THE IMPLICIT FUNCTION THEOREM FOR CONTINUOUS FUNCTIONS

In the present paper we obtain a new homological version of the implicit function theorem and some versions of the Darboux theorem. Such results are proved for continuous maps on topological manifolds. As a consequence. some versions of these classic theorems are proved when we consider differenciable (not necessarily C-1) maps.

Decay of geometry for Fibonacci critical covering maps of the circle

We study the growth of Df `` (f(c)) when f is a Fibonacci critical covering map of the circle with negative Schwarzian derivative, degree d >= 2 and critical point c of order l > 1. As an application we prove that f exhibits exponential decay of geometry if and only if l <= 2, and in this case it has an absolutely continuous invariant probability measure, although not satisfying the so-called Collet-Eckmann condition. (C) 2009 Elsevier Masson SAS. All rights reserved.

Fibonacci bimodal maps

We introduce the Fibonacci bimodal maps on the interval and show that their two turning points are both in the same minimal invariant Cantor set. Two of these maps with the same orientation have the same kneading sequences and, among bimodal maps without central returns, they exhibit turning points with the strongest recurrence as possible.

Henon-like maps with arbitrary stationary combinatorics

We extend the renormalization operator introduced in [A. de Carvalho, M. Martens and M. Lyubich. Renormalization in the Henon family, I: universality but non-rigidity. J. Stat. Phys. 121(5/6) (2005), 611-669] from period-doubling Henon-like maps to Henon-like maps with arbitrary stationary combinatorics. We show that the renonnalization picture also holds in this case if the maps are taken to be strongly dissipative. We study infinitely renormalizable maps F and show that they have an invariant Cantor set O on which F acts like a p-adic adding machine for some p > 1. We then show, as for the period-doubling case in the work of de Carvalho, Martens and Lyubich [Renormalization in the Henon family, I: universality but non-rigidity. J. Stat. Phys. 121(5/6) (2005), 611-669], that the sequence of renormalizations has a universal form, but that the invariant Cantor set O is non-rigid. We also show that O cannot possess a continuous invariant line field.

XMM-Newton temperature maps for five intermediate redshift clusters of galaxies

We have analyzed XMM-Newton archive data for five clusters of galaxies (redshifts 0.223-0.313) covering a wide range of dynamical states, from relaxed objects to clusters undergoing several mergers. We present here temperature maps of the X-ray gas together with a preliminary interpretation of the formation history of these clusters. (c) 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.

A two-armed pattern in flickering maps of the nova-like variable UU aquarii

We report the analysis of a uniform sample of 31 light curves of the nova-like variable UU Aqr with eclipse-mapping techniques. The data were combined to derive eclipse maps of the average steady-light component, the long-term brightness changes, and the low- and high-frequency flickering components. The long-term variability responsible for the ""low-brightness`` and ""high-brightness`` states is explained in terms of the response of a viscous disk to changes of 20%-50% in the mass transfer rate from the donor star. Low- and high-frequency flickering maps are dominated by emission from two asymmetric arcs reminiscent of those seen in the outbursting dwarf nova IP Peg, and they are similarly interpreted as manifestations of a tidally induced spiral shock wave in the outer regions of a large accretion disk. The asymmetric arcs are also seen in the map of the steady light aside from the broad brightness distribution of a roughly steady-state disk. The arcs account for 25% of the steady-light flux and are a long-lasting feature in the accretion disk of UU Aqr. We infer an opening angle of 10 degrees +/- 3 degrees for the spiral arcs. The results suggest that the flickering in UU Aqr is caused by turbulence generated after the collision of disk gas with the density-enhanced spiral wave in the accretion disk.

Note on ""Continuous matter creation and the acceleration of the universe: the growth of density fluctuations""

Recently, de Roany and Pacheco (Gen Relativ Gravit, doi:10.1007/s10714-010-1069-2) performed a Newtonian analysis on the evolution of perturbations for a class of relativistic cosmological models with Creation of Cold Dark Matter (CCDM) proposed by the present authors (Lima et al. in JCAP 1011:027, 2010). In this note we demonstrate that the basic equations adopted in their work do not recover the specific (unperturbed) CCDM model. Unlike to what happens in the original CCDM cosmology, their basic conclusions refer to a decelerating cosmological model in which there is no transition from a decelerating to an accelerating regime as required by SNe type Ia and complementary observations.

Cladistic analysis of continuous modularized traits provides phylogenetic signals in Homo evolution

Evolutionary novelties in the skeleton are usually expressed as changes in the timing of growth of features intrinsically integrated at different hierarchical levels of development(1). As a consequence, most of the shape- traits observed across species do vary quantitatively rather than qualitatively(2), in a multivariate space(3) and in a modularized way(4,5). Because most phylogenetic analyses normally use discrete, hypothetically independent characters(6), previous attempts have disregarded the phylogenetic signals potentially enclosed in the shape of morphological structures. When analysing low taxonomic levels, where most variation is quantitative in nature, solving basic requirements like the choice of characters and the capacity of using continuous, integrated traits is of crucial importance in recovering wider phylogenetic information. This is particularly relevant when analysing extinct lineages, where available data are limited to fossilized structures. Here we show that when continuous, multivariant and modularized characters are treated as such, cladistic analysis successfully solves relationships among main Homo taxa. Our attempt is based on a combination of cladistics, evolutionary- development- derived selection of characters, and geometric morphometrics methods. In contrast with previous cladistic analyses of hominid phylogeny, our method accounts for the quantitative nature of the traits, and respects their morphological integration patterns. Because complex phenotypes are observable across different taxonomic groups and are potentially informative about phylogenetic relationships, future analyses should point strongly to the incorporation of these types of trait.

A novel locus for split-hand/foot malformation associated with tibial hemimelia (SHFLD syndrome) maps to chromosome region 17p13.1-17p13.3

Split-hand/foot malformation (SHFM) associated with aplasia of long bones, SHFLD syndrome or Tibial hemimelia-ectrodactyly syndrome is a rare condition with autosomal dominant inheritance, reduced penetrance and an incidence estimated to be about 1 in 1,000,000 liveborns. To date, three chromosomal regions have been reported as strong candidates for harboring SHFLD syndrome genes: 1q42.2-q43, 6q14.1 and 2q14.2. We characterized the phenotype of nine affected individuals from a large family with the aim of mapping the causative gene. Among the nine affected patients, four had only SHFM of the hands and no tibial defects, three had both defects and two had only unilateral tibial hemimelia. In keeping with previous publications of this and other families, there was clear evidence of both variable expression and incomplete penetrance, the latter bearing hallmarks of anticipation. Segregation analysis and multipoint Lod scores calculations (maximum Lod score of 5.03 using the LINKMAP software) using all potentially informative family members, both affected and unaffected, identified the chromosomal region 17p13.1-17p13.3 as the best and only candidate for harboring a novel mutated gene responsible for the syndrome in this family. The candidate gene CRK located within this region was sequenced but no pathogenic mutation was detected.

Neuronal Expression of Cd36, Cd44, and Cd83 Antigen Transcripts Maps to Distinct and Specific Murine Brain Circuits

Cells recruited by the innate immune response rely on surface-expressed molecules in order to receive signals from the local environment and to perform phagocytosis, cell adhesion, and others processes linked to host defense. Hundreds of surface antigens designated through a cluster of differentiation (CD) number have been used to identify particular populations of leukocytes. Surprisingly, we verified that the genes that encode Cd36 and Cd83 are constitutively expressed in specific neuronal cells. For instance, Cd36 mRNA is expressed in some regions related to circuitry involved in pheromone responses and reproductive behavior. Cd44 expression, reanalyzed and detailed here, is associated with the laminar formation and midline thalamic nuclei in addition to striatum, extended amygdala, and a few hypothalamic, cortical, and hippocampal regions. A systemic immune challenge was able to increase Cd44 expression quickly in the area postrema and motor nucleus of the vagus but not in regions presenting expressive constitutive expression. In contrast to Cd36 and Cd44, Cd83 message was widely distributed from the olfactory bulb to the brain stem reticular formation, sparing the striatopallidum, olivary region, and cerebellum. Its pattern of expression nevertheless remained strongly associated with hypothalamic, thalamic, and hindbrain nuclei. Unlike the other transcripts, Cd83 mRNA was rapidly modulated by restraint stress. Our results indicate that these molecules might play a role in specific neural circuits and present functions other than those attributed to leukocyte biology. The data also suggest that these surface proteins, or their associated mRNA, could be used to label neurons in specific circuits/regions. J. Comp. Neurol. 517:906-924, 2009. (C) 2009 Wiley-Liss, Inc.

Continuous and High-Level In Vivo Delivery of Endostatin From Recombinant Cells Encapsulated in TheraCyte (R) Immunoisolation Devices

Endostatin (ES) is a potent inhibitor of angiogenesis and tumor growth. Continuous ES delivery of ES improves the efficacy and potency of the antitumoral therapy. The TheraCyte (R) system is a polytetrafluoroethylene (PTFE) semipermeable membrane macroencapsulation system for implantation of genetically engineered cells specially designed for the in vivo delivery of therapeutic proteins, such as ES, which circumvents the problem of limited half-life and variation in circulating levels. In order to enable neovascularization at the tissues adjacent to the devices prior to ES secretion by the cells inside them, we designed a scheme in which empty TheraCyte (R) devices were preimplanted SC into immunodeficient mice. Only after healing (17 days later) were Chinese hamster ovary cells expressing ES injected into the preimplanted devices. In another model for device implantation, the cells expressing ES where loaded into the immunoisolation devices prior to implantation into the animals, and the TheraCyte (R) were then immediately implanted SC into the mice. Throughout the 2-month study, constant high ES levels of up to 3.7 mu g/ml were detected in the plasma of the mice preimplanted with the devices, while lower but also constant levels of ES (up to 2.1 mu g/ml plasma) were detected in the mice that had received devices preloaded with the ES-expressing cells. Immunohistochemistry using anti-ES antibody showed reaction within the device and outside it, demonstrating that ES, secreted by the confined recombinant cells, permeated through the membrane and reached the surrounding tissues.

ROOT PROBLEM FOR CONVENIENT MAPS

In this paper we study when the minimal number of roots of the so-called convenient maps horn two-dimensional CW complexes into closed surfaces is zero We present several necessary and sufficient conditions for such a map to be root free Among these conditions we have the existence of specific fittings for the homomorphism induced by the map on the fundamental groups, existence of the so-called mutation of a specific homomorphism also induced by the map, and existence of particular solutions of specific systems of equations on free groups over specific subgroups

Strong surjectivity of maps from 2-complexes into the 2-sphere

Given a model 2-complex K(P) of a group presentation P, we associate to it an integer matrix Delta(P) and we prove that a cellular map f : K(P) -> S(2) is root free (is not strongly surjective) if and only if the diophantine linear system Delta(P) Y = (deg) over right arrow (f) has an integer solution, here (deg) over right arrow (f) is the so-called vector-degree of f

THE POINCARE-BENDIXSON THEOREM ON THE KLEIN BOTTLE FOR CONTINUOUS VECTOR FIELDS

We present a version of the Poincare-Bendixson Theorem on the Klein bottle K(2) for continuous vector fields. As a consequence, we obtain the fact that K(2) does not admit continuous vector fields having a omega-recurrent injective trajectory.

ON NONSYMMETRIC THEOREMS FOR (H, G)-COINCIDENCES

Let X be a compact Hausdorff space, phi: X -> S(n) a continuous map into the n-sphere S(n) that induces a nonzero homomorphism phi*: H(n)(S(n); Z(p)) -> H(n)(X; Z(p)), Y a k-dimensional CW-complex and f: X -> a continuous map. Let G a finite group which acts freely on S`. Suppose that H subset of G is a normal cyclic subgroup of a prime order. In this paper, we define and we estimate the cohomological dimension of the set A(phi)(f, H, G) of (H, G)-coincidence points of f relative to phi.