Periodic points of holomorphic maps via Lefschetz numbers

In this paper we study the set of periods of holomorphic maps on compact manifolds, using the periodic Lefschetz numbers introduced by Dold and Llibre, which can be computed from the homology class of the map. We show that these numbers contain information about the existence of periodic points of a given period; and, if we assume the map to be transversal, then they give us the exact number of such periodic orbits. We apply this result to the complex projective space of dimension n and to some special type of Hopf surfaces, partially characterizing their set of periods. In the first case we also show that any holomorphic map of CP(n) of degree greater than one has infinitely many distinct periodic orbits, hence generalizing a theorem of Fornaess and Sibony. We then characterize the set of periods of a holomorphic map on the Riemann sphere, hence giving an alternative proof of Baker's theorem.

Time consistent Pareto solutions in common access resource gameswith asymmetric players

In the analysis of equilibrium policies in a di erential game, if agents have different time preference rates, the cooperative (Pareto optimum) solution obtained by applying the Pontryagin's Maximum Principle becomes time inconsistent. In this work we derive a set of dynamic programming equations (in discrete and continuous time) whose solutions are time consistent equilibrium rules for N-player cooperative di erential games in which agents di er in their instantaneous utility functions and also in their discount rates of time preference. The results are applied to the study of a cake-eating problem describing the management of a common property exhaustible natural resource. The extension of the results to a simple common property renewable natural resource model in in nite horizon is also discussed.

Improved segmentation of deep brain grey matter structures using magnetization transfer (MT) parameter maps.

Basal ganglia and brain stem nuclei are involved in the pathophysiology of various neurological and neuropsychiatric disorders. Currently available structural T1-weighted (T1w) magnetic resonance images do not provide sufficient contrast for reliable automated segmentation of various subcortical grey matter structures. We use a novel, semi-quantitative magnetization transfer (MT) imaging protocol that overcomes limitations in T1w images, which are mainly due to their sensitivity to the high iron content in subcortical grey matter. We demonstrate improved automated segmentation of putamen, pallidum, pulvinar and substantia nigra using MT images. A comparison with segmentation of high-quality T1w images was performed in 49 healthy subjects. Our results show that MT maps are highly suitable for automated segmentation, and so for multi-subject morphometric studies with a focus on subcortical structures.

Backflow-induced asymmetric collapse of disclination lines in liquid crystals

We present experiments where opposed pairs of planar parallel disclination lines of topological strength s=±1 move due to their mutual attraction. Our measurements show that their motion is clearly asymmetric, with +1 defects moving up to twice as fast as -1 ones. This is a clear indication of backflow, given the intrinsic isotropic elasticity of our system. A phenomenological model is able to account for the experimental observations by renormalizing the orientational diffusivity estimated from the velocity of each defect.

Synthetic applications of chiral unsaturated epoxy alcohols prepared by sharpless asymmetric epoxidation

An overview of the synthesis and applications of chiral 2,3-epoxy alcohols containing unsaturated chains is presented. One of the fundamental synthetic routes to these compounds is Sharpless asymmetric epoxidation, which is reliable, highly chemoselective and enables easy prediction of the product enantioselectivity. Thus, unsaturated epoxy alcohols are readily obtained by selective oxidation of the allylic double bond in the presence of other carbon-carbon double or triple bonds. The wide availability of epoxy alcohols with unsaturated chains, the versatility of the epoxy alcohol functionality (e.g. regio- and stereo-selective ring opening; oxidation; and reduction), and the arsenal of established alkene chemistries, make unsaturated epoxy alcohols powerful starting materials for the synthesis of complex targets such as biologically active molecules. The popularization of ring-closing metathesis has further increased their value, making them excellent precursors to cyclic compounds.

Asymmetric cancer cell division regulated by AKT.

Human tumors often contain slowly proliferating cancer cells that resist treatment, but we do not know precisely how these cells arise. We show that rapidly proliferating cancer cells can divide asymmetrically to produce slowly proliferating "G0-like" progeny that are enriched following chemotherapy in breast cancer patients. Asymmetric cancer cell division results from asymmetric suppression of AKT/PKB kinase signaling in one daughter cell during telophase of mitosis. Moreover, inhibition of AKT signaling with small-molecule drugs can induce asymmetric cancer cell division and the production of slow proliferators. Cancer cells therefore appear to continuously flux between symmetric and asymmetric division depending on the precise state of their AKT signaling network. This model may have significant implications for understanding how tumors grow, evade treatment, and recur.

Geomorphological method in the elaboration of hazard maps for flash-floods in the municipality of Jucuarán (El Salvador)

This work deals with the elaboration of flood hazard maps. These maps reflect the areas prone to floods based on the effects of Hurricane Mitch in the Municipality of Jucuarán of El Salvador. Stream channels located in the coastal range in the SE of El Salvador flow into the Pacific Ocean and generate alluvial fans. Communities often inhabit these fans can be affected by floods. The geomorphology of these stream basins is associated with small areas, steep slopes, well developed regolite and extensive deforestation. These features play a key role in the generation of flash-floods. This zone lacks comprehensive rainfall data and gauging stations. The most detailed topographic maps are on a scale of 1:25 000. Given that the scale was not sufficiently detailed, we used aerial photographs enlarged to the scale of 1:8000. The effects of Hurricane Mitch mapped on these photographs were regarded as the reference event. Flood maps have a dual purpose (1) community emergency plans, (2) regional land use planning carried out by local authorities. The geomorphological method is based on mapping the geomorphological evidence (alluvial fans, preferential stream channels, erosion and sedimentation, man-made terraces). Following the interpretation of the photographs this information was validated on the field and complemented by eyewitness reports such as the height of water and flow typology. In addition, community workshops were organized to obtain information about the evolution and the impact of the phenomena. The superimposition of this information enables us to obtain a comprehensive geomorphological map. Another aim of the study was the calculation of the peak discharge using the Manning and the paleohydraulic methods and estimates based on geomorphologic criterion. The results were compared with those obtained using the rational method. Significant differences in the order of magnitude of the calculated discharges were noted. The rational method underestimated the results owing to short and discontinuous periods of rainfall data with the result that probabilistic equations cannot be applied. The Manning method yields a wide range of results because of its dependence on the roughness coefficient. The paleohydraulic method yielded higher values than the rational and Manning methods. However, it should be pointed out that it is possible that bigger boulders could have been moved had they existed. These discharge values are lower than those obtained by the geomorphological estimates, i.e. much closer to reality. The flood hazard maps were derived from the comprehensive geomorphological map. Three categories of hazard were established (very high, high and moderate) using flood energy, water height and velocity flow deduced from geomorphological and eyewitness reports.

Asymmetric giant magnetoresistance in Co10Cu90 magnetic granular alloys

We have observed a type of giant magnetoresistance (GMR) in magnetic granular Co10Cu90 alloys. The asymmetric GMR depends strongly on the size of magnetic Co particles, which exhibit superparamagnetic behavior at given measured temperature. The asymmetric GMR points to a metastable state that develops when the sample is field-cooled, which is lost after recycling. We propose that high-field cooling produces more effective parallel alignment of small unblocked Co particle moments and interfacial magnetizations, which contributes to the further decrease of the resistance in comparison with the samples zero-field-cooled, and then applied to the same field.

A new locus for congenital cataract, microcornea, microphthalmia, and atypical iris coloboma maps to chromosome 2.

OBJECTIVE: To report a novel phenotype of autosomal dominant atypical congenital cataract associated with variable expression of microcornea, microphthalmia, and iris coloboma linked to chromosome 2. Molecular analysis of this phenotype may improve our understanding of anterior segment development. DESIGN: Observational case study, genome linkage analysis, and gene mutation screening. PARTICIPANTS: Three families, 1 Egyptian and 2 Belgians, with a total of 31 affected were studied. METHODS: Twenty-one affected subjects and 9 first-degree relatives underwent complete ophthalmic examination. In the Egyptian family, exclusion of PAX6, CRYAA, and MAF genes was demonstrated by haplotype analysis using microsatellite markers on chromosomes 11, 16, and 21. Genome-wide linkage analysis was then performed using 385 microsatellite markers on this family. In the 2 Belgian families, the PAX6 gene was screened for mutations by direct sequencing of all exons. MAIN OUTCOME MEASURES: Phenotype description, genome-wide linkage of the phenotype, linkage to the PAX6, CRYAA, and MAF genes, and mutation detection in the PAX6 gene. RESULTS: Affected members of the 3 families had bilateral congenital cataracts inherited in an autosomal dominant pattern. A novel form of hexagonal nuclear cataract with cortical riders was expressed. Among affected subjects with available data, 95% had microcornea, 39% had microphthalmia, and 38% had iris coloboma. Seventy-five percent of the colobomata were atypical, showing a nasal superior location in 56%. A positive lod score of 4.86 was obtained at theta = 0 for D2S2309 on chromosome 2, a 4.9-Mb common haplotype flanked by D2S2309 and D2S2358 was obtained in the Egyptian family, and linkage to the PAX6, CRYAA, or MAF gene was excluded. In the 2 Belgian families, sequencing of the junctions and all coding exons of PAX6 did not reveal any molecular change. CONCLUSIONS: We describe a novel phenotype that includes the combination of a novel form of congenital hexagonal cataract, with variably expressed microcornea, microphthalmia, and atypical iris coloboma, not caused by PAX6 and mapping to chromosome 2. FINANCIAL DISCLOSURE(S): The authors have no proprietary or commercial interest in any materials discussed in this article.

Genetic linkage maps of 'Pêra' sweet orange and 'Cravo' mandarin with RAPD markers

The objective of this work was to construct linkage maps of 'Pêra' sweet orange [Citrus sinensis (L.) Osbeck] and 'Cravo' mandarin (Citrus reticulata Blanco) using RAPD markers and the pseudo-testcross strategy. The parents were chosen according to the resistance/susceptibility to citrus variegate chlorosis (CVC). The segregation of 176 markers was analyzed in 94 progeny of F1 hybrids, which were obtained from controlled crossings. The linkage map of 'Pêra' sweet orange had 117 markers defined by 12 linkage groups, which spanned 612.1 cM. Only six markers could not be linked to the linkage group and 48.7% of the markers showed segregation distortion. The linkage map of 'Cravo' mandarin had 51 markers defined by 12 linkage groups, which spanned 353.3 cM. Only two markers did not link to the groups and 15.7% showed segregation distortion. The construction of linkage maps is relevant to future mapping studies of the inheritance of CVC, citrus canker and leprosis.

Selective resonance suppression 1H-[13C] NMR spectroscopy with asymmetric adiabatic RF pulses.

Despite obvious improvements in spectral resolution at high magnetic field, the detection of 13C labeling by 1H-[13C] NMR spectroscopy remains hampered by spectral overlap, such as in the spectral region of 1H resonances bound to C3 of glutamate (Glu) and glutamine (Gln), and C6 of N-acetylaspartate (NAA). The aim of this study was to develop, implement, and apply a novel 1H-[13C] NMR spectroscopic editing scheme, dubbed "selective Resonance suppression by Adiabatic Carbon Editing and Decoupling single-voxel STimulated Echo Acquisition Mode" (RACED-STEAM). The sequence is based on the application of two asymmetric narrow-transition-band adiabatic RF inversion pulses at the resonance frequency of the 13C coupled to the protons that need to be suppressed during the mixing time (TM) period, alternating the inversion band downfield and upfield from the 13C resonance on odd and even scans, respectively, thus suppressing the detection of 1H resonances bound to 13C within the transition band of the inversion pulse. The results demonstrate the efficient suppression of 1H resonances bound to C3 of Glu and Gln, and C4 of Glu, which allows the 1H resonances bound to C6 of NAA and C4 of Gln to be revealed. The measured time course of the resolved labeling into NAA C6 with the new scheme was consistent with the slow turnover of NAA.

Let's K-Map Play: Juego de aprendizaje de Karnagh Maps para móvil

En este informe se describe el trabajo de fin de máster, centrado en el estudio de la gamificación como herramienta de aprendizaje aplicada a dispositivos móviles. Se ha realizado una revisión de los artículos científicos que tratan sobre el tema de la gamificación como herramienta educativa,para terminar el trabajo desarrollando un prototipo de juego para el aprendizaje de mapas de Karnaugh. Se ha optado por un desarrollo multiplataforma y se han revisado los frameworks de desarrollo más populares para desarrollo móvil multiplataforma así como los motores de juegos aplicables a este caso. Tras la implementación, se ha probado el prototipo en dos sistemas operativos móviles libres: Android y Firefox OS.

Global periodicity conditions for maps and recurrences via Normal Forms

We face the problem of characterizing the periodic cases in parametric families of (real or complex) rational diffeomorphisms having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary conditions for the existence of a formal linearization of the map, and on the introduction of a suitable rational parametrization of the parameters of the family. Using these tools we can find a finite set of values p for which the map can be p-periodic, reducing the problem of finding the parameters for which the periodic cases appear to simple computations. We apply our results to several two and three dimensional classes of polynomial or rational maps. In particular we find the global periodic cases for several Lyness type recurrences

Periodic orbits of integrable birational maps on the plane: blending dynamics and algebraic geometry, the Lyness' case

Contingut del Pòster presentat al congrés New Trends in Dynamical Systems