Random replicators with high-order interactions

We use tools of the equilibrium statistical mechanics of disordered systems to study analytically the statistical properties of an ecosystem composed of N species interacting via random mutual interactions, as well as via deterministic self-interactions of order p>/=2. We show that the main effect of increasing the order of the interactions among the species is to make the system less competitive, in the sense that the fraction of extinct species is greatly reduced. In addition, we find that for p>2 there is a threshold value which gives a lower bound to the concentration of the surviving species, preventing then the existence of rare species and, consequently, increasing the robustness of the ecosystem to external perturbations.     

Molecular structure and dynamics in the low temperature (orthorhombic) phase of NH3BH3

Variable temperature 2H NMR experiments on the orthorhombic phase of selectively deuterated NH3BH3 spanning the static to fast exchange limits of the borane and amine motions are reported. New values of the electric field gradient (EFG) tensor parameters have been obtained from the static 2H spectra of V(zz) = 1.652 (+/-0.082) x 10(21) V/m(2) and eta = 0.00 +/- 0.05 for the borane hydrogens and V(zz) = 2.883 (+/-0.144) x 10(21) V/m(2) and eta = 0.00 +/- 0.05 for the amine hydrogens. The molecular symmetry inferred from the observation of equal EFG tensors for the three borane hydrogens and likewise for the three amine hydrogens is in sharp contrast with the C(s) symmetry derived from diffraction studies. The origin of the apparent discrepancy has been investigated using molecular dynamics methods in combination with electronic structure calculations of NMR parameters, bond lengths, and bond angles. The computation of parameters from a statistical ensemble rather than from a single set of atomic Cartesian coordinates gives values that are in close quantitative agreement with the 2H NMR electric field gradient tensor measurements and are more consistent with the molecular symmetry revealed by the NMR spectra.     

Spectroscopic studies of the phase transition in ammonia borane: Raman spectroscopy of single crystal NH3BH3 as a function of temperature from 88 to 330 K

Raman spectra of single crystal ammonia borane, NH3BH3, were recorded as a function of temperature from 88 to 300 K using Raman microscopy and a variable temperature stage. The orthorhombic to orientationally disordered tetragonal phase transition at 225 K was clearly evident from the decrease in the number of vibrational modes. However, some of the modes in the orthorhombic phase appeared to merge 10-12 K below the phase transition perhaps suggesting the presence of an intermediate phase. Factor group analysis of vibrational spectra for both orthorhombic and tetragonal phase is provided. In addition, electronic structure calculations are used to assist in the interpretation and assignment of the normal modes.     

Weighted approximation by Baskakov-type operators

The uniform weighted approximation errors of Baskakov-type operators are characterized for weights of the form $\left(\dfrac{x}{1+x}\right)^{\gamma_{0}}{(1+x)}^{\gamma_{\infty}}$ for ?? ₀,?? _????[?1,0]. Direct and strong converse theorems are proved in terms of the weighted K-functional.     

Maturation of auditory temporal integration and inhibition assessed with event-related potentials (ERPs)

Background

We examined development of auditory temporal integration and inhibition by assessing electrophysiological responses to tone pairs separated by interstimulus intervals (ISIs) of 25, 50, 100, 200, 400, and 800 ms in 28 children aged 7 to 9 years, and 15 adults.

Results

In adults a distinct neural response was elicited to tones presented at ISIs of 25 ms or longer, whereas in children this was only seen in response to tones presented at ISIs above 100 ms. In adults, late N1 amplitude was larger for the second tone of the tone pair when separated by ISIs as short as 100 ms, consistent with the perceptual integration of successive stimuli within the temporal window of integration. In contrast, children showed enhanced negativity only when tone pairs were separated by ISIs of 200 ms. In children, the amplitude of the P1 component was attenuated at ISIs below 200 ms, consistent with a refractory process.

Conclusions

These results indicate that adults integrate sequential auditory information into smaller temporal segments than children. These results suggest that there are marked maturational changes from childhood to adulthood in the perceptual processes underpinning the grouping of incoming auditory sensory information, and that electrophysiological measures provide a sensitive, non-invasive method allowing further examination of these changes.     

On estimating the rate of best trigonometric approximation by a modulus of smoothness

Best trigonometric approximation in L _p , 1≦p≦∞, is characterized by a modulus of smoothness, which is equivalent to zero if the function is a trigonometric polynomial of a given degree. The characterization is similar to the one given by the classical modulus of smoothness. The modulus possesses properties similar to those of the classical one.     

3D structure of dendritic and hyper-branched macromolecules by X-ray diffraction

The atomic ordering in dendritic and hyper-branched macromolecules has been determined by X-ray diffraction. The approach of the atomic pair distribution function technique has been used due to the lack of 3D periodicity in these polymeric materials. Dendrimers are found to possess a semi-regular structure riddled with nanosize cavities. The cavities are joined into channels connecting dendrimer's surface and core. In contrast, hyper-branched polymers are rather irregular at the atomic scale and with less accessible interior.     

Three-dimensional structure of nanocomposites from atomic pair distribution function analysis: study of polyaniline and (polyaniline)(0.5)V(2)O(5) x 1.0 H(2)O

The three-dimensional structures of emeraldine base polyaniline (PANI) and (polyaniline)(0.5)V(2)O(5) x 1.0 H(2)O have been determined by total X-ray scattering experiments. Atomic pair distribution functions (PDF) were measured to obtain experimental observables against which structural models were tested and refined. The PDF approach is necessary because of the limited structural coherence in these nanostructured materials. Polyaniline possesses a well-defined local atomic arrangement that can be described in terms of an 84-atom orthorhombic unit cell. The nanocomposite (PANI)(0.5)V(2)O(5) x 1.0 H(2)O too is locally well ordered and may be described in terms of a small number of structure-sensible parameters. The PDF approach allows the construction of structure models of PANI and (PANI)(0.5)V(2)O(5) x 1.0 H(2)O on the basis of which important materials' properties can be explained predicted and possibly improved.     

Materials for hydrogen storage: structure and dynamics of borane ammonia complex

The activation energies for rotations in low-temperature orthorhombic ammonia borane were analyzed and characterized in terms of electronic structure theory. The perdeuterated (11)B-enriched ammonia borane, (11)BD(3)ND(3), sample was synthesized, and the structure was refined from neutron powder diffraction data at 175 K. This temperature has been chosen as median of the range of previously reported nuclear magnetic resonance spectroscopy measurements of these rotations. A representative molecular cluster model was assembled from the refined geometry, and the activation energies were calculated and characterized by analysis of the environmental factors that control the rotational dynamics. The barrier for independent NH(3) rotation, E(a) = 12.7 kJ mol(-1), largely depends on the molecular conformational torsion in the solid-state geometry. The barrier for independent BH(3) rotation, E(a) = 38.3 kJ mol(-1), results from the summation of the effect of molecular torsion and large repulsive intermolecular hydrogen-hydrogen interactions. However, a barrier of E(a) = 31.1 kJ mol(-1) was calculated for internally correlated rotation with preserved molecular conformation. Analysis of the barrier heights and the corresponding rotational pathways shows that rotation of the BH(3) group involves strongly correlated rotation of the NH(3) end of the molecule. This observation suggests that the barrier from previously reported measurement of BH(3) rotation corresponds to H(3)B-NH(3) correlated rotation.