Some results on stability of retarded functional differential equations using dichotomic map techniques

This paper deals with the study of the stability of nonautonomous retarded functional differential equations using the theory of dichotomic maps. After some preliminaries, we prove the theorems on simple and asymptotic stability. Some examples are given to illustrate the application of the method. Main results about asymptotic stability of the equation x′(t) = -b(t)x(t - r) and of its nonlinear generalization x′(t) = b(t) f (x(t - r)) are established. © 1998 Kluwer Academic Publishers.

Sistemas dinâmicos e equações diferenciais ordinárias

Pós-graduação em Matemática Universitária - IGCE

Wide vector solitons in systems with time- and space-modulated nonlinearities

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Terminal-repeat retrotransposons with GAG domain in plant genomes: a new testimony on the complex world of transposable elements

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Atratores pullback para equações parabólicas semilineares em domínios não cilíndricos

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Proximo–distal specification in the wing disc of Drosophila by the nubbin gene

Mutations in the nubbin (nub) gene have a phenotype consisting of a severe wing size reduction and pattern alterations, such as transformations of distal elements into proximal ones. nub expression is restricted to the wing pouch cells in wing discs since early larval development. These effects are also observed in genetic mosaics where cell proliferation is reduced in all wing blade regions autonomously, and transformation into proximal elements is observed in distal clones. Clones located in the proximal region of the wing blade cause in addition nonautonomous reduction of the whole wing. Cell lineage experiments in a nub mutant background show that clones respect neither the anterior–posterior nor the dorsal–ventral boundary but that the selector genes have been correctly expressed since early larval development. The phenotypes of nub el and nub dpp genetic combinations are synergistic and the overexpression of dpp in clones in nub wings does not result in overproliferation of the surrounding wild-type cells. We discuss the role of nub in the wing’s proximo–distal axis and in the formation of compartment boundaries.

Complex Proteolytic Processing Acts on Delta, a Transmembrane Ligand for Notch, during Drosophila Development

Delta functions as a cell nonautonomous membrane-bound ligand that binds to Notch, a cell-autonomous receptor, during cell fate specification. Interaction between Delta and Notch leads to signal transduction and elicitation of cellular responses. During our investigations to further understand the biochemical mechanism by which Delta signaling is regulated, we have identified four Delta isoforms in Drosophila embryonic and larval extracts. We have demonstrated that at least one of the smaller isoforms, Delta S, results from proteolysis. Using antibodies to the Delta extracellular and intracellular domains in colocalization experiments, we have found that at least three Delta isoforms exist in vivo, providing the first evidence that multiple forms of Delta exist during development. Finally, we demonstrate that Delta is a transmembrane ligand that can be taken up by Notch-expressing Drosophila cultured cells. Cell culture experiments imply that full-length Delta is taken up by Notch-expressing cells. We present evidence that suggests this uptake occurs by a nonphagocytic mechanism.

The complete genome of the crenarchaeon Sulfolobus solfataricus P2

The genome of the crenarchaeon Sulfolobus solfataricus P2 contains 2,992,245 bp on a single chromosome and encodes 2,977 proteins and many RNAs. One-third of the encoded proteins have no detectable homologs in other sequenced genomes. Moreover, 40% appear to be archaeal-specific, and only 12% and 2.3% are shared exclusively with bacteria and eukarya, respectively. The genome shows a high level of plasticity with 200 diverse insertion sequence elements, many putative nonautonomous mobile elements, and evidence of integrase-mediated insertion events. There are also long clusters of regularly spaced tandem repeats. Different transfer systems are used for the uptake of inorganic and organic solutes, and a wealth of intracellular and extracellular proteases, sugar, and sulfur metabolizing enzymes are encoded, as well as enzymes of the central metabolic pathways and motility proteins. The major metabolic electron carrier is not NADH as in bacteria and eukarya but probably ferredoxin. The essential components required for DNA replication, DNA repair and recombination, the cell cycle, transcriptional initiation and translation, but not DNA folding, show a strong eukaryal character with many archaeal-specific features. The results illustrate major differences between crenarchaea and euryarchaea, especially for their DNA replication mechanism and cell cycle processes and their translational apparatus.

Rolling-circle transposons in eukaryotes

All eukaryotic DNA transposons reported so far belong to a single category of elements transposed by the so-called “cut-and-paste” mechanism. Here, we report a previously unknown category of eukaryotic DNA transposons, Helitron, which transpose by rolling-circle replication. Autonomous Helitrons encode a 5′-to-3′ DNA helicase and nuclease/ligase similar to those encoded by known rolling-circle replicons. Helitron-like transposons have conservative 5′-TC and CTRR-3′ termini and do not have terminal inverted repeats. They contain 16- to 20-bp hairpins separated by 10–12 nucleotides from the 3′-end and transpose precisely between the 5′-A and T-3′, with no modifications of the AT target sites. Together with their multiple diverged nonautonomous descendants, Helitrons constitute ≈2% of both the Arabidopsis thaliana and Caenorhabditis elegans genomes and also colonize the Oriza sativa genome. Sequence conservation suggests that Helitrons continue to be transposed.

Dynamics and topographic organization of recursive self-organizing maps

Recently there has been an outburst of interest in extending topographic maps of vectorial data to more general data structures, such as sequences or trees. However, there is no general consensus as to how best to process sequences using topographicmaps, and this topic remains an active focus of neurocomputational research. The representational capabilities and internal representations of the models are not well understood. Here, we rigorously analyze a generalization of the self-organizingmap (SOM) for processing sequential data, recursive SOM (RecSOM) (Voegtlin, 2002), as a nonautonomous dynamical system consisting of a set of fixed input maps. We argue that contractive fixed-input maps are likely to produce Markovian organizations of receptive fields on the RecSOM map. We derive bounds on parameter β (weighting the importance of importing past information when processing sequences) under which contractiveness of the fixed-input maps is guaranteed. Some generalizations of SOM contain a dynamic module responsible for processing temporal contexts as an integral part of the model. We show that Markovian topographic maps of sequential data can be produced using a simple fixed (nonadaptable) dynamic module externally feeding a standard topographic model designed to process static vectorial data of fixed dimensionality (e.g., SOM). However, by allowing trainable feedback connections, one can obtain Markovian maps with superior memory depth and topography preservation. We elaborate on the importance of non-Markovian organizations in topographic maps of sequential data. © 2006 Massachusetts Institute of Technology.

Time-Dependent Differential Inclusions and Viability

AMS subject classification: Primary 34A60, Secondary 49J52.