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.

Female major histocompatibility complex type affects male testosterone levels and sperm number in the horse (Equus caballus).

Odours of vertebrates often contain information about the major histocompatibility complex (MHC), and are used in kin recognition, mate choice or female investment in pregnancy. It is, however, still unclear whether MHC-linked signals can also affect male reproductive strategies. We used horses (Equus caballus) to study this question under experimental conditions. Twelve stallions were individually exposed either to an unfamiliar MHC-similar mare and then to an unfamiliar MHC-dissimilar mare, or vice versa. Each exposure lasted over a period of four weeks. Peripheral blood testosterone levels were determined weekly. Three ejaculates each were collected in the week after exposure to both mares (i.e. in the ninth week) to determine mean sperm number and sperm velocity. We found high testosterone levels when stallions were kept close to MHC-dissimilar mares and significantly lower ones when kept close to MHC-similar mares. Mean sperm number per ejaculate (but not sperm velocity) was positively correlated to mean testosterone levels and also affected by the order of presentation of mares: sperm numbers were higher if MHC-dissimilar mares were presented last than if MHC-similar mares were presented last. We conclude that MHC-linked signals influence testosterone secretion and semen characteristics, two indicators of male reproductive strategies.

CFD simulation of complex phenomena containing suspensions and flow throughporous media

There is an increasing reliance on computers to solve complex engineering problems. This is because computers, in addition to supporting the development and implementation of adequate and clear models, can especially minimize the financial support required. The ability of computers to perform complex calculations at high speed has enabled the creation of highly complex systems to model real-world phenomena. The complexity of the fluid dynamics problem makes it difficult or impossible to solve equations of an object in a flow exactly. Approximate solutions can be obtained by construction and measurement of prototypes placed in a flow, or by use of a numerical simulation. Since usage of prototypes can be prohibitively time-consuming and expensive, many have turned to simulations to provide insight during the engineering process. In this case the simulation setup and parameters can be altered much more easily than one could with a real-world experiment. The objective of this research work is to develop numerical models for different suspensions (fiber suspensions, blood flow through microvessels and branching geometries, and magnetic fluids), and also fluid flow through porous media. The models will have merit as a scientific tool and will also have practical application in industries. Most of the numerical simulations were done by the commercial software, Fluent, and user defined functions were added to apply a multiscale method and magnetic field. The results from simulation of fiber suspension can elucidate the physics behind the break up of a fiber floc, opening the possibility for developing a meaningful numerical model of the fiber flow. The simulation of blood movement from an arteriole through a venule via a capillary showed that the model based on VOF can successfully predict the deformation and flow of RBCs in an arteriole. Furthermore, the result corresponds to the experimental observation illustrates that the RBC is deformed during the movement. The concluding remarks presented, provide a correct methodology and a mathematical and numerical framework for the simulation of blood flows in branching. Analysis of ferrofluids simulations indicate that the magnetic Soret effect can be even higher than the conventional one and its strength depends on the strength of magnetic field, confirmed experimentally by Völker and Odenbach. It was also shown that when a magnetic field is perpendicular to the temperature gradient, there will be additional increase in the heat transfer compared to the cases where the magnetic field is parallel to the temperature gradient. In addition, the statistical evaluation (Taguchi technique) on magnetic fluids showed that the temperature and initial concentration of the magnetic phase exert the maximum and minimum contribution to the thermodiffusion, respectively. In the simulation of flow through porous media, dimensionless pressure drop was studied at different Reynolds numbers, based on pore permeability and interstitial fluid velocity. The obtained results agreed well with the correlation of Macdonald et al. (1979) for the range of actual flow Reynolds studied. Furthermore, calculated results for the dispersion coefficients in the cylinder geometry were found to be in agreement with those of Seymour and Callaghan.

Temporal and spatial variability of mobile fauna on a submarine cliff and boulder scree complex: a community in flux

The mobile component of a community inhabiting a submarine boulder scree/cliff was investigated at Lough Hyne, Ireland at dawn, midday, dusk and night over a 1-week period. Line transects (50 m) were placed in the infralittoral (6 m) and circumlittoral (18 m) zones and also the interface between these two zones (12 m). The dominant mobile fauna of this cliff consisted of echinoderms (6 species), crustaceans (10 species) and fish (23 species). A different component community was identified at each time/depth interval using Multi-Dimensional Scaling (MDS) even though both species diversity (Shannon-Wiener indices) and richness (number of species) remained constant. These changes in community composition provided indirect evidence for migration by these mobile organisms. However, little evidence was found for migration between different zones with the exception of the several wrasse species. These species were observed to spend the daytime foraging in the deeper zone, but returned to the upper zone at night presumably for protection from predators. For the majority of species, migration was considered to occur to cryptic habitats such as holes and crevices. The number of organisms declined during the night, although crustacean numbers peaked, while fish and echinoderms were most abundant during day, possibly due to predator-prey interactions. This submarine community is in a state of flux, whereby, community characteristics, including trophic and energetic relationships, varied over small temporal (daily) and spatial (m) scales.

Bad reduction of genus three curves with complex multiplication

Let C be a smooth, absolutely irreducible genus 3 curve over a number field M. Suppose that the Jacobian of C has complex multiplication by a sextic CM-field K. Suppose further that K contains no imaginary quadratic subfield. We give a bound on the primes p of M such that the stable reduction of C at p contains three irreducible components of genus 1.

Complex meiotic configuration of the holocentric chromosomes: the intriguing case of the scorpion Tityus bahiensis

Mitotic and meiotic chromosomes of Tityus bahiensis were investigated using light (LM) and transmission electron microscopy (TEM) to determine the chromosomal characteristics and disclose the mechanisms responsible for intraspecific variability in chromosome number and for the presence of complex chromosome association during meiosis. This species is endemic to Brazilian fauna and belongs to the family Buthidae, which is considered phylogenetically basal within the order Scorpiones. In the sample examined, four sympatric and distinct diploid numbers were observed: 2n = 5, 2n = 6, 2n = 9, and 2 = 10. The origin of this remarkable chromosome variability was attributed to chromosome fissions and/or fusions, considering that the decrease in chromosome number was concomitant with the increase in chromosome size and vice versa. The LM and TEM analyses showed the presence of chromosomes without localised centromere, the lack of chiasmata and recombination nodules in male meiosis, and two nucleolar organiser regions carrier chromosomes. Furthermore, male prophase I cells revealed multivalent chromosome associations and/or unsynapsed or distinctly associated chromosome regions (gaps, less-condensed chromatin, or loop-like structure) that were continuous with synapsed chromosome segments. All these data permitted us to suggest that the chromosomal rearrangements of T. bahiensis occurred in a heterozygous state. A combination of various factors, such as correct disjunction and balanced segregation of the chromosomes involved in complex meiotic pairing, system of achiasmate meiosis, holocentric nature of the chromosomes, population structure, and species dispersion patterns, could have contributed to the high level of chromosome rearrangements present in T. bahiensis.

Comparison of microbial numbers in soils by using various culture media and temperatures

The influence of different media and incubation temperatures on the quantification of microbial populations in sorghum, eucalyptus and forest soils was evaluated. Microbial growth was compared by using complex (tryptone soybean agar, TSA, casein-starch, CS, and Martin) and saline (Thorton, M3, Czapeck) media and incubation temperatures of 25 and 30° C. Higher numbers of total bacterial. and fungal colony-forming units (CFU) were observed in sorghum soils, and of spore-forming and Gram-negative bacteria in forest soils than other soils. Actinomycetes counts were highest in forest soil when using CS medium at 30° C and in sorghum soil at 25° C in M3 medium. Microorganism counts were dependent on the media and incubation temperatures. The counts at temperatures of 30° C were significantly higher than at 25° C. Microbial quantification was best when using TSA medium for total. and spore-forming bacteria, Thorton for Gram-negative bacteria, M3 for actinomycetes, and Martin for fungi. © 2005 Elsevier GmbH. All rights reserved.

Complex meiotic configuration of the holocentric chromosomes: the intriguing case of the scorpion Tityus bahiensis

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Chromosome numbers and their taxonomic implications for eight Brazilian andropogons (Poaceae: Andropogoneae)

Eleven chromosome counts are reported for Brazilian populations of eight species of Andropogon. Counts for five of the species are first reports for the species. Four of these species, A. arenarius, A. glaziovii, A. lateralis, and A. lindmanii, are hexaploids (n=30) and belong to a group of about a dozen species informally referred to as the Andropogon lateralis complex. Two other species of this complex, A. bicornis and A. hypogynus, we also found to be hexaploids, in agreement with previous reports. Diploid counts (n=10) for A. macrothrix (a first report) and A. virgatus (the same as two previous reports) support the morphological affinities of these two species to other species complexes within Andropogon. © 1986 the New York Botanical Garden.

Cytogenetic analysis of Epicauta atomaria (Meloidae) and Palembus dermestoides (Tenebrionidae) with Xyp sex determination system using standard staining, C-bands, NOR and synaptonemal complex microspreading techniques

The mitotic and meiotic chromosomes of the beetles Epicauta atomaria (Meloidae) and Palembus dermestoides (Tenebrionidae) were analysed using standard staining, C-banding and silver impregnation techniques. We determine the diploid and haploid chromosome numbers, the sex determination system and describe the chromosomal morphology, the C-banding pattern and the chromosome(s) bearing NORs (nucleolar organizer regions). Both species shown 2n = 20 chromosomes, the chromosomal meioformula 9 + Xyp, and regular chromosome segregation during anaphases I and II. The chromosomes of E. atomaria are basically metacentric or submetacentric and P. dermestoides chromosomes are submetacentric or subtelocentric. In both beetles the constitutive heterochromatin is located in the pericentromeric region in all autosomes and in the Xp chromosome; additional C-bands were observed in telomeric region of the short arm in some autosomes in P. dermestoides. The yp chromosome did not show typical C-bands in these species. As for the synaptonemal complex, the nucleolar material is associated to the 7th bivalent in E. atomaria and 3rd and 7th bivalents in P. dermestoides. Strong silver impregnated material was observed in association with Xyp in light and electron microscopy preparations in these species and this material was interpreted to be related to nucleolar material.

Complex scalar dark matter in a B-L model

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Population biology and distribution of the portunid crab Callinectes ornatus (Decapoda: Brachyura) in an estuary-bay complex of southern Brazil

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Complex scalar dark matter in a B-L model

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Genetic differentiation among distinct karyomorphs of the wolf fish Hoplias malabaricus species complex (Characiformes, Erythrinidae) and report of unusual hybridization with natural triploidy

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Estimating persistent Betti numbers for discrete shape analysis

Persistent Topology is an innovative way of matching topology and geometry, and it proves to be an effective mathematical tool in shape analysis. In order to express its full potential for applications, it has to interface with the typical environment of Computer Science: It must be possible to deal with a finite sampling of the object of interest, and with combinatorial representations of it. Following that idea, the main result claims that it is possible to construct a relation between the persistent Betti numbers (PBNs; also called rank invariant) of a compact, Riemannian submanifold X of R^m and the ones of an approximation U of X itself, where U is generated by a ball covering centered in the points of the sampling. Moreover we can state a further result in which, this time, we relate X with a finite simplicial complex S generated, thanks to a particular construction, by the sampling points. To be more precise, strict inequalities hold only in "blind strips'', i.e narrow areas around the discontinuity sets of the PBNs of U (or S). Out of the blind strips, the values of the PBNs of the original object, of the ball covering of it, and of the simplicial complex coincide, respectively.