Дисертації з теми "Variational theory"
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Aghassi, Michele Leslie. "Robust optimization, game theory, and variational inequalities." Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/33670.
Повний текст джерелаIncludes bibliographical references (p. 193-109).
We propose a robust optimization approach to analyzing three distinct classes of problems related to the notion of equilibrium: the nominal variational inequality (VI) problem over a polyhedron, the finite game under payoff uncertainty, and the network design problem under demand uncertainty. In the first part of the thesis, we demonstrate that the nominal VI problem is in fact a special instance of a robust constraint. Using this insight and duality-based proof techniques from robust optimization, we reformulate the VI problem over a polyhedron as a single- level (and many-times continuously differentiable) optimization problem. This reformulation applies even if the associated cost function has an asymmetric Jacobian matrix. We give sufficient conditions for the convexity of this reformulation and thereby identify a class of VIs, of which monotone affine (and possibly asymmetric) VIs are a special case, which may be solved using widely-available and commercial-grade convex optimization software. In the second part of the thesis, we propose a distribution-free model of incomplete- information games, in which the players use a robust optimization approach to contend with payoff uncertainty.
(cont.) Our "robust game" model relaxes the assumptions of Harsanyi's Bayesian game model, and provides an alternative, distribution-free equilibrium concept, for which, in contrast to ex post equilibria, existence is guaranteed. We show that computation of "robust-optimization equilibria" is analogous to that of Nash equilibria of complete- information games. Our results cover incomplete-information games either involving or not involving private information. In the third part of the thesis, we consider uncertainty on the part of a mechanism designer. Specifically, we present a novel, robust optimization model of the network design problem (NDP) under demand uncertainty and congestion effects, and under either system- optimal or user-optimal routing. We propose a corresponding branch and bound algorithm which comprises the first constructive use of the price of anarchy concept. In addition, we characterize conditions under which the robust NDP reduces to a less computationally demanding problem, either a nominal counterpart or a single-level quadratic optimization problem. Finally, we present a novel traffic "paradox," illustrating counterintuitive behavior of changes in cost relative to changes in demand.
by Michele Leslie Aghassi.
Ph.D.
Worthing, Rodney A. (Rodney Alan). "Contributions to the variational theory of convection." Thesis, Massachusetts Institute of Technology, 1996. http://hdl.handle.net/1721.1/10577.
Повний текст джерелаGmeineder, Franz Xaver. "Regularity theory for variational problems on BD." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:1f412087-de70-44a8-a045-8923f1e29611.
Повний текст джерелаScott, Matthew. "Theory of electrode polarization, application of variational methods." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape3/PQDD_0015/MQ55238.pdf.
Повний текст джерелаTürköz, Ş. (Şemsettin). "Variational procedure for [phi]4-scalar field theory." Thesis, Massachusetts Institute of Technology, 1989. http://hdl.handle.net/1721.1/52913.
Повний текст джерелаOn t.p. "[phi]" is the original Greek letter.
Includes bibliographical references (leaves 81-83).
by Ş. Türköz.
Ph.D.
Santambrogio, Filippo. "Variational problems in transport theory with mass concentration." Doctoral thesis, Scuola Normale Superiore, 2006. http://hdl.handle.net/11384/85701.
Повний текст джерелаBuquicchio, Luke J. "Variational Open Set Recognition." Digital WPI, 2020. https://digitalcommons.wpi.edu/etd-theses/1377.
Повний текст джерелаBlack, Joshua. "Development and applications of Quasi-Variational Coupled-Cluster theory." Thesis, Cardiff University, 2017. http://orca.cf.ac.uk/105353/.
Повний текст джерелаBrown, Bruce J. L. "A variational approach to local optimality in control theory." Doctoral thesis, University of Cape Town, 2001. http://hdl.handle.net/11427/4869.
Повний текст джерелаA new approach to control theory is investigated in this thesis. The approach is based on a locally specified state space model of the control dynamics; together with a goal function, which defines a generalized distance from each state position to the desired equilibrium point or trajectory. A feedback control function is sought, which will result in a system response which approximates the gradient descent trajectories of the specified goal function. The approximation is chosen so that the resulting trajectories satisfy a certain local optimality criterion, involving the averaged second derivative of the goal function along the trajectories.
Laatz, C. D. "Cosmological perturbation theory and the variational principle in gravitation." Master's thesis, University of Cape Town, 2000. http://hdl.handle.net/11427/6671.
Повний текст джерелаInclude bibliographical references.
In this thesis firstly the theory of relativistic cosmological perturbations is studies, in the process being reviewed over the period 1960-1993. Secondly the variational principle, apropos of gravitation, is formulated and discussed. These two fields are then synthesised via a variational formulation of general relativity and cosmological perturbation theory. In the process new light is shed on Covariant Perturbation Theory via the development of generalised alternative variables, culminating in a unique variational formulation.
Lazzaroni, Giuliano. "Some results in the variational theory of crack growth." Doctoral thesis, SISSA, 2009. http://hdl.handle.net/20.500.11767/4621.
Повний текст джерелаAllagi, Mabruk Omar F. Mehemed. "Variational processing of Monte Carlo solutions in neutron transport theory." Thesis, University of Cambridge, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.624171.
Повний текст джерелаAlmoukhalalati, Adel. "Applications of variational perturbation theory in relativistic molecular quantum mechanics." Toulouse 3, 2016. http://www.theses.fr/2016TOU30172.
Повний текст джерелаThe father of relativistic quantum mechan ics P. A. M. Dirac predicted that, the more realistic version of quantum mechanics that he established wouId not offer much more when compared to the non-relativistic formulation of quantum mechanics when applied to ordinary atomic and molecular systems. When the relativistic quantum theory was around forty years old, people had started to recognize how important relativistic effects can beeven for the study of atomic and molecular systems. Relativistic effects are manifested via the contraction of atomics and p orbitais, the expansion of atomic d and 1 orbitais, and spin-orbit coupling. A classical example on t he importance of relativistic effects is the band struct ure of metallic gold for which non-relativistic caleulations will lead to an overestimation of the 5d-6p gap predicting a UV absorption band which is compatible with a metal that looks like silver. The thesis focuses on the atomic and molecular calculations within the 4-component relativistic framework. Ln particular, the use of the variational perturbation theory in relativistic framework. The perturbation theory in quantum mechanics is based on partitioning the Hamiltonian H into zeroth-order Hamiltonian Ho and V that forms the perturbation through a para meter lambda. Ln many-body (Rayleigh-Sch rodinger) perturbation theory, we have an exact solution of t he Hamiltonian l/0 , whereas in the variational perturbation theory, we assume to have anoptimized energy for any value of the parameter À. The thesis contains two principal projects, the first project concerns the description of the electron correlation in the relativistic framework. Ln this project , we focused on the perturbative approach to derive t he relativistic formulas nece~sary for the energy in two-electron atoms. T hecorrelation energy is the difference between the exact eigenvalue of the Ha mi ltonian and its expectation value in the Hartree-Fock approximation. The exact eigenvalue is not avail able, but in the non- relativistic domain t he best solution is a full Cl for a given basis. Our main goal, in this project , will be to show that the best solution of the wave equation for the embedded Dirac-Coulomb Hamil tonian, is not a Full Cl, as in thenon- relativistic case, but a MCSCF which uses a Cl development in positive-energy orbitais only, but which keeps rotations between the positive and negative energy orbitais to optimize the projection operator. The second project concerns a study of the effects of t he nuclear volume in the vibrational spectra of diatomic molecules. Ln the early 80s, Theg roup of Professor Eberhardt Tiemann in Hanover used the rotational spectroscopy with high resolution to study a series of diatomic molecules containing heavy a toms like lead in order to establish spectroscopie constants (R. Bond length, vibrational frequency W c etc. ) with a great precision. A molecule AB has several isotopomers according to isotopes atoms A and B and it was weil known at that t ime only the spectrum of eachisotopomer is slightly d iffe rent because of the mass differences between each isotope of the atoms A and B. Prof. Tiemann and his collaborators discovered that we must also take into account the difference in nuclear volume of each isotope. We provide an independent check on previous experimental and t heoretical studies of nuclear volume effects in rotational spectroscopy, notably re-derivation of theory and benchmark previous calculations by 4-component relativistic state of the art correlated calculations
Ding, Bingfeng. "Variational particle-antiparticle bound states in the scalar Yukawa model." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ59128.pdf.
Повний текст джерелаMosher, Scott William. "A Variational Transport Theory Method for Two-Dimensional Reactor Core Calculations." Diss., Georgia Institute of Technology, 2004. http://hdl.handle.net/1853/5070.
Повний текст джерелаIlas, Danut. "Coarse mesh transport theory model for heterogeneous systems." Diss., Georgia Institute of Technology, 2001. http://hdl.handle.net/1853/16089.
Повний текст джерелаFranklin, C. P. "Scattering theory with applications to muon catalysed fusion and positron H2+ collisions." Thesis, University of Nottingham, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.281636.
Повний текст джерелаKovvali, Ravi Kumar. "A nonlinear theory of Cosserat elastic plates using the variational-asymptotic method." Diss., Georgia Institute of Technology, 2015. http://hdl.handle.net/1853/54342.
Повний текст джерелаSADE, MARTIN CHARLES. "VARIATIONAL PRINCIPLES FOR FIELD VARIABLES SUBJECT TO GROUP ACTIONS (GAUGE)." Diss., The University of Arizona, 1985. http://hdl.handle.net/10150/188075.
Повний текст джерелаZhang, Chen-Song. "Adaptive finite element methods for variational inequalities theory and applications in finance /." College Park, Md. : University of Maryland, 2007. http://hdl.handle.net/1903/7167.
Повний текст джерелаThesis research directed by: Applied Mathematics and Scientific Computation Program. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
Doole, Stuart Harvey. "Steady gravity waves on flows with vorticity : bifurcation theory and variational principles." Thesis, University of Oxford, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.357537.
Повний текст джерелаChyou, Hui-Huang Abel. "Variational formulation and finite element implementation of Pagano's theory of laminated plates /." The Ohio State University, 1989. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487671108308444.
Повний текст джерелаGalbraith, Grant N. "Applications of variational analysis to optimal trajectories and nonsmooth Hamilton-Jacobi theory /." Thesis, Connect to this title online; UW restricted, 1999. http://hdl.handle.net/1773/5766.
Повний текст джерелаKim, Yunho. "Variational methods theory and its applications to image deblurring and denoising problems /." Diss., Restricted to subscribing institutions, 2009. http://proquest.umi.com/pqdweb?did=1872146111&sid=1&Fmt=2&clientId=1564&RQT=309&VName=PQD.
Повний текст джерелаMongiardo, Mauro. "Variational analysis of waveguide discontinuities by integral equation including the edge condition." Thesis, University of Bath, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.305044.
Повний текст джерелаPonsiglione, Marcello. "Stability of Neumann problems and applications to the variational theory of crack propagation." Doctoral thesis, SISSA, 2004. http://hdl.handle.net/20.500.11767/4175.
Повний текст джерелаChi, Xuguang. "A non-variational approach to the quantum three-body coulomb problem /." View abstract or full-text, 2004. http://library.ust.hk/cgi/db/thesis.pl?PHYS%202004%20CHI.
Повний текст джерелаWang, Jiabin. "Variational Bayes inference based segmentation algorithms for brain PET-CT images." Thesis, The University of Sydney, 2012. https://hdl.handle.net/2123/29251.
Повний текст джерелаSimo, Tao Lee Walter Cédric. "On the variational approach to mollification in the theory of ill-posed problems and applications." Thesis, Toulouse 3, 2020. http://www.theses.fr/2020TOU30130.
Повний текст джерелаInverse problems is a fast growing area in applied mathematics which has gained a great attention in the last decades due to its ubiquity in several fields of sciences and technology. Yet, most often, inverse problems result in mathematical equation which are unstable. That is, the solutions do not continuously depend on the data. As a matter of fact, very little perturbations on the data might cause arbitrary large errors on the solutions. Therefore, given that the noise is generally unavoidable in the data, direct attempts to solve the problem fail and one needs to apply a regularization method in order to recover stable approximates of the unknown solutions. In this respect, several regularization techniques have been developed in the literature. Globally, all these regularization methods can be split into two classes: A class of methods which attempt to reconstruct the unknown solutions and a class of methods which try to recover smooth versions of the unknown solutions. The aim of this thesis is to contribute to the promotion of the second class of regularization method via the study and application of the variational formulation of mollification. In this work, we show that the variational approach can be extended to the regularization of ill-posed problems involving non-compact operators. In this respect, we study and successfully apply the method to a problem coming from statistics namely the nonparametric instrumental regression. An additional contribution of this thesis is the design and study of a novel regularization method suitable for linear exponentially ill-posed problems. A numerical comparison of the new method to classical regularization methods such as Tikhonov, spectral cut-off, asymptotic regularization and conjugate gradient is carried out on three test problems from literature. The practical aspect of selection of the regularization parameter without knowledge of the noise level is also considered. Apart from the study and application of regularization methods, this thesis also focuses on the application of a very popular parameter selection rule known as the Morozov principle. Using Lagrange duality, we provide a simple and rapid algorithm for the computation of the regularization parameter corresponding to this rule for Tikhonov-like regularization methods. A relevance of this study is that it highlights a poorly known regularization method which yet has a great potential and is able to provide comparatively better approximate solutions compared to well-known classical regularization techniques. Another benefit of this thesis is the design of a new regularization method which, we believe, is promising in the regularization of exponentially ill-posed problems, especially for inverse heat conduction problems
Borghi, Giovanni. "Gutzwiller approximation applied to inhomogeneous lattice models and solid-state systems." Doctoral thesis, SISSA, 2011. http://hdl.handle.net/20.500.11767/4290.
Повний текст джерелаBui, Hoa. "Extremality and stationarity of collections of sets : metric, slope and normal cone characterisations." Thesis, Federation University of Australia, 2019. http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/178600.
Повний текст джерелаDoctor of Philosophy
Spencer, Paul. "Variational problems arising in classical mechanics and nonlinear elasticity." Thesis, University of Bath, 1999. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.323570.
Повний текст джерелаChen, Guang. "General Variational Principles : theory and applications to the approximate solutions of nonlinear and/or nonconservative oscillations." Diss., Georgia Institute of Technology, 1986. http://hdl.handle.net/1853/14996.
Повний текст джерелаCaruso, Valeria. "Variational inequalities and networks for organ transplants and for humanitarian organizations." Doctoral thesis, Università di Catania, 2018. http://hdl.handle.net/10761/3788.
Повний текст джерелаWarschkow, Oliver. "A divide-and-conquer implementation of the discrete variational DFT method for large molecular and solid systems." Thesis, University of Southampton, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.284652.
Повний текст джерелаSingh, Kumaresh. "Efficient Computational Tools for Variational Data Assimilation and Information Content Estimation." Diss., Virginia Tech, 2010. http://hdl.handle.net/10919/39125.
Повний текст джерелаPh. D.
Pontaza, Juan Pablo. "Least-squares variational principles and the finite element method: theory, formulations, and models for solid and fluid mechanics." Diss., Texas A&M University, 2003. http://hdl.handle.net/1969.1/288.
Повний текст джерелаVierling, Morten [Verfasser], and Michael [Akademischer Betreuer] Hinze. "Control-constrained parabolic optimal control problems on evolving surfaces : theory and variational discretization / Morten Vierling. Betreuer: Michael Hinze." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2013. http://d-nb.info/1042753873/34.
Повний текст джерелаHaro, Àlex. "The Primitive Function of an Exact Symplectomorphism. Variational principles, Converse KAM Theory and the problems of determination and interpolation." Doctoral thesis, Universitat de Barcelona, 1998. http://hdl.handle.net/10803/2116.
Повний текст джерелаa) PART I: Exact symplectic geometry (introduction of the problems). This part contains the basic tools of symplectic geometry and outlines the four subjects that we have study along the thesis: the determination problem, the interpolation problem, the variational problem and the breakdown problem.
b) PART II: On the standard symplectic manifold (analytical part). We recall the necessary tools to work on R(d) x R(d). That is we perform a coordinate treatment of the results. First of all we relate different kinds of generating functions to the primitive function and later we solve formally the determination problem. Then we introduce different variational principles: for fixed points, periodic orbits and orbital segments. Their invariance under certain kind of transformations of phase space is proved, and we interpret physically such results. Finally we give the basic properties of invariant exact Lagrangian graphs obtaining at last that if our graph is minimizing then its orbits are minimizing.
c) PART III: On the cotangent bundle (geometrical part). The first three chapters are similar to the three previous ones with the difference that we do an intrinsic treatment of the results by considering any cotangent bundle. The fourth chapter in this part deals with the solution of the interpolation problem given in analytic set up.
d) PART IV: Converse KAM theory (numerical part). The last part deals with the applications to converse Kolmogorv-Arnold-Moser (KAM) theory. First of all we give a small list of different examples that we shall study later. Then we generalize converse KAM theory and we related it to the Lipschitz theory by Birkhoff and Herman. Then we perform our variational Greene method and apply it to different examples. Also we study numerically the Aubry-Mather sets in higher dimensions. After this we apply our methods to the rotational standard map that is a symplectic skew product. Then we give some ideas about the geometrical obstructions for existence of invariant tori showing them with a simple example. We also find some known Birkhoff normal forms using our methods. Finally we explain briefly how our theory can be used for arbitrary Lagrangian foliations.
La present memòria es troba dividida en quatre parts ben diferenciades. La primera conté les eines bàsiques de la geometria simplèctica i planteja els quatre problemes que tractarem al llarg de la memòria: el problema de determinació, el problema d'interpolació, el problema variacional i el problema del trencament de tors invariants.
La segona part tracta sobre la varietat simpléctica estàndard, i vindria a ser la part analítica. Aquí hem treballat a R(d) x R(d), és a dir hem fet un tractament coordenat dels resultats. Primer relacionem les funcions generatrius amb la funció primitiva i després resolem formalment el problema de determinación. Tot seguit tractem diferents principis variacionals per als punts fixos per a les òrbites periòdiques i per als segments orbitals. La seva invariància respecte a certs tipus de transformacions de l'espai de fase és demostrada donant una interpretació física. Finalment donem les propietats bàsiques dels grafs Lagrangians invariants, especialment aquella que diu que les òrbites sobre un graf minimitzant són minimitzants.
La tercera part abraça el tema del fibrat cotangent, la part geométrica de l'obra. Els tres primers capítols segueixen més o menys la línia dels tres precedents amb la diferéncia fonamental que aquí considerem qualsevol fibrat cotangent. Fem llavors un tractament intrínsec. El quart capítol d'aquesta part està dedicat a resoldre el problema d'interpolació en el cas analític.
La quarta i darrera part (que vindria a ser la secció numèrica de la tesi), tracta de les aplicacions a la teoria Kolmogorv, Arnold i Moser (KAM) inversa o del trencament dels tors invariants. Primer donem una llista d'exemples que utilitzarem més endavant. Després generalitzem la teoria KAM inversa i la relacionem amb la teoria Lipschitziana de Birkhoff i Herman. Llavors implementem el nostre criteri de Greene variacional i l'apliquem a diferents exemples. També estudiem els equivalents dels conjunts d'Aubry-Mather en dimensió alta (bé = 4). Després apliquem aquesta metodologia a l'aplicació estàndard rotacional (3D), indicant abans la teoria necessària. Llavors donem algunes idees de com generalitzar els criteris obstruccionals a dimensions altes hi ho mostrem amb un petit exemple. Finalment retrobem algunes formes normals de Birkhoff utilitzant la nostra metodologia basada en la funcióprimitiva i expliquem una mica com es podria considerar la nostra teoria tenint en compte foliacions Lagrangianes arbitràries.
Goßler, Timo, Tina Wakolbinger, Anna Nagurney, and Patrizia Daniele. "How to increase the impact of disaster relief: a study of transportation rates, framework agreements and product distribution." Elsevier, 2019. http://dx.doi.org/10.1016/j.ejor.2018.09.045.
Повний текст джерелаBarbagallo, Mathias. "Statistical energy analysis and variational principles for the prediction of sound transmission in multilayered structures." Doctoral thesis, KTH, MWL Marcus Wallenberg Laboratoriet, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-118427.
Повний текст джерелаQC 20130218
Maad, Sara. "Critical point theory with applications to semilinear problems without compactness." Doctoral thesis, Uppsala : Matematiska institutionen, Univ. [distributör], 2002. http://publications.uu.se/theses/91-506-1557-2/.
Повний текст джерелаSmith, Todd Blanton. "Variational embedded solitons, and traveling wavetrains generated by generalized Hopf bifurcations, in some NLPDE systems." Doctoral diss., University of Central Florida, 2011. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/5042.
Повний текст джерелаID: 029809927; System requirements: World Wide Web browser and PDF reader.; Mode of access: World Wide Web.; Thesis (Ph.D.)--University of Central Florida, 2011.; Includes bibliographical references (p. 121-129).
Ph.D.
Doctorate
Mathematics
Sciences
Yu, Haofeng. "A Numerical Investigation Of The Canonical Duality Method For Non-Convex Variational Problems." Diss., Virginia Tech, 2011. http://hdl.handle.net/10919/29095.
Повний текст джерелаPh. D.
Aragão, Cristiane Moura Lima de. "Cálculo de integrais de trajetória em mecânica estatística e teoria de campos através de técnicas variacionais." Universidade de São Paulo, 2002. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-18022014-140626/.
Повний текст джерелаWe have extended the Kleinert variational technique to field theory. This method was first used in quantum mechanics and provides a convergent cumulate expansion that is extremely accurate. Its extension to field theory is non-trivial because of the ultraviolet divergences that appear when the space dimension is greater than 2. Due to these divergences the theory has to be regularized and renormalized. In addition to the usual difficulties associated with renormalization, one has to decide whether one calculates the optimum value of the variational parameter before or after renormalization. In this thesis we deal with the renormalization of the variational effective potential. Firstly, we show that the zero temperature regularized variational potential coincides with the post-Gaussian effective potential introduced by Stancu and Stenvenson. Secondly, we present a renormalization scheme that enables one to renormalize the theory before calculating the optimum variational parameter. Using this scheme we show that the usual 1-loop effective potential can be obtained from the Kleinert variational scheme by interacting only once the equation that determines the variational parameter. In this sense, the 1-loop expansion is contained within the variational scheme. For the 2-loop effective potential the same approximation is not so good. The renormalization of the theory before the calculation of the variational parameter allows one to study the variational effective potential numerically and in a non-pertubative way, as it was done in quantum mechanics by Kleinert.
Maslovaric, Marcel [Verfasser], Henrik [Akademischer Betreuer] Seppänen, Henrik [Gutachter] Seppänen, Viktor [Gutachter] Pidstrygach, and Daniel [Gutachter] Greb. "Variational Geometric Invariant Theory and Moduli of Quiver Sheaves / Marcel Maslovaric ; Gutachter: Henrik Seppänen, Viktor Pidstrygach, Daniel Greb ; Betreuer: Henrik Seppänen." Göttingen : Niedersächsische Staats- und Universitätsbibliothek Göttingen, 2018. http://d-nb.info/1161942149/34.
Повний текст джерелаHu, Xu. "Towards efficient learning of graphical models and neural networks with variational techniques." Thesis, Paris Est, 2019. http://www.theses.fr/2019PESC1037.
Повний текст джерелаIn this thesis, I will mainly focus on variational inference and probabilistic models. In particular, I will cover several projects I have been working on during my PhD about improving the efficiency of AI/ML systems with variational techniques. The thesis consists of two parts. In the first part, the computational efficiency of probabilistic graphical models is studied. In the second part, several problems of learning deep neural networks are investigated, which are related to either energy efficiency or sample efficiency
Silva, Edcarlos Domingos da. "Multiplicidade de soluções para sistemas gradientes semilineares ressonantes." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306981.
Повний текст джерелаTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
Made available in DSpace on 2018-08-13T06:21:00Z (GMT). No. of bitstreams: 1 Silva_EdcarlosDomingosda_D.pdf: 993704 bytes, checksum: d68d4e58a916f7d2428f76207a8cb4da (MD5) Previous issue date: 2009
Resumo: Nesta tese lidamos com três classes de sistemas gradientes ressonantes. A primeira classe é um sistema com ressonância do tipo Landesman-Lazer. A segunda classe é um sistema fortemente ressonante enquanto a terceira classe é um sistema com ressonância no infinito e na origem. Analisamos as questões de existência e multiplicidade de soluções em cada uma das classes mencionadas. Para obtermos os nossos principais resultados aplicamos alguns métodos variacionais, tais como, teoremas Min-Max e minimização. Além disso, usamos a Teoria de Morse para distinguirmos soluções dados por métodos variacionais distintos.
Abstract: In this thesis we deal with three classes of gradient elliptic systems with resonance. The first class is a resonant system of Landesman-Lazer type. The second class is a system of strong resonance type while the third class is a system with resonance at infinity and at origin. We are concerned about the questions of existence and multiplicity of solutions in each of the classes mentioned. To obtain our main results we apply variational methods, such as, Min-max theorems and minimization. Moreover, we use Morse Theory to distinguish the solutions given by different variational methods.
Doutorado
Doutor em Matemática
Gairing, Jan Martin. "Variational and Ergodic Methods for Stochastic Differential Equations Driven by Lévy Processes." Doctoral thesis, Humboldt-Universität zu Berlin, 2018. http://dx.doi.org/10.18452/18984.
Повний текст джерелаThe present thesis investigates certain aspects of the interplay between the ergodic long time behavior and the smoothing property of dynamical systems generated by stochastic differential equations (SDEs) with jumps, in particular SDEs driven by Lévy processes and the Marcus’ canonical equation. A variational approach to the Malliavin calculus generates an integration-by-parts formula that allows to transfer spatial variation to variation in the probability measure. The strong Feller property of the associated Markov semigroup and the existence of smooth transition densities are deduced from a non-standard ellipticity condition on a combination of the Gaussian and a jump covariance. Similar results on submanifolds are inferred from the ambient Euclidean space. These results are then applied to random dynamical systems generated by linear stochas- tic differential equations. Ruelle’s integrability condition translates into an integrability condition for the Lévy measure and ensures the validity of the multiplicative ergodic theo- rem (MET) of Oseledets. Hence the exponential growth rate is governed by the Lyapunov spectrum. Finally the top Lyapunov exponent is represented by a formula of Furstenberg– Khasminskii–type as an ergodic average of the infinitesimal growth rate over the unit sphere.
Eskandari, Aram. "VAE-clustering of neural signals and their association to cytokines." Thesis, KTH, Matematisk statistik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-273627.
Повний текст джерелаI detta examensarbete börjar vi med att reproducera tidigare experiment av Zanos et al., där dom visat att det är möjligt att associera nervsignaler med specifika cytokiner. Ett framtida mål med detta projekt är att skicka syntetiska nervsignaler till kroppen för att observera reaktioner utan motsvarande katalysator av symptomen. Vi använder en variational autoencoder (VAE) i våra experiment för att skapa en modell kapabel till att generera nya nervsignaler, och vi introducerar en ny klusterings-teknik kallad VAE-klustring, vilken kommer att användas för att klustra nervsignaler med dess associerade cytokiner. Fokuset i detta arbete ligger i implementationen av denna metod och applicerandet på nervsignaler. Efter att ha kört VAE-klustring på MNIST dataset fann vi att det det är användbart för att hitta detaljerade egenskaper hos ett dataset. Vi har även funnit att användningen av en VAE som en generativ modell för nervsignaler är ett bra sätt att återskapa detaljerade vågformer.