Letteratura scientifica selezionata sul tema "Noyau algébrique"
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Tesi sul tema "Noyau algébrique":
Ancona, Michele. "Moments en géométrie algébrique réelle". Thesis, Lyon, 2018. http://www.theses.fr/2018LYSE1274.
It is well known that the number of real roots of a real degree d polynomial is at most d. In the 90s, E. Kostlan proved that the average number of real roots equals the square root of d, once we equip the space of polynomials with some natural Gaussian measure. This result has a geometric interpretation, in which the real polynomials are sections of a line bundle over the Riemann sphere. We can extend this study in a more general case of a real Riemann surface equipped with ample line bundle and study the expected value of the number of real zeros of a random section. In this thesis, we compute all the central moments of these random variables. As an application, we prove that the measure of the space of real sections whose number of real zeros deviates from the expected one goes to zeros, as the degree of the line bundle goes to infinity.In a second part, we present analogues results in real Hurwitz theory, in which we study the real critical points of a random branched covering of the Riemann sphere. We compute the expected value of this number and also all the central moments.The techniques we use are of analytique nature (Bergman kernel, L^2 estimates) and gometric one (Olver multispaces, coarea formula)
Peñaranda, Luis. "Géométrie algorithmique non linéaire et courbes algébriques planaires". Electronic Thesis or Diss., Nancy 2, 2010. http://www.theses.fr/2010NAN23002.
We tackle in this thesis the problem of computing the topology of plane algebraic curves. We present an algorithm that avoids special treatment of degenerate cases, based on algebraic tools such as Gröbner bases and rational univariate representations. We implemented this algorithm and showed its performance by comparing to simi- lar existing programs. We also present an output-sensitive complexity analysis of this algorithm. We then discuss the tools that are necessary for the implementation of non- linear geometric algorithms in CGAL, the reference library in the computational geom- etry community. We present an univariate algebraic kernel for CGAL, a set of functions aimed to handle curved objects defined by univariate polynomials. We validated our approach by comparing it to other similar implementations
Validire, Romain. "Capitulation des noyaux sauvages étales". Phd thesis, Université de Limoges, 2008. http://tel.archives-ouvertes.fr/tel-00343427.
La structure de groupe abélien du p-groupe des classes des étages de $F_{\infty}/F$ est asymptotiquement bien connue : nous montrons, au moyen de la théorie d'Iwasawa des $\Z_p$-extensions, un analogue de ce résultat en $K$-théorie supérieure.
Dans un deuxième temps, nous étudions le groupe de Galois sur $F_{\infty}$ de la pro-p-extension, non ramifiée, p-décomposée maximale de $F_{\infty}$, lorsque $F_{\infty}$ est la $\Z_p$-extension cyclotomique de $F$. Après avoir établi un lien entre la structure de ce groupe et le comportement galoisien des noyaux sauvages étales, nous donnons divers critères effectifs de non pro-p-liberté pour ce groupe.
Laske, Michael. "Le K1 des courbes sur les corps globaux : conjecture de Bloch et noyaux sauvages". Thesis, Bordeaux 1, 2009. http://www.theses.fr/2009BOR13861/document.
For a smooth projective geometrically connected curve X over a global ?eld k, we determine the Q-structure of its ?rst Quillen K-group K1(X) by showing that dimQ K1(X) ? Q =2r, where r denotes the number of archimedean places of k (including the case r = 0 for k a function ?eld). This con?rms a conjecture of Bloch. In the language of Milnor K-theory, which we de?ne for varieties via Somekawa groups, the ?rst special Milnor K-group SKM 1 (X) is torsion. For the proof, we develop a theory of heights applicable to Milnor K-groups, and generalize the factor basis approach of Bass-Tate. A ?ner structure of SKM 1 (X) emerges when localizing the ground ?eld k, and we give an explicit description of the resulting decomposition. In particular, we identify a potentially ?nite subgroup WKl(X):= ker (SKM 1 (X) ? Zl ? Lv SKM 1 (Xv) ? Zl) for each rational prime l, named wild kernel
Sebti, Nadia. "Noyaux rationnels et automates d'arbres". Rouen, 2015. http://www.theses.fr/2015ROUES007.
In the case of words, a general scheme for computing rational kernels has been proposed. It is based on a general algorithm for composition of weighted transducers and a general algorithm computing smallest distance. Our goal is to generalize this computation scheme to the case of trees using tree automata. To do this we have established the following two main objectives : On the one hand,define tree automata for computing subtree kernel, subsettree kernel and tree factor kernel. On the other hand, from a regular tree expression, build a tree automaton to compute the various rational tree kernels described by regular tree expressions using the following scheme over two tree languages L1 and L2 : KE(L1;L2) = (AL1 \ AE \ AL1). We explored and proposed efficient algorithms for the conversion of a regular tree expression into tree automata. The first algorithm computes the Follow sets for a regular tree expression E of a size jEj and alphabetic width jjEjj in O(jjEjj jEj) time complexity. The second algorithm computes the equation tree automaton via the k-C-Continuations which is based on the acyclic minimization of Revuz. The algorithm is performed in an O(jQj jEj) time and space complexity, where jQj is the number of states of the produced automaton. Then we developed algorithms for the computation of subtree kernel, subsettree kernel and tree factor kernel. Our approach is based on the representation of all trees of the set S = fs1; : : : ; sng (resp. T = ft1; : : : ; tmg) by a particular weighted tree automaton called Root Weighted Tree Automaton the RWTA AS (resp. AT ) (equivalent to the prefix automaton in the case of words) such that jASj #Pn i=1 jsij = jSj (resp. JAT #Pm j=1 jtj j = jTj) ; then we compute the kernels between the two sets S and T. This amounts to compute the weight of the intersection automaton AS \ AT. We show that the computation of the kernel K(S; T) can be done in O(jASj jAT j) time and space complexity. Keywords: Finite Tree Automata, Rationnal Tree Languages, Regular Tree Expressions, Conversion of Regular Tree Expressions, Rational Kernels, Trees, Rational Tree Kernels
Lescop, Mikaël. "Sur les 2-extensions de Q dont la 2-partie du noyau sauvage est triviale". Limoges, 2003. http://aurore.unilim.fr/theses/nxfile/default/b1efa329-cc35-477d-9273-27ceca2d84b9/blobholder:0/2003LIMO0010.pdf.
In this thesis, we are interested in the study of the triviality of the 2-primary wild kernel of somme abelian 2-extensions of the rationals Q. Since the general case of multi-quadratic extensions has been already solved, we deal with the case of cyclic 2-extensions, and then with that of totally In this thesis, we are interested in the study of the triviality of the 2-primary wild kernel of some real abelian 2-extensions. The results we obtain are based on an improvement we propose of the genus formula proved by M. Kolster and A. Movahhedi. As a consequence, we also retrieve the 2-rank of the wild kernel of quadratic fields. We end the thesis by some examples illustrating the hurdles we have to overcome to determine the general case of abelian 2-extensions of Q
Carriere, Mathieu. "On Metric and Statistical Properties of Topological Descriptors for geometric Data". Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLS433/document.
In the context of supervised Machine Learning, finding alternate representations, or descriptors, for data is of primary interest since it can greatly enhance the performance of algorithms. Among them, topological descriptors focus on and encode the topological information contained in geometric data. One advantage of using these descriptors is that they enjoy many good and desireable properties, due to their topological nature. For instance, they are invariant to continuous deformations of data. However, the main drawback of these descriptors is that they often lack the structure and operations required by most Machine Learning algorithms, such as a means or scalar products. In this thesis, we study the metric and statistical properties of the most common topological descriptors, the persistence diagrams and the Mappers. In particular, we show that the Mapper, which is empirically instable, can be stabilized with an appropriate metric, that we use later on to conpute confidence regions and automatic tuning of its parameters. Concerning persistence diagrams, we show that scalar products can be defined with kernel methods by defining two kernels, or embeddings, into finite and infinite dimensional Hilbert spaces