The euler characteristic is the unique locally determined numerical homotopy invariant of finite complexes

If a numerical homotopy invariant of finite simplicial complexes has a local formula, then, up to multiplication by an obvious constant, the invariant is the Euler characteristic. Moreover, the Euler characteristic itself has a unique local formula.     

A solid-state NMR method for solution of zeolite crystal structures

Since zeolites are notoriously difficult to prepare as large single crystals, structure determination usually relies on powder X-ray diffraction (XRD). However, structure solution (i.e., deriving an initial structural model) directly from powder XRD data is often very difficult due to the diffraction phase problem and the high degree of overlap between the individual reflections, particularly for materials with the structural complexity of most zeolites. Here, we report a method for structure determination of zeolite crystal structures that combines powder XRD and nuclear magnetic resonance (NMR) spectroscopy in which the crucial step of structure solution is achieved using solid-state (29)Si double-quantum dipolar recoupling NMR, which probes the distance-dependent dipolar interactions between naturally abundant (29)Si nuclei in the zeolite framework. For two purely siliceous zeolite blind test samples, we demonstrate that the NMR data can be combined with the unit cell parameters and space group to solve structural models that refine successfully against the powder XRD data.     

Diversity and Popularity in Organizations and Communities

This paper examines social groupings whose structure depends only on the distribution of ability to attract attention. When people‘s attention is a scarce resource, those individuals who are rated highest by a large number of other individuals will have to ration their attention, resulting in constraints on the social structure of the group. The incidence of popular individuals by that definition reflects the extent to which individuals agree on who their highest-rated colleague is. We propose three basic distributions or ways to generate the matrix of perceived ability so as to yield popularity profiles that can be parametrically adjusted to match observations. We demonstrate that each of these assumption sets leads to a slightly different correlation between the value of the assumption‘s parameter and the set of observable popularity patterns. Since popularity, in real life, often determines such things as power, centrality, over-utilization and perhaps reduced accessibility, having more realistic ways of representing it is important for modeling and understanding virtual organizations and communities.     

Determination of molecular geometry by high-order multiple-quantum evolution in solid-state NMR

The principles of molecular geometry determination by high-quantum heteronuclear local field spectroscopy in solid-state NMR are discussed. The extreme multiple-quantum coherences in a cluster of nuclear spins are allowed to evolve in the presence of heteronuclear through-space couplings to two spins of a different type. The multiple-quantum dephasing curve is independent of the homonuclear spin-spin couplings and may be described in terms of geometric parameters. The triple-quantum version of the experiment is demonstrated by determining the psi torsion angle in a [(15)N(2), (13)C(3)]-labeled sample of the peptide ala-ala-gly. Two regions of torsion angle space fit the experimental data, one in the neighborhood of -152 degrees and one in the neighborhood of +161 degrees. The latter determination is in excellent agreement with the X-ray estimate of +160.5 degrees.     

Multiple-quantum relaxation in the magic-angle-spinning NMR of 13C spin pairs.

We determine the decay rate constants of zero-, double- and single-quantum coherence for 13C spin pairs in magic-angle-spinning solid-state NMR. The double-quantum coherence is excited by a C7 pulse sequence and converted into zero-quantum coherence by a frequency-selective pair of pi/2 pulses. The zero-quantum coherence is reconverted into observable magnetization by a second pair of pi/2 pulses followed by a second C7 sequence. In a magnetically dilute system where the 13C-13C distance is 0.296 nm, the relaxation rate constants are consistent with a model of uncorrelated random fields at the two labeled 13C sites. In a fully-labelled system with a short 13C-13C distance of 0.153 nm, the measured rate constants are inconsistent with the uncorrelated random field model.     

Vibrational spectra of alkali hydrogen selenites,selenous acid,and their deuterated analogs

The infrared and Raman spectra of alkali hydrogen selenites [(MHSeO₃), where M = Li, Na, K, or Cs], selenous acid (H₂Seo₃), and their deuterated analogs have been recorded and interpreted. The internal mode frequencies observed in sodium hydrogen selenite, selenous acid, and sodium trihydrogen selenite are used to generate general valence force constants for HSeO^?₃ and H₂SeO₃ under the assumption of C_s geometry for each species. Calculations of observed deuterium frequency shifts are made to aid in the assignments of the various internal modes. A low-temperature proton-triggered phase transition is observed in CsHSeO₃ and is confirmed in KHSeO₃. A discussion of the effects of proton order and disorder upon the selenite frequencies is also presented.     

The effect of timing errors on the intelligibility of deaf children's speech.

The purpose of this study was to quantify the effect of timing errors on the intelligibility of deaf children's speech. Deviant timing patterns were corrected in the recorded speech samples of six deaf children using digital speech processing techniques. The speech waveform was modified to correct timing errors only, leaving all other aspects of the speech unchanged. The following six-stage approximation procedure was used to correct the deviant timing patterns: (1) original, unaltered utterances, (2) correction of pauses only, (3) correction of relative timing, (4) correction of absolute syllable duration, (5) correction of relative timing and pauses, and (6) correction of absolute syllable duration and pauses. Measures of speech intelligibility were obtained for the original and the computer-modified utterances. On the average, the highest intelligibility score was obtained when relative timing errors only were corrected. The correction of this type of error improved the intelligibility of both stressed and unstressed words within a phrase. Improvements in word intelligibility, which occurred when relative timing was corrected, appeared to be closely related to the number of phonemic errors present within a word. The second highest intelligibility score was obtained for the original, unaltered sentences. On the average, the intelligibility scores obtained for the other four forms of timing modification were poorer than those obtained for the original sentences. Thus, the data show that intelligibility improved, on the average, when only one type of error, relative timing, was corrected.     

Direct enhancement of nuclear singlet order by dynamic nuclear polarization

Hyperpolarized singlet order is available immediately after dissolution DNP, avoiding need for additional preparation steps. We demonstrate this procedure on a sample of [1,2-(13)C(2)]pyruvic acid.     

Alkyl inductive effects on molecular ionization potentials—XV n-alkanes

The first ionisation potentials, E_I, of n-alkanes are found to be a linear function of the inductive substituent constants, Σσ_I. The correlation is obtained by considering that a σ-bonding electron is ejected from the most central CC bond in the alkane RR′. The equation for the regression is E_I = 17·19 + 60·2 Σσ_I ± 0·04 eV, with correlation coefficient 0·998. An equation is also deduced relating E_I to the number of carbon atoms, n_c, and hydrogen atoms, n_H, in the n-alkane: E_I = 4·70(n_H - 1)/n_c, from which E_I for polymethylene, (CH₂)_x, is found to be 9·40 eV.