Dissertations / Theses on the topic 'Probabilistic representation of PDEs'
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1
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.
Abstract:
Cette thèse s'intéresse aux équations différentielles stochastiques de type McKean(EDS) et à leur utilisation pour représenter des équations aux dérivées partielles (EDP) non linéaires. Ces équations ne dépendent pas seulement du temps et de la position d'une certaine particule mais également de sa loi. En particulier nous traitons le cas inhabituel de la représentation d'EDP de type Fokker-Planck avec condition terminale fixée. Nous discutons existence et unicité pour ces EDP et de leur représentation sous la forme d'une EDS de type McKean, dont l'unique solutioncorrespond à la dynamique du retourné dans le temps d'un processus de diffusion.Nous introduisons la notion de représentation complètement non-linéaire d'une EDP semilinéaire. Celle-ci consiste dans le couplage d'une EDS rétrograde et d'un processus solution d'une EDS évoluant de manière rétrograde dans le temps. Nous discutons également une application à la représentation d'une équation d'Hamilton-Jacobi-Bellman (HJB) en contrôle stochastique. Sur cette base, nous proposonsun algorithme de Monte-Carlo pour résoudre des problèmes de contrôle. Celui ciest avantageux en termes d'efficience calculatoire et de mémoire, en comparaisonavec les approches traditionnelles progressive rétrograde. Nous appliquons cette méthode dans le contexte de la gestion de la demande dans les réseaux électriques. Pour finir, nous faisons le point sur l'utilisation d'EDS de type McKean généralisées pour représenter des EDP non-linéaires et non-conservatives plus générales que Fokker-PlanckThis 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
2
Sabbagh, Wissal. "Some Contributions on Probabilistic Interpretation For Nonlinear Stochastic PDEs." Thesis, Le Mans, 2014. http://www.theses.fr/2014LEMA1019/document.
Abstract:
L'objectif de cette thèse est l'étude de la représentation probabiliste des différentes classes d'EDPSs non-linéaires(semi-linéaires, complètement non-linéaires, réfléchies dans un domaine) en utilisant les équations différentielles doublement stochastiques rétrogrades (EDDSRs). Cette thèse contient quatre parties différentes. Nous traitons dans la première partie les EDDSRs du second ordre (2EDDSRs). Nous montrons l'existence et l'unicité des solutions des EDDSRs en utilisant des techniques de contrôle stochastique quasi- sure. La motivation principale de cette étude est la représentation probabiliste des EDPSs complètement non-linéaires. Dans la deuxième partie, nous étudions les solutions faibles de type Sobolev du problème d'obstacle pour les équations à dérivées partielles inteégro-différentielles (EDPIDs). Plus précisément, nous montrons la formule de Feynman-Kac pour l'EDPIDs par l'intermédiaire des équations différentielles stochastiques rétrogrades réfléchies avec sauts (EDSRRs). Plus précisément, nous établissons l'existence et l'unicité de la solution du problème d'obstacle, qui est considérée comme un couple constitué de la solution et de la mesure de réflexion. L'approche utilisée est basée sur les techniques de flots stochastiques développées dans Bally et Matoussi (2001) mais les preuves sont beaucoup plus techniques. Dans la troisième partie, nous traitons l'existence et l'unicité pour les EDDSRRs dans un domaine convexe D sans aucune condition de régularité sur la frontière. De plus, en utilisant l'approche basée sur les techniques du flot stochastiques nous démontrons l'interprétation probabiliste de la solution faible de type Sobolev d'une classe d'EDPSs réfléchies dans un domaine convexe via les EDDSRRs. Enfin, nous nous intéressons à la résolution numérique des EDDSRs à temps terminal aléatoire. La motivation principale est de donner une représentation probabiliste des solutions de Sobolev d'EDPSs semi-linéaires avec condition de Dirichlet nul au bord. Dans cette partie, nous étudions l'approximation forte de cette classe d'EDDSRs quand le temps terminal aléatoire est le premier temps de sortie d'une EDS d'un domaine cylindrique. Ainsi, nous donnons les bornes pour l'erreur d'approximation en temps discret. Cette partie se conclut par des tests numériques qui démontrent que cette approche est effectiveThe 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
3
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.
Abstract:
Cette thèse porte sur les méthodes numériques pour les équations aux dérivées partielles (EDP) non-linéaires dégénérées, ainsi que pour des problèmes de contrôle d'EDP non-linéaires résultants d'un nouveau problème de transport optimal. Toutes ces questions sont motivées par des applications en mathématiques financières. La thèse est divisée en quatre parties. Dans une première partie, nous nous intéressons à la condition nécessaire et suffisante de la monotonie du thêta-schéma de différences finies pour l'équation de diffusion en dimension un. Nous donnons la formule explicite dans le cas de l'équation de la chaleur, qui est plus faible que la condition classique de Courant-Friedrichs-Lewy (CFL). Dans une seconde partie, nous considérons une EDP parabolique non-linéaire dégénérée et proposons un schéma de type ''splitting'' pour la résoudre. Ce schéma réunit un schéma probabiliste et un schéma semi-lagrangien. Au final, il peut être considéré comme un schéma Monte-Carlo. Nous donnons un résultat de convergence et également un taux de convergence du schéma. Dans une troisième partie, nous étudions un problème de transport optimal, où la masse est transportée par un processus d'état type ''drift-diffusion'' controllé. Le coût associé est dépendant des trajectoires de processus d'état, de son drift et de son coefficient de diffusion. Le problème de transport consiste à minimiser le coût parmi toutes les dynamiques vérifiant les contraintes initiales et terminales sur les distributions marginales. Nous prouvons une formule de dualité pour ce problème de transport, étendant ainsi la dualité de Kantorovich à notre contexte. La formulation duale maximise une fonction valeur sur l'espace des fonctions continues bornées, et la fonction valeur correspondante à chaque fonction continue bornée est la solution d'un problème de contrôle stochastique optimal. Dans le cas markovien, nous prouvons un principe de programmation dynamique pour ces problèmes de contrôle optimal, proposons un algorithme de gradient projeté pour la résolution numérique du problème dual, et en démontrons la convergence. Enfin dans une quatrième partie, nous continuons à développer l'approche duale pour le problème de transport optimal avec une application à la recherche de bornes de prix sans arbitrage des options sur variance étant donnés les prix des options européennes. Après une première approximation analytique, nous proposons un algorithme de gradient projeté pour approcher la borne et la stratégie statique correspondante en options vanillesThis 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
4
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.
5
Tarrago, Pierre. "Non-commutative generalization of some probabilistic results from representation theory." Thesis, Paris Est, 2015. http://www.theses.fr/2015PESC1123/document.
Abstract:
Le sujet de cette thèse est la généralisation non-commutative de résultats probabilistes venant de la théorie des représentations. Les résultats obtenus se divisent en trois parties distinctes. Dans la première partie de la thèse, le concept de groupe quantique easy est étendu au cas unitaire. Tout d'abord, nous donnons une classification de l'ensemble des groupes quantiques easy unitaires dans le cas libre et classique. Nous étendons ensuite les résultats probabilistes de au cas unitaire. La deuxième partie de la thèse est consacrée à une étude du produit en couronne libre. Dans un premier temps, nous décrivons les entrelaceurs des représentations dans le cas particulier d'un produit en couronne libre avec le groupe symétrique libre: cette description permet également d'obtenir plusieurs résultats probabilistes. Dans un deuxième temps, nous établissons un lien entre le produit en couronne libre et les algèbres planaires: ce lien mène à une preuve d'une conjecture de Banica et Bichon. Dans la troisième partie de la thèse, nous étudions un analoque du graphe de Young qui encode la structure multiplicative des fonctions fondamentales quasi-symétriques. La frontière minimale de ce graphe a déjà été décrite par Gnedin et Olshanski. Nous prouvons que la frontière minimale coïncide avec la frontière de Martin. Au cours de cette preuve, nous montrons plusieurs résultats combinatoires asymptotiques concernant les diagrammes de Young en rubanThe 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
6
Ugail, Hassan, and Eyad Elyan. "Efficient 3D data representation for biometric applications." IOS Press, 2007. http://hdl.handle.net/10454/2683.
Abstract:
YesAn 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.
7
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.
Abstract:
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1994.Includes bibliographical references (p. 145-149).
by Amelia Huimin Shen.
Ph.D.
8
Ugail, Hassan, and S. Kirmani. "Shape reconstruction using partial differential equations." World Scientific and Engineering Academy and Society (WSEAS), 2006. http://hdl.handle.net/10454/2645.
Abstract:
We present an efficient method for reconstructing complex geometry using an elliptic Partial Differential Equation (PDE) formulation. The integral part of this work is the use of three-dimensional curves within the physical space which act as boundary conditions to solve the PDE. The chosen PDE is solved explicitly for a given general set of curves representing the original shape and thus making the method very efficient. In order to improve the quality of results for shape representation we utilize an automatic parameterization scheme on the chosen curves. With this formulation we discuss our methodology for shape representation using a series of practical examples.
9
Vasudevan, 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.
10
Lloyd, 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.
11
Lavis, 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.
Abstract:
This thesis presents a means for representing and computing beliefs in the form of arbitrary probability density functions with a guarantee for the ongoing validity of such beliefs over indefinte time frames. The foremost aspect of this proposal is the introduction of a general, theoretical, solution to the guaranteed state estimation problem from within the recursive Bayesian estimation framework. The solution presented here determines the minimum space required, at each stage of the estimation process, to represent the belief with limited, or no, loss of information. Beyond this purely theoretical aspect, a number of numerical techniques, capable of determining the required space and performing the appropriate spatial reconfiguration, whilst also computing and representing the belief functions, are developed. This includes a new, hybrid particle-element approach to recursive Bayesian estimation. The advantage of spatial reconfiguration as presented here is that it ensures that the belief functions consider all plausible states of the target system, without altering the recursive Bayesian estimation equations used to form those beliefs. Furthermore, spatial reconfiguration as proposed in this dissertation enhances the estimation process since it allows computational resources to be concentrated on only those states considered plausible. Autonomous maritime search and rescue is used as a focus application throughout this dissertation since the searching-and-tracking requirements of the problem involve uncertainty, the use of arbitrary belief functions and dynamic target systems. Nevertheless, the theoretical development in this dissertation has been kept general and independent of an application, and as such the theory and techniques presented here may be applied to any problem involving dynamic Bayesian beliefs. A number of numerical experiments and simulations show the efficacy of the proposed spatially reconfigurable representations, not only in ensuring the validity of the belief functions over indefinite time frames, but also in reducing computation time and improving the accuracy of function approximation. Improvements of an order of magnitude were achieved when compared with traditional, spatially static representations.
12
Geilke, 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.
13
Zanitti, 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.
Abstract:
Grâce aux récents progrès technologiques, le chercheur en neurosciences dispose d'une quantité croissante de jeux de données pour étudier le cerveau. La multiplicité des travaux dédiés a également produit des ontologies encodant des connaissances à la pointe concernant les différentes aires, les schémas d'activation, les mots-clés associés aux études, etc. Il existe d'autre part une incertitude inhérente aux images cérébrales, du fait de la mise en correspondance entre voxels - ou pixels 3D - et points réels sur le cerveau de différents sujets. Malheureusement, à ce jour, aucun cadre unifié ne permet l'accès à cette mine de données hétérogènes avec l'incertitude associée, obligeant le chercheur à se tourner vers des outils ad hoc. Dans cette étude, nous présentons NeuroLang, un langage probabiliste basé sur de la logique de premier ordre, comprenant des règles existentielles, de l'incertitude probabiliste, l'intégration d'ontologies reposant sur l'hypothèse du monde ouvert, ainsi que des mécanismes garantissant une réponse aux requêtes résolvables, même sur de très grandes bases de données. Nous soutenons que NeuroLang, par l'expressivité de son langage de requête, contribuera à grandement améliorer la recherche en neurosciences, en donnant notamment la possibilité d'intégrer de manière transparente des données hétérogènes, telles que des ontologies avec des atlas cérébraux probabilistes. Dans ce cas-ci, des domaines cognitifs - à la granularité fine - et des régions cérébrales seront associés via un ensemble de critères formels, favorisant ainsi la communication et la reproductibilité des résultats d'études sur les fonctions cérébrales. Aussi croyons-nous que NeuroLang est à même de se positionner en tête sur ces approches numériques qui visent à formaliser la recherche neuroscientifique à grande échelle via la programmation probabiliste et logique du premier ordreResearchers 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
14
Tarrago, Pierre [Verfasser], and 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.
15
Nayak, Sunita. "Representation and learning for sign language recognition." [Tampa, Fla] : University of South Florida, 2008. http://purl.fcla.edu/usf/dc/et/SFE0002362.
16
El-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.
17
Paraschos, Alexandros [Verfasser], Jan [Akademischer Betreuer] Peters, Gerhard [Akademischer Betreuer] Neumann, and 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.
18
Elyan, Eyad, and Hassan Ugail. "Reconstruction of 3D human facial images using partial differential equations." Academy Publisher, 2007. http://hdl.handle.net/10454/2644.
Abstract:
One of the challenging problems in geometric
modeling and computer graphics is the construction of
realistic human facial geometry. Such geometry are
essential for a wide range of applications, such as 3D face
recognition, virtual reality applications, facial expression
simulation and computer based plastic surgery application.
This paper addresses a method for the construction of 3D
geometry of human faces based on the use of Elliptic Partial
Differential Equations (PDE). Here the geometry
corresponding to a human face is treated as a set of surface
patches, whereby each surface patch is represented using
four boundary curves in the 3-space that formulate the
appropriate boundary conditions for the chosen PDE. These
boundary curves are extracted automatically using 3D data
of human faces obtained using a 3D scanner. The solution of
the PDE generates a continuous single surface patch
describing the geometry of the original scanned data. In this
study, through a number of experimental verifications we
have shown the efficiency of the PDE based method for 3D
facial surface reconstruction using scan data. In addition to
this, we also show that our approach provides an efficient
way of facial representation using a small set of parameters
that could be utilized for efficient facial data storage and
verification purposes.
19
Ogul, 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.
Abstract:
Machine learning techniques have been widely used for classification problems in computational biology. They require that the input must be a collection of fixedlength feature vectors. Since proteins are of varying lengths, there is a need for a
means of representing protein sequences by a fixed-number of features. This thesis
introduces three novel methods for this purpose: n-peptide compositions with
reduced alphabets, pairwise similarity scores by maximal unique matches, and
pairwise similarity scores by probabilistic suffix trees.
New sequence representations described in the thesis are applied on three
challenging problems of computational biology: remote homology detection,
subcellular localization prediction, and solvent accessibility prediction, with some
problem-specific modifications. Rigorous experiments are conducted on common
benchmarking datasets, and a comparative analysis is performed between the new
methods and the existing ones for each problem.
On remote homology detection tests, all three methods achieve competitive
accuracies with the state-of-the-art methods, while being much more efficient. A
combination of new representations are used to devise a hybrid system, called
PredLOC, for predicting subcellular localization of proteins and it is tested on two
distinct eukaryotic datasets. To the best of author&rsquos 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.
20
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.
Abstract:
Les problèmes de contrôle stochastique optimal à horizon fini forment une classe de problèmes de contrôle optimal où interviennent des processus stochastiques considérés sur un intervalle de temps borné. Tout comme beaucoup de problème de contrôle optimal, ces problèmes sont résolus en utilisant le principe de la programmation dynamique qui induit une équation aux dérivées partielles (EDP) appelée équation d'Hamilton-Jacobi-Bellman. Les méthodes basées sur la discrétisation de l’espace sous forme de grille, les méthodes probabilistes ou plus récemment les méthodes max-plus peuvent alors être utilisées pour résoudre cette équation. Cependant, le premier type de méthode est mis en défaut quand un espace à dimension grande est considéré à cause de la malédiction de la dimension tandis que le deuxième type de méthode ne permettait jusqu'ici que de résoudre des problèmes où la non linéarité de l'équation aux dérivées partielles par rapport à la Hessienne n'est pas trop forte. Quant au troisième type de méthode, il entraine une explosion de la complexité de la fonction valeur. Nous introduisons dans cette thèse deux nouveaux schémas probabilistes permettant d'agrandir la classe des problèmes pouvant être résolus par les méthodes probabilistes. L'une est adaptée aux EDP à coefficients bornés tandis que l'autre peut être appliqué aux EDP à coefficients bornés ou non bornés. Nous prouvons la convergence des deux schémas probabilistes et obtenons des estimées de l'erreur de convergence dans le cas d'EDP à coefficients bornés. Nous donnons également quelques résultats sur le comportement du deuxième schéma dans le cas d'EDP à coefficients non bornés. Ensuite, nous introduisons une méthode complètement nouvelle pour résoudre les problèmes de contrôle stochastique optimal à horizon fini que nous appelons la méthode max-plus probabiliste. Elle permet d'utiliser le caractère non linéaire des méthodes max-plus dans un contexte probabiliste tout en contrôlant la complexité de la fonction valeur. Une application au calcul du prix de sur-réplication d'une option dans un modèle de corrélation incertaine est donnée dans le cas d’un espace à dimension 2 et 5Stochastic 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
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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.
Abstract:
Doctor of Philosophy (PhD)This 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.
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Ramos, Fabio Tozeto. "Recognising, Representing and Mapping Natural Features in Unstructured Environments." Thesis, The University of Sydney, 2007. http://hdl.handle.net/2123/2322.
Abstract:
This 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.
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GARBARINO, 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.
Abstract:
In the artificial intelligence community there is a growing consensus that real
world data is naturally represented as graphs because they can easily incorporate complexity at several levels, e.g. hierarchies or time dependencies. In this context, this thesis studies two main branches for structured data.
In the first part we explore how state-of-the-art machine learning methods can be extended to graph modeled data provided that one is able to represent graphs in vector spaces. Such extensions can be applied to analyze several kinds of real-world data and tackle different problems. Here we study the
following problems: a) understand the relational nature and evolution of websites which belong to different categories (e-commerce, academic (p.a.) and encyclopedic (forum)); b) model tennis players scores based on different game surfaces and tournaments in order to predict matches results; c) analyze preter-
m-infants motion patterns able to characterize possible neuro degenerative disorders and d) build an academic collaboration recommender system able to model academic groups and individual research interest while suggesting possible researchers to connect with, topics of interest and representative publications to external users.
In the second part we focus on graphs inference methods from data which present two main challenges: missing data and non-stationary time dependency. In particular, we study the problem of inferring Gaussian Graphical
Models in the following settings: a) inference of Gaussian Graphical Models when data are missing or latent in the context of multiclass or temporal network inference and b) inference of time-varying Gaussian Graphical Models
when data is multivariate and non-stationary. Such methods have a natural application in the composition of an optimized stock markets portfolio. Overall this work sheds light on how to acknowledge the intrinsic structure
of data with the aim of building statistical models that are able to capture the actual complexity of the real world.
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Schustek, Philipp. "Probabilistic models for human judgments about uncertainty in intuitive inference tasks." Doctoral thesis, Universitat Pompeu Fabra, 2018. http://hdl.handle.net/10803/586057.
Abstract:
Updating beliefs to maintain coherence with observational evidence is a cornerstone of rationality. This entails the compliance with probabilistic principles which acknowledge that real-world observations are consistent with several possible interpretations. This work presents two novel experimental paradigms and computational analyses of how human participants quantify uncertainty in perceptual inference tasks. Their behavioral responses feature non-trivial patterns of probabilistic inference such as reliability-based belief updating over hierarchical state representations of the environment. Despite characteristic generalization biases, behavior cannot be explained well by alternative heuristic accounts. These results suggest that uncertainty is an integral part of our inferences and that we indeed have the potential to resort to rational inference mechanisms that adhere to probabilistic principles. Furthermore, they appear consistent with ubiquitous representations of uncertainty posited by framework theories such as Bayesian hierarchical modeling and predictive coding.Un 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.
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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.
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Chrastansky, Alena [Verfasser], and 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.
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Nyga, Daniel [Verfasser], Michael [Akademischer Betreuer] [Gutachter] Beetz, and 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.
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Lee, Wooyoung. "Learning Statistical Features of Scene Images." Research Showcase @ CMU, 2014. http://repository.cmu.edu/dissertations/540.
Abstract:
Scene perception is a fundamental aspect of vision. Humans are capable of analyzing behaviorally-relevant scene properties such as spatial layouts or scene categories very quickly, even from low resolution versions of scenes. Although humans perform these tasks effortlessly, they are very challenging for machines. Developing methods that well capture the properties of the representation used by the visual system will be useful for building computational models that are more consistent with perception. While it is common to use hand-engineered features that extract information from predefined dimensions, they require careful tuning of parameters and do not generalize well to other tasks or larger datasets. This thesis is driven by the hypothesis that the perceptual representations are adapted to the statistical properties of natural visual scenes. For developing statistical features for global-scale structures (low spatial frequency information that encompasses entire scenes), I propose to train hierarchical probabilistic models on whole scene images. I first investigate statistical clusters of scene images by training a mixture model under the assumption that each image can be decoded by sparse and independent coefficients. Each cluster discovered by the unsupervised classifier is consistent with the high-level semantic categories (such as indoor, outdoor-natural and outdoor-manmade) as well as perceptual layout properties (mean depth, openness and perspective). To address the limitation of mixture models in their assumptions of a discrete number of underlying clusters, I further investigate a continuous representation for the distributions of whole scenes. The model parameters optimized for natural visual scenes reveal a compact representation that encodes their global-scale structures. I develop a probabilistic similarity measure based on the model and demonstrate its consistency with the perceptual similarities. Lastly, to learn the representations that better encode the manifold structures in general high-dimensional image space, I develop the image normalization process to find a set of canonical images that anchors the probabilistic distributions around the real data manifolds. The canonical images are employed as the centers of the conditional multivariate Gaussian distributions. This approach allows to learn more detailed structures of the local manifolds resulting in improved representation of the high level properties of scene images.
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Yan, 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.
Abstract:
Die Erforschung der neuronaler Grundlagen des Arbeitsgedächtnisses (WM) fand breite Aufmerksamkeit, konzentrierte sich aber auf die Speicherung sensorischer Inhalte. Beweise für die kurzfristige Aufrechterhaltung abstrakter, verbaler oder kategorischer Informationen sind selten. Ziel dieser Arbeit ist die Untersuchung der neuronalen Repräsentation von WM-Inhalten auf verschiedenen Abstraktionsebenen. Ich stelle hier drei empirische Studien vor, in denen fMRT, multivariate Musteranalyse oder probabilistische Modelle als Hauptmethoden eingesetzt wurden. Die erste Studie identifizierte kortikale Regionen, die den WM-Inhalt eines Skripts behielten. Chinesische Muttersprachler wurden gebeten, sich bekannte chinesische Zeichen zu merken, was die verbale Kodierung stark fördern. Die Ergebnisse zeigten links lateralisierte sprachbezogene Hirnareale als Kandidatenspeicher für verbale Inhalte. Die zweite und dritte Studie zielten darauf ab, die Hypothese zu testen, dass Farbe als eine Kombination aus einer visuellen Repräsentation und einer kategorischen Repräsentation gespeichert wird. Die zweite Studie verwendete ein sensorisches Kodierungsmodell und ein empirisch basiertes kategorisches Kodierungsmodell, um jeweils zwei Quellen neuronaler Repräsentationen zu charakterisieren. Farbinformationen wurden in drei farbbezogenen ROIs dekodiert: V1, V4, VO1, und insbesondere wurde eine Erhöhung der kategorischen Repräsentation in vorderen kortikalen Arealen beobachtet. In der dritten Studie wurde die verzögerte Verhaltensreaktion untersucht, die ein systematisches Bias-Muster zeigte; es wurde ein probabilistisches Dual-Content-Modell implementiert, das ein mit den experimentellen Ergebnissen hoch korreliertes Antwortmuster erzeugte; dies bestätigte die Hypothese der mnemonischen Dual-Content Repräsentation. Diese Studien zusammen schlagen eine Arbeitsteilung entlang der rostro-kaudalen Achse des Gehirns, die auf der Abstraktionsebene der gespeicherten Inhalte basiert.Research 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.
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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.
Abstract:
As Redes Bayesianas constituem um modelo computacional adequado para a realização de inferências probabilísticas em domínios que envolvem a incerteza. O raciocínio diagnóstico médico pode ser caracterizado como um ato de inferência probabilística em um domínio incerto, onde a elaboração de hipóteses diagnósticas é representada pela estratificação de doenças em função das probabilidades a elas associadas. A presente dissertação faz uma pesquisa sobre a metodologia para construção/validação de redes bayesianas voltadas à área médica, e utiliza estes conhecimentos para o desenvolvimento de uma rede probabilística para o auxílio diagnóstico da Insuficiência Cardíaca (IC). Esta rede bayesiana, implementada como parte do sistema SEAMED/AMPLIA, teria o papel de alerta para o diagnóstico e tratamento precoce da IC, o que proporcionaria uma maior agilidade e eficiência no atendimento de pacientes portadores desta patologia.Bayesian 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.
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Jain, Dominik [Verfasser], Michael [Akademischer Betreuer] Beetz, and 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.
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Shan, 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.
Abstract:
This thesis studies grammar-based approaches in the application of Estimation of Distribution Algorithms (EDA) to the tree representation widely used in Genetic Programming (GP). Although EDA is becoming one of the most active fields in Evolutionary computation (EC), the solution representation in most EDA is a Genetic Algorithms (GA) style linear representation. The more complex tree representations, resembling GP, have received only limited exploration. This is unfortunate, because tree representations provide a natural and expressive way of representing solutions for many problems. This thesis aims to help fill this gap, exploring grammar-based approaches to extending EDA to GP-style tree representations. This thesis firstly provides a comprehensive survey of current research on EDA with emphasis on EDA with GP-style tree representation. The thesis attempts to clarify the relationship between EDA with conventional linear representations and those with a GP-style tree representation, and to reveal the unique difficulties which face this research. Secondly, the thesis identifies desirable properties of probabilistic models for EDA with GP-style tree representation, and derives the PRODIGY framework as a consequence. Thirdly, following the PRODIGY framework, three methods are proposed. The first method is Program Evolution with Explicit Learning (PEEL). Its incremental general-to-specific grammar learning method balances the effectiveness and efficiency of the grammar learning. The second method is Grammar Model-based Program Evolution (GMPE). GMPE realises the PRODIGY framework by introducing elegant inference methods from the formal grammar field. GMPE provides good performance on some problems, but also provides a means to better understand some aspects of conventional GP, especially the building block hypothesis. The third method is Swift GMPE (sGMPE), which is an extension of GMPE, aiming at reducing the computational cost. Fourthly, a more accurate Minimum Message Length metric for grammar learning in PRODIGY is derived in this thesis. This metric leads to improved performance in the GMPE system, but may also be useful in grammar learning in general. It is also relevant to the learning of other probabilistic graphical models.
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Moraes, 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.
Abstract:
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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.
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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.
Abstract:
En chimiotaxie, le modèle parabolique-parabolique classique de Keller-Segel en dimension d décrit l’évolution en temps de la densité d'une population de cellules et de la concentration d'un attracteur chimique. Cette thèse porte sur l’étude des équations de Keller-Segel parabolique-parabolique par des méthodes probabilistes. Dans ce but, nous construisons une équation différentielle stochastique non linéaire au sens de McKean-Vlasov dont le coefficient dont le coefficient de dérive dépend, de manière singulière, de tout le passé des lois marginales en temps du processus. Ces lois marginales couplées avec une transformation judicieuse permettent d’interpréter les équations de Keller-Segel de manière probabiliste. En ce qui concerne l'approximation particulaire il faut surmonter une difficulté intéressante et, nous semble-t-il, originale et difficile chaque particule interagit avec le passé de toutes les autres par l’intermédiaire d'un noyau espace-temps fortement singulier. En dimension 1, quelles que soient les valeurs des paramètres de modèle, nous prouvons que les équations de Keller-Segel sont bien posées dans tout l'espace et qu'il en est de même pour l’équation différentielle stochastique de McKean-Vlasov correspondante. Ensuite, nous prouvons caractère bien posé du système associé des particules en interaction non markovien et singulière. Nous établissons aussi la propagation du chaos vers une unique limite champ moyen dont les lois marginales en temps résolvent le système Keller-Segel parabolique-parabolique. En dimension 2, des paramètres de modèle trop grands peuvent conduire à une explosion en temps fini de la solution aux équations du Keller-Segel. De fait, nous montrons le caractère bien posé du processus non-linéaire au sens de McKean-Vlasov en imposant des contraintes sur les paramètres et données initiales. Pour obtenir ce résultat, nous combinons des techniques d'analyse d’équations aux dérivées partielles et d'analyse stochastique. Finalement, nous proposons une méthode numérique totalement probabiliste pour approcher les solutions du système Keller-Segel bi-dimensionnel et nous présentons les principaux résultats de nos expérimentations numériquesThe 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
35
Spiegel, Christoph. "Additive structures and randomness in combinatorics." Doctoral thesis, Universitat Politècnica de Catalunya, 2020. http://hdl.handle.net/10803/669327.
Abstract:
Arithmetic Combinatorics, Combinatorial Number Theory, Structural Additive Theory and Additive Number Theory are just some of the terms used to describe the vast field that sits at the intersection of Number Theory and Combinatorics and which will be the focus of this thesis. Its contents are divided into two main parts, each containing several thematically related results.
The first part deals with the question under what circumstances solutions to arbitrary linear systems of equations usually occur in combinatorial structures..The properties we will be interested in studying in this part relate to the solutions to linear systems of equations.
A first question one might ask concerns the point at which sets of a given size will typically contain a solution. We will establish a threshold and also study the distribution of the number of solutions at that threshold, showing that it converges to a Poisson distribution in certain cases.
Next, Van der Waerden’s Theorem, stating that every finite coloring of the integers contains monochromatic arithmetic progression of arbitrary length, is by some considered to be the first result in Ramsey Theory. Rado generalized van der Waerden’s result by characterizing those linear systems whose solutions satisfy a similar property and Szemerédi strengthened it to a statement concerning density rather than colorings. We will turn our attention towards versions of Rado’s and Szemerédi’s Theorem in random sets, extending previous work of Friedgut, Rödl, Rucin´ski and Schacht in the case of the former and of Conlon, Gowers and Schacht for the latter to include a larger variety of systems and solutions.
Lastly, Chvátal and Erdo¿s suggested studying Maker-Breaker games. These games have deep connections to the theory of random structures and we will build on work of Bednarska and Luczak to establish the threshold for how much a large variety of games need to be biased in favor of the second player. These include games in which the first player wants to occupy a solution to some given linear system, generalizing the van der Waerden games introduced by Beck.
The second part deals with the extremal behavior of sets with interesting additive properties. In particular, we will be interested in bounds or structural descriptions for sets exhibiting some restrictions with regards to either their representation function or their sumset.
First, we will consider Sidon sets, that is sets of integers with pairwise unique differences. We will study a generalization of Sidon sets proposed very recently by Kohayakawa, Lee, Moreira and Rödl, where the pairwise differences are not just distinct, but in fact far apart by a certain measure. We will obtain strong lower bounds for such infinite sets using an approach of Cilleruelo. As a consequence of these bounds, we will also obtain the best current lower bound for Sidon sets in randomly generated infinite sets of integers of high density.
Next, one of the central results at the intersection of Combinatorics and Number Theory is the Freiman–Ruzsa Theorem stating that any finite set of integers of given doubling can be efficiently covered by a generalized arithmetic progression. In the case of particularly small doubling, more precise structural descriptions exist. We will first study results going beyond Freiman’s well-known 3k–4 Theorem in the integers. We will then see an application of these results to sets of small doubling in finite cyclic groups.
Lastly, we will turn our attention towards sets with near-constant representation functions. Erdo¿s and Fuchs established that representation functions of arbitrary sets of integers cannot be too close to being constant. We will first extend the result of Erdo¿s and Fuchs to ordered representation functions. We will then address a related question of Sárközy and Sós regarding weighted representation function.La 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.
36
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.
Abstract:
In this thesis we study quantum-like representation and simulation of quantum algorithms by using classical computers.The quantum--like representation algorithm (QLRA) was introduced by A. Khrennikov (1997) to solve the ``inverse Born's rule problem'', i.e. to construct a representation of probabilistic data-- measured in any context of science-- and represent this data by a complex or more general probability amplitude which matches a generalization of Born's rule.The outcome from QLRA matches the formula of total probability with an additional trigonometric, hyperbolic or hyper-trigonometric interference term and this is in fact a generalization of the familiar formula of interference of probabilities. We study representation of statistical data (of any origin) by a probability amplitude in a complex algebra and a Clifford algebra (algebra of hyperbolic numbers). The statistical data is collected from measurements of two dichotomous and trichotomous observables respectively. We see that only special statistical data (satisfying a number of nonlinear constraints) have a quantum--like representation. We also study simulations of quantum computers on classical computers.Although it can not be denied that great progress have been made in quantum technologies, it is clear that there is still a huge gap between the creation of experimental quantum computers and realization of a quantum computer that can be used in applications. Therefore the simulation of quantum computations on classical computers became an important part in the attempt to cover this gap between the theoretical mathematical formulation of quantum mechanics and the realization of quantum computers. Of course, it can not be expected that quantum algorithms would help to solve NP problems for polynomial time on classical computers. However, this is not at all the aim of classical simulation. The second part of this thesis is devoted to adaptation of the Mathematica symbolic language to known quantum algorithms and corresponding simulations on classical computers. Concretely we represent Simon's algorithm, Deutsch-Josza algorithm, Shor's algorithm, Grover's algorithm and quantum error-correcting codes in the Mathematica symbolic language. We see that the same framework can be used for all these algorithms. This framework will contain the characteristic property of the symbolic language representation of quantum computing and it will be a straightforward matter to include future algorithms in this framework.
37
Aliakbari, 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.
Abstract:
Cette thèse est centralisée sur cette question : comment est-ce que le système visuel peut coder efficacement la position des objets en mouvement, en dépit des diverses sources d'incertitude ? Cette étude déploie une hypothèse sur la connaissance a priori de la cohérence temporelle du mouvement (Burgi et al 2000; Yuille and Grzywacz 1989). Nous avons ici étendu le cadre de modélisation précédemment proposé pour expliquer le problème de l'ouverture (Perrinet and Masson, 2012). C'est un cadre d'estimation de mouvement Bayésien mis en oeuvre par un filtrage particulaire, que l'on appelle la prévision basé sur le mouvement (MBP). Sur cette base, nous avons introduit une théorie du codage de position basée sur le mouvement, et étudié comment les mécanismes neuronaux codant la position instantanée de l'objet en mouvement pourraient être affectés par le signal de mouvement le long d'une trajectoire. Les résultats de cette thèse suggèrent que le codage de la position basé sur le mouvement peut constituer un calcul neuronal générique parmi toutes les étapes du système visuel. Cela peut en partie compenser les effets cumulatifs des délais neuronaux dans le codage de la position. En outre, il peut expliquer des changements de position basés sur le mouvement, comme par example, l'Effect de Saut de Flash. Comme un cas particulier, nous avons introduit le modèle de MBP diagonal et avons reproduit la réponse anticipée de populations de neurones dans l'aire cortical V1. Nos résultats indiquent qu'un codage en position efficace et robuste peut être fortement dépendant de l'intégration le long de la trajectoireCoding 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
38
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.
Abstract:
Dans cette thèse, nous proposons une approche progressive (forward) pour la représentation probabiliste d'Equations aux Dérivées Partielles (EDP) nonlinéaires et nonconservatives, permettant ainsi de développer un algorithme particulaire afin d'en estimer numériquement les solutions. Les Equations Différentielles Stochastiques Nonlinéaires de type McKean (NLSDE) étudiées dans la littérature constituent une formulation microscopique d'un phénomène modélisé macroscopiquement par une EDP conservative. Une solution d'une telle NLSDE est la donnée d'un couple $(Y,u)$ où $Y$ est une solution d' équation différentielle stochastique (EDS) dont les coefficients dépendent de $u$ et de $t$ telle que $u(t,cdot)$ est la densité de $Y_t$. La principale contribution de cette thèse est de considérer des EDP nonconservatives, c'est-à- dire des EDP conservatives perturbées par un terme nonlinéaire de la forme $Lambda(u,nabla u)u$. Ceci implique qu'un couple $(Y,u)$ sera solution de la représentation probabiliste associée si $Y$ est un encore un processus stochastique et la relation entre $Y$ et la fonction $u$ sera alors plus complexe. Etant donnée la loi de $Y$, l'existence et l'unicité de $u$ sont démontrées par un argument de type point fixe via une formulation originale de type Feynmann-KacThis 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
39
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.
Abstract:
Dans cette thèse, nous proposons une approche progressive (forward) pour la représentation probabiliste d'Equations aux Dérivées Partielles (EDP) nonlinéaires et nonconservatives, permettant ainsi de développer un algorithme particulaire afin d'en estimer numériquement les solutions. Les Equations Différentielles Stochastiques Nonlinéaires de type McKean (NLSDE) étudiées dans la littérature constituent une formulation microscopique d'un phénomène modélisé macroscopiquement par une EDP conservative. Une solution d'une telle NLSDE est la donnée d'un couple (Y,u) où Y est une solution d' équation différentielle stochastique (EDS) dont les coefficients dépendent de u et de t telle que u(t,.) est la densité de Yt. La principale contribution de cette thèse est de considérer des EDP nonconservatives, c'est-à- dire des EDP conservatives perturbées par un terme nonlinéaire de la forme Lambda(u,nabla u)u. Ceci implique qu'un couple (Y,u) sera solution de la représentation probabiliste associée si Y est un encore un processus stochastique et la relation entre Y et la fonction u sera alors plus complexe. Etant donnée la loi de Y, l'existence et l'unicité de u sont démontrées par un argument de type point fixe via une formulation originale de type Feynmann-KacThis 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
40
Chen, Sih-Huei, and 陳思卉. "Probabilistic Latent Variable Model for Learning Data Representation." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/4xt8z4.
Abstract:
博士國立中央大學
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.
41
Cheuk, Adrian Y. W. "Stochastic simulation in dynamic probabilistic networks using compact representation." Thesis, 1996. http://hdl.handle.net/2429/6018.
Abstract:
In recent years, researchers in the A l domain have used Bayesian belief networks to build
models of expert opinion. Though computationally expensive deterministic algorithms have been devised,
it has been shown that exact probabilistic inference in belief networks, especially multiply connected
ones, is intractable. In view of this, various approximation methods based on stochastic simulation
appeared in an attempt to perform efficient approximate inference in large and richly interconnected
models. However, due to convergence problems, approximation in dynamic probabilistic networks
has seemed unpromising. Reversing arcs into evidence nodes can improve convergence performance
in simulation, but the resulting exponential increase in network complexity and, in particular,
the size of the conditional probability tables (CPTs) can often render this evidence reversal
method computationally inefficient.
In this thesis, we describe a structured simulation algorithm that uses the evidence reversal
technique based on a tree-structured representation for CPTs. Most real systems exhibit a large
amount of local structure. The tree can reduce network complexity by exploiting this structure to keep
CPTs in a compact way even after arcs have been reversed. The tree also has a major impact on improving
computational efficiency by capturing context-specific independence during simulation. Experimental
results show that in general our structured evidence reversal algorithm improves convergence
performance significantly while being both spatially and computationally much more efficient
than its unstructured counterpart.
42
Wong, Alexander. "Probabilistic complex phase representation objective function for multimodal image registration." Thesis, 2010. http://hdl.handle.net/10012/5326.
Abstract:
An interesting problem in computer vision is that of image registration, which plays an important role in many vision-based recognition and motion analysis applications. Of particular interest among data registration problems are multimodal image registration problems, where the image data sets are acquired using different imaging modalities. There are several important issues that make real-world multimodal registration a difficult problem to solve. First, images are often characterized by illumination and contrast non-uniformities. Such image non-uniformities result in local minima along the convergence plane that make it difficult for local optimization schemes to converge to the correct solution. Second, real-world images are often contaminated with signal noise, making the extraction of meaningful features for comparison purposes difficult to accomplish. Third, feature space differences make performing direct comparisons between the different data sets with a reasonable level of accuracy a challenging problem. Finally, solving the multimodal registration problem can be computationally expensive for large images. This thesis presents a probabilistic complex phase representation (PCPR) objective function for registering images acquired using different imaging modalities. A probabilistic multi-scale approach is introduced to create image representations based on local phase relationships extracted using complex wavelets. An objective function is introduced for assessing the alignment between the images based on a Geman-McClure error distribution model between the probabilistic complex phase representations of the images. Experimental results show that the proposed PCPR objective function can provide improved registration accuracies when compared to existing objective functions.
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Paraschos, Alexandros. "Robot Skill Representation, Learning and Control with Probabilistic Movement Primitives." Phd thesis, 2017. http://tuprints.ulb.tu-darmstadt.de/6947/1/root.pdf.
Abstract:
Robotic technology has made significant advances in the recent years, yet
robots have not been fully incorporated in our every day lives. Current
robots are executing a set of pre-programmed skills, that can not adapt to
environmental changes, and acquiring new skills is difficult and time
consuming. Additionally, current approaches for robot control focus on
accurately reproducing a task, but rarely consider safety aspects that could
enable the robots to share the same environment with humans. In this thesis, we
develop a framework that allows robots to rapidly acquire new skills, to adapt
skills to environmental changes, and to be controlled accurately and in a safe
manner.
Our framework is based on movement primitives, a well-established concept for
representing modular and reusable robot skills. In this thesis, we introduce a
novel movement primitive representation that not only models the shape of the
movement but also its uncertainty in time. We choose to rely on probability
theory, creating a mathematically sound framework that is capable of adapting
skills to environmental changes as well as adapting the execution speed online.
Our probabilistic framework allows training the robot with imitation learning,
speeding up significantly the process of novel skill acquisition. Hence, our
approach unifies all the significant properties of existing movement primitive
representations and, additionally, provides new properties, such as
conditioning and combination of primitives.
By modeling the variance of the trajectories, our framework enables standard
probabilistic operations to be applied on movement primitives. First, we
present a generalization operator that can modify a given trajectory
distribution to new situations and has improved performance over the current
approaches. Secondly, we define a novel combination operator for the
co-activating of multiple primitives, enabling the resulting primitive to
concurrently solve multiple tasks. Finally, we demonstrate that smoothly
sequencing primitives is simply a special case of movement combination. All
aforementioned operators for our model were derived analytically.
In noisy environments, coordinated movements have better recovery from
perturbations when compared to controlling each degree of freedom
independently. While many movement primitive representations use time as a
reference signal for synchronization, our approach, in addition, synchronizes
complete movement sequences in the full state of the robot. The skill's
correlations are encoded in the covariance matrix of our probabilistic model
that we estimate from demonstrations. Furthermore, by encoding the
correlations between the state of the robot and force/torque sensors, we
demonstrate that our approach has improved performance during physical
interaction tasks.
A movement generation framework would have limited application without a
control approach that can reproduce the learned primitives in a physical
system. Therefore, we derive two control approaches that are capable of
reproducing exactly the encoded trajectory distribution. When the dynamics of
the system are known, we derive a model-based stochastic feedback controller.
The controller has time-varying feedback gains that depend on the variance of
the trajectory distribution. We compute the gains in closed form. When the
dynamics of the system are unknown or are difficult to obtain, e.g., during
physical interaction scenarios, we propose a model-free controller. This
model-free controller has the same structure as the model-based controller,
i.e. a stochastic feedback controller, with time-varying gains, where the
gains can also be computed in closed form.
Complex robots with redundant degrees of freedom can in principle perform
multiple tasks at the same time, for example, reaching for an object with a
robotic arm while avoiding an obstacle. However, simultaneously performing
multiple tasks using the same degrees of freedom, requires combining control
signals from all the tasks. We developed a novel prioritization approach where
we utilize the variance of the movement as a priority measure. We demonstrate
how the task priorities can be obtained from imitation learning and how
different primitives can be combined to solve unseen previously unobserved
task-combinations. Due to the prioritization, we can efficiently learn a
combination of tasks without requiring individual models per task combination.
Additionally, existing primitive libraries can be adapted to environmental
changes by means of a single primitive, prioritized to compensate for the
change. Therefore, we avoid retraining the entire primitive library. The
prioritization controller can still be computed in closed form.
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Ahmat, Norhayati, Hassan Ugail, and Castro Gabriela Gonzalez. "Modelling the Mechanical Behaviour of a Pharmaceutical Tablet Using PDEs." 2012. http://hdl.handle.net/10454/5428.
Abstract:
yesDetailed 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.
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"Reasoning and Learning with Probabilistic Answer Set Programming." Doctoral diss., 2019. http://hdl.handle.net/2286/R.I.53736.
Abstract:
abstract: Knowledge Representation (KR) is one of the prominent approaches to Artificial Intelligence (AI) that is concerned with representing knowledge in a form that computer systems can utilize to solve complex problems. Answer Set Programming (ASP), based on the stable model semantics, is a widely-used KR framework that facilitates elegant and efficient representations for many problem domains that require complex reasoning.
However, while ASP is effective on deterministic problem domains, it is not suitable for applications involving quantitative uncertainty, for example, those that require probabilistic reasoning. Furthermore, it is hard to utilize information that can be statistically induced from data with ASP problem modeling.
This dissertation presents the language LP^MLN, which is a probabilistic extension of the stable model semantics with the concept of weighted rules, inspired by Markov Logic. An LP^MLN program defines a probability distribution over "soft" stable models, which may not satisfy all rules, but the more rules with the bigger weights they satisfy, the bigger their probabilities. LP^MLN takes advantage of both ASP and Markov Logic in a single framework, allowing representation of problems that require both logical and probabilistic reasoning in an intuitive and elaboration tolerant way.
This dissertation establishes formal relations between LP^MLN and several other formalisms, discusses inference and weight learning algorithms under LP^MLN, and presents systems implementing the algorithms. LP^MLN systems can be used to compute other languages translatable into LP^MLN.
The advantage of LP^MLN for probabilistic reasoning is illustrated by a probabilistic extension of the action language BC+, called pBC+, defined as a high-level notation of LP^MLN for describing transition systems. Various probabilistic reasoning about transition systems, especially probabilistic diagnosis, can be modeled in pBC+ and computed using LP^MLN systems. pBC+ is further extended with the notion of utility, through a decision-theoretic extension of LP^MLN, and related with Markov Decision Process (MDP) in terms of policy optimization problems. pBC+ can be used to represent (PO)MDP in a succinct and elaboration tolerant way, which enables planning with (PO)MDP algorithms in action domains whose description requires rich KR constructs, such as recursive definitions and indirect effects of actions.Dissertation/Thesis
Doctoral Dissertation Computer Science 2019
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Lian, Wenzhao. "Modeling Time Series and Sequences: Learning Representations and Making Predictions." Diss., 2015. http://hdl.handle.net/10161/11362.
Abstract:
The 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
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Liu, Bozhong. "Towards effective spatial data mining : uncertainty, condensity and privacy." Thesis, 2017. http://hdl.handle.net/10453/116219.
Abstract:
University of Technology Sydney. Faculty of Engineering and Information Technology.Spatial 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.