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Documents : Multi angle  Conférences Vidéo | enregistrements trouvés : 585

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We will show that there exists a correspondence between smooth $l$-adic sheaves and overconvergent $F$-isocrystals over a curve preserving the Frobenius eigenvalues. Moreover, we show the existence of $l$-adic companions associated to overconvergent $F$-isocrystals for smooth varieties.
Some part of the work is done jointly with Esnault.

12H25 ; 14F30 ; 14F10

I will describe joint work with Thomas Kragh proving that closed exact Lagrangians in cotangent bundles are simply homotopy equivalent to the base. The main two ideas are (i) a Floer theoretic model for the Whitehead torsion of the projection from the Lagrangian to the base, and (ii) a large scale deformation of the Lagrangian which allows a computation of this torsion.

53D40 ; 55P35 ; 55P42

Reidemeister torsion was the first topological invariant that could distinguish between spaces which were homotopy equivalent but not homeomorphic. The Cheeger-Müller theorem established that the Reidemeister torsion of a closed manifold can be computed analytically. I will report on joint work with Frédéric Rochon and David Sher on finding a topological expression for the analytic torsion of a manifold with fibered cusp ends. Examples of these manifolds include most locally symmetric spaces of rank one. We establish our theorem by controlling the behavior of analytic torsion as a space degenerates to form hyperbolic cusp ends. Reidemeister torsion was the first topological invariant that could distinguish between spaces which were homotopy equivalent but not homeomorphic. The Cheeger-Müller theorem established that the Reidemeister torsion of a closed manifold can be computed analytically. I will report on joint work with Frédéric Rochon and David Sher on finding a topological expression for the analytic torsion of a manifold with fibered cusp ends. Examples of these ...

58J52 ; 58J05 ; 58J50 ; 58J35 ; 55N25 ; 55N33

Multi angle  Logarithms and deformation quantization
Alekseev, Anton (Auteur de la Conférence) | CIRM (Editeur )

We prove the statement$/$conjecture of M. Kontsevich on the existence of the logarithmic formality morphism $\mathcal{U}^{log}$. This question was open since 1999, and the main obstacle was the presence of $dr/r$ type singularities near the boundary $r = 0$ in the integrals over compactified configuration spaces. The novelty of our approach is the use of local torus actions on configuration spaces of points in the upper half-plane. It gives rise to a version of Stokes' formula for differential forms with singularities at the boundary which implies the formality property of $\mathcal{U}^{log}$. We also show that the logarithmic formality morphism admits a globalization from $\mathbb{R}^{d}$ to an arbitrary smooth manifold. We prove the statement$/$conjecture of M. Kontsevich on the existence of the logarithmic formality morphism $\mathcal{U}^{log}$. This question was open since 1999, and the main obstacle was the presence of $dr/r$ type singularities near the boundary $r = 0$ in the integrals over compactified configuration spaces. The novelty of our approach is the use of local torus actions on configuration spaces of points in the upper half-plane. It gives rise ...

53D55 ; 17B56

When solving wave scattering problems with the Boundary Element Method (BEM), one usually faces the problem of storing a dense matrix of huge size which size is proportional to the (square of) the number N of unknowns on the boundary of the scattering object. Several methods, among which the Fast Multipole Method (FMM) or the H-matrices are celebrated, were developed to circumvent this obstruction. In both cases an approximation of the matrix is obtained with a O(N log(N)) storage and the matrix-vector product has the same complexity. This permits to solve the problem, replacing the direct solver with an iterative method.
The aim of the talk is to present an alternative method which is based on an accurate version of the Fourier based convolution. Based on the non-uniform FFT, the method, called the sparse cardinal sine decomposition (SCSD) ends up to have the same complexity than the FMM for much less complexity in the implementation. We show in practice how the method works, and give applications in as different domains as Laplace, Helmholtz, Maxwell or Stokes equations.
This is a joint work with Matthieu Aussal.
When solving wave scattering problems with the Boundary Element Method (BEM), one usually faces the problem of storing a dense matrix of huge size which size is proportional to the (square of) the number N of unknowns on the boundary of the scattering object. Several methods, among which the Fast Multipole Method (FMM) or the H-matrices are celebrated, were developed to circumvent this obstruction. In both cases an approximation of the matrix is ...

65T50 ; 65R10 ; 65T40

Multi angle  From metronomic to... chaotic therapy ?
André, Nicolas (Auteur de la Conférence) | CIRM (Editeur )

définition of the quotient norm - basic properties - existence of minimal liftings: von Neumann algebras - finite dimensional cases - non-uniqueness results - counter-examples: the unitary Fredholm group

Multi angle  Recurrence of half plane maps
Angel, Omer (Auteur de la Conférence) | CIRM (Editeur )

On a graph $G$, we consider the bootstrap model: some vertices are infected and any vertex with 2 infected vertices becomes infected. We identify the location of the threshold for the event that the Erdos-Renyi graph $G(n, p)$ can be fully infected by a seed of only two infected vertices. Joint work with Brett Kolesnik.

05C80 ; 60K35 ; 60C05

We start by recalling the essential features of frames, both discrete and continuous, with some emphasis on the notion of frame duality. Then we turn to generalizations, namely upper and lower semi-frames, and their duality. Next we consider arbitrary measurable maps and examine the standard operators, analysis, synthesis and frame operators, and study their properties. Finally we analyze the recent notion of reproducing pairs. In view of their duality structure, we introduce two natural partial inner product spaces and formulate a number of open questions.

Keywords: continuous frames - semi-frames - frame duality - reproducing pairs - partial inner product spaces
We start by recalling the essential features of frames, both discrete and continuous, with some emphasis on the notion of frame duality. Then we turn to generalizations, namely upper and lower semi-frames, and their duality. Next we consider arbitrary measurable maps and examine the standard operators, analysis, synthesis and frame operators, and study their properties. Finally we analyze the recent notion of reproducing pairs. In view of their ...

42C15 ; 42C40 ; 46C50 ; 65T60

Multi angle  New hints from the reward system
Apicella, Paul (Auteur de la Conférence) ; Loewenstein, Yonatan (Auteur de la Conférence) | CIRM (Editeur )

Start the video and click on the track button in the timeline to move to talk 1, 2 and to the discussion.

- Talk 1: Paul Apicella - Striatal dopamine and acetylcholine mechanisms involved in reward-related learning

The midbrain dopamine system has been identified as a major component of motivation and reward processing. One of its main targets is the striatum which plays an important role in motor control and learning functions. Other subcortical neurons work in parallel with dopamine neurons. In particular, striatal cholinergic interneurons participate in signaling the reward-related significance of stimuli and they may act in concert with dopamine to encode prediction error signals and control the learning of stimulus­response associations. Recent studies have revealed functional cooperativity between these two neuromodulatory systems of a complexity far greater than previously appreciated. In this talk I will review the difference and similarities between dopamine and acetylcholine reward-signaling systems, the possible nature of reward representation in each system, and discuss the involvement of striatal dopamine-acetylcholine interactions during leaning and behavior.

- Talk 2: Yonatan Loewenstein - Modeling operant learning: from synaptic plasticity to behavior

- Discussion with Paul Apicella and Yonatan Loewenstein
Start the video and click on the track button in the timeline to move to talk 1, 2 and to the discussion.

- Talk 1: Paul Apicella - Striatal dopamine and acetylcholine mechanisms involved in reward-related learning

The midbrain dopamine system has been identified as a major component of motivation and reward processing. One of its main targets is the striatum which plays an important role in motor control and learning functions. Other ...

68T05 ; 68Uxx ; 92B20 ; 92C20 ; 92C40

To illustrate specifically quantum behaviours, the talk will consider three typical problems for non-linear kinetic models evolving through pair collisions at temperatures not far from absolute zero. Based on those examples, a number of differences between quantum and classical Boltzmann theory is discussed in more general term.

82D50 ; 76Y05 ; 82D30 ; 35Q60 ; 35Q55

Breast cancer is the most common type of cancer among women and despite recent advances in the medical field, there are still some inherent limitations in the currently used screening techniques. The radiological interpretation of X-ray mammograms often leads to over-diagnosis and, as a consequence, to unnecessary traumatic and painful biopsies. First we use the 1D Wavelet Transform Modulus Maxima (WTMM) method to reveal changes in skin temperature dynamics of women breasts with and without malignant tumor. We show that the statistics of temperature temporal fluctuations about the cardiogenic and vasomotor perfusion oscillations do not change across time-scales for cancerous breasts as the signature of homogeneous monofractal fluctuations. This contrasts with the continuous change of temperature fluctuation statistics observed for healthy breasts as the hallmark of complex multifractal scaling. When using the 2D WTMM method to analyze the roughness fluctuations of X-ray mammograms, we reveal some drastic loss of roughness spatial correlations that likely results from some deep architectural change in the microenvironment of a breast tumor. This local breast disorganisation may deeply affect heat transfer and related thermomechanics in the breast tissue and in turn explain the loss of multifractal complexity of temperature temporal fluctuations previously observed in mammary glands with malignant tumor. These promising findings could lead to the future use of combined wavelet-based multifractal processing of dynamic IR thermograms and X-ray mammograms to help identifying women with high risk of breast cancer prior to more traumatic examinations. Besides potential clinical impact, these results shed a new light on physiological changes that may precede anatomical alterations in breast cancer development.

Keywords: breast cancer - X-ray mammography - infrared thermography - multifractal analysis - wavelet transform - wavelet transform modulus maxima method
Breast cancer is the most common type of cancer among women and despite recent advances in the medical field, there are still some inherent limitations in the currently used screening techniques. The radiological interpretation of X-ray mammograms often leads to over-diagnosis and, as a consequence, to unnecessary traumatic and painful biopsies. First we use the 1D Wavelet Transform Modulus Maxima (WTMM) method to reveal changes in skin ...

92-08 ; 92C50 ; 92C55

Multi angle  Présentation de la "Journée Formation"
Arnoux, Pierre (Auteur de la Conférence) ; Bourgeois, Gérald (Auteur de la Conférence) | CIRM (Editeur )

La Commission française pour l'enseignement des mathématiques (CFEM) et ses composantes ont décidé d'organiser, en clôture de la semaine nationale des mathématiques, les 20-21-22 mars 2015, un forum intitulé "Mathématiques vivantes, de l'école au monde". Le forum a pris la forme d'un réseau d'évènements, à Paris, Lyon et Marseille. Le dimanche s'est tenue au CIRM une journée pour les enseignants, avec un public de 80 personnes. Une présentation des différentes interventions et de la Société mathématique de France (SMF) introduisent cette journée. La Commission française pour l'enseignement des mathématiques (CFEM) et ses composantes ont décidé d'organiser, en clôture de la semaine nationale des mathématiques, les 20-21-22 mars 2015, un forum intitulé "Mathématiques vivantes, de l'école au monde". Le forum a pris la forme d'un réseau d'évènements, à Paris, Lyon et Marseille. Le dimanche s'est tenue au CIRM une journée pour les enseignants, avec un public de 80 personnes. Une présentation ...

00A05 ; 00A09

The concept of a "transseries" is a natural extension of that of a Laurent series, allowing for exponential and logarithmic terms. Transseries were introduced in the 1980s by the analyst Écalle and also, independently, by the logicians Dahn and Göring. The germs of many naturally occurring real-valued functions of one variable have asymptotic expansions which are transseries. Since the late 1990s, van den Dries, van der Hoeven, and myself, have pursued a program to understand the algebraic and model-theoretic aspects of this intricate but fascinating mathematical object. A differential analogue of "henselianity" is central to this program. Last year we were able to make a significant step forward, and established a quantifier elimination theorem for the differential field of transseries in a natural language. My goal for this talk is to introduce transseries without prior knowledge of the subject, and to explain our recent work. The concept of a "transseries" is a natural extension of that of a Laurent series, allowing for exponential and logarithmic terms. Transseries were introduced in the 1980s by the analyst Écalle and also, independently, by the logicians Dahn and Göring. The germs of many naturally occurring real-valued functions of one variable have asymptotic expansions which are transseries. Since the late 1990s, van den Dries, van der Hoeven, and myself, have ...

03C10 ; 03C64 ; 26A12

Subshifts of finite type are of high interest from a computational point of view, since they can be described by a finite amount of information - a set of forbidden patterns that defines the subshift - and thus decidability and algorithmic questions can be addressed. Given an SFT $X$, the simplest question one can formulate is the following: does $X$ contain a configuration? This is the so-called domino problem, or emptiness problem: for a given finitely presented group $0$, is there an algorithm that determines if the group $G$ is tilable with a finite set of tiles? In this lecture I will start with a presentation of two different proofs of the undecidability of the domino problem on $Z^2$. Then we will discuss the case of finitely generated groups. Finally, the emptiness problem for general subshifts will be tackled. Subshifts of finite type are of high interest from a computational point of view, since they can be described by a finite amount of information - a set of forbidden patterns that defines the subshift - and thus decidability and algorithmic questions can be addressed. Given an SFT $X$, the simplest question one can formulate is the following: does $X$ contain a configuration? This is the so-called domino problem, or emptiness problem: for a given ...

68Q45 ; 03B25 ; 37B50

Energy investment into maturation encompasses any expenses linked to tissue differentiation, i.e. re-organization of body structure during development. This is different from growth which can be conceptualized as synthesis of more of the same. Energy invested into growth is fixed into the biomass of the organism (with some overheads), but energy invested in maturation is oxidized as metabolic work making it more difficult to quantify in practice. Nonetheless it can be quantified and it can even represent a substantial part of the energy budget of living organisms. In this talk I will give an overview of different studies where investment in maturity was quantified. The focus will be on 4 different types of organisms: cnidarians, ctenophores, teleost fish and frogs. I will further discuss what type of eco-physiological effects might be expected when an organism modifies its investment into these processes. Some intriguing literature studies will be presented which can be re-interpreted in perhaps unexpected ways when investment into maturation is taken into account. This raises the question of just how important and how flexible such costs might actually be. Maturity can be used as a quantifier for internal time. Seven criteria were proposed which should be respected by any such metric: (1) independent of morphology, (2) independent of body size, (3) depend on one a priori homologous event, (4) unaffected by changes in temperature, (5) similar between closely related species, (6) increase with clock time, and (7) physically quantifiable (Reiss 1989). We showed that the maturity concept of Dynamic Energy Budget theory complies with all those criteria and on the basis of this information and the studies presented above I will finish by discussing the potential role of maturity in shaping metabolic flexibility. Energy investment into maturation encompasses any expenses linked to tissue differentiation, i.e. re-organization of body structure during development. This is different from growth which can be conceptualized as synthesis of more of the same. Energy invested into growth is fixed into the biomass of the organism (with some overheads), but energy invested in maturation is oxidized as metabolic work making it more difficult to quantify in ...

92D25 ; 92D40 ; 92C30

Multi angle  Correspondants Mathrice
Azema, Laurent (Auteur de la Conférence) | CIRM (Editeur )

Les missions des correspondants Mathrice pour l'agenda, l'annuaire...

68U35

Many machine learning and signal processing problems are traditionally cast as convex optimization problems. A common difficulty in solving these problems is the size of the data, where there are many observations ("large n") and each of these is large ("large p"). In this setting, online algorithms such as stochastic gradient descent which pass over the data only once, are usually preferred over batch algorithms, which require multiple passes over the data. Given n observations/iterations, the optimal convergence rates of these algorithms are $O(1/\sqrt{n})$ for general convex functions and reaches $O(1/n)$ for strongly-convex functions. In this tutorial, I will first present the classical results in stochastic approximation and relate them to classical optimization and statistics results. I will then show how the smoothness of loss functions may be used to design novel algorithms with improved behavior, both in theory and practice: in the ideal infinite-data setting, an efficient novel Newton-based stochastic approximation algorithm leads to a convergence rate of $O(1/n)$ without strong convexity assumptions, while in the practical finite-data setting, an appropriate combination of batch and online algorithms leads to unexpected behaviors, such as a linear convergence rate for strongly convex problems, with an iteration cost similar to stochastic gradient descent. Many machine learning and signal processing problems are traditionally cast as convex optimization problems. A common difficulty in solving these problems is the size of the data, where there are many observations ("large n") and each of these is large ("large p"). In this setting, online algorithms such as stochastic gradient descent which pass over the data only once, are usually preferred over batch algorithms, which require multiple passes ...

62L20 ; 68T05 ; 90C06 ; 90C25

Many machine learning and signal processing problems are traditionally cast as convex optimization problems. A common difficulty in solving these problems is the size of the data, where there are many observations ("large n") and each of these is large ("large p"). In this setting, online algorithms such as stochastic gradient descent which pass over the data only once, are usually preferred over batch algorithms, which require multiple passes over the data. Given n observations/iterations, the optimal convergence rates of these algorithms are $O(1/\sqrt{n})$ for general convex functions and reaches $O(1/n)$ for strongly-convex functions. In this tutorial, I will first present the classical results in stochastic approximation and relate them to classical optimization and statistics results. I will then show how the smoothness of loss functions may be used to design novel algorithms with improved behavior, both in theory and practice: in the ideal infinite-data setting, an efficient novel Newton-based stochastic approximation algorithm leads to a convergence rate of $O(1/n)$ without strong convexity assumptions, while in the practical finite-data setting, an appropriate combination of batch and online algorithms leads to unexpected behaviors, such as a linear convergence rate for strongly convex problems, with an iteration cost similar to stochastic gradient descent. Many machine learning and signal processing problems are traditionally cast as convex optimization problems. A common difficulty in solving these problems is the size of the data, where there are many observations ("large n") and each of these is large ("large p"). In this setting, online algorithms such as stochastic gradient descent which pass over the data only once, are usually preferred over batch algorithms, which require multiple passes ...

62L20 ; 68T05 ; 90C06 ; 90C25

A quantum phase transition is commonly referred to as a point in a family of gapped Hamiltonians where the spectral gap closes. In the absence of a general perturbation theory for quantum spin systems in the thermodynamic limit, I will discuss necessary, and sufficient, conditions for a transition, and present explicit constructions of paths of uniformly gapped Hamiltonians in one dimension.

Z