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Mathematics in Science and Technology   | enregistrements trouvés : 71

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Lecture 1. Collective dynamics and self-organization in biological systems : challenges and some examples.

Lecture 2. The Vicsek model as a paradigm for self-organization : from particles to fluid via kinetic descriptions

Lecture 3. Phase transitions in the Vicsek model : mathematical analyses in the kinetic framework.

35L60 ; 82C22 ; 82B26 ; 82C26 ; 92D50

Inspired by modeling in neurosciences, we here discuss the well-posedness of a networked integrate-and-fire model describing an infinite population of companies which interact with one another through their common statistical distribution. The interaction is of the self-excitatory type as, at any time, the debt of a company increases when some of the others default: precisely, the loss it receives is proportional to the instantaneous proportion of companies that default at the same time. From a mathematical point of view, the coefficient of proportionality, denoted by a, is of great importance as the resulting system is known to blow-up when a takes large values, a blow-up meaning that a macroscopic proportion of companies may default at the same time. In the current talk, we focus on the complementary regime and prove that existence and uniqueness hold in arbitrary time without any blow-up when the excitatory parameter is small enough. Inspired by modeling in neurosciences, we here discuss the well-posedness of a networked integrate-and-fire model describing an infinite population of companies which interact with one another through their common statistical distribution. The interaction is of the self-excitatory type as, at any time, the debt of a company increases when some of the others default: precisely, the loss it receives is proportional to the instantaneous proportion ...

35K60 ; 82C31 ; 92B20

The aim is to describe the distribution of immune status in an age-structured population on the basis of a within-host sub-model [1] for continuous waning and occasional boosting. Inspired by both Feller's fundamental work [2] and the more recent delay equation formulation of physiologically structured populations [3,4], we derive, for a given force of infection, a linear renewal equation that can be solved by successive approximation, i.e., by generation expansion (with the generation number corresponding to the number of times an individual became infected).
In joint work in progress with Wilfred de Graaf, Peter Teunis and Mirjam Kretzschmar we want to use either the generation expansion or an invariant/stable distribution as the starting point for the efficient computation of coarse statistics.
The aim is to describe the distribution of immune status in an age-structured population on the basis of a within-host sub-model [1] for continuous waning and occasional boosting. Inspired by both Feller's fundamental work [2] and the more recent delay equation formulation of physiologically structured populations [3,4], we derive, for a given force of infection, a linear renewal equation that can be solved by successive approximation, i.e., by ...

92D30 ; 60J75 ; 45D05

Motivated by the spectrogram (or short-time Fourier transform) basic principles of linear algebra are explained, preparing for the more general case of Gabor frames in time-frequency analysis. The importance of the singular value decomposition and the four spaces associated with a matrix is pointed out, and based on this the pseudo-inverse (leading later to the dual Gabor frame) and the Loewdin (symmetric) orthogonalization are explained.

15-XX ; 41-XX ; 42-XX ; 46-XX

Post-edited  Le problème Graph Motif - Partie 1
Fertin, Guillaume (Auteur de la Conférence) | CIRM (Editeur )

Le problème Graph Motif est défini comme suit : étant donné un graphe sommet colorié G=(V,E) et un multi-ensemble M de couleurs, déterminer s'il existe une occurrence de M dans G, c'est-à-dire un sous ensemble V' de V tel que
(1) le multi-ensemble des couleurs de V' correspond à M,
(2) le sous-graphe G' induit par V' est connexe.
Ce problème a été introduit, il y a un peu plus de 10 ans, dans le but de rechercher des motifs fonctionnels dans des réseaux biologiques, comme par exemple des réseaux d'interaction de protéines ou des réseaux métaboliques. Graph Motif a fait depuis l'objet d'une attention particulière qui se traduit par un nombre relativement élevé de publications, essentiellement orientées autour de sa complexité algorithmique.
Je présenterai un certain nombre de résultats algorithmiques concernant le problème Graph Motif, en particulier des résultats de FPT (Fixed-Parameter Tractability), ainsi que des bornes inférieures de complexité algorithmique.
Ceci m'amènera à détailler diverses techniques de preuves dont certaines sont plutôt originales, et qui seront je l'espère d'intérêt pour le public.
Le problème Graph Motif est défini comme suit : étant donné un graphe sommet colorié G=(V,E) et un multi-ensemble M de couleurs, déterminer s'il existe une occurrence de M dans G, c'est-à-dire un sous ensemble V' de V tel que
(1) le multi-ensemble des couleurs de V' correspond à M,
(2) le sous-graphe G' induit par V' est connexe.
Ce problème a été introduit, il y a un peu plus de 10 ans, dans le but de rechercher des motifs fonctionnels dans des ...

05C15 ; 05C85 ; 05C90 ; 68Q17 ; 68Q25 ; 68R10 ; 92C42 ; 92D20

Le principe de décision en démocratie consiste à produire, de l'expression des opinions individuelles, un consensus. Il existe de multiples procédures pour passer des unes à l'autre variant suivant les pays, les jurys... Le Président n'est pas élu de la même façon en France, aux USA ou en Irlande. Quelles seraient les procédures qui répondraient à des critères "raisonnables" de qualité ?
Des mathématiciens se sont intéressés à ce type de questions. Du paradoxe de Condorcet au théorème de Black en passant par le théorème de Arrow, leurs réponses sont parfois déconcertantes.
Le principe de décision en démocratie consiste à produire, de l'expression des opinions individuelles, un consensus. Il existe de multiples procédures pour passer des unes à l'autre variant suivant les pays, les jurys... Le Président n'est pas élu de la même façon en France, aux USA ou en Irlande. Quelles seraient les procédures qui répondraient à des critères "raisonnables" de qualité ?
Des mathématiciens se sont intéressés à ce type de ...

91B12 ; 91B08 ; 91B14 ; 91F10

In this international farewell address about 35 years of research on Dynamic energy Budget theory, I review the ontogeny of the theory, and discuss background, motivation, start, milestones and outlook from a personal perspective. The effort is framed as a case study in Theoretical Biology.

A popular line of research in evolutionary biology is to use time-calibrated phylogenies in order to infer the underlying diversification process. This involves the use of stochastic models of ultrametric trees, i.e., trees whose tips lie at the same distance from the root. We recast some well-known models of ultrametric trees (infinite regular trees, exchangeable coalescents, coalescent point processes) in the framework of so-called comb metric spaces and give some applications of coalescent point processes to the phylogeny of bird species.

However, these models of diversification assume that species are exchangeable particles, and this always leads to the same (Yule) tree shape in distribution. Here, we propose a non-exchangeable, individual-based, point mutation model of diversification, where interspecific pairwise competition is only felt from the part of individuals belonging to younger species. As the initial (meta)population size grows to infinity, the properly rescaled dynamics of species lineages converge to a one-parameter family of coalescent trees interpolating between the caterpillar tree and the Kingman coalescent.

Keywords: ultrametric tree, inference, phylogenetic tree, phylogeny, birth-death process, population dynamics, evolution
A popular line of research in evolutionary biology is to use time-calibrated phylogenies in order to infer the underlying diversification process. This involves the use of stochastic models of ultrametric trees, i.e., trees whose tips lie at the same distance from the root. We recast some well-known models of ultrametric trees (infinite regular trees, exchangeable coalescents, coalescent point processes) in the framework of so-called comb metric ...

60J80 ; 60J85 ; 92D15 ; 92D25 ; 54E45 ; 54E70

Mathematical modeling and numerical mathematics of today is very much Lagrangian and modern automated modeling techniques lead to differential-algebraic systems. The optimal control for such systems in general cannot be obtained using the classical Euler-Lagrange approach or the maximum principle, but it is shown how this approach can be extended.
differential-algebraic equations - optimal control - Lagrangian subspace - necessary optimality conditions - Hamiltonian system - symplectic flow
Mathematical modeling and numerical mathematics of today is very much Lagrangian and modern automated modeling techniques lead to differential-algebraic systems. The optimal control for such systems in general cannot be obtained using the classical Euler-Lagrange approach or the maximum principle, but it is shown how this approach can be extended.
differential-algebraic equations - optimal control - Lagrangian subspace - necessary optimality ...

93C05 ; 93C15 ; 49K15 ; 34H05

In this talk, we investigate in a unified way the structural properties of a large class of convex regularizers for linear inverse problems. These penalty functionals are crucial to force the regularized solution to conform to some notion of simplicity/low complexity. Classical priors of this kind includes sparsity, piecewise regularity and low-rank. These are natural assumptions for many applications, ranging from medical imaging to machine learning.
imaging - image processing - sparsity - convex optimization - inverse problem - super-resolution
In this talk, we investigate in a unified way the structural properties of a large class of convex regularizers for linear inverse problems. These penalty functionals are crucial to force the regularized solution to conform to some notion of simplicity/low complexity. Classical priors of this kind includes sparsity, piecewise regularity and low-rank. These are natural assumptions for many applications, ranging from medical imaging to machine ...

62H35 ; 65D18 ; 94A08 ; 68U10 ; 90C31 ; 80M50 ; 47N10

In this talk, I will focus on a Fokker-Planck equation modeling interacting neurons in a network where each neuron is governed by an Integrate and Fire dynamic type. When the network is excitatory, neurons that discharge, instantaneously increased the membrane potential of the neurons of the network with a speed which is proportional to the amplitude of the global activity of the network. The self-excitable nature of these neurons in the case of excitatory networks leads to phenomena of blow-up, once the proportion of neurons that are close to their action potential is too high. In this talk, we are interested in understanding the regimes where solutions globally exist. By new methods of entropy and upper-solution, we give criteria where the phenomena of blow-up can not appear and specify, in some cases, the asymptotic behavior of the solution.

integrate-and-fire - neural networks - Fokker-Planck equation - blow-up
In this talk, I will focus on a Fokker-Planck equation modeling interacting neurons in a network where each neuron is governed by an Integrate and Fire dynamic type. When the network is excitatory, neurons that discharge, instantaneously increased the membrane potential of the neurons of the network with a speed which is proportional to the amplitude of the global activity of the network. The self-excitable nature of these neurons in the case of ...

92B20 ; 82C32 ; 35Q84

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 )

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

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

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

Quel rapport entre la forme d'un chou-fleur des côtes de Bretagne, des vaisseaux sanguins et les structures fractales ?
Quel rapport entre une maladie génétique et un fichier de musique mp3 ?
Quel rapport entre des dessins faits par Léonard de Vinci et les lois mathématiques gouvernant la forme des plantes ou la reproduction des lapins ?
Quel rapport entre la forme de la terre, le GPS de ma voiture et un vieux puits d'Egypte ?
Pourquoi les météorologues sont capables de prédire une hausse du niveau des océans dans 100 ans mais incapables de prévoir s'il va pleuvoir dans 15 jours ?
Quel rapport entre le cerveau humain et le cerveau d'un ordinateur ?
Nous répondrons à toutes ces questions via des mathématiques simples et élégantes, accessibles à tous.
Quel rapport entre la forme d'un chou-fleur des côtes de Bretagne, des vaisseaux sanguins et les structures fractales ?
Quel rapport entre une maladie génétique et un fichier de musique mp3 ?
Quel rapport entre des dessins faits par Léonard de Vinci et les lois mathématiques gouvernant la forme des plantes ou la reproduction des lapins ?
Quel rapport entre la forme de la terre, le GPS de ma voiture et un vieux puits d'Egypte ?
Pourquoi les ...

00A06 ; 00A08 ; 68-XX ; 92-XX

Il sera exposé divers exemples de modélisation en médecine (biologie du cancer, pharmacologie, imagerie fonctionnelle) pouvant donner lieu à des activités pédagogiques reposant de manières essentielles sur l'utilisation de l'informatique.

92C50 ; 65C20

Il sera exposé divers exemples de modélisation en médecine (biologie du cancer, pharmacologie, imagerie fonctionnelle) pouvant donner lieu à des activités pédagogiques reposant de manières essentielles sur l'utilisation de l'informatique.

92C50 ; 65C20

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