Factorizations of and by powers of complete graphs

Let K-k(d) denote the Cartesian product of d copies of the complete graph K-k. We prove necessary and sufficient conditions for the existence of a K-k(r)-factorization of K-pn(s), where p is prime and k > 1, n, r and s are positive integers. (C) 2002 Elsevier Science B.V. All rights reserved.

R-matrices and the tensor product graph method

A systematic method for constructing trigonometric R-matrices corresponding to the (multiplicity-free) tensor product of any two affinizable representations of a quantum algebra or superalgebra has been developed by the Brisbane group and its collaborators. This method has been referred to as the Tensor Product Graph Method. Here we describe applications of this method to untwisted and twisted quantum affine superalgebras.

Branching processes and computational collapse of discretized unimodal mappings

In computer simulations of smooth dynamical systems, the original phase space is replaced by machine arithmetic, which is a finite set. The resulting spatially discretized dynamical systems do not inherit all functional properties of the original systems, such as surjectivity and existence of absolutely continuous invariant measures. This can lead to computational collapse to fixed points or short cycles. The paper studies loss of such properties in spatial discretizations of dynamical systems induced by unimodal mappings of the unit interval. The problem reduces to studying set-valued negative semitrajectories of the discretized system. As the grid is refined, the asymptotic behavior of the cardinality structure of the semitrajectories follows probabilistic laws corresponding to a branching process. The transition probabilities of this process are explicitly calculated. These results are illustrated by the example of the discretized logistic mapping.

Multiple axon guidance cues establish the olfactory topographic map: how do these cues interact?

Each primary olfactory neuron stochastically expresses one of similar to1000 odorant receptors. The total population of these neurons therefore consists of similar to1,000 distinct subpopulations, each of which are mosaically dispersed throughout one of four semi-annular zones in the nasal cavity. The axons of these different subpopulations are initially intermingled within the olfactory nerve. However, upon reaching the olfactory bulb, they sort out and converge so that axons expressing the same odorant receptor typically target one or two glomeruli. The spatial location of each of these 1800 glomeruli are topographically-fixed in the olfactory bulb and are invariant from animal to animal. Thus, while odorant receptors are expressed mosaically by neurons throughout the olfactory neuroepithelium their axons sort out, converge and target the same glomerulus within the olfactory bulb. How is such precise and reproducible topographic targeting generated? While some of the mechanisms governing the growth cone guidance of olfactory sensory neurons are understood, the cues responsible for homing axons to their target site remain elusive.

Partitioning sets of triples into small planes

We study partitions of the set of all ((v)(3)) triples chosen from a v-set into pairwise disjoint planes with three points per line. Our partitions may contain copies of PG(2, 2) only (Fano partitions) or copies of AG(2, 3) only (affine partitions) or copies of some planes of each type (mixed partitions). We find necessary conditions for Fano or affine partitions to exist. Such partitions are already known in several cases: Fano partitions for v = 8 and affine partitions for v = 9 or 10. We construct such partitions for several sporadic orders, namely, Fano partitions for v = 14, 16, 22, 23, 28, and an affine partition for v = 18. Using these as starter partitions, we prove that Fano partitions exist for v = 7(n) + 1, 13(n) + 1, 27(n) + 1, and affine partitions for v = 8(n) + 1, 9(n) + 1, 17(n) + 1. In particular, both Fano and affine partitions exist for v = 3(6n) + 1. Using properties of 3-wise balanced designs, we extend these results to show that affine partitions also exist for v = 3(2n). Similarly, mixed partitions are shown to exist for v = 8(n), 9(n), 11(n) + 1.

DNA sequence variation in the ITS-1 rDNA subunit and host relationships in sorghum midge, Stenodiplosis sorghicola (Coquillett) (Diptera : Cecidomyiidae), in Australia

Sequence variation in the internal transcribed spacer (ITS-1) ribosomal DNA subunit was examined for sorghum midge obtained from introduced and native hosts in south-eastern and central Queensland. No variation was observed relative to host plant or geographical distance for midges collected from two introduced hosts, grain sorghum (Sorghum bicolor ) and Johnson grass (S. halepense ); however, sequence differences were observed between midges from introduced and native hosts and among midges from a single native host, slender bluegrass (Dichanthium affine ). No evidence was observed of introduced midges on native hosts, or vice versa. These results agree with previously hypothesised host distributions for native and introduced midges in Australia, and expand the sample of introduced hosts to include Johnson grass. They suggest that Stenodiplosis sorghicola , the principal midge infesting grain sorghum, is also the most common species on Johnson grass. This confirms that Johnson grass plays a role in the population dynamics of S. sorghicola and suggests that midges originating from Johnson grass may influence levels of infestation in grain sorghum.

The embryonic development of the bodywall and nervous system of the cestode flatworm Hymenolepis diminuta

Cestodes (tapeworms) are a derived, parasitic clade of the phylum Platyhelminthes (flatworms). The cestode body wall represents an adaptation to its endoparasitic lifestyle. The epidermis forms a nonciliated syncytium, and both muscular and nervous system are reduced. Morphological differences between cestodes and free-living flatworms become apparent already during early embryogenesis. Cestodes have a complex life cycle that begins with an infectious larva, called the oncosphere. In regard to cell number, cestode oncospheres are among the simplest multicellular organisms, containing in the order of 50-100 cells. As part of our continuing effort to analyze embryonic development in flatworms, we describe here the staining pattern obtained with acTub in embryos and larvae of the cestode Hymenolepis diminuta and, briefly, the monogenean Neoheterocotyle rhinobatidis. In addition, we labeled the embryonic musculature of Hymenolepis with phalloidin. In Hymenolepis embryos, two different cell types that we interpret as neurons and epidermal gland cells express acTub. There exist only two neurons that develop close to the midline at the anterior pole of the embryo. The axons of these two neurons project posteriorly into the center of the oncosphere, where they innervate the complex of muscles that is attached to the booklets. In addition to neurons, acTub labels a small and invariant set of epidermal gland cells that develop at superficial positions, anteriorly adjacent to the neurons, in the dorsal midline, and around the posteriorly located hooklets. During late stages of embryogenesis they spread and form a complete covering of the embryo. We discuss these data in the broader context of platyhelminth embryology.

New Zealand climate in the Neogene and implications for global atmospheric circulation

New Zealand has a good Neogene plant fossil record. During the Miocene it was without high topography and it was highly maritime, meaning that its climate, and the resulting vegetation, would be controlled dominantly by zonal climate conditions. Its vegetation record during this time suggests the climate passed from an ever-wet and cool but frostless phase in the Early Miocene in which Nothofagus subgenus Brassospora was prominent. Then it became seasonally dry, with vegetation in which palms and Eucalyptus were prominent and fires were frequent, and in the mid-Miocene, it developed a dry-climate vegetation dominated by Casuarinaceae. These changes are reflected in a sedimentological change from acidic to alkaline chemistry and the appearance of regular charcoal in the record. The vegetation then changed again to include a prominent herb component including Chenopodiaceae and Asteraceae. Sphagnum became prominent, and Nothofagus returned, but mainly as the subgenus Fuscospora (presently restricted to temperate climates). This is interpreted as a return to a generally wet, but now cold climate, in which outbreaks of cold polar air and frost were frequent. The transient drying out of a small maritime island and the accompanying vegetation/climate sequence could be explained by a higher frequency of the Sub-Tropical High Pressure (STHP) cells (the descending limbs of the Hadley cells) over New Zealand during the Miocene. This may have resulted from an increased frequency of 'blocking', a synoptic situation which occurs in the region today. An alternative hypothesis, that the global STHP belt lay at a significantly higher latitude in the early Neogene (perhaps 55degreesS) than today (about 30degreesS), is considered less likely because of physical constraints on STHP belt latitude. In either case, the difference between the early Neogene and present situation may have been a response to an increased polar-equatorial temperature gradient. This contrasts with current climate models for the geological past in which the latitude of the High Pressure belt impact is held invariant though geological time. (C) 2003 Elsevier Science B.V. All rights reserved.

Link invariants associated with gauge equivalent solutions of the Yang-Baxter equation: The one-parameter family of minimal typical representations of Uq[gl(2|1)]

In this paper we investigate the construction of state models for link invariants using representations of the braid group obtained from various gauge choices for a solution of the trigonometric Yang-Baxter equation. Our results show that it is possible to obtain invariants of regular isotopy (as defined by Kauffman) which may not be ambient isotopic. We illustrate our results with explicit computations using solutions of the trigonometric Yang-Baxter equation associated with the one-parameter family of minimal typical representations of the quantum superalgebra U-q,[gl(2/1)]. We have implemented MATHEMATICA code to evaluate the invariants for all prime knots up to 10 crossings.

Virtual simulation of the postsurgical cosmetic outcome in patientswith pectus excavatum

Pectus excavatum is the most common congenital deformity of the anterior chest wall, in which several ribs and the sternum grow abnormally. Nowadays, the surgical correction is carried out in children and adults through Nuss technic. This technic has been shown to be safe with major drivers as cosmesis and the prevention of psychological problems and social stress. Nowadays, no application is known to predict the cosmetic outcome of the pectus excavatum surgical correction. Such tool could be used to help the surgeon and the patient in the moment of deciding the need for surgery correction. This work is a first step to predict postsurgical outcome in pectus excavatum surgery correction. Facing this goal, it was firstly determined a point cloud of the skin surface along the thoracic wall using Computed Tomography (before surgical correction) and the Polhemus FastSCAN (after the surgical correction). Then, a surface mesh was reconstructed from the two point clouds using a Radial Basis Function algorithm for further affine registration between the meshes. After registration, one studied the surgical correction influence area (SCIA) of the thoracic wall. This SCIA was used to train, test and validate artificial neural networks in order to predict the surgical outcome of pectus excavatum correction and to determine the degree of convergence of SCIA in different patients. Often, ANN did not converge to a satisfactory solution (each patient had its own deformity characteristics), thus invalidating the creation of a mathematical model capable of estimating, with satisfactory results, the postsurgical outcome

Measuring and Controlling the Chaotic Motion of Profits

The study of economic systems has generated deep interest in exploring the complexity of chaotic motions in economy. Due to important developments in nonlinear dynamics, the last two decades have witnessed strong revival of interest in nonlinear endogenous business chaotic models. The inability to predict the behavior of dynamical systems in the presence of chaos suggests the application of chaos control methods, when we are more interested in obtaining regular behavior. In the present article, we study a specific economic model from the literature. More precisely, a system of three ordinary differential equations gather the variables of profits, reinvestments and financial flow of borrowings in the structure of a firm. Firstly, using results of symbolic dynamics, we characterize the topological entropy and the parameter space ordering of kneading sequences, associated with one-dimensional maps that reproduce significant aspects of the model dynamics. The analysis of the variation of this numerical invariant, in some realistic system parameter region, allows us to quantify and to distinguish different chaotic regimes. Finally, we show that complicated behavior arising from the chaotic firm model can be controlled without changing its original properties and the dynamics can be turned into the desired attracting time periodic motion (a stable steady state or into a regular cycle). The orbit stabilization is illustrated by the application of a feedback control technique initially developed by Romeiras et al. [1992]. This work provides another illustration of how our understanding of economic models can be enhanced by the theoretical and numerical investigation of nonlinear dynamical systems modeled by ordinary differential equations.

Lanczos algorithm on the grassmann manifold

5th. European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008) 8th. World Congress on Computational Mechanics (WCCM8)

Genus and Braid Index Associated to Sequences of Renormalizable Lorenz Maps

We describe the Lorenz links generated by renormalizable Lorenz maps with reducible kneading invariant (K(f)(-), = K(f)(+)) = (X, Y) * (S, W) in terms of the links corresponding to each factor. This gives one new kind of operation that permits us to generate new knots and links from the ones corresponding to the factors of the *-product. Using this result we obtain explicit formulas for the genus and the braid index of this renormalizable Lorenz knots and links. Then we obtain explicit formulas for sequences of these invariants, associated to sequences of renormalizable Lorenz maps with kneading invariant (X, Y) * (S,W)*(n), concluding that both grow exponentially. This is specially relevant, since it is known that topological entropy is constant on the archipelagoes of renormalization.

New physics contributions to A(FB)(t(t)over-bar) at the Tevatron

The Tevatron has measured a discrepancy relative to the standard model prediction in the forward-backward asymmetry in top quark pair production. This asymmetry grows with the rapidity difference of the two top quarks. It also increases with the invariant mass of the t (t) over bar pair, reaching, for high invariant masses, 3.4 standard deviations above the next-to-leading order prediction for the charge asymmetry of QCD. However, perfect agreement between experiment and the standard model was found in both total and differential cross section of top quark pair production. As this result could be a sign of new physics we have parametrized this new physics in terms of a complete set of dimension six operators involving the top quark. We have then used a Markov chain Monte Carlo approach in order to find the best set of parameters that fits the data, using all available data regarding top quark pair production at the Tevatron. We have found that just a very small number of operators are able to fit the data better than the standard model.

Spatio-temporal alignment of pedobarographic image sequences

O documento em anexo encontra-se na versão post-print (versão corrigida pelo editor).