47 degrees . A synchronized, coregistered video system recorded animal location and orientation. To highlight differences between animals, a frequency correlation matrix was computed from the observed wide-band power spectra of the scattered sound. Significant differences in the slopes and shapes of the eigenvalue spectra of this matrix were found for mysids versus copepods. These results support the idea that broadband, multiple-angle scatter can be used to classify organisms of different sizes and shapes.     

On distributive residuated groupoids

In this note we extend the well-known fact (see [1], p. 45) that an implicative (or Brouwerian) lattice is distributive to a large class of residuated groupoids.     

Structural and electronic model of negative electron affinity on the Si/Cs/O surface

Structural and electronic models are proposed which correlate Goldstein's LEED, Auger, photo-emission, plasmon, and desorption data for negative electron affinity (NEA) on Si(100) surfaces. In the structural model, the surface Si atoms group into adjacent rows of surface “pedestals” and surface “caves”. Their density is 3.4 × 10¹⁴ cm^?2 each, as inferred from the LEED 2 × 2 reconstruction pattern and other data. Adsorbed Cs resides in fourfold coordination with Si atop the pedestals. Adsorbed oxygen is completely submerged in the caves of aperture 2.98Å to give a Cs-O dipole length of 2.9Å. Similar structural arguments show why Cs must be adsorbed before O₂, and why Si(111) does not exhibit NEA. In the electronic model, the surface dielectric constant, 5.3. obtained from the surface plasmon energy, 7 eV, is used to compute the dipole length from the final work function, 0.9 eV. It is 2.8Å in excellent agreement with the dipole length computed from the above structural model. Some properties of the “induced” surface states in the presence of Cs and O are also described.     

HF dimer in small helium clusters: interchange-tunneling dynamics in a quantum environment

We present diffusion quantum Monte Carlo calculations of the interchange tunneling splitting of (4)He(n)(HF)(2) clusters, n = 1-10. The tunneling splitting decreases rapidly for n = 1-4 clusters, and much more slowly for n>4. The decrease calculated for (4)He(n)(HF)(2) represents 74% of the reduction in the tunneling splitting measured recently for HF dimer in nanodroplets of more than 2000 He atoms. The first four He atoms quench the interchange tunneling very efficiently by virtue of occupying the equatorial ring which encircles the C(2h) transition state of the tunneling pathway.     

First example of high loaded polymer-stabilized nanoclusters immobilized on hydrotalcite: effects in alkyne hydrogenation

Poly(N-vinyl-2-pyrrolidone)-stabilized Pd-nanoclusters, for the first time exclusively supported on the hydrotalcite lateral surface, showed a remarkable catalytic performance in the selective hydrogenation of 3-hexyn-1-ol, which can be ascribed to both the influence of the protecting polymer PVP as well as the nature of the support.     

Multiple angle acoustic classification of zooplankton

The use of multiple angle acoustic scatter to discriminate between two taxa of fluid-like zooplankton, copepods and euphausiids, is explored. Using computer modeling, feature extraction, and subsequent classification, the accuracy in discriminating between the two taxa is characterized via computer simulations. The model applies the distorted wave Born approximation together with a simple system geometry, a linear array, to predict a set of noisy training and test data. Three feature spaces are designed, exploiting the relationship between the shape of the scatterer and angularly varying scattering amplitude, to extract discriminant features from these data. Under the assumption of uniform random length and uniform three-dimensional orientation distributions for each class of scatterers, the performance of several classification algorithms is evaluated. Simulations reveal that the incorporation of multiple angle data leads to a marked improvement in classification performance over single angle methods. The improvement is more substantial using broadband scatter. The simulations indicate that under the stated assumptions, a low classification error can be obtained. The use of multiple angle scatter therefore holds promise to substantially improve the in situ acoustic classification of fluid-like zooplankton using simple observation geometries.     

Size-Controlled Hapticity Switching in [Ln(C9H9)(C8H8)] Sandwiches

Sandwich complexes of lanthanides have recently attracted a considerable amount of interest due to their applications as Single Molecule Magnet (SMM). Herein, a comprehensive series of heteroleptic lanthanide sandwich complexes ligated by the cyclononatetraenyl (Cnt) and the cyclooctatetraenyl (Cot) ligand [Ln(Cot)(Cnt)] (Ln=Tb, Dy, Er, Ho, Yb, and Lu) is reported. The coordination behavior of the Cnt ligand has been investigated along the series and shows different coordination patterns in the solid-state depending on the size of the corresponding lanthanide ion without altering its overall anisotropy. Besides the characterization in the solid state by single-crystal X-ray diffraction and in solution by ¹H NMR, static magnetic studies and ab initio computational studies were performed.     

Mathematical analysis of a two-patch model of tuberculosis disease with staged progression

The spread of tuberculosis is studied through a two-patch epidemiological system SE₁ ? E_nI which incorporates migrations from one patch to another just by susceptible individuals. Our model is consider with bilinear incidence and migration between two patches, where infected and infectious individuals cannot migrate from one patch to another, due to medical reasons. The existence and uniqueness of the associated endemic equilibria are discussed. Quadratic forms and Lyapunov functions are used to show that when the basic reproduction ratio is less than one, the disease-free equilibrium (DFE) is globally asymptotically stable, and when it is greater than one there exists in each case a unique endemic equilibrium (boundary equilibria and endemic equilibrium) which is globally asymptotically stable. Numerical simulation results are provided to illustrate the theoretical results.     

Co-evolution of insect proteases and plant protease inhibitors

Plants are at the basis of the food chain, but there is no such thing as a "free lunch" for herbivores. To promote reproductive success, plants evolved multi-layered defensive tactics to avoid or discourage herbivory. To the detriment of plants, herbivores, in turn, evolved intricate strategies to find, eat, and successfully digest essential plant parts to raise their own offspring. In this battle the digestive tract is the arena determining final victory or defeat as measured by growth or starvation of the herbivore. Earlier, specific molecular opponents were identified as proteases and inhibitors: digestive proteases of herbivores evolved structural motifs to occlude plant protease inhibitors, or alternatively, the insects evolved proteases capable of specifically degrading the host plant inhibitors. In response plant inhibitors evolved hyper-variable and novel protein folds to remain active against potential herbivores. At the level of protease regulation in herbivorous insects, it was shown that inhibition-insensitive digestive proteases are up-regulated when sensitive proteases are inhibited. The way this regulation operates in mammals is known as negative feedback by gut-luminal factors, so-called 'monitor peptides' that are sensitive to the concentration of active enzymes. We propose that regulation of gut enzymes by endogenous luminal factors has been an open invitation to plants to "hijack" this regulation by evolving receptor antagonists, although yet these plant factors have not been identified. In future research the question of the co-evolution of insect proteases and plant inhibitors should, therefore, be better approached from a systems level keeping in mind that evolution is fundamentally opportunistic and that the plant's fitness is primarily improved by lowering the availability of essential amino acids to an herbivore by any available mechanism.