Documents  | enregistrements trouvés : 200

Research talks;Dynamical Systems and Ordinary Differential Equations

In a joint work with Sebastien Biebler, we show the existence of a locally dense set of real polynomial automorphisms of $\mathbb{C}^{2}$ displaying a stable wandering Fatou component; in particular this solves the problem of their existence, reported by Bedford and Smillie in 1991. These wandering Fatou components have non-empty real trace and their statistical behavior is historical with high emergence. The proof follows from a real geometrical model which enables us to show the existence of an open and dense set of $C^{r}$ families of surface diffeomorphisms in the Newhouse domain, each of which displaying a historical, high emergent, wandering domain at a dense set of parameters, for every $2\leq r\leq \infty $ and $r=\omega $. Hence, this also complements the recent work of Kiriki and Soma, by proving the last Taken's problem in the $C^{\infty }$ and $C^{\omega }$-case. In a joint work with Sebastien Biebler, we show the existence of a locally dense set of real polynomial automorphisms of $\mathbb{C}^{2}$ displaying a stable wandering Fatou component; in particular this solves the problem of their existence, reported by Bedford and Smillie in 1991. These wandering Fatou components have non-empty real trace and their statistical behavior is historical with high emergence. The proof follows from a real g...

37Bxx ; 37Dxx ; 37FXX ; 32Hxx

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Research talks;Probability and Statistics

60B20 ; 60J80 ; 15B05

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Research talks;Numerical Analysis and Scientific Computing;Computer Science;Mathematical Physics

Quantum walks are widely and successfully used to model diverse physical processes. This leads to computation of the models, to explore their properties. Quantum walks have also been shown to be universal for quantum computing. This is a more subtle result than is often appreciated, since it applies to computations run on qubit-based quantum computers in the single walker case, and physical quantum walkers in the multi-walker case (quantum cellular automata). Nonetheless, quantum walks are powerful tools for quantum computing when correctly applied. I will explain the relationship between quantum walks as models and quantum walks as computational tools, and give some examples of their application in both contexts. Quantum walks are widely and successfully used to model diverse physical processes. This leads to computation of the models, to explore their properties. Quantum walks have also been shown to be universal for quantum computing. This is a more subtle result than is often appreciated, since it applies to computations run on qubit-based quantum computers in the single walker case, and physical quantum walkers in the multi-walker case (quantum ...

68Q12 ; 68W40

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Research talks;Dynamical Systems and Ordinary Differential Equations;Algebraic and Complex Geometry

How to study the dynamics of a holomorphic polynomial vector field in $\mathbb{C}^{2}$? What is the replacement of invariant measure? I will survey some surprising rigidity results concerning the behavior of these dynamical system. It is helpful to consider the extension of this dynamical system to the projective plane.
Consider a foliation in the projective plane admitting a unique invariant algebraic curve. Assume that the foliation is generic in the sense that its singular points are hyperbolic. With T.-C. Dinh, we showed that there is a unique positive $dd^{c}$-closed (1, 1)-current of mass 1 which is directed by the foliation. This is the current of integration on the invariant curve. A unique ergodicity theorem for the distribution of leaves follows: for any leaf $L$, appropriate averages on $L$ converge to the current of integration on the invariant curve (although generically the leaves are dense). The result uses our theory of densities for currents. It extends to Foliations on Kähler surfaces.
I will describe a recent result, with T.-C. Dinh and V.-A. Nguyen, dealing with foliations on compact Kähler surfaces. If the foliation, has only hyperbolic singularities and does not admit a transverse measure, in particular no invariant compact curve, then there exists a unique positive $dd^{c}$-closed (1, 1)-current of mass 1 which is directed by the foliation( it’s like uniqueness of invariant measure for discrete dynamical systems). This improves on previous results, with J.-E. Fornæss, for foliations (without invariant algebraic curves) on the projective plane. The proof uses a theory of densities for positive $dd^{c}$-closed currents (an intersection theory). How to study the dynamics of a holomorphic polynomial vector field in $\mathbb{C}^{2}$? What is the replacement of invariant measure? I will survey some surprising rigidity results concerning the behavior of these dynamical system. It is helpful to consider the extension of this dynamical system to the projective plane.
Consider a foliation in the projective plane admitting a unique invariant algebraic curve. Assume that the foliation is ...

37F75 ; 37Axx

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Research talks;Dynamical Systems and Ordinary Differential Equations;Partial Differential Equations

Evolutionary rescue (ER) is the process by which a population, initially destined to extinction due to environmental stress, avoids extinction via adaptive evolution. One of the widely observed pattern of ER (especially in the study of antibiotic resistance) is that it is more likely to occur in mild than in strong stress. This may be due either to purely demographic effects (extinction is faster in strong stress) or to evolutionary effects (adaptation is harder in strong stress). Disentangling the two and predicting the likelihood of ER has important medical or agronomic implications, but also has a strong potential for empirical testing of eco-evolutionary theory, as ER experiments are widespread (at least in microbial systems) and fairly rapid to perform.
Here, I will present results from three recent articles [1-3] where we considered the probability of ER, and the distribution of extinction times, in a classic phenotype-fitness landscape: Fisher’s geometric model (FGM). In our (classic) version of the FGM, fitness is a quadratic function of traits, with an optimum that depends on the environment. This model has received some empirical support with respects to its ability to reproduce or even predict patterns of context dependence in mutation effects on fitness (be it environmental or genetic context).
In our FGM-ER scenario, a population is initially adapted to the current optimum (either a clone or at mutation selection balance). The environment shifts abruptly and the optimum position, plus possibly peak height and width are modified. We follow the evolutionary and demographic response to this change, assuming a density-independent demography (which we approximate by continuous branching process CB process or Feller process).
In spite of its simplicity, the FGM displays fairly distinct behaviors depending on the relative strength of selection and mutation: this yields different approaches to deal with the FGM-ER scenario. I will thus present the different approaches we have used so far: from the strong selection, weak mutation regime to the weak mutation strong selection regime, and discuss possible extensions at the transition between these regimes. Evolutionary rescue (ER) is the process by which a population, initially destined to extinction due to environmental stress, avoids extinction via adaptive evolution. One of the widely observed pattern of ER (especially in the study of antibiotic resistance) is that it is more likely to occur in mild than in strong stress. This may be due either to purely demographic effects (extinction is faster in strong stress) or to evolutionary effects ...

35K58 ; 35Q92 ; 37N25 ; 60G99

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Research talks;Mathematics in Science and Technology;Probability and Statistics

In recent years, new pandemic threats have become more and more frequent (SARS, bird flu, swine flu, Ebola, MERS, nCoV...) and analyses of data from the early spread more and more common and rapid. Particular interest is usually focused on the estimation of $ R_{0}$ and various methods, essentially based estimates of exponential growth rate and generation time distribution, have been proposed. Other parameters, such as fatality rate, are also of interest. In this talk, various sources of bias arising because observations are made in the early phase of spread will be discussed and also possible remedies proposed. In recent years, new pandemic threats have become more and more frequent (SARS, bird flu, swine flu, Ebola, MERS, nCoV...) and analyses of data from the early spread more and more common and rapid. Particular interest is usually focused on the estimation of $ R_{0}$ and various methods, essentially based estimates of exponential growth rate and generation time distribution, have been proposed. Other parameters, such as fatality rate, are also of ...

92B05 ; 92B15 ; 62P10

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Research talks;Analysis and its Applications;Dynamical Systems and Ordinary Differential Equations;Partial Differential Equations

We introduce and analyze a mathematical model for the regeneration of planarian flatworms. This system of differential equations incorporates dynamics of head and tail cells which express positional control genes that in turn translate into localized signals that guide stem cell differentiation. Orientation and positional information is encoded in the dynamics of a long range wnt-related signaling gradient.
We motivate our model in relation to experimental data and demonstrate how it correctly reproduces cut and graft experiments. In particular, our system improves on previous models by preserving polarity in regeneration, over orders of magnitude in body size during cutting experiments and growth phases. Our model relies on tristability in cell density dynamics, between head, trunk, and tail. In addition, key to polarity preservation in regeneration, our system includes sensitivity of cell differentiation to gradients of wnt-related signals measured relative to the tissue surface. This process is particularly relevant in a small tissue layer close to wounds during their healing, and modeled here in a robust fashion through dynamic boundary conditions. We introduce and analyze a mathematical model for the regeneration of planarian flatworms. This system of differential equations incorporates dynamics of head and tail cells which express positional control genes that in turn translate into localized signals that guide stem cell differentiation. Orientation and positional information is encoded in the dynamics of a long range wnt-related signaling gradient.
We motivate our model in relation to ...

92C15 ; 35B36 ; 35Q92 ; 37N25 ; 35K40

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Research talks;Computer Science;Control Theory and Optimization

Machine learning pipelines often rely on optimization procedures to make discrete decisions (e.g. sorting, picking closest neighbors, finding shortest paths or optimal matchings). Although these discrete decisions are easily computed in a forward manner, they cannot be used to modify model parameters using first-order optimization techniques because they break the back-propagation of computational graphs. In order to expand the scope of learning problems that can be solved in an end-to-end fashion, we propose a systematic method to transform a block that outputs an optimal discrete decision into a differentiable operation. Our approach relies on stochastic perturbations of these parameters, and can be used readily within existing solvers without the need for ad hoc regularization or smoothing. These perturbed optimizers yield solutions that are differentiable and never locally constant. The amount of smoothness can be tuned via the chosen noise amplitude, whose impact we analyze. The derivatives of these perturbed solvers can be evaluated eciently. We also show how this framework can be connected to a family of losses developed in structured prediction, and describe how these can be used in unsupervised and supervised learning, with theoretical guarantees.
We demonstrate the performance of our approach on several machine learning tasks in experiments on synthetic and real data. Machine learning pipelines often rely on optimization procedures to make discrete decisions (e.g. sorting, picking closest neighbors, finding shortest paths or optimal matchings). Although these discrete decisions are easily computed in a forward manner, they cannot be used to modify model parameters using first-order optimization techniques because they break the back-propagation of computational graphs. In order to expand the scope of learning ...

90C06 ; 68W20 ; 62F99

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Research talks;Probability and Statistics

Differences in disease predisposition or response to treatment can be explained in great part by genomic differences between individuals. This has given birth to precision medicine, where treatment is tailored to the genome of patients. This field depends on collecting considerable amounts of molecular data for large numbers of individuals, which is being enabled by thriving developments in genome sequencing and other high-throughput experimental technologies.
Unfortunately, we still lack effective methods to reliably detect, from this data, which of the genomic features determine a phenotype such as disease predisposition or response to treatment. One of the major issues is that the number of features that can be measured is large (easily reaching tens of millions) with respect to the number of samples for which they can be collected (more usually of the order of hundreds or thousands), posing both computational and statistical difficulties.
In my talk I will discuss how to use biological networks, which allow us to understand mutations in their genomic context, to address these issues. All the methods I will present share the common hypotheses that genomic regions that are involved in a given phenotype are more likely to be connected on a given biological network than not. Differences in disease predisposition or response to treatment can be explained in great part by genomic differences between individuals. This has given birth to precision medicine, where treatment is tailored to the genome of patients. This field depends on collecting considerable amounts of molecular data for large numbers of individuals, which is being enabled by thriving developments in genome sequencing and other high-throughput ex...

92C42 ; 92-08 ; 92B15 ; 62P10

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- viii; 174 p.
ISBN 978-0-691-19377-9

Annals of mathematics studies , 0202

Localisation : Ouvrage RdC (ARIT)

géométrie algébrique # variété de Shimura # fraction continue hyperelliptique # Jacobien # hauteur de Faltings # conjecture locale de Langlands # équation de Pell

00B25 ; 11-06 ; 11Fxx ; 14G22 ; 14G35 ; 11Gxx ; 11Dxx ; 11Mxx

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- 218 p.
ISBN 978-4-86497-079-2

Advanced studies in pure mathematics , 0080

Localisation : Collection 1er étage

théorie des opérateurs # algèbre d'opérateurs # physique mathématique # opérateur vertex # théorie quantique des champs # hypergroupe # K-théorie # automorphisme # flip # groupe quantique # chaîne de spins

46-06 ; 81-06 ; 46Lxx ; 81Rxx ; 81Txx ; 00B25

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- 541 p.
ISBN 978-4-86497-050-1

Advanced Studies in Pure Mathematics , 0076

Localisation : Collection 1er étage

Masatoshi Noumi # équation différentielle fonctionnelle # théorie de la représentation # fonction spéciale # équation de Painlevé

33-06 ; 17-06 ; 81-06 ; 33D90 ; 34M55 ; 00B30 ; 39-06

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- 469 p.
ISBN 978-4-86497-055-6

Advanced studies in pure mathematics , 0078

Localisation : Collection 1er étage

cavenas de Wulff # méthode sphérique # propagation de front d'onde # caustique # courbe partiellement nulle # surface gaussienne # variété symplectique # contrainte symplectique # diagramme de Heegaard # point d'inflexion # singularité lagrangienne # cohomologie locale # courbe plane # indice de Whitney # invariant isotopique # géométrie différentielle discrète # représentation de Weierstrass # système différentiel implicite # système Hamiltonien implicite # espace de Minkowski # surface minimale conforme cavenas de Wulff # méthode sphérique # propagation de front d'onde # caustique # courbe partiellement nulle # surface gaussienne # variété symplectique # contrainte symplectique # diagramme de Heegaard # point d'inflexion # singularité lagrangienne # cohomologie locale # courbe plane # indice de Whitney # invariant isotopique # géométrie différentielle discrète # représentation de Weierstrass # système différentiel implicite # système H...

37K25 ; 53A10 ; 53C42 ; 53A35 ; 58k99 ; 53A99

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- xiii; 289 p.
ISBN 978-981-13-6627-7

Progress in mathematics , 0328

Localisation : Collection 1er étage

théorie des groupes # groupe topologique # analyse harmonique # groupe réductif p-adique # conjecture de Langlands

11-06 ; 11F70 ; 11F85 ; 22E50 ; 00B25

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- vii; 265 p.
ISBN 978-1-108-74072-2

London mathematical society lecture note series , 0456

Localisation : Collection 1er étage

analyse combinatoire # théorie des graphes # cryptographie # matroïde # géométrie d'incidence

05-06

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- xvi; 453 p.
ISBN 978-1-108-43163-7

London mathematical society lecture note series , 0450

Localisation : Collection 1er étage

Abbas Bahri # hommage # équation aux dérivées partielles # physique mathématique # équation d'onde # équation de réaction-diffusion # équation de Ginzburg-Landau # équation de Yamabe

35-06 ; 35Qxx ; 58J90 ; 81Q05 ; 00B15 ; 00B30

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- xv; 193 p.
ISBN 978-1-108-43762-2

London mathematical society lecture note series , 0451

Localisation : Collection 1er étage

Ross Geoghegan # théorie des groupes # groupe topologique # variété topologique

20-06 ; 20F65 ; 57Mxx ; 00B25

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- vi; 501 p.
ISBN 978-1-108-72874-4

London mathematical society lecture note series , 0455

Localisation : Collection 1er étage

théorie des groupes # génération de groupes simples finis # théorie des blocs # système de fusion # groupe algébrique # groupe à un seul corrélateur # théorie géométrique des groupes # groupe de Beauville

20-06 ; 20Dxx ; 20Exx ; 20F65 ; 20Gxx ; 14L10 ; 00B25

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- ix; 326 p.
ISBN 978-1-108-46096-5

London mathematical society lecture note series , 0452

Localisation : Collection 1er étage

mécanique des fluides # équation aux dérivées partielles # conjecture d'Onsager # unicité faible-fort # équation de Navier-Stokes

35-06 ; 35Q35 ; 35Q30 ; 76D03 ; 76D05 ; 76D07 ; 76M25 ; 00B25

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