Some remarks about Poincaré duality pairs

Bieri-Eckmann [6] introduced the concept of relative cohomology for a group pair (G, S), where G is a group and S is a family of subgroups of G and, by using that theory, they introduced the concept of Poincaré duality pairs (G, S) and provided a topological interpretation for such pairs through Eilenberg-MacLane pairs K(G, S, 1). A Poincaré duality pair is a pair (G, S) that satisfies two isomorphisms, one between absolute cohomology and relative homology and the second between relative cohomology and absolute homology. In this paper, we present a proof that those two isomorphisms are equivalent. We also present some calculations on duality pairs by using the cohomological invariant defined in [1] and studied in [2-4]. © 2012 Pushpa PublishingHouse.

T-duality in 2D integrable models

The non-conformal analogue of Abelian T-duality transformations relating pairs of axial and vector integrable models from the non-Abelian affine Toda family is constructed and studied in detail.

A RELATIVE COHOMOLOGICAL INVARIANT FOR GROUP PAIRS

We define a cohomological invariant E(G, S, M) where G is a group, S is a non empty family of (not necessarily distinct) subgroups of infinite index in G and M is a F2G-module (F2 is the field of two elements). In this paper we are interested in the special case where the family of subgroups consists of just one subgroup, and M is the F2G-module F2(G/S). The invariant E(G, {S}, F2(G/S)) will be denoted by E(G, S). We study the relations of this invariant with other ends e(G) , e(G, S) and e(G, S), and some results are obtained in the case where G and S have certain properties of duality.

Relationship among malocclusion, number of occlusal pairs and mastication

This study evaluated the relationship among malocclusion, number of occlusal pairs, masticatory performance, masticatory time and masticatory ability in completely dentate subjects. Eighty healthy subjects (mean age = 19.40 ± 4.14 years) were grouped according to malocclusion diagnosis (n = 16): Class I, Class Class II-2, Class III and Normocclusion (control). Number of occlusal pairs was determined clinically. Masticatory performance was evaluated by the sieving method, and the time used for the comminute test food was registered as the masticatory time. Masticatory ability was measured by a dichotomic self-perception questionnaire. Statistical analysis was done by one-way ANOVA, ANOVA on ranks, Chi-Square and Spearman tests. Class II-1 and III malocclusion groups presented a smaller number of occlusal pairs than Normocclusion (p < 0.0001), Class I (p < 0.001) and II-2 (p < 0.0001) malocclusion groups. Class I, and III malocclusion groups showed lower masticatory performance values compared to Normocclusion (p < 0.05) and Class II-2 (p < 0.05) malocclusion groups. There were no differences in masticatory time (p = 0.156) and ability (χ2 = 3.58/p= 0.465) among groups. Occlusal pairs were associated with malocclusion (rho = 0.444/p < 0.0001) and masticatory performance (rho = 0.393/p < 0.0001), but malocclusion was not correlated with masticatory performance (rho = 0.116/p= 0.306). In conclusion, masticatory performance and ability were not related to malocclusion, and subjects with Class I, II-1 and III malocclusions presented lower masticatory performance because of their smaller number of occlusal pairs.

Cosmic distance duality relation and the shape of galaxy clusters

Context. Observations in the cosmological domain are heavily dependent on the validity of the cosmic distance-duality (DD) relation, eta = D(L)(z)(1+ z)(2)/D(A)(z) = 1, an exact result required by the Etherington reciprocity theorem where D(L)(z) and D(A)(z) are, respectively, the luminosity and angular diameter distances. In the limit of very small redshifts D(A)(z) = D(L)(z) and this ratio is trivially satisfied. Measurements of Sunyaev-Zeldovich effect (SZE) and X-rays combined with the DD relation have been used to determine D(A)(z) from galaxy clusters. This combination offers the possibility of testing the validity of the DD relation, as well as determining which physical processes occur in galaxy clusters via their shapes. Aims. We use WMAP (7 years) results by fixing the conventional Lambda CDM model to verify the consistence between the validity of DD relation and different assumptions about galaxy cluster geometries usually adopted in the literature. Methods. We assume that. is a function of the redshift parametrized by two different relations: eta(z) = 1+eta(0)z, and eta(z) = 1+eta(0)z/(1+z), where eta(0) is a constant parameter quantifying the possible departure from the strict validity of the DD relation. In order to determine the probability density function (PDF) of eta(0), we consider the angular diameter distances from galaxy clusters recently studied by two different groups by assuming elliptical (isothermal) and spherical (non-isothermal) beta models. The strict validity of the DD relation will occur only if the maximum value of eta(0) PDF is centered on eta(0) = 0. Results. It was found that the elliptical beta model is in good agreement with the data, showing no violation of the DD relation (PDF peaked close to eta(0) = 0 at 1 sigma), while the spherical (non-isothermal) one is only marginally compatible at 3 sigma. Conclusions. The present results derived by combining the SZE and X-ray surface brightness data from galaxy clusters with the latest WMAP results (7-years) favors the elliptical geometry for galaxy clusters. It is remarkable that a local property like the geometry of galaxy clusters might be constrained by a global argument provided by the cosmic DD relation.

TESTING THE DISTANCE-DUALITY RELATION WITH GALAXY CLUSTERS AND TYPE Ia SUPERNOVAE

In this Letter, we propose a new and model-independent cosmological test for the distance-duality (DD) relation, eta = D(L)(z)(1 + z)(-2)/D(A)(z) = 1, where D(L) and D(A) are, respectively, the luminosity and angular diameter distances. For D(L) we consider two sub-samples of Type Ia supernovae (SNe Ia) taken from Constitution data whereas D(A) distances are provided by two samples of galaxy clusters compiled by De Filippis et al. and Bonamente et al. by combining Sunyaev-Zeldovich effect and X-ray surface brightness. The SNe Ia redshifts of each sub-sample were carefully chosen to coincide with the ones of the associated galaxy cluster sample (Delta z < 0.005), thereby allowing a direct test of the DD relation. Since for very low redshifts, D(A)(z) approximate to D(L)(z), we have tested the DD relation by assuming that. is a function of the redshift parameterized by two different expressions: eta(z) = 1 + eta(0)z and eta(z) = 1 +eta(0)z/(1 + z), where eta(0) is a constant parameter quantifying a possible departure from the strict validity of the reciprocity relation (eta(0) = 0). In the best scenario (linear parameterization), we obtain eta(0) = -0.28(-0.44)(+0.44) (2 sigma, statistical + systematic errors) for the De Filippis et al. sample (elliptical geometry), a result only marginally compatible with the DD relation. However, for the Bonamente et al. sample (spherical geometry) the constraint is eta(0) = -0.42(-0.34)(+0.34) (3 sigma, statistical + systematic errors), which is clearly incompatible with the duality-distance relation.

Aspects of a noncommutative scalar/tensor duality

We study the noncommutative massless Kalb-Ramond gauge field coupled to a dynamical U(1) gauge field in the adjoint representation together with a compensating vector field. We derive the Seiberg-Witten map and obtain the corresponding mapped action to first order in theta. The (emergent) gravity structure found in other situations is not present here. The off-shell dual scalar theory is derived and it does not coincide with the Seiberg-Witten mapped scalar theory. Dispersion relations are also discussed. The p-form generalization of the Seiberg-Witten map to order theta is also derived.

Duality linking standard and tachyon scalar field cosmologies

In this work we investigate the duality linking standard and tachyon scalar field homogeneous and isotropic cosmologies in N + 1 dimensions. We determine the transformation between standard and tachyon scalar fields and between their associated potentials, corresponding to the same background evolution. We show that, in general, the duality is broken at a perturbative level, when deviations from a homogeneous and isotropic background are taken into account. However, we find that for slow-rolling fields the duality is still preserved at a linear level. We illustrate our results with specific examples of cosmological relevance, where the correspondence between scalar and tachyon scalar field models can be calculated explicitly.

Electric Field Effects in the Excitation of Cold Rydberg-Atom Pairs

In this work, we study the role of the ac Stark effects on the excitation of nS(1/2) cold Rydberg atoms produced in a rubidium magneto-optical trap. We have observed an atomic population in the nP(3/2) state after excitation of nS(1/2) for 29 <= n <= 37. Such an observation is normally attributed to binary collisions; however, the interaction between Rb nS(1/2) atoms is repulsive. To explain our results, the dipole-dipole interaction and ac Stark shifts from the excitation laser must be considered. We find that the Rydberg-atom-pair state asymptotically correlating to nP(3/2)+(n-1)P(3/2) is excited directly.

Cost functions and duality for stochastic technologies

Cost functions dual to stochastic production technologies are derived and their properties are discussed. These cost functions are shown to be consistent with expected-utility maximization without placing serious structural restrictions on the underlying technology.

DISCORDANCE FOR RETINITIS PIGMENTOSA IN TWO MONOZYGOTIC TWIN PAIRS

Background: Retinitis pigmentosa (RP) is a group of genetically heterogeneous diseases with progressive degeneration of the retina. The condition can be inherited as an autosomal dominant, autosomal recessive, and X-linked trait. Methods: We report on two female twin pairs. One twin of each pair is affected with RP, the other twin is unaffected, both clinically and functionally. Molecular analysis in both twins included zygosity determination, arrayed primer extension chip analysis for autosomal recessive and dominant RP, sequencing of the entire RPGR gene, and analysis of X-chromosome inactivation status. Results: Both unrelated twin pairs were genetically identical. Of the potential pathogenetic mechanisms, skewed X-inactivation was excluded on leukocytes. Autosomal recessive RP and autosomal dominant RP arrayed primer extension chip analysis result was completely normal, excluding known mutations in known genes as the cause of disease in the affected twins. Sequencing excluded mutations in RPGR. A postzygotic recessive or dominant genetic mutation of an RP gene is not impossible. A postfertilization error as a potential cause of uniparental isodisomy is unlikely albeit not entirely impossible. Conclusion: The authors report on the second and third unrelated identical twin pair discordant for RP. The exact cause of the condition and the explanation of the clinical discordance remain elusive. RETINA 31:1164-1169, 2011

Searching behaviour and diet of Oystercatcher Haematopus ostralegus pairs feeding in their territories

Search path, searching behaviour and diet of pairs of Oystercatchers feeding in mudflat territories were studied during spring. females ate Nereis, Mya, small unidentified prey, probably Corophium, and a few Macoma, whereas males primarily ate Macoma. Even when female and male foraged in the same site, they often caught different prey. The combination of 'The Search-rate/Detection Model' (Gendron & Staddon 1983) and 'The Harvestable Prey Model' (Zwarts & Wanink 1993) provide the theoretical framework in which to explain these differences in diet. Macoma are thought to be more cryptic than Nereis, Mya and Corophium. Therefore females, while searching at a faster rate than their respective mates, caught far fewer cryptic prey, but a greater number of more conspicuous prey than their mates. On the basis of distances moved before and after capturing prey, males exhibited area-restricted searching for Macoma and Corophium. In contrast, females did not exhibit any area-restricted searching. it is suggested that the distribution of Macoma and Corophium available to males searching slowly was more clumped than that of these two prey species available to females searching more quickly.

A comparison of family functioning, temperament, and childhood conditions in monozygotic twin pairs discordant for lifetime bulimia nervosa

Objective: The authors investigated differences between twins in nine pairs of female monozygotic twins in the Australian Twin Registry who were discordant for lifetime bulimia nervosa. Method: The twins affected and unaffected by lifetime bulimia nervosa were compared on self-report measures, including a measure of parental bonding, four measures of temperament, and six early-childhood medical conditions. Results: No twins had current bulimia nervosa, and there was no difference in weight or eating status between the affected and unaffected twins. The affected twins reported significantly lower self-esteem and less warmth but more overprotection by their mothers during childhood. Conclusions: Although limited by the small number of discordant twin pairs and the inability to detect causal relationships, these results suggest that environmental influences that promote low self-esteem may also increase the risk for bulimia nervosa. These temperamental differences may explain the discrepancies in parenting or perceived parenting.

Concordance of iron indices in homozygote and heterozygote sibling pairs in hemochromatosis families: implications for family screening

Background/Aims: Concordance of iron indices between same sex siblings homozygous for the cysteine-to-tyrosine substitution at amino acid 282 (C282Y) mutation suggests that the variable phenotype in hereditary hemochromatosis is caused by genetic factors. Concordance of iron indices between same-sex heterozygous sibling pairs would provide further evidence of genetic modifiers of disease expression, and guidance for family screening strategies of subjects heterozygous for the C282Y mutation. Methods: We compared the iron indices of 35 C282Y homozygous and 35 C282Y heterozygous same-sex sibling pairs. To clarify whether concordance between siblings was due to environmental or genetic factors we compared the iron indices of 164 C282Y homozygous-normal, same-sex dizygotic twins. Results: Serum ferritin (r = 0.50, P = 0.003), hepatic iron concentration (r = 0.61, P = 0.025) and hepatic iron index (r = 0.67, P = 0.01) were highly concordant in C282Y homozygotes. Heterozygote siblings were concordant for serum ferritin (r = 0.76, P = 0.0001) and transferrin saturation (r = 0.79, P = 0.0001). Homozygote-normal same-sex dizygotic twins were concordant for serum ferritin (r = 0.62, P = 0.0001) but not for transferrin saturation. Conclusions: Concordance of iron indices exists in C282Y homozygote and heterozygote sibling pairs. Siblings of expressing C282Y heterozygotes require phenotypic assessment. These data provide evidence for modifying genes influencing disease expression in hemochromatosis. (C) 2002 European Association for the Study of the Liver. Published by Elsevier Science B.V. All rights reserved.