Connections between signal processing and complex analysis

We describe one of the research lines of the Grup de Teoria de Funcions de la UAB UB, which deals with sampling and interpolation problems in signal analysis and their connections with complex function theory.

Fuzzy subgroups, algebraic and topological points of view and complex analysis

Fuzzy subsets and fuzzy subgroups are basic concepts in fuzzy mathematics. We shall concentrate on fuzzy subgroups dealing with some of their algebraic, topological and complex analytical properties. Explorations are theoretical belonging to pure mathematics. One of our ideas is to show how widely fuzzy subgroups can be used in mathematics, which brings out the wealth of this concept. In complex analysis we focus on Möbius transformations, combining them with fuzzy subgroups in the algebraic and topological sense. We also survey MV spaces with or without a link to fuzzy subgroups. Spectral space is known in MV algebra. We are interested in its topological properties in MV-semilinear space. Later on, we shall study MV algebras in connection with Riemann surfaces. In fact, the Riemann surface as a concept belongs to complex analysis. On the other hand, Möbius transformations form a part of the theory of Riemann surfaces. In general, this work gives a good understanding how it is possible to fit together different fields of mathematics.

Synaptonemal complex analysis of the Holstein-Friesian, Piemontese and Simmental breeds of Bos taurus taurus

The synaptonemal complex (SC) of specimens of Sos taurus taurus from the Holstein-Friesian, Piemontese, and Simmental breeds, was analysed. The analysis included quantification of the frequency of various types of abnormalities in the SC, and the frequency of calls with SC abnormalities. All animals had 29 autosomal bivalents and one sexual bivalent and the most frequently recorded abnormality was pairing failure. The number of cells with abnormalities in the Holstein-Friesian breed was 29.41%, in the Piemontese breed was 30.00% and in the Simmental breed it was 29.54%. The subspecies Bos taurus taurus had 29.63% of cells showing abnormalities with 57.33% of these abnormalities occurring in zygotene and 42.67% occurring in pachytene. Statistical analyses showed that there were no significant differences in the number of cells with SC abnormalities among the breeds studied. The frequency of cells with abnormalities, and the efect on the fertility of the Holstein-Friesian, Piemontese and Simmental breeds are discussed.

SYNAPTONEMAL COMPLEX-ANALYSIS OF THE SEX BIVALENT IN GOATS

Synaptonemal complex (SC) analysis of XY pairing in the goat (Capra hircus; 2n = 60) was investigated by electron microscopy for the first time in this species. Synapsis of the X and Y chromosomes begins during the mid-late zygotene stage as the autosomes complete their pairing. Only a small portion of the total length of the Y is paired with the X chromosome at this time. By the early pachytene, almost 90% of the Y is paired with the X. All the observed stages of the sex bivalent pairing showed the structural difference between the differential and pairing regions. In the pairing region, a synaptonemal complex is formed, while in the differential region the chromosome axes remain free.

SYNAPTONEMAL COMPLEX-ANALYSIS IN SPERMATOCYTES AND OOCYTES OF RAINBOW-TROUT, ONCORHYNCHUS-MYKISS (PISCES, SALMONIDAE) - THE PROCESS OF AUTOSOME AND SEX-CHROMOSOME SYNAPSIS

The surface-spreading synaptonemal complex (SC) technique was employed to analyze spermatocytes and oocytes of rainbow trout in order to visualize the process of autosome and sex chromosome synapsis in this species. The structure of lateral elements (LEs) of the SC and the chromosome synapsis process at the stages of leptotene, zygotene and pachytene are described. Comparative analysis of SCs of spermatocytes and oocytes showed a difference in the synaptic process, i.e. in spermatocytes all LEs were synapsed before the appearance of centromeric regions in the biarmed elements, while in the oocytes some fully synapsed LEs, including the centromeric region of the biarmed elements, were found together with fully or partially unsynapsed LEs. In males the sex chromosome synapsis starts only after all autosomes have synapsed. Irregular synapses involving three or four LEs were found in 3.4% of the cells analyzed in mid or late zygotene. Multivalents were found in males and females. Some aspects of initial meiotic development and their implications in rainbow trout cytogenetics, genetics and evolution are discussed.

SYNAPTONEMAL COMPLEX-ANALYSIS IN GOATS CARRYING THE 5/15 ROBERTSONIAN TRANSLOCATION

Synaptonemal complexes were analysed by electron microscopy in 2 bucks heterozygous for the 5/15 Robertsonian translocation. The cis configuration (free homologous 5 and 15 chromosomes on the same side of the 5/15 translocated chromosome) was found in all 50 cells examined. This feature is considered a prerequisite for the development of balanced gametes. No association between the sex bivalent and trivalent was observed.

SYNAPTONEMAL COMPLEX-ANALYSIS IN SPERMATOCYTES OF TILAPIA, OREOCHROMIS-NILOTICUS (PISCES, CICHLIDAE)

Some adaptations of the synaptonemal complex (SC) whole-mounting technique first used in plants permitted its application to meiotic studies in tilapia, Oreochromis niloticus. Direct observation of the chromosome pairing process and bivalent structure during the meiotic prophase of this fish species by light and electron microscopy permitted the analysis of SCs in autosomes and the possible identification of sex chromosomes. The analysis of SCs in spermatocytes of 0. niloticus revealed that all 22 bivalent chromosomes completely paired, except for the occurrence of a size heteromorphism in the terminal region of the largest bivalent associated with the presence of an incompletely paired segment during the synapsis process, which may be the cytological visualization of an XX/XY sex chromosome system in this species.

Synaptonemal complex analysis of Nellore and Gyr breeds of Bos taurus indicus

A synaptonemal complex (SC) study of specimens of Nellore and Gyr breeds of Bos taurus indicus was performed with the main objective to identify and determinate the frequency of abnormalities of SC and the frequency of cells with abnormalities. All animals analyzed had 29 autosomal bivalents and one sexual bivalent. The Nellore breed had 30.00% of cells with SC abnormalities while the Gyr breed had only 11.11%. Statistical analyses showed that there were not significant differences for the number of cells with abnormalities among the breeds studied. The subspecies Bos taurus indicus had 16.92% of cells showing abnormalities, being 62.82% of these abnormalities in zygotene and 37.18% in pachytene. Some aspects regarding the frequency of cells with abnormalities and the fertility of Nellore and Gyr breeds are discussed.

Synaptonemal complex analysis in the fish species Piaractus mesopotamicus and Colossoma macropomum, and in their interspecific hybrid

The surface-spreading technique for visualization of whole cell synaptonemal complex (SC) complements was employed to study the chromosome synapsis in spermatocytes of P. mesopotamicus, C. macropomum and in their interspecific hybrid (tambacu) with the main objective to analyze possible errors in chromosome pairing that could result in hybrid sterility. SC analysis showed that the parental species P. mesopotamicus and C. macropomum have 27 bivalents homogeneously synapsed. The SC in spermatocytes from the hybrid tambacu showed gross meiotic configurations in all cells analyzed. The spermatocytes exhibited a few chromosomes or well synapsed chromosome segments, while many chromosome segments did not have any synapsis. This result, allied to other genetical and cytogenetical evidence, reinforces the hypothesis that the hybrid tambacu is sterile. Further studies involving other aspects, such as behavior and physiology, should be conduced before the introduction of these hybrids in rivers and lakes.

Synaptomenal complex analysis of four breeds of Bos taurus taurus x B. taurus indicus hybrids

The synaptonemal complex (SC) was analyzed in four F1 hybrids of Bos taurus taurus and B. taurus indicus including Gyr-Simmental (G-S), Nelore Simmental (N-S), Gyr-Holstein-Friesian (G-H) and Nelore-Piemontese (N-P). We analysed the frequency of various types of SC abnormalities and the frequency of cells with SC abnormalities. The results were compared with similar observations made on purebred animals. All the animals studied possessed 29 autosomal and one sex bivalent. The frequency of cells with abnormalities in the hybrids were 28.0% in the N-P, 29.1% in the G-S, 33.3% in the N-S and 40.0% in the G-H. The frequency of cells with abnormalities in the four hybrids was 31.5%; 57.9% of these abnormalities occurred in zygotene and 42.0% occurred in pachytene. The comparisons among the hybrids and among the hybrids and their parental breeds showed that the only significant difference was between Gyr and Gyr-Holstein-Friesian animals. Some aspects of the relationship between the frequency of cells with anomalies and the fertility of hybrids are discussed.

Flexibility Properties in Complex Analysis and Affine Algebraic Geometry

In the last decades affine algebraic varieties and Stein manifolds with big (infinite-dimensional) automorphism groups have been intensively studied. Several notions expressing that the automorphisms group is big have been proposed. All of them imply that the manifold in question is an Oka–Forstnerič manifold. This important notion has also recently merged from the intensive studies around the homotopy principle in Complex Analysis. This homotopy principle, which goes back to the 1930s, has had an enormous impact on the development of the area of Several Complex Variables and the number of its applications is constantly growing. In this overview chapter we present three classes of properties: (1) density property, (2) flexibility, and (3) Oka–Forstnerič. For each class we give the relevant definitions, its most significant features and explain the known implications between all these properties. Many difficult mathematical problems could be solved by applying the developed theory, we indicate some of the most spectacular ones.

Statnote 13: a more complex analysis of variance incorporating a 'repeated measures' factor

Experiments combining different groups or factors and which use ANOVA are a powerful method of investigation in applied microbiology. ANOVA enables not only the effect of individual factors to be estimated but also their interactions; information which cannot be obtained readily when factors are investigated separately. In addition, combining different treatments or factors in a single experiment is more efficient and often reduces the sample size required to estimate treatment effects adequately. Because of the treatment combinations used in a factorial experiment, the degrees of freedom (DF) of the error term in the ANOVA is a more important indicator of the ‘power’ of the experiment than the number of replicates. A good method is to ensure, where possible, that sufficient replication is present to achieve 15 DF for the error term of the ANOVA testing effects of particular interest. Finally, it is important to always consider the design of the experiment because this determines the appropriate ANOVA to use. Hence, it is necessary to be able to identify the different forms of ANOVA appropriate to different experimental designs and to recognise when a design is a split-plot or incorporates a repeated measure. If there is any doubt about which ANOVA to use in a specific circumstance, the researcher should seek advice from a statistician with experience of research in applied microbiology.

New occurrence of microchromosomes B in Moenkhausia sanctaefilomenae (Pisces, Characidae) from the Parana River of Brazil: analysis of the synaptonemal complex

The Moenkhausia sanctaefilomenae specimens showed a karyotype consisting of 2n = 50 chromosomes with 12 metacentrics, 36 submetacentrics and two subtelocentrics. In addition to the basic karyotype, all the males specimens have cells ranging from zero to two B microchromosomes in mitotic metaphases. These chromosomes were not observed in the female specimens. C-band analysis showed a distribution pattern of characteristic heterochromatin with interstitial and centromeric blocks. However, the B chromosomes were faintly stained with C-banding and were not fluorescent with CMA(3) staining. The meiotic studies showed the formation of bivalents in metaphase I and in pachytene under an optical microscope. Through synaptonemal complex analysis with an electron microscope, the pachytene showed 25 bivalents completely paired and a small bivalent corresponding to the B chromosomes. In the same preparation, one of the B chromosomes was observed in a univalent form. on the basis of pairing behavior and morphology it is assumed that B chromosomes of M. sanctaefilomenae show homology between them and their evolutionary aspects are discussed.

Complex modal analysis of a slender vertical rotor by finite elements method

In this paper, natural frequencies were analyzed (axial, torsional and flexural) and frequency response of a vertical rotor with a hard disk at the edge through the classical modal and complex analysis. The equation that rules the movement was obtained through the Lagrangian formulation. The model considered the effects of bending, torsion and axial deformation of the shaft, besides the gravitational and gyroscopic effects. The finite element method was used to discretize the structure into hollow cylindrical elements with 12 degrees of freedom. Mass, stiffness and gyroscopic matrices were explained consistently. The classical modal analysis, usually applied to stationary structures, does not consider an important characteristic of rotating machinery which are the methods of forward and backward whirl. Initially, through the traditional modal analysis, axial and torsional natural frequencies were obtained in a static shaft, since they do not suffer the influence of gyroscopic effects. Later research was performed by complex modal analysis. This type of tool, based on the use of complex coordinates to describe the dynamic behavior of rotating shaft, allows the decomposition of the system in two submodes, backward and forward. Thus, it is possible to clearly visualize that the orbit and direction of the precessional motion around the line of the rotating shaft is not deformed. A finite element program was developed using MATLAB (TM) and numerical simulations were performed to validate this model. Natural frequencies and directional frequency forced response (dFRF) were obtained using the complex modal analysis for a simple vertical rotor and also for a typical drill string used in the construction of oil wells.