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.

Spectral invariants of periodic nonautonomous discrete dynamical systems

For an interval map, the poles of the Artin-Mazur zeta function provide topological invariants which are closely connected to topological entropy. It is known that for a time-periodic nonautonomous dynamical system F with period p, the p-th power [zeta(F) (z)](p) of its zeta function is meromorphic in the unit disk. Unlike in the autonomous case, where the zeta function zeta(f)(z) only has poles in the unit disk, in the p-periodic nonautonomous case [zeta(F)(z)](p) may have zeros. In this paper we introduce the concept of spectral invariants of p-periodic nonautonomous discrete dynamical systems and study the role played by the zeros of [zeta(F)(z)](p) in this context. As we will see, these zeros play an important role in the spectral classification of these systems.

Chains of Infinite Order, Chains with Memory of Variable Length, and Maps of the Interval

We show how to construct a topological Markov map of the interval whose invariant probability measure is the stationary law of a given stochastic chain of infinite order. In particular we characterize the maps corresponding to stochastic chains with memory of variable length. The problem treated here is the converse of the classical construction of the Gibbs formalism for Markov expanding maps of the interval.

The bovine dilated cardiomyopathy locus maps to a 1.0-Mb interval on chromosome 18

Cardiomyopathies are myocardial diseases that lead to cardiac dysfunction, heart failure, arrhythmia, and sudden death. In human medicine, cardiomyopathies frequently warrant heart transplantation in children and adults. Bovine dilated cardiomyopathy (BDCMP) is a heart muscle disorder that has been observed during the last 30 years in cattle of Holstein-Friesian origin. In Switzerland BDCMP affects Swiss Fleckvieh and Red Holstein breeds. BDCMP is characterized by a cardiac enlargement with ventricular remodeling and chamber dilatation. The common symptoms in affected animals are subacute subcutaneous edema, congestion of the jugular veins, and tachycardia with gallop rhythm. A cardiomegaly with dilatation and hypertrophy of all heart chambers, myocardial degeneration, and fibrosis are typical postmortem findings. It was shown that all BDCMP cases reported worldwide traced back to a red factor-carrying Holstein-Friesian bull, ABC Reflection Sovereign. An autosomal recessive mode of inheritance was proposed for BDCMP. Recently, the disease locus was mapped to a 6.7-Mb interval MSBDCMP06-BMS2785 on bovine Chr 18 (BTA18). In the present study the BDCMP locus was fine mapped by using a combined strategy of homozygosity mapping and association study. A BAC contig of 2.9 Mb encompassing the crucial interval was constructed to establish the correct marker order on BTA18. We show that the disease locus is located in a gene-rich interval of 1.0 Mb and is flanked by the microsatellite markers DIK3006 and MSBDCMP51.

Precision of distances and ordering of microsatellite markers in consensus linkage maps of chromosomes 1, 3 and 4 from two reciprocal chicken populations using bootstrap sampling

Some factors complicate comparisons between linkage maps from different studies. This problem can be resolved if measures of precision, such as confidence intervals and frequency distributions, are associated with markers. We examined the precision of distances and ordering of microsatellite markers in the consensus linkage maps of chromosomes 1, 3 and 4 from two F 2 reciprocal Brazilian chicken populations, using bootstrap sampling. Single and consensus maps were constructed. The consensus map was compared with the International Consensus Linkage Map and with the whole genome sequence. Some loci showed segregation distortion and missing data, but this did not affect the analyses negatively. Several inversions and position shifts were detected, based on 95% confidence intervals and frequency distributions of loci. Some discrepancies in distances between loci and in ordering were due to chance, whereas others could be attributed to other effects, including reciprocal crosses, sampling error of the founder animals from the two populations, F(2) population structure, number of and distance between microsatellite markers, number of informative meioses, loci segregation patterns, and sex. In the Brazilian consensus GGA1, locus LEI1038 was in a position closer to the true genome sequence than in the International Consensus Map, whereas for GGA3 and GGA4, no such differences were found. Extending these analyses to the remaining chromosomes should facilitate comparisons and the integration of several available genetic maps, allowing meta-analyses for map construction and quantitative trait loci (QTL) mapping. The precision of the estimates of QTL positions and their effects would be increased with such information.

AFFINE INTERVAL EXCHANGE TRANSFORMATIONS WITH FLIPS AND WANDERING INTERVALS

There exist uniquely ergodic affine interval exchange transformations of [0,1] with flips which have wandering intervals and are such that the support of the invariant measure is a Cantor set.

Toplological Entropy in the Syncronization of Piecewise Linear and Monotone Maps. Coupled Duffing Oscillators

In this paper is presented a relationship between the synchronization and the topological entropy. We obtain the values for the coupling parameter, in terms of the topological entropy, to achieve synchronization of two unidirectional and bidirectional coupled piecewise linear maps. In addition, we prove a result that relates the synchronizability of two m-modal maps with the synchronizability of two conjugated piecewise linear maps. An application to the unidirectional and bidirectional coupled identical chaotic Duffing equations is given. We discuss the complete synchronization of two identical double-well Duffing oscillators, from the point of view of symbolic dynamics. Working with Poincare cross-sections and the return maps associated, the synchronization of the two oscillators, in terms of the coupling strength, is characterized.

A progressive autosomal recessive cataract locus maps to chromosome 9q13-q22.

Cataracts are the leading cause of blindness in most countries. Although most hereditary cases appear to follow an autosomal dominant pattern of inheritance, autosomal recessive inheritance has been clearly documented and is probably underrecognized. We studied a large family-from a relatively isolated geographic region-whose members were affected by autosomal recessive adult-onset pulverulent cataracts. We mapped the disease locus to a 14-cM interval at a novel disease locus, 9q13-q22 (between markers D9S1123 and D9S257), with a LOD score of 4.7. The study of this progressive and age-related cataract phenotype may provide insight into the cause of the more common sporadic form of age-related cataracts.

Investigations on the Dynamics of Combination Maps and the Analysis of Bifurcation in a Discontinuous Logistic Map

This thesis is a study of discrete nonlinear systems represented by one dimensional mappings.As one dimensional interative maps represent Poincarre sections of higher dimensional flows,they offer a convenient means to understand the dynamical evolution of many physical systems.It highlighting the basic ideas of deterministic chaos.Qualitative and quantitative measures for the detection and characterization of chaos in nonlinear systems are discussed.Some simple mathematical models exhibiting chaos are presented.The bifurcation scenario and the possible routes to chaos are explained.It present the results of the numerical computational of the Lyapunov exponents (λ) of one dimensional maps.This thesis focuses on the results obtained by our investigations on combinations maps,scaling behaviour of the Lyapunov characteristic exponents of one dimensional maps and the nature of bifurcations in a discontinous logistic map.It gives a review of the major routes to chaos in dissipative systems,namely, Period-doubling ,Intermittency and Crises.This study gives a theoretical understanding of the route to chaos in discontinous systems.A detailed analysis of the dynamics of a discontinous logistic map is carried out, both analytically and numerically ,to understand the route it follows to chaos.The present analysis deals only with the case of the discontinuity parameter applied to the right half of the interval of mapping.A detailed analysis for the n –furcations of various periodicities can be made and a more general theory for the map with discontinuities applied at different positions can be on a similar footing

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.

Precision of distances and ordering of microsatellite markers in consensus linkage maps of chromosomes 1, 3 and 4 from two reciprocal chicken populations using bootstrap sampling

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

The locus for bovine dilated cardiomyopathy maps to chromosome 18

Bovine dilated cardiomyopathy (BDCMP) is a severe and terminal disease of the heart muscle observed in Holstein-Friesian cattle over the last 30 years. There is strong evidence for an autosomal recessive mode of inheritance for BDCMP. The objective of this study was to genetically map BDCMP, with the ultimate goal of identifying the causative mutation. A whole-genome scan using 199 microsatellite markers and one SNP revealed an assignment of BDCMP to BTA18. Fine-mapping on BTA18 refined the candidate region to the MSBDCMP06-BMS2785 interval. The interval containing the BDCMP locus was confirmed by multipoint linkage analysis using the software loki. The interval is about 6.7 Mb on the bovine genome sequence (Btau 3.1). The corresponding region of HSA19 is very gene-rich and contains roughly 200 genes. Although telomeric of the marker interval, TNNI3 is a possible positional and a functional candidate for BDCMP given its involvement in a human form of dilated cardiomyopathy. Sequence analysis of TNNI3 in cattle revealed no mutation in the coding sequence, but there was a G-to-A transition in intron 6 (AJ842179:c.378+315G>A). The analysis of this SNP using the study's BDCMP pedigree did not conclusively exclude TNNI3 as a candidate gene for BDCMP. Considering the high density of genes on the homologous region of HSA19, further refinement of the interval on BTA18 containing the BDCMP locus is needed.

Arachnomelia in Brown Swiss cattle maps to chromosome 5

Arachnomelia in Brown Swiss cattle is a monogenic autosomal recessive inherited congenital disorder of the skeletal system giving affected calves a spidery look (OMIA ID 000059). Over a period of 20 years 15 cases were sampled in the Swiss and Italian Brown cattle population. Pedigree data revealed that all affected individuals trace back to a single acknowledged carrier founder sire. A genome scan using 240 microsatellites spanning the 29 bovine autosomes showed homozygosity at three adjacent microsatellite markers on bovine Chr 5 in all cases. Linkage analysis confirmed the localization of the arachnomelia mutation in the region of the marker ETH10. Fine-mapping and haplotype analysis using a total of 34 markers in this region refined the critical region of the arachnomelia locus to a 7.19-Mb interval on bovine Chr 5. The disease-associated IBD haplotype was shared by 36 proven carrier animals and allows marker-assisted selection. As the corresponding human and mouse chromosome segments do not contain any clear functional candidate genes for this disorder, the mutation causing arachnomelia in the Brown Swiss cattle might help to identify an unknown gene in bone development.

Maps of Waxeggkees glacier 1950-2000

Photogrammetric surveys have been made and maps drawn of a number of glaciers in the eastern Alps, among them the Waxeggkees in the Zillertal Alps of Tyrol, at approximately ten-year intervals since 1950. Terrestrial photogrammetry was used for the pictures taken in 1950, 1960, 1980, 1989 and 2000, while aerial photogrammetry was employed for the 1969 photo. These maps were subsequently used to calculate the changes in area, elevation and volume for elevational zones of 50 m. The numeric values are given in two tables. The illustration of surface changes in Waxeggkees is continued cartographically on 5 map sheets at the scale of 1 : 15.000 and a vertical interval of the contour lines of 50 m. Changes in glacier area are marked in light red to indicate a decrease in area, and in light blue for an increase. Changes in elevation can only be indicated indirectly, namely in the form of vertical interval bands, referring to the surface areas that arise due to the relocation of the contour lines, resulting from an elevational change. Decrease in elevation is indicated in red, increase in blue, on 100 m contour lines.

A novel modifier gene for plasma von Willebrand factor level maps to distal mouse chromosome 11

Type 1 von Willebrand disease (VWD), characterized by reduced levels of plasma von Willebrand factor (VWF), is the most common inherited bleeding disorder in humans. Penetrance of VWD is incomplete, and expression of the bleeding phenotype is highly variable. In addition, plasma VWF levels vary widely among normal individuals. To identify genes that influence VWF level, we analyzed a genetic cross between RIIIS/J and CASA/Rk, two strains of mice that exhibit a 20-fold difference in plasma VWF level. DNA samples from F2 progeny demonstrating either extremely high or extremely low plasma VWF levels were pooled and genotyped for 41 markers spanning the autosomal genome. A novel locus accounting for 63% of the total variance in VWF level was mapped to distal mouse chromosome 11, which is distinct from the murine Vwf locus on chromosome 6. We designated this locus Mvwf for “modifier of VWF.” Additional genotyping of as many as 2407 meioses established a high resolution genetic map with gene order Cola1-Itg3a-Ngfr-Mvwf/Gip-Hoxb9-Hoxb1-Cbx·rs2-Cox5a-Gfap. The Mvwf candidate interval between Ngfr and Hoxb9 is ≈0.5 centimorgan (cM). These results demonstrate that a single dominant gene accounts for the low VWF phenotype of RIIIS/J mice in crosses with several other strains. The pattern of inheritance suggests a gain-of-function mutation in a unique component of VWF biosynthesis or processing. Characterization of the human homologue for Mvwf may have relevance for a subset of type 1 VWD cases and may define an important genetic factor modifying penetrance and expression of mutations at the VWF locus.