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This thesis aims to expose several applications of artificial intelligence (AI) for medical data processing and understanding. Medical imaging is a domain generating massive data, which thus requires more and more time for clinicians to process and analyze them. In this manuscript, we show how generative learning can help in many aspects of the processing, understanding, and modeling of CT images of the inner ear. First, we develop a deep generative model to solve a commonly encountered problem in CT imaging: the presence of metal artifacts. This model may allow clinicians to better assess the quality of cochlea implant (CI) positioning with a reduced presence of artifacts. To this end, a generative adversarial neural network (GAN) framework equipped with a specially designed loss function is proposed. That network was trained on a synthetic CT volume dataset resulting from the application of X-ray physics simulations. Second, since many deep learning segmentation methods fail to cope with explicit shape representations, we propose a Bayesian generative framework that addresses the issues of shape model inference in 3D images. We focus on the balance between shape and appearance through an Expectation-Maximisation (EM) approach. The method is applied to the segmentation of more than 200 patient CT volumes. The results show performances that are comparable to supervised methods and better than previously proposed unsupervised ones. Besides, we show how the proposed framework can estimate the uncertainty in the shape parameters. Third, we tackle the issue of the compact representation of CT images through a novel flow-based deep generative network. Generative models can create an implicit distribution of the imaging dataset from which one can generate samples. For a better representation, we proposed a Quasi-symplectic Langevin Variational Autoencoder (Langevin-VAE) that improves the current gradients, flow-based generative models. Finally, we propose an online framework for medical landmarks detection that can cope with the difficulty to manually position landmarks in volumetric images. The one shot training framework includes an offline step that only requires a single annotated image for training and is applied to the annotation of hundreds of images.; Cette thèse vise à exposer plusieurs applications de l'intelligence artificielle (IA) pour le traitement et la compréhension des données médicales. L'imagerie médicale est un domaine générant des données massives, qui nécessitent donc de plus en plus de temps aux cliniciens pour être traitées et analysées. Dans ce manuscrit, nous montrons comment l'apprentissage génératif peut aider dans de nombreux aspects pour le traitement, la compréhension et la modélisation des images scanner de l'oreille interne. Tout d'abord, nous développons un modèle génératif profond pour résoudre un problème couramment rencontré en imagerie CT : la présence d'artefacts métalliques. Ce modèle peut permettre aux cliniciens de mieux évaluer la qualité du positionnement des électrodes d'un implant cochléaire avec une présence réduite d'artefacts. Pour cela, un réseau de neurones antagoniste et génératif (GAN) est proposé intégrant une fonction de perte spécifique. Ce réseau a été entrainé sur un ensemble d'images volumiques scanner synthétiques résultant de l'application de simulations de la physique des rayons X. Deuxièmement, étant donné que de nombreuses méthodes de segmentation d'apprentissage profond ne parviennent pas à gérer explicitement les modèles de forme, nous proposons un cadre génératif bayésien qui aborde les problèmes d'inférence de modèle de forme dans les images médicales 3D. Notre approche permet de faire un compromis entre les informations de forme et d'apparence issus de l'image à travers une approche d'espérance-maximisation (EM). Celle-ci est appliquée à la segmentation de plus de 200 volumes tomodensitométriques de patients. Les résultats indiquent des performances comparables aux méthodes supervisées et meilleures que les méthodes non supervisées proposées précédemment. En outre, nous montrons comment ce cadre méthodologique proposé peut estimer l'incertitude dans les paramètres de forme. Troisièmement, nous abordons le problème de la représentation compacte des images scanner à travers un nouveau réseau génératif profond basé sur les flux. Les modèles génératifs peuvent créer une distribution implicite de l'ensemble de données d'imagerie à partir duquel on peut générer des échantillons. Pour une meilleure représentation, nous avons proposé un Auto-encodeur Variationnel Quasi-symplectique avec une dynamique de Langevin (Langevin-VAE) qui améliore les gradients actuels des modèles génératifs basés sur les flux. Enfin, nous proposons une méthode pour la détection de points caractéristiques qui permet de s'affranchir de la difficulté de positionner manuellement ces points dans des images volumiques. Cette approche comprend une étape préalable d'apprentissage ne nécessitant qu'une seule image annotée pour l'entrainement. Elle est appliquée à l'annotation de centaines d'images scanner de l'oreille interne.

Orientador: Paulo Regis Caron Ruffino Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica Resumo: Neste trabalho tratamos de dois aspectos relativos à fluxos estocásticos em folheações. Na primeira parte tratamos da decomposição de um fluxo f(t,.)=h(t,v(t,.)) em uma variedade diferenciável com duas folheações transversais entre si (M,H, V) de modo que h(t,.) preserva as folhas de H e v(t,.) preserva as folhas de V. Nesta parte estudamos como certas propriedades topológicas das folheações, tais como interseções de folhas e atingibilidade, influenciam na decomposição. Por fim mostramos que quando H é transversalmente orientável, um fluxo é decomponível se e somente se preserva esta orientação. Como aplicação deste resultado obtemos uma condição suficiente para que o fluxo de uma e.d.e. de Stratonovich seja decomponível. Na segunda parte obtemos uma medida \nu definida em subvariedades de M transversais à H a qual é invariante pelo fluxo f(t,.) gerado por uma equação de Stratonovich. Posteriormente estudamos recorrência destes fluxos em relação à topologia gerada por abertos H-saturados Abstract: This work approaches two problems concerning flows in foliated manifolds. The first part deals with the decomposition of a flow f(t,.) =h(t,v(t,.)) in a bifoliated differentiable manifold (M, H, V), where h(t,.) preserves the leaves of H and v(t,.) preserves V. In this part we study the way topological features, such as attainability and intersection of leaves, influence the decomposition. Finally, we present a complete description of decomposability in terms of the topology of the foliations by proving that when H is transversaly orientable f(t,.) is decomposable if and only if it preserves the transversal orientation. Afterwards we give a sufficient condition for the flow of an Stratonovich s.d.e to be decomposable. In the second part we provide an invariant measure on submanifolds of M that are transversal to H, and we use it to study recurrence Doutorado Matemática Doutor em Matemática CNPQ 142084/2012-3 CAPES

We have studied the efficiency of organization of transfer trains at developed railroad junctions based on the criterion of total hours of railroad wagon downtime under accumulation. We have constructed discrete-event simulation models (Java SE, AnyLogic) of the organization of transfer trains in line with a "rigid schedule" and under accumulation to the standard for trains. The models take into consideration the stochastic nature of wagon arrivals to the accumulation points and meeting the established norm for the mass of trains. It is considered at modeling that track development of railroad stations and intranodal passages is rational and does not significantly affect delay in the motion of transfer trains. The transfer trains schedule is rational and rhythmic. The throughput capacity of open tracks at a node and the processing capability of subsystems at railroad stations are sufficient. We have experimentally compared the efficiency of four models of the organization of transfer trains, including a "flexible model", which combines dispatch upon accumulation to the standard of a train and a "rigid schedule" at the same time. It was established that the minimal hours of wagon accumulation are achieved when transfer trains are organized via a combined variant: a simultaneous dispatch in line with a "rigid schedule" and at accumulation to the standard. Organization of transfer trains in line with a "rigid schedule" requires the organization of additional trains, otherwise there is an increase in the queue of wagons at accumulation points. When increasing the number of daily trains by 10‒11 %, the process of forming and dispatching becomes sufficiently reliable and efficient. The specified recommendations would make it possible to improve the typical process of operation of railroad junctions in terms of dispatcher control over the formation, dispatch, and passing of transfer trains during intranodal traffic

Monocrystalline, cast aluminium microwires of diameter (D) below 25 mu m free of micromilling artefacts are annealed under protective atmosphere. Annealing increases the flow stress of all tested microwires, by an amount that is found, in a Haasen plot of measured activation area values, to be an athermal contribution to the flow stress that is attributed to surface oxide layer thickening. Microwires oriented for single slip with D similar to 14 mu m behave as do as-cast microwires with D similar to 7 mu m, showing a transition to higher and more stochastic flow stress values; this effect is attributed to a greater scarcity of dislocation sources after annealing. (C) 2018 Acta Materialia Inc. Published by Elsevier Ltd.

In a stochastic-flow network with budget constraint, the network reliability for level (d, b), i.e., R(d,b), where d is a given demand value and b is a budget limit, is the probability of transmitt...

We consider the following stochastic partial differential equation, $$\begin{array}{@{}rcl@{}} &&dY_{t} = L^{\ast} Y_{t} dt + A^{\ast} Y_{t} \cdot dB_{t}\\ &&Y_{0} = \psi, \end{array} $$ associated with a stochastic flow {X(t,x)}, for t ≥ 0, $x \in \mathbb {R}^{d}$ , as in Rajeev and Thangavelu (Potential Anal. 28(2), 139–162, 2008). We show that the strong solutions constructed there are ‘locally of compact support’. Using this notion,we define the mild solutions of the above equation and show the equivalence between strong and mild solutions in the multi Hilbertian space $\mathscr{S}^{\prime }$ . We show uniqueness of solutions in the case when ψ is smooth via the ‘monotonicity inequality’ for (L∗,A∗), which is a known criterion for uniqueness.

In this paper, we give a probabilistic interpretation of Sobolev solutions to parabolic semilinear McKean–Vlasov partial differential equations (PDEs for short) in terms of mean-field backward stochastic differential equations (BSDEs for short). This probabilistic interpretation can be viewed as a generalization of the Feynman–Kac formula. The method is based on the stochastic flow technique which is different from classical stochastic differential equations (SDEs for short) due to the influence of mean-field term in McKean–Vlasov SDEs.

The applicability of differential equations to description of integer values dynamics in bio-informatics is investigated. It is shown that a differential model may be interpreted as a continuous analogue of a stochastic flow. The method of construction of a quasi-Poisson flow on the base of multi-dimension differential equations is proposed. Mathematical correctness of the algorithm is proven. The system has been studied by a computer simulation and a discrete nature of processes has been taken into account. The proposed schema has been applied to the classical Volterra's models, which are widely used for description of biological systems. It has been demonstrated that although behaviour of discrete and continuous models is similar, some essential qualitative and quantitative differences in their dynamics take place.

Sufficient conditions as well as necessary and sufficient ones are found for the completeness of the stochastic flow generated by equations with the so-called current velocities (Nelson's symmetric...

This paper contains a list of corrections to the paper ‘ Solutions of SPDEs associated with a stochastic flow’.

The paper is devoted to the modeling of a single-phase flow through saturated porous media. A statistical approach where permeability is considered as a lognormal random field is applied. The impact of permeability, random boundary conditions and wells pressure on the flow in a production well is studied. A numerical procedure to generate an ensemble of realizations of the numerical solution of the problem is developed. A global sensitivity analysis is performed using Sobol indices. The impact of different model parameters on the total model uncertainty is studied.

The method of characteristics is a powerful tool to solve some nonlinear second order stochastic PDEs like those satisfied by a consistent dynamic utilities, see [EM13, MM20]. In this situation the solution V (t, z) is theoretically of the formX t V (0,ξ t (z)) whereX and Y are solutions of a system of two SDEs,ξ is the inverse flow ofȲ and V (0, .) is the initial condition. Unfortunately this representation is not explicit except in simple cases whereX andȲ are solutions of linear equations. The objective of this work is to take advantage of this representation to establish a numerical scheme approximating the solution V using Euler approximations X N and ξ N of X and ξ. This allows us to avoid a complicated discretizations in time and space of the SPDE for which it seems really difficult to obtain error estimates. We place ourselves in the framework of SDEs driven by Lévy noise and we establish at first a strong convergence result, in L p-norms, of the compound approximation X N t (Y N t (z)) to the compound variable X t (Y t (z)), in terms of the approximations of X and Y which are solutions of two SDEs with jumps. We then apply this result to Utility-SPDEs of HJB type after inverting monotonic stochastic flows.

A network with multi-state arcs or nodes is commonly called a multi-state network. In the real world, the system reliability of a multi-state network can vary over time. Hence, a critical issue emerges to characterize the time attribute in a stochastic flow network. To solve this issue, this study bridges conventional reliability theory and the reliability of multi-state network. This study utilizes exponential distribution as a possible reliability function to quantify the time attribute in a multi-state network. First, the reliability of every single component is modeled by exponential distribution, where such components comprise a multi-state element. Once the time constraint is given, the capacity probability distribution of arcs can be derived. Second, an algorithm to generate minimal capacity vectors for given demand is provided. Finally, the system reliability can be calculated in terms of the derived capacity probability distribution and the generated minimal capacity vectors. A maintenance issue is further discussed according to the result of system reliability.

For stochastic flow network (SFN), given all the lower (or upper) boundary points, the classic problem is to calculate the probability that the capacity vectors are greater than or equal to the lower boundary points (less than or equal to the upper boundary points). However, in some practical cases, SFN reliability would be evaluated between the lower and upper boundary points at the same time. The evaluation of SFN reliability with upper and lower boundary points at the same time is the focus of this paper. Because of intricate relationships among upper and lower boundary points, a decomposition approach is developed to obtain several simplified subsets. SFN reliability is calculated according to these subsets by means of the inclusion-exclusion principle. Two heuristic options are then established in order to calculate SFN reliability in an efficient direction based on the lower and upper boundary points.

Industry 4.0 is widely accepted in manufacturing industry since it guides a novel and promising production paradigm. A new characteristic in Industry 4.0-based manufacturing systems is that the applications of advanced intelligent machines which have communication, self-optimization and self-training behaviors. Based on this new change, this study investigates a flow-shop scheduling problem under the consideration of multiple objectives, time-dependent processing time and uncertainty. A mixed integer programming model is formulated for this problem, and a fireworks algorithm is developed where some special strategies are designed, e.g., explosion sparks procedure and selection solution procedure. Simulation experiments on a set of test problems are carried out, and the experimental results demonstrate that the model and proposed algorithm can achieve a satisfactory performance by comparing with three state-of-the-art multi-objective optimization algorithms.

In the case of an existing limited capacity of the system called required system capacity, in this study a new method is presented to determine the disjoint paths to send data from the source to the sink. System reliability is evaluated as the probability that a specified amount of data can be transmitted from a source to a sink through two disjoint paths, subject to a time threshold and a required capacity. In addition, we study the effect of using the proposed method on the reliability evaluation in comparison with other previous methods.

We study the dynamic transition of the Swift-Hohenberg equation (SHE) when linear multiplicative noise acting on a finite set of modes of the dominant linear flow is introduced. Existence of a stochastic flow and a local stochastic invariant manifold for this stochastic form of SHE are both addressed in this work. We show that the approximate reduced system corresponding to the invariant manifold undergoes a stochastic pitchfork bifurcation, and obtain numerical evidence suggesting that this picture is a good approximation for the full system as well.

Formation of rational delivery routes is the main way to increase the effectiveness of client services for freight forwarding companies. The main part of the requests for transport services comes from occasional (non-constant) clients. The set of those requests forms a stochastic flow. For stochastic requests flow, the delivery routes are formed in the process of the requests receipt. Therefore, the standard approaches for merging of requests from multiple clients into routes, based on linear programming techniques, cannot be used in such conditions. An algorithm of formation under the stochastic demand conditions of such delivery routes, which allow servicing of two or more shippers, is proposed in the paper. The author has developed a specialized software to support decisions made by dispatchers of forwarding companies.

In this paper, we will try to study the same result proved in \cite{10}. So, on the same model and with some assumptions, we will study the property of homeomorphism of the stochastic flow generated by the natural model in a one-dimensional case and with some modifications, based on an important theory of Hiroshi Kunita. This is the main motivation of our research.

In this paper we investigate the regularity properties of strong solutions to SDEs driven by L\'evy processes with irregular drift coefficients. Under some mild conditions, we show that the singular SDE has a unique strong solution for each starting point and the family of all the solutions forms a stochastic flow. Moreover, the Malliavin differentiability of the strong solutions is also obtained. As an application, we also prove a path-by-path uniqueness result for some related random ODEs., Comment: 28 pages

This paper evaluates the standard empirical methods employed in the study of foreign aid, when the data generating process is a calibrated stochastic growth model in which aid recipients make optimal investment and consumption decisions. When recipients receive a stochastic flow of aid and wish to smooth consumption, standard methods fail to distinguish between the response to transient and permanent aid shocks, and hence yield misleading results concerning the object of interest to policy makers: the long-run impact of aid.