Weak and Semi Compatible Maps in Probabilistic Metric Space Using Implicit Relation

2000 Mathematics Subject Classification: 54H25, 47H10.

Results on proximal and generalized weak proximal contractions including the case of iteration-dependent range sets

This paper presents some further results on proximal and asymptotic proximal contractions and on a class of generalized weak proximal contractions in metric spaces. The generalizations are stated for non-self-mappings of the forms for and , or , subject to and , such that converges uniformly to T, and the distances are iteration-dependent, where , , and are non-empty subsets of X, for , where is a metric space, provided that the set-theoretic limit of the sequences of closed sets and exist as and that the countable infinite unions of the closed sets are closed. The convergence of the sequences in the domain and the image sets of the non-self-mapping, as well as the existence and uniqueness of the best proximity points, are also investigated if the metric space is complete. Two application examples are also given, being concerned, respectively, with the solutions through pseudo-inverses of both compatible and incompatible linear algebraic systems and with the parametrical

THE EFFECT of WEAK DISSIPATION IN TWO-DIMENSIONAL MAPPING

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

CYP19A1 fine-mapping and Mendelian randomization: Estradiol is causal for endometrial cancer

Candidate gene studies have reported CYP19A1 variants to be associated with endometrial cancer and with estradiol (E2) concentrations. We analyzed 2937 single nucleotide polymorphisms (SNPs) in 6608 endometrial cancer cases and 37 925 controls and report the first genome wide-significant association between endometrial cancer and a CYP19A1 SNP (rs727479 in intron 2, P=4.8x10(-11)). SNP rs727479 was also among those most strongly associated with circulating E2 concentrations in 2767 post-menopausal controls (P=7.4x10(-8)). The observed endometrial cancer odds ratio per rs727479 A-allele (1.15, CI=1.11-1.21) is compatible with that predicted by the observed effect on E2 concentrations (1.09, CI=1.03-1.21), consistent with the hypothesis that endometrial cancer risk is driven by E2. From 28 candidate-causal SNPs, 12 co-located with three putative gene-regulatory elements and their risk alleles associated with higher CYP19A1 expression in bioinformatical analyses. For both phenotypes, the associations with rs727479 were stronger among women with a higher BMI (Pinteraction=0.034 and 0.066 respectively), suggesting a biologically plausible gene-environment interaction.

Rapid genome wide mapping of phosphine resistance loci by a simple regional averaging analysis in the red flour beetle, Tribolium castaneum

Background Next-generation sequencing technology is an important tool for the rapid, genome-wide identification of genetic variations. However, it is difficult to resolve the ‘signal’ of variations of interest and the ‘noise’ of stochastic sequencing and bioinformatic errors in the large datasets that are generated. We report a simple approach to identify regional linkage to a trait that requires only two pools of DNA to be sequenced from progeny of a defined genetic cross (i.e. bulk segregant analysis) at low coverage (<10×) and without parentage assignment of individual SNPs. The analysis relies on regional averaging of pooled SNP frequencies to rapidly scan polymorphisms across the genome for differential regional homozygosity, which is then displayed graphically. Results Progeny from defined genetic crosses of Tribolium castaneum (F4 and F19) segregating for the phosphine resistance trait were exposed to phosphine to select for the resistance trait while the remainders were left unexposed. Next generation sequencing was then carried out on the genomic DNA from each pool of selected and unselected insects from each generation. The reads were mapped against the annotated T. castaneum genome from NCBI (v3.0) and analysed for SNP variations. Since it is difficult to accurately call individual SNP frequencies when the depth of sequence coverage is low, variant frequencies were averaged across larger regions. Results from regional SNP frequency averaging identified two loci, tc_rph1 on chromosome 8 and tc_rph2 on chromosome 9, which together are responsible for high level resistance. Identification of the two loci was possible with only 5-7× average coverage of the genome per dataset. These loci were subsequently confirmed by direct SNP marker analysis and fine-scale mapping. Individually, homozygosity of tc_rph1 or tc_rph2 results in only weak resistance to phosphine (estimated at up to 1.5-2.5× and 3-5× respectively), whereas in combination they interact synergistically to provide a high-level resistance >200×. The tc_rph2 resistance allele resulted in a significant fitness cost relative to the wild type allele in unselected beetles over eighteen generations. Conclusion We have validated the technique of linkage mapping by low-coverage sequencing of progeny from a simple genetic cross. The approach relied on regional averaging of SNP frequencies and was used to successfully identify candidate gene loci for phosphine resistance in T. castaneum. This is a relatively simple and rapid approach to identifying genomic regions associated with traits in defined genetic crosses that does not require any specialised statistical analysis.

A Pd-24 Pregnant Molecular Nanoball: Self-Templated Stellation by Precise Mapping of Coordination Sites

We found that Pd(II) ion (M) and the smallest 120 bidentate donor pyrimidine (L-a) self-assemble into a mononuclear M(L-a)(4) complex (1a) instead of the expected smallest M-12(L-a)(24) molecular ball (1), presumably due to the weak coordination nature of the pyrimidine. To construct such a pyrimidine bridged nanoball, we employed a new donor tris(4-(pyrimidin-5-yl)phenyl)amine (L); which upon selective complexation with Pd(II) ions resulted in the formation of a pregnant M24L24 molecular nanoball (2) consisting of a pyrimidine-bridged Pd-12 baby-ball supported by a Pd-12 larger mother-ball. The formation of the baby-ball was not successful without the support of the mother-ball. Thus, we created an example of a self-assembly where the inner baby-ball resembling to the predicted M-12(L-a)(24) ball (1) was incarcerated by the giant outer mother-ball by means of geometrical constraints. Facile conversion of the pregnant ball 2 to a smaller M-12(L-b)(24) ball 3 with dipyridyl donor was achieved in a single step.

Cortical thickness mapping to identify focal osteoporosis in patients with hip fracture.

BACKGROUND: Individuals with osteoporosis are predisposed to hip fracture during trips, stumbles or falls, but half of all hip fractures occur in those without generalised osteoporosis. By analysing ordinary clinical CT scans using a novel cortical thickness mapping technique, we discovered patches of markedly thinner bone at fracture-prone regions in the femurs of women with acute hip fracture compared with controls. METHODS: We analysed CT scans from 75 female volunteers with acute fracture and 75 age- and sex-matched controls. We classified the fracture location as femoral neck or trochanteric before creating bone thickness maps of the outer 'cortical' shell of the intact contra-lateral hip. After registration of each bone to an average femur shape and statistical parametric mapping, we were able to visualise and quantify statistically significant foci of thinner cortical bone associated with each fracture type, assuming good symmetry of bone structure between the intact and fractured hip. The technique allowed us to pinpoint systematic differences and display the results on a 3D average femur shape model. FINDINGS: The cortex was generally thinner in femoral neck fracture cases than controls. More striking were several discrete patches of statistically significant thinner bone of up to 30%, which coincided with common sites of fracture initiation (femoral neck or trochanteric). INTERPRETATION: Femoral neck fracture patients had a thumbnail-sized patch of focal osteoporosis at the upper head-neck junction. This region coincided with a weak part of the femur, prone to both spontaneous 'tensile' fractures of the femoral neck, and as a site of crack initiation when falling sideways. Current hip fracture prevention strategies are based on case finding: they involve clinical risk factor estimation to determine the need for single-plane bone density measurement within a standard region of interest (ROI) of the femoral neck. The precise sites of focal osteoporosis that we have identified are overlooked by current 2D bone densitometry methods.

On weak and strong Peano theorems

We say that the Peano theorem holds for a topological vector space $E$ if, for any continuous mapping $f : {\Bbb R}\times E \to E$ and any $(t(0), x(0))$ is an element of ${\Bbb R}\times E$, the Cauchy problem $\dot x(t) = f(t,x(t))$, $x(t(0)) = x(0)$, has a solution in some neighborhood of $t(0)$. We say that the weak version of Peano theorem holds for $E$ if, for any continuous map $f : {\Bbb R}\times E \to E$, the equation $\dot x(t) = f (t, x(t))$ has a solution on some interval. We construct an example (answering a question posed by S. G. Lobanov) of a Hausdorff locally convex topological vector space E for which the weak version of Peano theorem holds and the Peano theorem fails to hold. We also construct a Hausdorff locally convex topological vector space E for which the Peano theorem holds and any barrel in E is neither compact nor sequentially compact.

Architecture and other Architectures: Mapping the Production of Insular Space in the Pearl River Delta (China) and Jakarta (Indonesia)

Globalization is widely regarded as the rise of the borderless world. However in practice, true globalization points rather to a “spatial logic” by which globalization is manifested locally in the shape of insular space. Globalization in this sense is not merely about the creation of physical fragmentation of space but also the creation of social disintegration. This study tries to proof that global processes also create various forms of insular space leading also to specific social implications. In order to examine the problem this study looks at two cases: China’s Pearl River Delta (PRD) and Jakarta in Indonesia. The PRD case reveals three forms of insular space namely the modular, concealed and the hierarchical. The modular points to the form of enclosed factories where workers are vulnerable for human-right violations due to the absent of public control. The concealed refers to the production of insular space by subtle discrimination against certain social groups in urban space. And the hierarchical points to a production of insular space that is formed by an imbalanced population flow. The Jakarta case attempts to show more types of insularity in relation to the complexity of a mega-city which is shaped by a culture of exclusion. Those are dormant and hollow insularity. The dormant refers to the genesis of insular– radical – community from a culture of resistance. The last type, the hollow, points to the process of making a “pseudo community” where sense of community is not really developed as well as weak social relationship with its surrounding. Although global process creates various expressions of territorial insularization, however, this study finds that the “line of flight” is always present, where the border of insularity is crossed. The PRD’s produces vernacular modernization done by peasants which is less likely to be controlled by the politics of insularization. In Jakarta, the culture of insularization causes urban informalities that have no space, neither spatially nor socially; hence their state of ephemerality continues as a tactic of place-making. This study argues that these crossings possess the potential for reconciling venue to defuse the power of insularity.

Genome-wide association mapping in a wild avian population identifies a link between genetic and phenotypic variation in a life-history trait

Understanding the genetic basis of traits involved in adaptation is a major challenge in evolutionary biology but remains poorly understood. Here, we use genome-wide association mapping using a custom 50 k single nucleotide polymorphism (SNP) array in a natural population of collared flycatchers to examine the genetic basis of clutch size, an important life-history trait in many animal species. We found evidence for an association on chromosome 18 where one SNP significant at the genome-wide level explained 3.9% of the phenotypic variance. We also detected two suggestive quantitative trait loci (QTLs) on chromosomes 9 and 26. Fitness differences among genotypes were generally weak and not significant, although there was some indication of a sex-by-genotype interaction for lifetime reproductive success at the suggestive QTL on chromosome 26. This implies that sexual antagonism may play a role in maintaining genetic variation at this QTL. Our findings provide candidate regions for a classic avian life-history trait that will be useful for future studies examining the molecular and cellular function of, as well as evolutionary mechanisms operating at, these loci.

Mapping QTLs for aluminum tolerance in maize

Aluminum toxicity is one of the major constraints for plant development in acid soils, limiting food production in many countries. Cultivars genetically adapted to acid soils may offer an environmental compatible solution, providing a sustainable agriculture system. The aim of this work was to identify genomic regions associated with Al tolerance in maize, and to quantify the genetic effects on the phenotypic variation. A population of 168 F-3:4 families derived from a cross between two contrasting maize inbred lines for Al tolerance was evaluated using the NSRL and RSRL parameters in nutrient solution containing toxic level of aluminum. Variance analyses indicated that the NSRL was the most reliable phenotypic index to measure Al tolerance in the population, being used for further QTL mapping analysis. RFLP and SSR markers were selected for bulked segregant analysis, and additional SSR markers, flanking the polymorphisms of interest, were chosen in order to saturate the putative target regions. Seven linkage groups were constructed using 17 RFLP and 34 SSR markers. Five QTLs were mapped on chromosomes 2, 6 and 8, explaining 60% of the phenotypic variation. QTL(4) and marker umc043 were located on chromosomes 8 and 5, close to genes encoding for enzymes involved in the organic acids synthesis pathways, a widely proposed mechanism for Al tolerance in plants. QTL(2) was mapped in the same region as Alm2, also associated with Al tolerance in maize. In addition, dominant and additive effects were important in the control of this trait in maize.

SOME CONSEQUENCES IN WEAK PROCESSES OF 3-GENERATION MIXING IN THE LEPTONIC SECTOR

We investigate the sensitivity of some weak processes to a Cabibbo-Kobayashi-Maskawa in the leptonic sector. Values for mixing angles and masses compatible with several experimental accelerator data were found. We discuss in this context neutrino oscillations and cosmological and astrophysical consequences as well.

Evidence of weak ferromagnetism in doped plasticized polyaniline (PANI-DDoESSA)0.5 from electron spin resonance measurements

X-band electron spin resonance (ESR) measurements have been performed on a conducting free-standing film of polyaniline plasticized and protonated with di-n-dodecyl ester of sulfosuccinic acid (DDoESSA). The magnetic field was applied parallel and perpendicular to the plane of the film. At around 75 K a transition is observed from Pauli susceptibility to a localized state in which the spin 1/2 polarons behave as spin 1/2 dimers. A rough estimation of the intradimer and interdimer exchange constants is obtained. Below 5 K, ESR data reveal a weak ferromagnetism with the Dzyaloshinskii-Moriya vector mainly oriented in the plane of the film. The existence of a relatively well-defined n-fold axis along the chain direction in the crystalline regions confers a symmetry compatible with such analysis. © 2013 IOP Publishing Ltd.

Flavor tagged time-dependent angular analysis of the B0s → J/ψΦ decay and extraction of Δ Γs and the weak phase Φs in ATLAS

A measurement of the B 0 s →J/ψϕ decay parameters, updated to include flavor tagging is reported using 4.9  fb −1 of integrated luminosity collected by the ATLAS detector from s √ =7  TeV pp collisions recorded in 2011 at the LHC. The values measured for the physical parameters are ϕ s 0.12±0.25(stat)±0.05(syst)  rad ΔΓ s 0.053±0.021(stat)±0.010(syst)  ps −1 Γ s 0.677±0.007(stat)±0.004(syst)  ps −1 |A ∥ (0)| 2 0.220±0.008(stat)±0.009(syst) |A 0 (0)| 2 0.529±0.006(stat)±0.012(syst) δ ⊥ =3.89±0.47(stat)±0.11(syst)  rad where the parameter ΔΓ s is constrained to be positive. The S -wave contribution was measured and found to be compatible with zero. Results for ϕ s and ΔΓ s are also presented as 68% and 95% likelihood contours, which show agreement with the Standard Model expectations.

Spatial variability and potential impacts of climate change on flood and debris flow hazard zone mapping and implications for risk management

The main goals of this study were to identifythe alpine torrent catchments that are sensitive to climatic changes and to assess the robustness of the methods for the elaboration of flood and debris flow hazard zone maps to specific effects of climate changes. In this study, a procedure for the identification and localization of torrent catchments in which the climate scenarios will modify the hazard situation was developed. In two case studies, the impacts of a potential increase of precipitation intensities to the delimited hazard zones were studied. The identification and localization of the torrent and river catchments, where unfavourable changes in the hazard situation occur, could eliminate speculative and unnecessary measures against the impacts of climate changes like a general enlargement of hazard zones or a general over dimensioning of protection structures for the whole territory. The results showed a high spatial variability of the sensitivity of catchments to climate changes. In sensitive catchments, the sediment management in alpine torrents will meet future challenges due to a higher rate for sediment removal from retention basins. The case studies showed a remarkable increase of the areas affected by floods and debris flow when considering possible future precipitation intensities in hazard mapping. But, the calculated increase in extent of future hazard zones lay within the uncertainty of the methods used today for the delimitation of the hazard zones. Thus, the consideration of the uncertainties laying in the methods for the elaboration of hazard zone maps in the torrent and river catchments sensitive to climate changes would provide a useful instrument for the consideration of potential future climate conditions. The study demonstrated that weak points in protection structures in future will become more important in risk management activities.