Baire and automata

In his thesis Baire defined functions of Baire class 1. A function f is of Baire class 1 if it is the pointwise limit of a sequence of continuous functions. Baire proves the following theorem. A function f is not of class 1 if and only if there exists a closed nonempty set F such that the restriction of f to F has no point of continuity. We prove the automaton version of this theorem. An ω-rational function is not of class 1 if and only if there exists a closed nonempty set F recognized by a Büchi automaton such that the restriction of f to F has no point of continuity. This gives us the opportunity for a discussion on Hausdorff's analysis of Δ°2, ordinals, transfinite induction and some applications of computer science

The geological-event reference system, a step towards geological data harmonization

The temporal dimension is an inherent component of geology. In this regard, traditional geological maps can represent a few geological events, yet they hardly account for the entire complex rock history whether sedimentary, crystalline or volcanic. Here, using the RGF research program (French Geological Reference platform) we propose a new methodology based on digital technology and the French historical collection of 1:50 000-scale geological maps. This innovative approach consists of describing, organizing and hierarchizing a series of geological events within a reference framework and linking it to GIS map geometries (polygons, faults, points). In this way, the complete history of geological features can be compiled and stored in digital maps, combining distinct geological events and properties. For a single event, all associated transformations can be represented on maps, facilitating the production of real “palaeo-geological” maps that consider not only traditional sedimentary environments but also possible synchronous weathering, metamorphism, and volcanism. We discuss here an example of French orogenic history. The approach demonstrated here on geological maps can be used with other geological data media (boreholes, seismic reflection profiles, etc.) and thus facilitate a 3D-to-4D scale, with a significant ability to address not only academic community needs, but also themes or issues related to applications required by politics, civil engineering, and society itself, to confront challenges such as natural and anthropic risk reduction and subsurface uses

Angiotensin II Facilitates Breast Cancer Cell Migration and Metastasis

Breast cancer metastasis is a leading cause of death by malignancy in women worldwide. Efforts are being made to further characterize the rate-limiting steps of cancer metastasis, i.e. extravasation of circulating tumor cells and colonization of secondary organs. In this study, we investigated whether angiotensin II, a major vasoactive peptide both produced locally and released in the bloodstream, may trigger activating signals that contribute to cancer cell extravasation and metastasis. We used an experimental in vivo model of cancer metastasis in which bioluminescent breast tumor cells (D3H2LN) were injected intra-cardiacally into nude mice in order to recapitulate the late and essential steps of metastatic dissemination. Real-time intravital imaging studies revealed that angiotensin II accelerates the formation of metastatic foci at secondary sites. Pre-treatment of cancer cells with the peptide increases the number of mice with metastases, as well as the number and size of metastases per mouse. In vitro, angiotensin II contributes to each sequential step of cancer metastasis by promoting cancer cell adhesion to endothelial cells, trans-endothelial migration and tumor cell migration across extracellular matrix. At the molecular level, a total of 102 genes differentially expressed following angiotensin II pre-treatment were identified by comparative DNA microarray. Angiotensin II regulates two groups of connected genes related to its precursor angiotensinogen. Among those, up-regulated MMP2/MMP9 and ICAM1 stand at the crossroad of a network of genes involved in cell adhesion, migration and invasion. Our data suggest that targeting angiotensin II production or action may represent a valuable therapeutic option to prevent metastatic progression of invasive breast tumors

Type I interferon-mediated autoinflammation due to DNase II deficiency

Microbial nucleic acid recognition serves as the major stimulus to an antiviral response, implying a requirement to limit the misrepresentation of self nucleic acids as non-self and the induction of autoinflammation. By systematic screening using a panel of interferon-stimulated genes we identify two siblings and a singleton variably demonstrating severe neonatal anemia, membranoproliferative glomerulonephritis, liver fibrosis, deforming arthropathy and increased anti-DNA antibodies. In both families we identify biallelic mutations in DNASE2, associated with a loss of DNase II endonuclease activity. We record increased interferon alpha protein levels using digital ELISA, enhanced interferon signaling by RNA-Seq analysis and constitutive upregulation of phosphorylated STAT1 and STAT3 in patient lymphocytes and monocytes. A hematological disease transcriptomic signature and increased numbers of erythroblasts are recorded in patient peripheral blood, suggesting that interferon might have a particular effect on hematopoiesis. These data define a type I interferonopathy due to DNase II deficiency in humans

Etude topologique de fonctions définissables par automates

The subject of this thesis is the study of the topological complexity of omega-rationals functions : functions of finite words which graph is recognizable by finite automaton. The universe of our study is the borelian hierarchy and Baire classes. We first note that that such function are at most of Baire class 2. Christophe Prieur has shown that the problem of the continuity is decidable. We prove that to be of class 1 is also decidable in the synchronous case : we adapt a result of Sierpinski on sub-graph. Then we focus on continuity points of such functions. A result of Baire says that a function is not of Baire class 1 if and only if there exists a closed non empty set with no continuity point of the function. We prove an automaton version of this theorem : an omega-rational function is not of Baire class 1 if and only if there exists a closed non empty set recognizable by Büchy automaton with no continuity point of the function. For this we use the Hausdorff derivation which stop in finite time on omega-rational functions. We conclude this work with the study of orbits of real functions definable in Pisot basis by synchronous tansductors. One can use the Sarkovski's order to make a classification of orders of orbits of real continuous functions. The principal result is the following : for any integer n one can decide if there exists periodic orbits of cardinality n or less in the Sarkovski's order.L'objet de cette thèse est l'étude de la complexité topologique de fonctions omega-rationnelles : fonctions de mots infinis dont le graphe est reconnaissable par automate fini. Le cadre de notre étude est celui de la hiérarchie des boréliens et des classes de Baire. On remarque tout d'abord que ces fonctions sont au plus de classe 2. Christophe Prieur a montré que le problème de la continuité est décidable. Nous avons montré qu'être de classe 1 est aussi décidable dans le cas synchrone en adaptant un résultat de Sierpinski portant sur les sur et sous-graphes à notre contexte. Notre attention s'est ensuite portée aux points de continuité de telles fonctions. Un résultat de Baire dit qu'une fonction n'est pas de classe 1 si et seulement si il existe un fermé non vide sur lequel la fonction n'admet aucun point de continuité. Nous prouvons une version automate de ce théorème : Une fonction omega-rationnelle n'est pas de classe 1 si et seulement si il existe un fermé non vide reconnaissable par un automate de Büchi tel que la restriction de la fonction à ce fermé n'ait aucun point de continuité. Ce résultat est prouvé en utilisant la dérivation de Hausdorff qui s'arrête au bout d'un nombre fini d'étapes sur les langages omega-rationnels Ce travail s'est conclu par l'étude des orbites des fonctions réelles définissables en base Pisot par des transducteurs synchrones. L'ordre de Sarkovski permet de classifier les ordres des orbites périodiques des fonction réelles continues. Le résultat principal obtenu est la décidabilité pour tout entier n de l'existence d'orbites périodiques de cardinalité n et par suite de toute cardinalité inférieure dans l'ordre de Sarkovski

Suivi longitudinal de la densité minérale osseuse dans la maladie de Crohn de l'enfant

RENNES1-BU Santé (352382103) / SudocPARIS-BIUM (751062103) / SudocSudocFranceF

Baire and automata

In his thesis Baire defined functions of Baire class 1. A function f is of Baire class 1 if it is the pointwise limit of a sequence of continuous functions. Baire proves the following theorem. A function f is not of class 1 if and only if there exists a closed nonempty set F such that the restriction of f to F has no point of continuity. We prove the automaton version of this theorem. An ω-rational function is not of class 1 if and only if there exists a closed nonempty set F recognized by a Büchi automaton such that the restriction of f to F has no point of continuity. This gives us the opportunity for a discussion on Hausdorff's analysis of Δ°2, ordinals, transfinite induction and some applications of computer science

Automata, Borel functions and real numbers in Pisot base

This note is about functions ƒ : Aω → Bω whose graph is recognized by a Büchi finite automaton on the product alphabet A x B. These functions are Baire class 2 in the Baire hierarchy of Borel functions and it is decidable whether such function are continuous or not. In 1920 W. Sierpinski showed that a function $f : \mathbb{ R} \rightarrow \mathbb{R}$ is Baire class 1 if and only if both the overgraph and the undergraph of f are Fσ. We show that such characterization is also true for functions on infinite words if we replace the real ordering by the lexicographical ordering on Bω. From this we deduce that it is decidable whether such function are of Baire class 1 or not. We extend this result to real functions definable by automata in Pisot base

The geological-event reference system, a step towards geological data harmonization

The temporal dimension is an inherent component of geology. In this regard, traditional geological maps can represent a few geological events, yet they hardly account for the entire complex rock history whether sedimentary, crystalline or volcanic. Here, using the RGF research program (French Geological Reference platform) we propose a new methodology based on digital technology and the French historical collection of 1:50 000-scale geological maps. This innovative approach consists of describing, organizing and hierarchizing a series of geological events within a reference framework and linking it to GIS map geometries (polygons, faults, points). In this way, the complete history of geological features can be compiled and stored in digital maps, combining distinct geological events and properties. For a single event, all associated transformations can be represented on maps, facilitating the production of real “palaeo-geological” maps that consider not only traditional sedimentary environments but also possible synchronous weathering, metamorphism, and volcanism. We discuss here an example of French orogenic history. The approach demonstrated here on geological maps can be used with other geological data media (boreholes, seismic reflection profiles, etc.) and thus facilitate a 3D-to-4D scale, with a significant ability to address not only academic community needs, but also themes or issues related to applications required by politics, civil engineering, and society itself, to confront challenges such as natural and anthropic risk reduction and subsurface uses