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Introduction to the Modern Theory of Dynamical Systems

The human T-cell leukemia virus type 1 (HTLV-1), identified as the first human oncogenic retrovirus 30 years ago, is not an ubiquitous virus. HTLV-1 is present throughout the world, with clusters of high endemicity located often nearby areas where the virus is nearly absent. The main HTLV-1 highly endemic regions are the Southwestern part of Japan, sub-Saharan Africa and South America, the Caribbean area and foci in Middle East and Australo-Melanesia. The origin of this puzzling geographical or rather ethnic repartition is probably linked to a founder effect in some groups with the persistence of a high viral transmission rate. Despite different socio-economic and cultural environments, the HTLV-1 prevalence increases gradually with age, especially among women in all highly endemic areas. The three modes of HTLV-1 transmission are mother to child, sexual transmission and transmission with contaminated blood products. Twenty years ago, de The and Bomford estimated the total number of HTLV-1 carriers to be 10-20 millions people. At that time, large regions had not been investigated, few population-based studies were available and the assays used for HTLV-1 serology were not enough specific. Despite the fact that there is still a lot of data lacking in large areas of the world and that most of the HTLV-1 studies concern only blood donors, pregnant women or different selected patients or high-risk groups, we shall try based on the most recent data, to revisit the world distribution and the estimates of the number of HTLV-1 infected persons. Our best estimates range from 5-10 millions HTLV-1 infected individuals. However, these results were based on approximately 1.5 billion of individuals originating from known endemic areas with reliable available epidemiological data. Correct estimates in other highly populated regions such as China, India, the Maghreb and East Africa is currently not possible, thus, the current number of HTLV-1 carriers is very probably much higher.

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Epidemiological Aspects and World Distribution of HTLV-1 Infection

Epidemiologic aspects of human T-lymphotropic virus type I (HTLV-I) infection have been thoroughly studied over the course of approximately 25 years since its first description. The geographic distribution of the virus has been defined, with Japan, Africa, Caribbean islands and South America emerging as the areas of highest prevalence. The reasons for HTLV-I clustering, such as the high ubiquity in southwestern Japan but low prevalence in neighboring regions of Korea, China and eastern Russia are still unknown. The major modes of transmission are well understood, although better quantitative data on the incidence of transmission, and on promoting/inhibiting factors, are needed. Epidemiologic proof has been obtained for HTLV-I's causative role in major disease associations: adult T-cell leukemia (ATL), HTLV-associated myelopathy/tropical spastic paraparesis (HAM/TSP), HTLV-associated uveitis and infective dermatitis. However, more and better studies are needed for other apparent disease outcomes such as rheumatologic, psychiatric and infectious diseases. Since curative treatment of ATL and HAM/TSP is lacking and a vaccine is unavailable, the social and financial cost for the individual, his/her family and the health system is immense. For this reason, public health interventions aimed at counseling and educating high-risk individuals and populations are of paramount importance.

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Global epidemiology of HTLV-I infection and associated diseases.

Part I. Examples and Fundamental Concepts Introduction 1. First examples 2. Equivalence, classification, and invariants 3. Principle classes of asymptotic invariants 4. Statistical behavior of the orbits and introduction to ergodic theory 5. Smooth invariant measures and more examples Part II. Local Analysis and Orbit Growth 6. Local hyperbolic theory and its applications 7. Transversality and genericity 8. Orbit growth arising from topology 9. Variational aspects of dynamics Part III. Low-Dimensional Phenomena 10. Introduction: What is low dimensional dynamics 11. Homeomorphisms of the circle 12. Circle diffeomorphisms 13. Twist maps 14. Flows on surfaces and related dynamical systems 15. Continuous maps of the interval 16. Smooth maps of the interval Part IV. Hyperbolic Dynamical Systems 17. Survey of examples 18. Topological properties of hyperbolic sets 19. Metric structure of hyperbolic sets 20. Equilibrium states and smooth invariant measures Part V. Sopplement and Appendix 21. Dynamical systems with nonuniformly hyperbolic behavior Anatole Katok and Leonardo Mendoza.

Introduction to the Modern Theory of Dynamical Systems: EQUILIBRIUM STATES AND SMOOTH INVARIANT MEASURES

Introduction to the Modern Theory of Dynamical Systems: INTRODUCTION: WHAT IS LOW-DIMENSIONAL DYNAMICS?

https://www.arca.fiocruz.br/bitstream/icict/8199/1/Castro-Filho%20BG%20Distribution....pdf

Distribution of human T-lymphotropic virus type I among blood donors: a nationwide Brazilian study.

Sickle cell disease has a worldwide distribution and is a public health problem in Brazil. Although vaso-occlusive crisis (VOC) is one of the most important clinical features of the disease, there are still several steps of its pathogenesis which are unknown. The increase of the chemotactic factor interleukin 8 (IL-8) has been reported to be involved in sickle cell disease crisis, but this has not been demonstrated conclusively. In the present study we analyzed serum IL-8 levels by ELISA and hematological parameters and hemoglobin patterns by standard techniques in 23 (21 SS and 2 SC) Brazilian patients with sickle cell syndromes during VOC caused by different inducing factors, 22 (21 SS and 1 SC) sickle cell patients out of crisis, and 11 healthy controls. Increased IL-8 levels were observed in 19 of 23 VOC patients (79.2%), 3 of them with more than 1,000 pg/ml. Seventeen of 22 (77.3%) non-crisis patients showed low IL-8 levels (less than 15 pg/ml). Healthy controls had low IL-8 levels. A significant difference in serum IL-8 levels was observed between crisis and non-crisis sickle cell patients (P<0.0001). There was no correlation between IL-8 levels and hematological data or hemoglobin patterns. High serum IL-8 levels were observed in VOC patients independently of the crisis-inducing factor. We conclude that in the studied population, IL-8 concentration may be a useful VOC marker, although the mechanism of the pathogenic process of sickle cell VOC syndromes remains unclear.

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Interleukin 8 as a vaso-occlusive marker in Brazilian patients with sickle cell disease

Let G be a noncompact semi-simple Lie group and \(\) a Lie semigroup with nonempty interior. We study the homotopy groups \(\), \(\), of S. Generalizing a well known fact for G, it is proved that there exists a compact and connected subgroup \(\) such that \(\) is isomorphic to \(\). Furthermore, there exists a coset \(\)z contained in int S which is a deformation retract of S.

The Homotopy Type of Lie Semigroups in Semi-Simple Lie Groups

For linear control systems in discrete time controllability properties are characterized. In particular, a unique control set with nonvoid interior exists and it is bounded in the hyperbolic case. Then a formula for the invariance pressure of this control set is proved.

/pdf/controllability-properties-and-invariance-pressure-for-58sk5gefmx.pdf

Controllability Properties and Invariance Pressure for Linear Discrete-Time Systems

Notions of invariance pressure for control systems are introduced based on weights for the control values. The equivalence is shown between inner invariance pressure based on spanning sets of controls and on invariant open covers, respectively. Furthermore, a number of properties of invariance pressure are derived and it is computed for a class of linear systems.

Alexandre J. Santana

Papers

Distribution of human T-lymphotropic virus type I among blood donors: a nationwide Brazilian study.

Interleukin 8 as a vaso-occlusive marker in Brazilian patients with sickle cell disease

The Homotopy Type of Lie Semigroups in Semi-Simple Lie Groups

Controllability Properties and Invariance Pressure for Linear Discrete-Time Systems

Invariance Pressure for Control Systems