The isocohomological property, higher Dehn functions, and relatively hyperbolic groups

The property that the polynomial cohomology with coefficients of a finitely generated discrete group is canonically isomorphic to the group cohomology is called the (weak) isocohomological property for the group. In the case when a group is of type $HF^\infty$, i.e. that has a classifying space with the homotopy type of a cellular complex with finitely many cells in each dimension, we show that the isocohomological property is equivalent to the universal cover of the classifying space satisfying polynomially bounded higher Dehn functions. If a group is hyperbolic relative to a collection of subgroups, each of which is polynomially combable (respectively $HF^\infty$ and isocohomological), then we show that the group itself has these respective properties too. Combining with the results of Connes-Moscovici and Dru{\c{t}}u-Sapir we conclude that a group satisfies the Novikov conjecture if it is relatively hyperbolic to subgroups that are of property RD, of type $HF^\infty$ and isocohomological.Comment: 35 pages, no figure

OPE analysis for polarized deep inelastic scattering

We present an explicit OPE analysis for the first moment of $g_1$ up to order $M^2/Q^2$. This result allows to calculate power corrections to the Bjorken and Ellis--Jaffe sum rules.Comment: 10 pages, minor modifications, revised version for the journa

On the Q^2 Dependence of Measured Polarized Structure Funtions

We analyse the available data on the polarized asymmetries $A_1$ for proton, neutron and deuteron targets. We use a homogeneous and updated set of unpolarized structure functions to derive $g_1$ from $A_1$, and we accurately correct for the scaling violations in order to obtain $g_1(x,Q^2)$ with the same $Q^2$ for all $x$ values. The contribution to the $Q^2$ evolution of a possible large gluon polarized density is also considered. The implications for the Ellis-Jaffe and for the Bjorken sum rules are discussed.Comment: 11 pages (LaTex) + 4 figures (topdrawer, included at the end) CERN-TH 7023/9

Testing the handbag contribution to exclusive virtual Compton scattering

We discuss the handbag approximation to exclusive deep virtual Compton scattering. After defining the kinematical region where this approximation can be valid, we propose tests for its relevance in planned electroproduction experiments, e + p -> e + p + gamma. We focus on scaling laws in the cross section, and the distribution in the angle between the lepton and hadron planes, which contains valuable information on the angular momentum structure of the Compton process. We advocate to measure weighted cross sections, which make use of the data in the full range of this angle and do not require very high event statistics.Comment: 14 pages, LaTeX, 3 figures included using epsf.st

Molecular evolution of dimeric α-amylase inhibitor genes in wild emmer wheat and its ecological association

<p>Abstract</p> <p>Background</p> <p>α-Amylase inhibitors are attractive candidates for the control of seed weevils, as these insects are highly dependent on starch as an energy source. In this study, we aimed to reveal the structure and diversity of dimeric α-amylase inhibitor genes in wild emmer wheat from Israel and to elucidate the relationship between the emmer wheat genes and ecological factors using single nucleotide polymorphism (SNP) markers. Another objective of this study was to find out whether there were any correlations between SNPs in functional protein-coding genes and the environment.</p> <p>Results</p> <p>The influence of ecological factors on the genetic structure of dimeric α-amylase inhibitor genes was evaluated by specific SNP markers. A total of 244 dimeric α-amylase inhibitor genes were obtained from 13 accessions in 10 populations. Seventy-five polymorphic positions and 74 haplotypes were defined by sequence analysis. Sixteen out of the 75 SNP markers were designed to detect SNP variations in wild emmer wheat accessions from different populations in Israel. The proportion of polymorphic loci <it>P </it>(5%), the expected heterozygosity <it>He</it>, and Shannon's information index in the 16 populations were 0.887, 0.404, and 0.589, respectively. The populations of wild emmer wheat showed great diversity in gene loci both between and within populations. Based on the SNP marker data, the genetic distance of pair-wise comparisons of the 16 populations displayed a sharp genetic differentiation over long geographic distances. The values of <it>P</it>, <it>He</it>, and Shannon's information index were negatively correlated with three climatic moisture factors, whereas the same values were positively correlated by Spearman rank correlation coefficients' analysis with some of the other ecological factors.</p> <p>Conclusion</p> <p>The populations of wild emmer wheat showed a wide range of diversity in dimeric α-amylase inhibitors, both between and within populations. We suggested that SNP markers are useful for the estimation of genetic diversity of functional genes in wild emmer wheat. These results show significant correlations between SNPs in the α-amylase inhibitor genes and ecological factors affecting diversity. Ecological factors, singly or in combination, explained a significant proportion of the variations in the SNPs, and the SNPs could be classified into several categories as ecogeographical predictors. It was suggested that the SNPs in the α-amylase inhibitor genes have been subjected to natural selection, and ecological factors had an important evolutionary influence on gene differentiation at specific loci.</p

Gluon Polarization from QCD Sum Rules

The gluon polarization $\Delta G$ in a nucleon can be defined in a gauge invariant way as the integral over the Ioffe-time distribution of polarized gluons. We argue that for sufficiently regular polarized gluon distributions $\Delta G$ is dominated by contributions from small and moderate values of the Ioffe-time z < 10. As a consequence $\Delta G$ can be estimated with 20% accuracy from the first two even moments of the polarized gluon distribution, and its behavior at small values of Bjorken x or, equivalently, at large Ioffe-times z. We employ this idea and compute the first two moments of the polarized gluon distribution within the framework of QCD sum rules. Combined with the color coherence hypothesis we obtain an upper limit for $\Delta G \sim 2 \pm 0.5$ at a typical scale $\mu^2 \sim 1 GeV^2$.Comment: 12 pages, Latex, 2 figures include

The GDH Sum Rule and Related Integrals

The spin structure of the nucleon resonance region is analyzed on the basis of our phenomenological model MAID. Predictions are given for the Gerasimov-Drell-Hearn sum rule as well as generalized integrals over spin structure functions. The dependence of these integrals on momentum transfer is studied and rigorous relationships between various definitions of generalized Gerasimov-Drell-Hearn integrals and spin polarizabilities are derived. These results are compared to the predictions of chiral perturbation theory and phenomenological models.Comment: 15 pages LaTeX including 5 figure

Noncommutative elliptic theory. Examples

We study differential operators, whose coefficients define noncommutative algebras. As algebra of coefficients, we consider crossed products, corresponding to action of a discrete group on a smooth manifold. We give index formulas for Euler, signature and Dirac operators twisted by projections over the crossed product. Index of Connes operators on the noncommutative torus is computed.Comment: 23 pages, 1 figur

Target Independence of the Emc-SMC Effect

An approach to deep inelastic scattering is described in which the matrix elements arising from the operator product expansion are factorised into composite operator propagators and proper vertex functions. In the case of polarised \m p scattering, the composite operator propagator is identified with the square root of the QCD topological susceptibility $\sqrt{\chi^{\prime}(0)}$, while the corresponding proper vertex is a renormalisation group invariant. We estimate $\chi^{\prime}(0)$ using QCD spectral sum rules and find that it is significantly suppressed relative to the OZI expectation. Assuming OZI is a good approximation for the proper vertex, our predictions, \int_{0}^{1}dx g_1^p (x;Q^2=10\GV^2)= 0.143 \pm 0.005 and $G^{(0)}_A \equiv \Delta \Sigma = 0.353 \pm 0.052$, are in excellent agreement with the new SMC data. This result, together with one confirming the validity of the OZI rule in the \hp radiative decay, supports our earlier conjecture that the suppression in the flavour singlet component of the first moment of $g_1^p$ observed by the EMC-SMC collaboration is a target-independent feature of QCD related to the $U(1)$ anomaly and is not a property of the proton structure. As a corollary, we extract the magnitude of higher twist effects from the neutron and Bjorken sum rules.Comment: 22 pages, 8 figures available on request