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Izydorczyk, Lucas. "Probabilistic backward McKean numerical methods for PDEs and one application to energy management". Electronic Thesis or Diss., Institut polytechnique de Paris, 2021. http://www.theses.fr/2021IPPAE008.
Pełny tekst źródłaThis thesis concerns McKean Stochastic Differential Equations (SDEs) to representpossibly non-linear Partial Differential Equations (PDEs). Those depend not onlyon the time and position of a given particle, but also on its probability law. In particular, we treat the unusual case of Fokker-Planck type PDEs with prescribed final data. We discuss existence and uniqueness for those equations and provide a probabilistic representation in the form of McKean type equation, whose unique solution corresponds to the time-reversal dynamics of a diffusion process.We introduce the notion of fully backward representation of a semilinear PDE: thatconsists in fact in the coupling of a classical Backward SDE with an underlying processevolving backwardly in time. We also discuss an application to the representationof Hamilton-Jacobi-Bellman Equation (HJB) in stochastic control. Based on this, we propose a Monte-Carlo algorithm to solve some control problems which has advantages in terms of computational efficiency and memory whencompared to traditional forward-backward approaches. We apply this method in the context of demand side management problems occurring in power systems. Finally, we survey the use of generalized McKean SDEs to represent non-linear and non-conservative extensions of Fokker-Planck type PDEs
Sabbagh, Wissal. "Some Contributions on Probabilistic Interpretation For Nonlinear Stochastic PDEs". Thesis, Le Mans, 2014. http://www.theses.fr/2014LEMA1019/document.
Pełny tekst źródłaThe objective of this thesis is to study the probabilistic representation (Feynman-Kac for- mula) of different classes ofStochastic Nonlinear PDEs (semilinear, fully nonlinear, reflected in a domain) by means of backward doubly stochastic differential equations (BDSDEs). This thesis contains four different parts. We deal in the first part with the second order BDS- DEs (2BDSDEs). We show the existence and uniqueness of solutions of 2BDSDEs using quasi sure stochastic control technics. The main motivation of this study is the probabilistic representation for solution of fully nonlinear SPDEs. First, under regularity assumptions on the coefficients, we give a Feynman-Kac formula for classical solution of fully nonlinear SPDEs and we generalize the work of Soner, Touzi and Zhang (2010-2012) for deterministic fully nonlinear PDE. Then, under weaker assumptions on the coefficients, we prove the probabilistic representation for stochastic viscosity solution of fully nonlinear SPDEs. In the second part, we study the Sobolev solution of obstacle problem for partial integro-differentialequations (PIDEs). Specifically, we show the Feynman-Kac formula for PIDEs via reflected backward stochastic differentialequations with jumps (BSDEs). Specifically, we establish the existence and uniqueness of the solution of the obstacle problem, which is regarded as a pair consisting of the solution and the measure of reflection. The approach is based on stochastic flow technics developed in Bally and Matoussi (2001) but the proofs are more technical. In the third part, we discuss the existence and uniqueness for RBDSDEs in a convex domain D without any regularity condition on the boundary. In addition, using the approach based on the technics of stochastic flow we provide the probabilistic interpretation of Sobolev solution of a class of reflected SPDEs in a convex domain via RBDSDEs. Finally, we are interested in the numerical solution of BDSDEs with random terminal time. The main motivation is to give a probabilistic representation of Sobolev solution of semilinear SPDEs with Dirichlet null condition. In this part, we study the strong approximation of this class of BDSDEs when the random terminal time is the first exit time of an SDE from a cylindrical domain. Thus, we give bounds for the discrete-time approximation error.. We conclude this part with numerical tests showing that this approach is effective
Tan, Xiaolu. "Stochastic control methods for optimal transportation and probabilistic numerical schemes for PDEs". Palaiseau, Ecole polytechnique, 2011. https://theses.hal.science/docs/00/66/10/86/PDF/These_TanXiaolu.pdf.
Pełny tekst źródłaThis thesis deals with the numerical methods for a fully nonlinear degenerate parabolic partial differential equations (PDEs), and for a controlled nonlinear PDEs problem which results from a mass transportation problem. The manuscript is divided into four parts. In a first part of the thesis, we are interested in the necessary and sufficient condition of the monotonicity of finite difference thêta-scheme for a one-dimensional diffusion equations. An explicit formula is given in case of the heat equation, which is weaker than the classical Courant-Friedrichs-Lewy (CFL) condition. In a second part, we consider a fully nonlinear degenerate parabolic PDE and propose a splitting scheme for its numerical resolution. The splitting scheme combines a probabilistic scheme and the semi-Lagrangian scheme, and in total, it can be viewed as a Monte-Carlo scheme for PDEs. We provide a convergence result as well as a rate of convergence. In the third part of the thesis, we study an optimal mass transportation problem. The mass is transported by the controlled drift-diffusion dynamics, and the associated cost depends on the trajectories, the drift as well as the diffusion coefficient of the dynamics. We prove a strong duality result for the transportation problem, thus extending the Kantorovich duality to our context. The dual formulation maximizes a value function on the space of all bounded continuous functions, and every value function corresponding to a bounded continuous function is the solution to a stochastic control problem. In the Markovian cases, we prove the dynamic programming principle of the optimal control problems, and we propose a gradient-projection algorithm for the numerical resolution of the dual problem, and provide a convergence result. Finally, in a fourth part, we continue to develop the dual approach of mass transportation problem with its applications in the computation of the model-independent no-arbitrage price bound of the variance option in a vanilla-liquid market. After a first analytic approximation, we propose a gradient-projection algorithm to approximate the bound as well as the corresponding static strategy in vanilla options
Helmkay, Owen. "Information representation, problem format, and mental algorithms in probabilistic reasoning". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/NQ66153.pdf.
Pełny tekst źródłaTarrago, Pierre. "Non-commutative generalization of some probabilistic results from representation theory". Thesis, Paris Est, 2015. http://www.theses.fr/2015PESC1123/document.
Pełny tekst źródłaThe subject of this thesis is the non-commutative generalization of some probabilistic results that occur in representation theory. The results of the thesis are divided into three different parts. In the first part of the thesis, we classify all unitary easy quantum groups whose intertwiner spaces are described by non-crossing partitions, and develop the Weingarten calculus on these quantum groups. As an application of the previous work, we recover the results of Diaconis and Shahshahani on the unitary group and extend those results to the free unitary group. In the second part of the thesis, we study the free wreath product. First, we study the free wreath product with the free symmetric group by giving a description of the intertwiner spaces: several probabilistic results are deduced from this description. Then, we relate the intertwiner spaces of a free wreath product with the free product of planar algebras, an object which has been defined by Bisch and Jones. This relation allows us to prove the conjecture of Banica and Bichon. In the last part of the thesis, we prove that the minimal and the Martin boundaries of a graph introduced by Gnedin and Olshanski are the same. In order to prove this, we give some precise estimates on the uniform standard filling of a large ribbon Young diagram. This yields several asymptotic results on the filling of large ribbon Young diagrams
Ugail, Hassan, i Eyad Elyan. "Efficient 3D data representation for biometric applications". IOS Press, 2007. http://hdl.handle.net/10454/2683.
Pełny tekst źródłaAn important issue in many of today's biometric applications is the development of efficient and accurate techniques for representing related 3D data. Such data is often available through the process of digitization of complex geometric objects which are of importance to biometric applications. For example, in the area of 3D face recognition a digital point cloud of data corresponding to a given face is usually provided by a 3D digital scanner. For efficient data storage and for identification/authentication in a timely fashion such data requires to be represented using a few parameters or variables which are meaningful. Here we show how mathematical techniques based on Partial Differential Equations (PDEs) can be utilized to represent complex 3D data where the data can be parameterized in an efficient way. For example, in the case of a 3D face we show how it can be represented using PDEs whereby a handful of key facial parameters can be identified for efficient storage and verification.
Shen, Amelia H. (Amelia Huimin). "Probabilistic representation and manipulation of Boolean functions using free Boolean diagrams". Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/34087.
Pełny tekst źródłaIncludes bibliographical references (p. 145-149).
by Amelia Huimin Shen.
Ph.D.
Ugail, Hassan, i S. Kirmani. "Shape reconstruction using partial differential equations". World Scientific and Engineering Academy and Society (WSEAS), 2006. http://hdl.handle.net/10454/2645.
Pełny tekst źródłaVasudevan, Shrihari. "Spatial cognition for mobile robots : a hierarchical probabilistic concept-oriented representation of space". Zürich : ETH, 2008. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=17612.
Pełny tekst źródłaLloyd, James Robert. "Representation, learning, description and criticism of probabilistic models with applications to networks, functions and relational data". Thesis, University of Cambridge, 2015. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.709264.
Pełny tekst źródłaLavis, Benjamin Mark Mechanical & Manufacturing Engineering Faculty of Engineering UNSW. "Spatially reconfigurable and non-parametric representation of dynamic bayesian beliefs". Publisher:University of New South Wales. Mechanical & Manufacturing Engineering, 2008. http://handle.unsw.edu.au/1959.4/41468.
Pełny tekst źródłaGeilke, Michael [Verfasser]. "Online density estimates : a probabilistic condensed representation of data for knowledge discovery / Michael Geilke". Mainz : Universitätsbibliothek Mainz, 2017. http://d-nb.info/1147611165/34.
Pełny tekst źródłaZanitti, Gaston Ezequiel. "Development of a probabilistic domain-specific language for brain connectivity including heterogeneous knowledge representation". Electronic Thesis or Diss., université Paris-Saclay, 2023. http://www.theses.fr/2023UPASG022.
Pełny tekst źródłaResearchers in neuroscience have a growing number of datasets available to study the brain, which is made possible by recent technological advances. Given the extent to which the brain has been studied, there is also available ontological knowledge encoding the current state of the art regarding its different areas, activation patterns, keywords associated with studies, etc. Furthermore, there is inherent uncertainty associated with brain scans arising from the mapping between voxels -3D pixels- and actual points in different individual brains. Unfortunately, there is currently no unifying framework for accessing such collections of rich heterogeneous data under uncertainty, making it necessary for researchers to rely on ad hoc tools. In this work we introduce NeuroLang, a probabilistic language based on first-order logic with existential rules, probabilistic uncertainty, ontologies integration under the open world assumption, and built-in mechanisms to guarantee tractable query answering over very large datasets. We propose that NeuroLang provides a substantial improvement to cognitive neuroscience research through the expressive power of its query language. We can leverage the ability of NeuroLang to seamlessly integrate useful heterogeneous data, such as ontologies and probabilistic brain atlases, to map fine-grained cognitive domains to brain regions through a set of formal criteria, promoting shareable and highly reproducible research on the domains of brain function. We believe that NeuroLang is well suited for leading computational approaches to formalize large-scale neuroscience research through probabilistic first-order logic programming
Tarrago, Pierre [Verfasser], i Roland [Akademischer Betreuer] Speicher. "Non-commutative generalization of some probabilistic results from representation theory / Pierre Tarrago. Betreuer: Roland Speicher". Saarbrücken : Saarländische Universitäts- und Landesbibliothek, 2015. http://d-nb.info/1079840249/34.
Pełny tekst źródłaNayak, Sunita. "Representation and learning for sign language recognition". [Tampa, Fla] : University of South Florida, 2008. http://purl.fcla.edu/usf/dc/et/SFE0002362.
Pełny tekst źródłaEl-Shaer, Mennat Allah. "An Experimental Evaluation of Probabilistic Deep Networks for Real-time Traffic Scene Representation using Graphical Processing Units". The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1546539166677894.
Pełny tekst źródłaParaschos, Alexandros [Verfasser], Jan [Akademischer Betreuer] Peters, Gerhard [Akademischer Betreuer] Neumann i Sylvain [Akademischer Betreuer] Calinon. "Robot Skill Representation, Learning and Control with Probabilistic Movement Primitives / Alexandros Paraschos ; Jan Peters, Gerhard Neumann, Sylvain Calinon". Darmstadt : Universitäts- und Landesbibliothek Darmstadt, 2017. http://d-nb.info/1147968381/34.
Pełny tekst źródłaElyan, Eyad, i Hassan Ugail. "Reconstruction of 3D human facial images using partial differential equations". Academy Publisher, 2007. http://hdl.handle.net/10454/2644.
Pełny tekst źródłaOgul, Hasan. "Computational Representation Of Protein Sequences For Homology Detection And Classification". Phd thesis, METU, 2006. http://etd.lib.metu.edu.tr/upload/12606997/index.pdf.
Pełny tekst źródłas knowledge, the accuracy achieved by PredLOC is the highest one ever reported on those datasets. The maximal unique match method is resulted with only a slight improvement in solvent accessibility predictions.
Fodjo, Eric. "Algorithms for the resolution of stochastic control problems in high dimension by using probabilistic and max-plus methods". Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLX034/document.
Pełny tekst źródłaStochastic optimal control problems with finite horizon are a class of optimal control problems where intervene stochastic processes in a bounded time. As many optimal control problems, they are often solved using a dynamic programming approach which results in a second order Partial Differential Equation (PDE) called the Hamilton-Jacobi-Bellman equation. Grid-based methods, probabilistic methods or more recently max-plus methods can be used then to solve this PDE. However, the first type of methods default in a space of high dimension because of the curse of dimensionality while the second type of methods allowed till now to solve only problems where the nonlinearity of the PDE with respect to the second order derivatives is not very high. As for the third type of method, it results in an explosion of the complexity of the value function. We introduce two new probabilistic schemes in order to enlarge the class of problems that can be solved with probabilistic methods. One is adapted to PDE with bounded coefficients while the other can be applied to PDE with bounded or unbounded coefficients. We prove the convergence of the two probabilistic scheme and obtain error estimates in the case of a PDE with bounded coefficients. We also give some results about the behavior of the second probabilistic scheme in the case of a PDE with unbounded coefficients. After that, we introduce a completely new type of method to solve stochastic optimal control problems with finite horizon that we call the max-plus probabilistic method. It allows to add the non linearity feature of max-plus methods to a probabilistic method while controlling the complexity of the value function. An application to the computation of the optimal super replication price of an option in an uncertain correlation model is given in a 5 dimensional space
Ramos, Fabio Tozeto. "Recognising, Representing and Mapping Natural Features in Unstructured Environments". Australian Centre for Field Robotics, Department of Aerospace, Mechanical and Mechatronic Engineering, 2008. http://hdl.handle.net/2123/2322.
Pełny tekst źródłaThis thesis addresses the problem of building statistical models for multi-sensor perception in unstructured outdoor environments. The perception problem is divided into three distinct tasks: recognition, representation and association. Recognition is cast as a statistical classification problem where inputs are images or a combination of images and ranging information. Given the complexity and variability of natural environments, this thesis investigates the use of Bayesian statistics and supervised dimensionality reduction to incorporate prior information and fuse sensory data. A compact probabilistic representation of natural objects is essential for many problems in field robotics. This thesis presents techniques for combining non-linear dimensionality reduction with parametric learning through Expectation Maximisation to build general representations of natural features. Once created these models need to be rapidly processed to account for incoming information. To this end, techniques for efficient probabilistic inference are proposed. The robustness of localisation and mapping algorithms is directly related to reliable data association. Conventional algorithms employ only geometric information which can become inconsistent for large trajectories. A new data association algorithm incorporating visual and geometric information is proposed to improve the reliability of this task. The method uses a compact probabilistic representation of objects to fuse visual and geometric information for the association decision. The main contributions of this thesis are: 1) a stochastic representation of objects through non-linear dimensionality reduction; 2) a landmark recognition system using a visual and ranging sensors; 3) a data association algorithm combining appearance and position properties; 4) a real-time algorithm for detection and segmentation of natural objects from few training images and 5) a real-time place recognition system combining dimensionality reduction and Bayesian learning. The theoretical contributions of this thesis are demonstrated with a series of experiments in unstructured environments. In particular, the combination of recognition, representation and association algorithms is applied to the Simultaneous Localisation and Mapping problem (SLAM) to close large loops in outdoor trajectories, proving the benefits of the proposed methodology.
Ramos, Fabio Tozeto. "Recognising, Representing and Mapping Natural Features in Unstructured Environments". Thesis, The University of Sydney, 2007. http://hdl.handle.net/2123/2322.
Pełny tekst źródłaGARBARINO, DAVIDE. "Acknowledging the structured nature of real-world data with graphs embeddings and probabilistic inference methods". Doctoral thesis, Università degli studi di Genova, 2022. http://hdl.handle.net/11567/1092453.
Pełny tekst źródłaSchustek, Philipp. "Probabilistic models for human judgments about uncertainty in intuitive inference tasks". Doctoral thesis, Universitat Pompeu Fabra, 2018. http://hdl.handle.net/10803/586057.
Pełny tekst źródłaUn pilar fundamental de la racionalidad es actualizar las creencias con la finalidad de mantener la coherencia con la evidencia observacional. Esto implica cumplir con principios probabilísticos, los cuales reconocen que las observaciones del mundo real son consistentes con varias interpretaciones posibles. Este estudio presenta dos novedosas pruebas experimentales, así como análisis computacionales, de cómo participantes humanos cuantifican la incertidumbre en tareas de inferencia perceptiva. Sus respuestas conductuales muestran patrones no triviales de inferencia probabilística, tales como la actualización de creencias basadas en la confiabilidad sobre las representaciones jerárquicas del estado del entorno. A pesar de los sesgos característicos de generalización, el comportamiento no puede ser correctamente explicado con descripciones heurísticas alternativas. Estos resultados sugieren que la incertidumbre es una parte integral de nuestras inferencias y que efectivamente tenemos el potencial para recurrir a mecanismos de inferencia racional, los cuales adhieren a principios probabilísticos. Además, dichos resultados son compatibles con la idea de que representaciones de incertidumbre internas son ubicuas, lo cual presuponen teorías generales como Bayesian hierarchical modeling y predictive coding.
Stenson, Matthew P. "Analysis of higher order terms in the Gram-Charlier type a representation of equivalent load used in probabilistic simulation of electric power systems". Ohio University / OhioLINK, 1987. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1183062589.
Pełny tekst źródłaChrastansky, Alena [Verfasser], i Hans Von [Akademischer Betreuer] Storch. "Multi-decadal reconstruction and probabilistic representation of weather-related variability in North Sea coast chronic oil pollution / Alena Chrastansky. Betreuer: Hans von Storch". Hamburg : Staats- und Universitätsbibliothek Hamburg, 2011. http://d-nb.info/102042236X/34.
Pełny tekst źródłaNyga, Daniel [Verfasser], Michael [Akademischer Betreuer] [Gutachter] Beetz i Anthony G. [Gutachter] Cohn. "Interpretation of Natural-language Robot Instructions: Probabilistic Knowledge Representation, Learning, and Reasoning / Daniel Nyga ; Gutachter: Michael Beetz, Anthony G. Cohn ; Betreuer: Michael Beetz". Bremen : Staats- und Universitätsbibliothek Bremen, 2017. http://d-nb.info/1132756944/34.
Pełny tekst źródłaLee, Wooyoung. "Learning Statistical Features of Scene Images". Research Showcase @ CMU, 2014. http://repository.cmu.edu/dissertations/540.
Pełny tekst źródłaYan, Chang. "Neural Representation of Working Memory Contents at Different Levels of Abstraction". Doctoral thesis, Humboldt-Universität zu Berlin, 2020. http://dx.doi.org/10.18452/22232.
Pełny tekst źródłaResearch on the neural basis of working memory (WM) has received broad attention but has focused on storage of sensory content. Evidence on short-term maintenance of abstract verbal or categorical information is scarce. This thesis aims to investigate neural representation of WM content at different levels of abstraction. I present here three empirical studies that employed fMRI, multivariate pattern analysis or probabilistic modeling as major methods. The first study identified cortical regions that retained WM content of a script. Native Chinese speakers were asked to memorize well-known Chinese characters which strongly facilitated verbal coding. Results indicated left lateralized language-related brain areas as candidate stores for verbal content. The second and the third studies aimed to test the hypothesis that color is memorized as a combination of the low-level visual representation and the abstract categorical representation. The second study utilized a conventional sensory encoding model and a novel empirical-based categorical encoding model to characterize two sources of neural representations. Color information was decoded in three color-related ROIs: V1, V4, VO1, and notably, an elevation in categorical representation was observed in more anterior cortices. In the third study, the delayed behavioral response was examined, which exhibited a systematic bias pattern; a probabilistic dual-content model was implemented, which produced response patterns highly correlated with experimental results; this confirmed the hypothesis of dual-content mnemonic representations. These studies together suggest a division of labor along the rostral-caudal axis of the brain, based on the abstraction level of memorized contents.
Silvestre, André Meyer. "Raciocínio probabilístico aplicado ao diagnóstico de insuficiência cardíaca congestiva (ICC)". reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2003. http://hdl.handle.net/10183/12679.
Pełny tekst źródłaBayesian networks (BN) constitute an adequate computational model to make probabilistic inference in domains that involve uncertainty. Medical diagnostic reasoning may be characterized as an act of probabilistic inference in an uncertain domain, where diagnostic hypotheses elaboration is represented by the stratification of diseases according to the related probabilities. The present dissertation researches the methodology used in the construction/validation of Bayesian Networks related to the medical field, and makes use of this knowledge for the development of a probabilistic network to aid in the diagnosis of Heart Failure (HF). This BN, implemented as part of the SEAMED/AMPLIA System, would engage in the role of alerting for early diagnosis and treatment of HF, which could provide faster and more efficient healthcare of patients carrying this pathology.
Jain, Dominik [Verfasser], Michael [Akademischer Betreuer] Beetz i Marc [Akademischer Betreuer] Toussaint. "Probabilistic Cognition for Technical Systems : Statistical Relational Models for High-Level Knowledge Representation, Learning and Reasoning / Dominik Jain. Gutachter: Michael Beetz ; Marc Toussaint. Betreuer: Michael Beetz". München : Universitätsbibliothek der TU München, 2012. http://d-nb.info/1031076190/34.
Pełny tekst źródłaShan, Yin Information Technology & Electrical Engineering Australian Defence Force Academy UNSW. "Program distribution estimation with grammar models". Awarded by:University of New South Wales - Australian Defence Force Academy. School of Information Technology and Electrical Engineering, 2005. http://handle.unsw.edu.au/1959.4/38737.
Pełny tekst źródłaMoraes, Carlos Afonso Silveira. "Registros de Representação Semiótica: Contribuições para o letramento probabilístico no 9º ano do Ensino Fundamental". Universidade Federal de São Carlos, 2017. https://repositorio.ufscar.br/handle/ufscar/9234.
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This research had the objective of describing and analyzing a teaching-learning concept of Probability in two classes of the ninth elementary school, in a municipal public school in Salto de Pirapora, in the interior of the State of São Paulo. The acquisition of probabilistic language in learning concept of probability was a motivating factor for the research project. The theoretical contributions of this research involved the records of semiotic representation by Raymond Duval and the literary probabilistic in the perspective of Iddo Gal. The guiding question of the research was: "How are records of semiotic representation mobilized and coordinated in tasks involving the context probabilistic? "A field work was elaborated with activities involving classical and frequentist probability, counting and statistics and a didactic sequence using experiments sample space, probability of simple events, events composites, bar graphs, relative frequency, frequency distribution and the tree diagram. As a teacher-researcher, the production of information originated from activities developed by students in the form of written protocols, in addition to audio records of dialogues that occurred in the correction of activities and records in the logbook. The results of the analysis of the empirical material of the research revealed that the students used different registers of semiotic representation in the resolution of tasks. The mobilization and coordination of these registers support the development of students' probabilistic literacy. Like this work was derived from the analysis of a pedagogical practice, it is expected there are contributions to the teaching practice in content involving combinatorial, statistical and probability for elementary school.
Esta pesquisa teve por objetivo descrever e analisar um cenário de ensinoaprendizagem do conceito de Probabilidade em duas classes do nono ano do Ensino Fundamental, em uma escola pública da rede municipal de ensino do município de Salto de Pirapora, interior do Estado de São Paulo. A aquisição da linguagem probabilística na aprendizagem de conceitos relativos à probabilidade foi um elemento motivador para o projeto de pesquisa. Os aportes teóricos dessa pesquisa envolveu os registros de representação semiótica por Raymond Duval e o letramento probabilístico na perspectiva de Iddo Gal. A questão orientadora da investigação foi: “Como os registros de representação semiótica são mobilizados e coordenados em tarefas envolvendo o contexto probabilístico?” Foi elaborado um trabalho de campo com atividades envolvendo a probabilidade clássica e frequentista, processos de contagem e estatística e uma sequência didática que utiliza experimentos aleatórios, espaço amostral, probabilidade de eventos simples, eventos compostos, gráficos de barra, frequência relativa, tabela de distribuição de frequência e o diagrama da árvore. Na condição de professor-pesquisador, a produção de informações foi oriunda de atividades desenvolvidas pelos alunos na forma de protocolos escritos, além de registros em áudio de diálogos ocorridos na correção das atividades e registros elaborados no diário de bordo. Os resultados da análise do material empírico da pesquisa revelaram nessa pesquisa de que os alunos utilizaram diferentes registros de representação semiótica na resolução das tarefas. A mobilização e coordenação desses registros favoreceram o desenvolvimento do letramento probabilístico dos alunos. Como este trabalho foi oriundo da análise de uma prática pedagógica, espera-se que haja contribuições para a prática docente em conteúdos envolvendo combinatória, estatística e probabilidade para o Ensino Fundamental.
Tomasevic, Milica. "Sur une interprétation probabiliste des équations de Keller-Segel de type parabolique-parabolique". Thesis, Université Côte d'Azur (ComUE), 2018. http://www.theses.fr/2018AZUR4097/document.
Pełny tekst źródłaThe standard d-dimensional parabolic--parabolic Keller--Segel model for chemotaxis describes the time evolution of the density of a cell population and of the concentration of a chemical attractant. This thesis is devoted to the study of the parabolic--parabolic Keller-Segel equations using probabilistic methods. To this aim, we give rise to a non linear stochastic differential equation of McKean-Vlasov type whose drift involves all the past of one dimensional time marginal distributions of the process in a singular way. These marginal distributions coupled with a suitable transformation of them are our probabilistic interpretation of a solution to the Keller Segel model. In terms of approximations by particle systems, an interesting and, to the best of our knowledge, new and challenging difficulty arises: each particle interacts with all the past of the other ones by means of a highly singular space-time kernel. In the one-dimensional case, we prove that the parabolic-parabolic Keller-Segel system in the whole Euclidean space and the corresponding McKean-Vlasov stochastic differential equation are well-posed in well chosen space of solutions for any values of the parameters of the model. Then, we prove the well-posedness of the corresponding singularly interacting and non-Markovian stochastic particle system. Furthermore, we establish its propagation of chaos towards a unique mean-field limit whose time marginal distributions solve the one-dimensional parabolic-parabolic Keller-Segel model. In the two-dimensional case there exists a possibility of a blow-up in finite time for the Keller-Segel system if some parameters of the model are large. Indeed, we prove the well-posedness of the mean field limit under some constraints on the parameters and initial datum. Under these constraints, we prove the well-posedness of the Keller-Segel model in the plane. To obtain this result, we combine PDE analysis and stochastic analysis techniques. Finally, we propose a fully probabilistic numerical method for approximating the two-dimensional Keller-Segel model and survey our main numerical results
Spiegel, Christoph. "Additive structures and randomness in combinatorics". Doctoral thesis, Universitat Politècnica de Catalunya, 2020. http://hdl.handle.net/10803/669327.
Pełny tekst źródłaLa combinatòria aritmètica, la teoria combinatòria dels nombres, la teoria additiva estructural i la teoria additiva de nombres són alguns dels termes que es fan servir per descriure una branca extensa i activa que es troba en la intersecció de la teoria de nombres i de la combinatòria, i que serà el motiu d'aquesta tesi doctoral. La primera part tracta la qüestió de sota quines circumstàncies es solen produir solucions a sistemes lineals d’equacions arbitràries en estructures additives. Una primera pregunta que s'estudia es refereix al punt en que conjunts d’una mida determinada contindran normalment una solució. Establirem un llindar i estudiarem també la distribució del nombre de solucions en aquest llindar, tot demostrant que en certs casos aquesta distribució convergeix a una distribució de Poisson. El següent tema de la tesis es relaciona amb el teorema de Van der Waerden, que afirma que cada coloració finita dels nombres enters conté una progressió aritmètica monocromàtica de longitud arbitrària. Aquest es considera el primer resultat en la teoria de Ramsey. Rado va generalitzar el resultat de van der Waerden tot caracteritzant en aquells sistemes lineals les solucions de les quals satisfan una propietat similar i Szemerédi la va reforçar amb una versió de densitat del resultat. Centrarem la nostra atenció cap a versions del teorema de Rado i Szemerédi en conjunts aleatoris, ampliant els treballs anteriors de Friedgut, Rödl, Rucinski i Schacht i de Conlon, Gowers i Schacht. Per últim, Chvátal i Erdos van suggerir estudiar estudiar jocs posicionals del tipus Maker-Breaker. Aquests jocs tenen una connexió profunda amb la teoria de les estructures aleatòries i ens basarem en el treball de Bednarska i Luczak per establir el llindar de la quantitat que necessitem per analitzar una gran varietat de jocs en favor del segon jugador. S'inclouen jocs en què el primer jugador vol ocupar una solució d'un sistema lineal d'equacions donat, generalitzant els jocs de van der Waerden introduïts per Beck. La segona part de la tesis tracta sobre el comportament extrem dels conjunts amb propietats additives interessants. Primer, considerarem els conjunts de Sidon, és a dir, conjunts d’enters amb diferències úniques quan es consideren parelles d'elements. Estudiarem una generalització dels conjunts de Sidons proposats recentment per Kohayakawa, Lee, Moreira i Rödl, en que les diferències entre parelles no són només diferents, sinó que, en realitat, estan allunyades una certa proporció en relació a l'element més gran. Obtindrem límits més baixos per a conjunts infinits que els obtinguts pels anteriors autors tot usant una construcció de conjunts de Sidon infinits deguda a Cilleruelo. Com a conseqüència d'aquests límits, obtindrem també el millor límit inferior actual per als conjunts de Sidon en conjunts infinits generats aleatòriament de nombres enters d'alta densitat. A continuació, un dels resultats centrals a la intersecció de la combinatòria i la teoria dels nombres és el teorema de Freiman-Ruzsa, que afirma que el conjunt suma d'un conjunt finit d’enters donats pot ser cobert de manera eficient per una progressió aritmètica generalitzada. En el cas de que el conjunt suma sigui de mida petita, existeixen descripcions estructurals més precises. Primer estudiarem els resultats que van més enllà del conegut teorema de Freiman 3k-4 en els enters. Llavors veurem una aplicació d’aquests resultats a conjunts de dobles petits en grups cíclics finits. Finalment, dirigirem l’atenció cap a conjunts amb funcions de representació gairebé constants. Erdos i Fuchs van establir que les funcions de representació de conjunts arbitraris d’enters no poden estar massa a prop de ser constants. Primer estendrem el resultat d’Erdos i Fuchs a funcions de representació ordenades. A continuació, abordarem una pregunta relacionada de Sárközy i Sós sobre funció de representació ponderada.
Nyman, Peter. "On relations between classical and quantum theories of information and probability". Doctoral thesis, Linnéuniversitetet, Institutionen för datavetenskap, fysik och matematik, DFM, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-13830.
Pełny tekst źródłaAliakbari, khoei Mina. "Une approche computationnelle de la dépendance au mouvement du codage de la position dans la système visuel". Thesis, Aix-Marseille, 2014. http://www.theses.fr/2014AIXM4041/document.
Pełny tekst źródłaCoding the position of moving objects is an essential ability of the visual system in fulfilling precise and robust tracking tasks. This thesis is focalized upon this question: How does the visual system efficiently encode the position of moving objects, despite various sources of uncertainty? This study deploys the hypothesis that the visual systems uses prior knowledge on the temporal coherency of motion (Burgi et al 2000; Yuille and Grzywacz 1989). We implemented this prior by extending the modeling framework previously proposed to explain the aperture problem (Perrinet and Masson, 2012), so-called motion-based prediction (MBP). This model is a Bayesian motion estimation framework implemented by particle filtering. Based on that, we have introduced a theory on motion-based position coding, to investigate how neural mechanisms encoding the instantaneous position of moving objects might be affected by motion. Results of this thesis suggest that motion-based position coding might be a generic neural computation among all stages of the visual system. This mechanism might partially compensate the accumulative and restrictive effects of neural delays in position coding. Also it may account for motion-based position shifts as the flash lag effect. As a specific case, results of diagonal MBP model reproduced the anticipatory response of neural populations in the primary visual cortex of macaque monkey. Our results imply that an efficient and robust position coding might be highly dependent on trajectory integration and that it constitutes a key neural signature to study the more general problem of predictive coding in sensory areas
Le, cavil Anthony. "Représentation probabiliste de type progressif d'EDP nonlinéaires nonconservatives et algorithmes particulaires". Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLY023.
Pełny tekst źródłaThis thesis performs forward probabilistic representations of nonlinear and nonconservative Partial Differential Equations (PDEs), which allowto numerically estimate the corresponding solutions via an interacting particle system algorithm, mixing Monte-Carlo methods and non-parametric density estimates.In the literature, McKean typeNonlinear Stochastic Differential Equations (NLSDEs) constitute the microscopic modelof a class of PDEs which are conservative. The solution of a NLSDEis generally a couple $(Y,u)$ where $Y$ is a stochastic process solving a stochastic differential equation whose coefficients depend on $u$ and at each time $t$, $u(t,cdot)$ is the law density of the random variable $Y_t$.The main idea of this thesis is to consider this time a non-conservative PDE which is the result of a conservative PDE perturbed by a term of the type $Lambda(u, nabla u) u$. In this case, the solution of the corresponding NLSDE is again a couple $(Y,u)$, where again $Y$ is a stochastic processbut where the link between the function $u$ and $Y$ is more complicated and once fixed the law of $Y$, $u$ is determined by a fixed pointargument via an innovating Feynmann-Kac type formula
Le, cavil Anthony. "Représentation probabiliste de type progressif d'EDP nonlinéaires nonconservatives et algorithmes particulaires". Electronic Thesis or Diss., Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLY023.
Pełny tekst źródłaThis thesis performs forward probabilistic representations of nonlinear and nonconservative Partial Differential Equations (PDEs), which allowto numerically estimate the corresponding solutions via an interacting particle system algorithm, mixing Monte-Carlo methods and non-parametric density estimates.In the literature, McKean typeNonlinear Stochastic Differential Equations (NLSDEs) constitute the microscopic modelof a class of PDEs which are conservative. The solution of a NLSDEis generally a couple (Y,u) where Y is a stochastic process solving a stochastic differential equation whose coefficients depend on u and at each time t, u(t,.) is the law density of the random variable Yt.The main idea of this thesis is to consider this time a non-conservative PDE which is the result of a conservative PDE perturbed by a term of the type Lambda(u, nabla u) u. In this case, the solution of the corresponding NLSDE is again a couple (Y,u), where again Y is a stochastic processbut where the link between the function u and Y is more complicated and once fixed the law of Y, u is determined by a fixed pointargument via an innovating Feynmann-Kac type formula
Chen, Sih-Huei, i 陳思卉. "Probabilistic Latent Variable Model for Learning Data Representation". Thesis, 2017. http://ndltd.ncl.edu.tw/handle/4xt8z4.
Pełny tekst źródła國立中央大學
資訊工程學系
106
Probabilistic framework has emerged as a powerful technique for representation learning. This dissertation proposes probabilistic latent variable model-based representation learning methods that involve both discrete and continuous latent spaces. For a discrete latent space, a hierarchical representation that is based on the Gaussian hierarchical latent Dirichlet allocation (G-hLDA) is proposed for capturing the latent characteristics of low-level features. Representation is learned by constructing an infinitely deep and branching tree-structured mixture model, which effectively models the subtle differences among classes. For a continuous latent space, a novel complex-valued latent variable model, named the complex-valued Gaussian process latent variable model (CGPLVM), is developed for discovering a compressed complex-valued representation of complex-valued data. The key concept of CGPLVM is that complex-valued data is approximated by a low-dimensional complex-valued latent representation through a function that is drawn from a complex Gaussian process. Additionally, we attempt to preserve both global and local data structures while promoting discrimination. A new objective function that incorporates a locality-preserving and a discriminative term for complex-valued data is presented. Then, a deep collaborative learning framework that is based on a variational autoencoder (VAE) and a Gaussian process (GP) is proposed to represent multimedia data with greater discriminative power than previously achieved. A Gaussian process classifier is incorporated into the VAE to guide a VAE-based representation, which distinguishes variations of data among classes and achieves the dual goals of reconstruction and classification. The developed methods are evaluated using multimedia data. The experimental results demonstrate the superior performances of the proposed methods, especially for situations with only a small number of training data.
Cheuk, Adrian Y. W. "Stochastic simulation in dynamic probabilistic networks using compact representation". Thesis, 1996. http://hdl.handle.net/2429/6018.
Pełny tekst źródłaWong, Alexander. "Probabilistic complex phase representation objective function for multimodal image registration". Thesis, 2010. http://hdl.handle.net/10012/5326.
Pełny tekst źródłaParaschos, Alexandros. "Robot Skill Representation, Learning and Control with Probabilistic Movement Primitives". Phd thesis, 2017. http://tuprints.ulb.tu-darmstadt.de/6947/1/root.pdf.
Pełny tekst źródłaAhmat, Norhayati, Hassan Ugail i Castro Gabriela Gonzalez. "Modelling the Mechanical Behaviour of a Pharmaceutical Tablet Using PDEs". 2012. http://hdl.handle.net/10454/5428.
Pełny tekst źródłaDetailed design of pharmaceutical tablets is essential nowadays in order to produce robust tablets with tailor-made properties. Compressibility and compactibility are the main compaction properties involved in the design and development of solid dosage forms. The data obtained from measured forces and displacements of the punch are normally analysed using the Heckel model to assess the mechanical behaviour of pharmaceutical powders. In this paper, we present a technique for shape modelling of pharmaceutical tablets based on the PDE method. We extended the formulation of the PDE method to a higher dimensional space in order to generate a solid tablet and a cuboid mesh is created to represent the tablet¿s components. We also modelled the displacement components of a compressed PDE- based representation of a tablet by utilising the solution of the axisymmetric boundary value problem for a finite cylinder subject to a uniform axial load. The experimental data and the results obtained from the developed model are shown in Heckel plots and a good agreement is found between both.
Available in full text since 5th Feb 2013 following the publisher's embargo period.
"Reasoning and Learning with Probabilistic Answer Set Programming". Doctoral diss., 2019. http://hdl.handle.net/2286/R.I.53736.
Pełny tekst źródłaDissertation/Thesis
Doctoral Dissertation Computer Science 2019
Lian, Wenzhao. "Modeling Time Series and Sequences: Learning Representations and Making Predictions". Diss., 2015. http://hdl.handle.net/10161/11362.
Pełny tekst źródłaThe analysis of time series and sequences has been challenging in both statistics and machine learning community, because of their properties including high dimensionality, pattern dynamics, and irregular observations. In this thesis, novel methods are proposed to handle the difficulties mentioned above, thus enabling representation learning (dimension reduction and pattern extraction), and prediction making (classification and forecasting). This thesis consists of three main parts.
The first part analyzes multivariate time series, which is often non-stationary due to high levels of ambient noise and various interferences. We propose a nonlinear dimensionality reduction framework using diffusion maps on a learned statistical manifold, which gives rise to the construction of a low-dimensional representation of the high-dimensional non-stationary time series. We show that diffusion maps, with affinity kernels based on the Kullback-Leibler divergence between the local statistics of samples, allow for efficient approximation of pairwise geodesic distances. To construct the statistical manifold, we estimate time-evolving parametric distributions by designing a family of Bayesian generative models. The proposed framework can be applied to problems in which the time-evolving distributions (of temporally localized data), rather than the samples themselves, are driven by a low-dimensional underlying process. We provide efficient parameter estimation and dimensionality reduction methodology and apply it to two applications: music analysis and epileptic-seizure prediction.
The second part focuses on a time series classification task, where we want to leverage the temporal dynamic information in the classifier design. In many time series classification problems including fraud detection, a low false alarm rate is required; meanwhile, we enhance the positive detection rate. Therefore, we directly optimize the partial area under the curve (PAUC), which maximizes the accuracy in low false alarm rate regions. Latent variables are introduced to incorporate the temporal information, while maintaining a max-margin based method solvable. An optimization routine is proposed with its properties analyzed; the algorithm is designed as scalable to web-scale data. Simulation results demonstrate the effectiveness of optimizing the performance in the low false alarm rate regions.
The third part focuses on pattern extraction from correlated point process data, which consist of multiple correlated sequences observed at irregular times. The analysis of correlated point process data has wide applications, ranging from biomedical research to network analysis. We model such data as generated by a latent collection of continuous-time binary semi-Markov processes, corresponding to external events appearing and disappearing. A continuous-time modeling framework is more appropriate for multichannel point process data than a binning approach requiring time discretization, and we show connections between our model and recent ideas from the discrete-time literature. We describe an efficient MCMC algorithm for posterior inference, and apply our ideas to both synthetic data and a real-world biometrics application.
Dissertation
Liu, Bozhong. "Towards effective spatial data mining : uncertainty, condensity and privacy". Thesis, 2017. http://hdl.handle.net/10453/116219.
Pełny tekst źródłaSpatial data mining (SDM) is a process of knowledge discovery that the observing data is related to geographical information. It has become an important data mining task due to the explosive growth and pervasive use of spatial data. It is more difficult to extract interesting and useful patterns from spatial datasets due to the complexity of spatial data types, spatial relationships, and spatial autocorrelation. Although existing methods can handle the spatial mining task properly, as the arrival of the big data era, new challenges for SDM are arising. Firstly, traditional SDM methods usually focus on deterministic datasets, where spatial events occur affirmatively at precise locations. However, the inherent uncertainty of spatial data makes the mining process more difficult. Classical spatial data mining algorithms are no longer applicable or need delicate modification. Secondly, traditional SDM frameworks produce an exponential number of patterns, which makes it hard for users to understand or apply. To solve the condensity issue, novel techniques such as summarization or representation must be carefully investigated. Thirdly, spatial data usually involves an individual’s location information, which incurs location privacy problem. It would be a challenge to protect location privacy with enhanced data security and improved resulting accuracy. To address the uncertainty issue, we study the problem of discovering co-location patterns in the context of continuously distributed uncertain data, namely Probabilistic Co-location Patterns Mining (PCPM). We develop an effective probabilistic co-location mining framework integrated with optimization strategies to address the challenges. To address the condensity issue, we investigate the problem of Representative Co-location Patterns Mining (RCPM). We define a new measure to quantify the distance between co-location patterns, and develop two efficient algorithms for summarization. To address the privacy issue, we solve the problem of protecting Location Privacy in Spatial Crowdsourcing (LPSC). We propose a secure spatial crowdsourcing framework based on encryption, and devise a novel secure indexing technique for efficient querying. The experimental results demonstrate the effectiveness and efficiency of our proposed solutions. The methods and techniques used in solving concrete SDM tasks can also be applied or extended to other SDM scenarios.