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Yuan, Rui. "Stochastic Second Order Methods and Finite Time Analysis of Policy Gradient Methods". Electronic Thesis or Diss., Institut polytechnique de Paris, 2023. http://www.theses.fr/2023IPPAT010.
Pełny tekst źródłaTo solve large scale machine learning problems, first-order methods such as stochastic gradient descent and ADAM are the methods of choice because of their low cost per iteration. The issue with first order methods is that they can require extensive parameter tuning, and/or knowledge of the parameters of the problem. There is now a concerted effort to develop efficient stochastic second order methods to solve large scale machine learning problems. The motivation is that they require less parameter tuning and converge for wider variety of models and datasets. In the first part of the thesis, we presented a principled approach for designing stochastic Newton methods for solving both nonlinear equations and optimization problems in an efficient manner. Our approach has two steps. First, we can re-write the nonlinear equations or the optimization problem as desired nonlinear equations. Second, we apply new stochastic second order methods to solve this system of nonlinear equations. Through our general approach, we showcase many specific new second-order algorithms that can solve the large machine learning problems efficiently without requiring knowledge of the problem nor parameter tuning. In the second part of the thesis, we then focus on optimization algorithms applied in a specific domain: reinforcement learning (RL). This part is independent to the first part of the thesis. To achieve such high performance of RL problems, policy gradient (PG) and its variant, natural policy gradient (NPG), are the foundations of the several state of the art algorithms (e.g., TRPO and PPO) used in deep RL. In spite of the empirical success of RL and PG methods, a solid theoretical understanding of even the “vanilla” PG has long been elusive. By leveraging the RL structure of the problem together with modern optimization proof techniques, we derive new finite time analysis of both PG and NPG. Through our analysis, we also bring new insights to the methods with better hyperparameter choices
Auffredic, Jérémy. "A second order Runge–Kutta method for the Gatheral model". Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-49170.
Pełny tekst źródłaCheng, Jianqiang. "Stochastic Combinatorial Optimization". Thesis, Paris 11, 2013. http://www.theses.fr/2013PA112261.
Pełny tekst źródłaIn this thesis, we studied three types of stochastic problems: chance constrained problems, distributionally robust problems as well as the simple recourse problems. For the stochastic programming problems, there are two main difficulties. One is that feasible sets of stochastic problems is not convex in general. The other main challenge arises from the need to calculate conditional expectation or probability both of which are involving multi-dimensional integrations. Due to the two major difficulties, for all three studied problems, we solved them with approximation approaches.We first study two types of chance constrained problems: linear program with joint chance constraints problem (LPPC) as well as maximum probability problem (MPP). For both problems, we assume that the random matrix is normally distributed and its vector rows are independent. We first dealt with LPPC which is generally not convex. We approximate it with two second-order cone programming (SOCP) problems. Furthermore under mild conditions, the optimal values of the two SOCP problems are a lower and upper bounds of the original problem respectively. For the second problem, we studied a variant of stochastic resource constrained shortest path problem (called SRCSP for short), which is to maximize probability of resource constraints. To solve the problem, we proposed to use a branch-and-bound framework to come up with the optimal solution. As its corresponding linear relaxation is generally not convex, we give a convex approximation. Finally, numerical tests on the random instances were conducted for both problems. With respect to LPPC, the numerical results showed that the approach we proposed outperforms Bonferroni and Jagannathan approximations. While for the MPP, the numerical results on generated instances substantiated that the convex approximation outperforms the individual approximation method.Then we study a distributionally robust stochastic quadratic knapsack problems, where we only know part of information about the random variables, such as its first and second moments. We proved that the single knapsack problem (SKP) is a semedefinite problem (SDP) after applying the SDP relaxation scheme to the binary constraints. Despite the fact that it is not the case for the multidimensional knapsack problem (MKP), two good approximations of the relaxed version of the problem are provided which obtain upper and lower bounds that appear numerically close to each other for a range of problem instances. Our numerical experiments also indicated that our proposed lower bounding approximation outperforms the approximations that are based on Bonferroni's inequality and the work by Zymler et al.. Besides, an extensive set of experiments were conducted to illustrate how the conservativeness of the robust solutions does pay off in terms of ensuring the chance constraint is satisfied (or nearly satisfied) under a wide range of distribution fluctuations. Moreover, our approach can be applied to a large number of stochastic optimization problems with binary variables.Finally, a stochastic version of the shortest path problem is studied. We proved that in some cases the stochastic shortest path problem can be greatly simplified by reformulating it as the classic shortest path problem, which can be solved in polynomial time. To solve the general problem, we proposed to use a branch-and-bound framework to search the set of feasible paths. Lower bounds are obtained by solving the corresponding linear relaxation which in turn is done using a Stochastic Projected Gradient algorithm involving an active set method. Meanwhile, numerical examples were conducted to illustrate the effectiveness of the obtained algorithm. Concerning the resolution of the continuous relaxation, our Stochastic Projected Gradient algorithm clearly outperforms Matlab optimization toolbox on large graphs
Sabbagh, Wissal. "Some Contributions on Probabilistic Interpretation For Nonlinear Stochastic PDEs". Thesis, Le Mans, 2014. http://www.theses.fr/2014LEMA1019/document.
Pełny tekst źródłaThe objective of this thesis is to study the probabilistic representation (Feynman-Kac for- mula) of different classes ofStochastic Nonlinear PDEs (semilinear, fully nonlinear, reflected in a domain) by means of backward doubly stochastic differential equations (BDSDEs). This thesis contains four different parts. We deal in the first part with the second order BDS- DEs (2BDSDEs). We show the existence and uniqueness of solutions of 2BDSDEs using quasi sure stochastic control technics. The main motivation of this study is the probabilistic representation for solution of fully nonlinear SPDEs. First, under regularity assumptions on the coefficients, we give a Feynman-Kac formula for classical solution of fully nonlinear SPDEs and we generalize the work of Soner, Touzi and Zhang (2010-2012) for deterministic fully nonlinear PDE. Then, under weaker assumptions on the coefficients, we prove the probabilistic representation for stochastic viscosity solution of fully nonlinear SPDEs. In the second part, we study the Sobolev solution of obstacle problem for partial integro-differentialequations (PIDEs). Specifically, we show the Feynman-Kac formula for PIDEs via reflected backward stochastic differentialequations with jumps (BSDEs). Specifically, we establish the existence and uniqueness of the solution of the obstacle problem, which is regarded as a pair consisting of the solution and the measure of reflection. The approach is based on stochastic flow technics developed in Bally and Matoussi (2001) but the proofs are more technical. In the third part, we discuss the existence and uniqueness for RBDSDEs in a convex domain D without any regularity condition on the boundary. In addition, using the approach based on the technics of stochastic flow we provide the probabilistic interpretation of Sobolev solution of a class of reflected SPDEs in a convex domain via RBDSDEs. Finally, we are interested in the numerical solution of BDSDEs with random terminal time. The main motivation is to give a probabilistic representation of Sobolev solution of semilinear SPDEs with Dirichlet null condition. In this part, we study the strong approximation of this class of BDSDEs when the random terminal time is the first exit time of an SDE from a cylindrical domain. Thus, we give bounds for the discrete-time approximation error.. We conclude this part with numerical tests showing that this approach is effective
El-Sharif, Najla Saleh Ahmed. "Second-order methods for some nonlinear second-order initial-value problems with forcing". Thesis, Brunel University, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.309501.
Pełny tekst źródłaNoubiagain, Chomchie Fanny Larissa. "Contributions to second order reflected backward stochastic differentials equations". Thesis, Le Mans, 2017. http://www.theses.fr/2017LEMA1016/document.
Pełny tekst źródłaThis thesis deals with the second-order reflected backward stochastic differential equations (2RBSDEs) in general filtration. In the first part , we consider the reflection with a lower obstacle and then extended the result in the case of an upper obstacle . Our main contribution consists in demonstrating the existence and the uniqueness of the solution of these equations defined in the general filtration under weak assumptions. We replace the uniform regularity by the Borel regularity(through analytic measurability). The dynamic programming principle for the robust stochastic control problem is thus demonstrated under weak assumptions, that is to say without regularity on the generator, the terminal condition and the obstacle. In the standard Backward Stochastic Differential Equations (BSDEs) framework, there is a symmetry between lower and upper obstacles reflection problem. On the contrary, in the context of second order BSDEs, this symmetry is no longer satisfy because of the nonlinearity of the expectation under which our robust stochastic non-dominated stochastic control problem is defined. In the second part , we get a numerical approximation scheme of a class of second-order reflected BSDEs. In particular we show the convergence of our scheme and we test numerically the results
Karlgaard, Christopher David. "Second-Order Relative Motion Equations". Thesis, Virginia Tech, 2001. http://hdl.handle.net/10919/34025.
Pełny tekst źródłaMaster of Science
Rodríguez, Cuesta Mª José. "Limit of detection for second-order calibration methods". Doctoral thesis, Universitat Rovira i Virgili, 2006. http://hdl.handle.net/10803/9013.
Pełny tekst źródłaThe lowest quantity of a substance that can be distinguished from the absence of that substance (a blank value) is called the detection limit or limit of detection (LOD). Traditionally, in the context of simple measurements where the instrumental signal only depends on the amount of analyte, a multiple of the blank value is taken to calculate the LOD (traditionally, the blank value plus three times the standard deviation of the measurement). However, the increasing complexity of the data that analytical instruments can provide for incoming samples leads to situations in which the LOD cannot be calculated as reliably as before.
Measurements, instruments and mathematical models can be classified according to the type of data they use. Tensorial theory provides a unified language that is useful for describing the chemical measurements, analytical instruments and calibration methods. Instruments that generate two-dimensional arrays of data are second-order instruments. A typical example is a spectrofluorometer, which provides a set of emission spectra obtained at different excitation wavelengths.
The calibration methods used with each type of data have different features and complexity. In this thesis, the most commonly used calibration methods are reviewed, from zero-order (or univariate) to second-order (or multi-linears) calibration models. Second-order calibration models are treated in details since they have been applied in the thesis.
Concretely, the following methods are described:
- PARAFAC (Parallel Factor Analysis)
- ITTFA (Iterative Target Transformation Analysis)
- MCR-ALS (Multivariate Curve Resolution-Alternating Least Squares)
- N-PLS (Multi-linear Partial Least Squares)
Analytical methods should be validated. The validation process typically starts by defining the scope of the analytical procedure, which includes the matrix, target analyte(s), analytical technique and intended purpose. The next step is to identify the performance characteristics that must be validated, which may depend on the purpose of the procedure, and the experiments for determining them. Finally, validation results should be documented, reviewed and maintained (if not, the procedure should be revalidated) as long as the procedure is applied in routine work.
The figures of merit of a chemical analytical process are 'those quantifiable terms which may indicate the extent of quality of the process. They include those terms that are closely related to the method and to the analyte (sensitivity, selectivity, limit of detection, limit of quantification, ...) and those which are concerned with the final results (traceability, uncertainty and representativity) (Inczédy et al., 1998). The aim of this thesis is to develop theoretical and practical strategies for calculating the limit of detection for complex analytical situations. Specifically, I focus on second-order calibration methods, i.e. when a matrix of data is available for each sample.
The methods most often used for making detection decisions are based on statistical hypothesis testing and involve a choice between two hypotheses about the sample. The first hypothesis is the "null hypothesis": the sample is analyte-free. The second hypothesis is the "alternative hypothesis": the sample is not analyte-free. In the hypothesis test there are two possible types of decision errors. An error of the first type occurs when the signal for an analyte-free sample exceeds the critical value, leading one to conclude incorrectly that the sample contains a positive amount of the analyte. This type of error is sometimes called a "false positive". An error of the second type occurs if one concludes that a sample does not contain the analyte when it actually does and it is known as a "false negative". In zero-order calibration, this hypothesis test is applied to the confidence intervals of the calibration model to estimate the LOD as proposed by Hubaux and Vos (A. Hubaux, G. Vos, Anal. Chem. 42: 849-855, 1970).
One strategy for estimating multivariate limits of detection is to transform the multivariate model into a univariate one. This strategy has been applied in this thesis in three practical applications:
1. LOD for PARAFAC (Parallel Factor Analysis).
2. LOD for ITTFA (Iterative Target Transformation Factor Analysis).
3. LOD for MCR-ALS (Multivariate Curve Resolution - Alternating Least Squares)
In addition, the thesis includes a theoretical contribution with the proposal of a sample-dependent LOD in the context of multivariate (PLS) and multi-linear (N-PLS) Partial Least Squares.
La Química Analítica es pot dividir en dos tipus d'anàlisis, l'anàlisi quantitativa i l'anàlisi qualitativa. La gran part de la química analítica moderna és quantitativa i fins i tot els govern fan ús d'aquesta ciència per establir regulacions que controlen, per exemple, nivells d'exposició a substàncies tòxiques que poden afectar la salut pública. El concepte de mínima quantitat d'un analit o component que es pot detectar apareix en moltes d'aquestes regulacions, en general com una part de la validació dels mètodes per tal de garantir la qualitat i la validesa dels resultats.
La mínima quantitat d'una substància que pot ser diferenciada de l'absència d'aquesta substància (el que es coneix com un blanc) s'anomena límit de detecció (limit of detection, LOD). En procediments on es treballa amb mesures analítiques que són degudes només a la quantitat d'analit present a la mostra (situació d'ordre zero) el LOD es pot calcular com un múltiple de la mesura del blanc (tradicionalment, 3 vegades la desviació d'aquesta mesura). Tanmateix, l'evolució dels instruments analítics i la complexitat creixent de les dades que generen, porta a situacions en les que el LOD no es pot calcular fiablement d'una forma tan senzilla. Les mesures, els instruments i els models de calibratge es poden classificar en funció del tipus de dades que utilitzen. La Teoria Tensorial s'ha utilitzat en aquesta tesi per fer aquesta classificació amb un llenguatge útil i unificat. Els instruments que generen dades en dues dimensions s'anomenen instruments de segon ordre i un exemple típic és l'espectrofluorímetre d'excitació-emissió, que proporciona un conjunt d'espectres d'emissió obtinguts a diferents longituds d'ona d'excitació.
Els mètodes de calibratge emprats amb cada tipus de dades tenen diferents característiques i complexitat. En aquesta tesi, es fa una revisió dels models de calibratge més habituals d'ordre zero (univariants), de primer ordre (multivariants) i de segon ordre (multilinears). Els mètodes de segon ordre estan tractats amb més detall donat que són els que s'han emprat en les aplicacions pràctiques portades a terme.
Concretament es descriuen:
- PARAFAC (Parallel Factor Analysis)
- ITTFA (Iterative Target Transformation Analysis)
- MCR-ALS (Multivariate Curve Resolution-Alternating Least Squares)
- N-PLS (Multi-linear Partial Least Squares)
Com s'ha avançat al principi, els mètodes analítics s'han de validar. El procés de validació inclou la definició dels límits d'aplicació del procediment analític (des del tipus de mostres o matrius fins l'analit o components d'interès, la tècnica analítica i l'objectiu del procediment). La següent etapa consisteix en identificar i estimar els paràmetres de qualitat (figures of merit, FOM) que s'han de validar per, finalment, documentar els resultats de la validació i mantenir-los mentre sigui aplicable el procediment descrit.
Algunes FOM dels processos químics de mesura són: sensibilitat, selectivitat, límit de detecció, exactitud, precisió, etc. L'objectiu principal d'aquesta tesi és desenvolupar estratègies teòriques i pràctiques per calcular el límit de detecció per problemes analítics complexos. Concretament, està centrat en els mètodes de calibratge que treballen amb dades de segon ordre.
Els mètodes més emprats per definir criteris de detecció estan basats en proves d'hipòtesis i impliquen una elecció entre dues hipòtesis sobre la mostra. La primera hipòtesi és la hipòtesi nul·la: a la mostra no hi ha analit. La segona hipòtesis és la hipòtesis alternativa: a la mostra hi ha analit. En aquest context, hi ha dos tipus d'errors en la decisió. L'error de primer tipus té lloc quan es determina que la mostra conté analit quan no en té i la probabilitat de cometre l'error de primer tipus s'anomena fals positiu. L'error de segon tipus té lloc quan es determina que la mostra no conté analit quan en realitat si en conté i la probabilitat d'aquest error s'anomena fals negatiu. En calibratges d'ordre zero, aquesta prova d'hipòtesi s'aplica als intervals de confiança de la recta de calibratge per calcular el LOD mitjançant les fórmules d'Hubaux i Vos (A. Hubaux, G. Vos, Anal. Chem. 42: 849-855, 1970)
Una estratègia per a calcular límits de detecció quan es treballa amb dades de segon ordre es transformar el model multivariant en un model univariant. Aquesta estratègia s'ha fet servir en la tesi en tres aplicacions diferents::
1. LOD per PARAFAC (Parallel Factor Analysis).
2. LOD per ITTFA (Iterative Target Transformation Factor Analysis).
3. LOD per MCR-ALS (Multivariate Curve Resolution - Alternating Least Squares)
A més, la tesi inclou una contribució teòrica amb la proposta d'un LOD que és específic per cada mostra, en el context del mètode multivariant PLS i del multilinear N-PLS.
Snyman, H. "Second order analyses methods for stirling engine design". Thesis, Stellenbosch : University of Stellenbosch, 2007. http://hdl.handle.net/10019.1/16102.
Pełny tekst źródła121 Leaves printed single pages, preliminary pages a-l and numbered pages 1-81.
ENGLISH ABSTRACT:In the midst of the current non-renewable energy crises specifically with regard to fossil fuel, various research institutions across the world have turned their focus to renewable and sustainable development. Using our available non.renewable resources as efficiently as possible has been a focal point the past decades and will certainly be as long as these resources exist Various means to utilize the world's abundant and freely available renewable energy has been studied and some even introduced and installed as sustainable energy sources, Electricity generation by means of wind powered turbines, photo-voltaic cells, and tidal and wave energy are but a few examples. Modern photo-voltaic cells are known to have a solar to electricity conversion efficiency of 12% (Van Heerden, 2003) while wind turbines have an approximate wind to electricity conversion efficiency of 50% (Twele et aI., 2002). This low solar to electricity conversion efficiency together with the fact that renewable energy research is a relatively modern development, lead to the investigation into methods capable of higher solar to electricity conversion efficiencies. One such method could be to use the relatively old technology of the Stirling cycle developed in the early 1800's (solar to electricity conversion efficiency in the range of 20.24 % according Van Heerden, 2003). The Stirling cycle provides a method for converting thermal energy to mechanical power which can be used to generate electricity, One of the main advantages of Stirling machines is that they are capable of using any form of heat source ranging from solar to biomass and waste heat. This document provides a discussion of some of the available methods for the analysis of Stirling machines. The six (6) different methods considered include: the method of Beale, West, mean-pressurepower- formula (MPPF), Schmidt, idea! adiabatic and the simple analysis methods. The first three (3) are known to be good back-of-the-envelope methods specifically for application as synthesis tools during initialisation of design procedures, while the latter three (3) are analysis tools finding application during Stirling engine design and analysis procedures. These analysis methods are based on the work done by Berchowitz and Urieli (1984) and form the centre of this document. Sections to follow provide a discussion of the mathematical model as well as the MATlAB implementation thereof. Experimental tests were conducted on the Heinrici engine to provide verification of the simulated resutls. Shortcomings of these analyses methods are also discussed in the sections to follow. Recommendations regarding improvements of the simulation program, possible fields of application for Stirling technology, as well as future fields of study are made in the final chapter of this document. A review of relevanl literature regarding modern applications of Stirling technology and listings of companies currently manufacturing and developing Stirling machines and findings of research done at various other institutions are provided.
AFRIKAANSE OPSOMMING:Die tempo van uitputling van die wereld se nie-hernubare energiebronne die afgelope jare het aanleiding gegee daartoe dal daar loenemend fokus toegespits word op die ontwikkeling van hernubare alternatiewe. Meer doeltreffende benutting van die wereld se nie-hernubare energie is reeds 'n fokus punt, vir navorsers reg oor die wereld, vir die afgelope dekades. Die aarde se oorvloedryke hernubare energie bronne word reeds met verskeie metodes ontgin. Die omskakeling van wind-, son- en gety energie na elektrisieteids is net 'n paar voorbeelde. Die effektiwiteid van sonkrag na elektrisietyds omskakeling van moderne fotovo!la'iese selle is in die orde van 12% (Van Heerden, 2003) terwyl die doeltreffendeid van wind energie na elektrisiteit omskakelling in die orde van 50% (Twele et at, 2002) is. Hierdie relatief lae omskelings doeltreffendeid van sonkrag na elektrisietyd, tesame met die feit dat die hernubare industrie nag relatief jonk is, lei lot die soeke na ander meer doellreffende moontlikhede Die Stirling siklus is nie 'n mod erne beginsel nie, maar die toepassing daarvan veral in die hernubare energie industrie is wei 'n relatiewe nuwe beg rip, veral in teme van die omskakeling van sonkrag na elektriese energie (gemiddelde sonkrag na lektriese energie omskakelings doellreffendeid in die orde van 20-24% is gevind deur Van Heerden, 2003). Die omskakeling van lermiese energie na meganiese energie is sekerlik die hoof uitkomsle van die Stirling siklus, alhoewel dit ook toepassing vind in die verkoefingsindustrie. Die feit dat die Stirling siklus van enige vorm van termiese energie (bv. son. biomassa, asook hilte geproduseer as byproduk tydens sekere prosesse) gebruik kan maak. is een van die redes wat die tegnologie 56 aanloklik maak, spesifiek !.o,v. die hernubare energie sektor. Ses (6) metodes vir die analise van die Stirling siklus word in hierdie dokument bespreek. Dit slui! die volgnde in: Beale-, West-, die gemiddelde-druk-krag-metode (GDKM), Schmidt-, adiabatiese- en die eenvoudige analise melodes. Die eerste drie (3) metodes is handige berekenings metodes Iydens die aanvangs en sinlesefase van Stirling enjin ontwerp, lerwyl die laaste drie (3) meer loegespils is op die volledige ontwerps- en analisefases gedurende die Stirling eniin ontwerps proses. Die drie (3) analise melodes is gebaseer op die werk wat deur Berchowitz en Urieli (1984) gedoen is en maak die kern van die dokument uit. Die wiskundige model, implimentering daarvan in MATlAB, sowel as die eksperimentele verifieering van die resultate word bespreek. Tekortkominge van die analise metodes word ook aangespreek in elke hoofsluk. Moontlikke verbeterings len opsigte van die verskeie aannames word in die finale hoofsluk van die dokumenl aangespreek. Verskeie voorgestelde riglings vir toekomslige navorsings projekle word ook in die finale hoofstuk van die dokument genoem. 'n Kort oorsig van die relevanle lileraluur in verband mel huidige loepassings van die Stirling legnologie, asook die name van maatskappye wal tans hierdie tegnologiee ontwikkel en vervaardig, word genoem.
Zhou, Chao. "Model Uncertainty in Finance and Second Order Backward Stochastic Differential Equations". Palaiseau, Ecole polytechnique, 2012. https://pastel.hal.science/docs/00/77/14/37/PDF/Thesis_ZHOU_Chao_Pastel.pdfcc.
Pełny tekst źródłaThe main objective of this PhD thesis is to study some financial mathematics problems in an incomplete market with model uncertainty. In recent years, the theory of second order backward stochastic differential equations (2BSDEs for short) has been developed by Soner, Touzi and Zhang on this topic. In this thesis, we adopt their point of view. This thesis contains of four key parts related to 2BSDEs. In the first part, we generalize the 2BSDEs theory initially introduced in the case of Lipschitz continuous generators to quadratic growth generators. This new class of 2BSDEs will then allow us to consider the robust utility maximization problem in non-dominated models. In the second part, we study this problem for exponential utility, power utility and logarithmic utility. In each case, we give a characterization of the value function and an optimal investment strategy via the solution to a 2BSDE. In the third part, we provide an existence and uniqueness result for second order reflected BSDEs with lower obstacles and Lipschitz generators, and then we apply this result to study the problem of American contingent claims pricing with uncertain volatility. In the fourth part, we define a notion of 2BSDEs with jumps, for which we prove the existence and uniqueness of solutions in appropriate spaces. We can interpret these equations as standard BSDEs with jumps, under both volatility and jump measure uncertainty. As an application of these results, we shall study a robust exponential utility maximization problem under model uncertainty, where the uncertainty affects both the volatility process and the jump measure
Crews, Hugh Bates. "Fast FSR Methods for Second-Order Linear Regression Models". NCSU, 2008. http://www.lib.ncsu.edu/theses/available/etd-04282008-151809/.
Pełny tekst źródłaBrabazon, Keeran J. "Multigrid methods for nonlinear second order partial differential operators". Thesis, University of Leeds, 2014. http://etheses.whiterose.ac.uk/8481/.
Pełny tekst źródłaDobrev, Veselin Asenov. "Preconditioning of discontinuous Galerkin methods for second order elliptic problems". [College Station, Tex. : Texas A&M University, 2007. http://hdl.handle.net/1969.1/ETD-TAMU-2531.
Pełny tekst źródłaYildirim, Ufuk. "Assessment Of Second-order Analysis Methods Presented In Design Codes". Master's thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/12610498/index.pdf.
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effects. In addition, the approximate methods defined in AISC 2005 (B1 &ndash
B2 Method), and TS648 (1980) will be discussed in detail. Then, example problems will be solved for the demonstration of theoretical formulations for members with and without end translation cases. Also, the results obtained from the structural analysis software, SAP2000, will be compared with the results acquired from the exact and the approximate methods. Finally, conclusions related to the study will be stated.
Abuazoum, Latifa Abdalla. "Advanced model updating methods for generally damped second order systems". Thesis, University of Nottingham, 2011. http://eprints.nottingham.ac.uk/12063/.
Pełny tekst źródłaFleming, Cliona Mary. "Second order chemometric methods and the analysis of complex data /". Thesis, Connect to this title online; UW restricted, 1999. http://hdl.handle.net/1773/8552.
Pełny tekst źródłaDavis, Benjamin J. "A study into discontinuous Galerkin methods for the second order wave equation". Thesis, Monterey, California: Naval Postgraduate School, 2015. http://hdl.handle.net/10945/45836.
Pełny tekst źródłaThere are numerous numerical methods for solving different types of partial differential equations (PDEs) that describe the physical dynamics of the world. For instance, PDEs are used to understand fluid flow for aerodynamics, wave dynamics for seismic exploration, and orbital mechanics. The goal of these numerical methods is to approximate the solution to a continuous PDE with an accurate discrete representation. The focus of this thesis is to explore a new Discontinuous Galerkin (DG) method for approximating the second order wave equation in complex geometries with curved elements. We begin by briefly highlighting some of the numerical methods used to solve PDEs and discuss the necessary concepts to understand DG methods. These concepts are used to develop a one- and two-dimensional DG method with an upwind flux, boundary conditions, and curved elements. We demonstrate convergence numerically and prove discrete stability of the method through an energy analysis.
Pefferly, Robert J. "Finite difference approximations of second order quasi-linear elliptic and hyperbolic stochastic partial differential equations". Thesis, University of Edinburgh, 2001. http://hdl.handle.net/1842/11244.
Pełny tekst źródłaSilveti, Falls Antonio. "First-order noneuclidean splitting methods for large-scale optimization : deterministic and stochastic algorithms". Thesis, Normandie, 2021. http://www.theses.fr/2021NORMC204.
Pełny tekst źródłaIn this work we develop and examine two novel first-order splitting algorithms for solving large-scale composite optimization problems in infinite-dimensional spaces. Such problems are ubiquitous in many areas of science and engineering, particularly in data science and imaging sciences. Our work is focused on relaxing the Lipschitz-smoothness assumptions generally required by first-order splitting algorithms by replacing the Euclidean energy with a Bregman divergence. These developments allow one to solve problems having more exotic geometry than that of the usual Euclidean setting. One algorithm is hybridization of the conditional gradient algorithm, making use of a linear minimization oracle at each iteration, with an augmented Lagrangian algorithm, allowing for affine constraints. The other algorithm is a primal-dual splitting algorithm incorporating Bregman divergences for computing the associated proximal operators. For both of these algorithms, our analysis shows convergence of the Lagrangian values, subsequential weak convergence of the iterates to solutions, and rates of convergence. In addition to these novel deterministic algorithms, we introduce and study also the stochastic extensions of these algorithms through a perturbation perspective. Our results in this part include almost sure convergence results for all the same quantities as in the deterministic setting, with rates as well. Finally, we tackle new problems that are only accessible through the relaxed assumptions our algorithms allow. We demonstrate numerical efficiency and verify our theoretical results on problems like low rank, sparse matrix completion, inverse problems on the simplex, and entropically regularized Wasserstein inverse problems
Dufrêne, Krzysztof. "Analysis and cancellation methods of second order intermodulation distortion in RFIC downconversion mixers". [S.l.] : [s.n.], 2007. http://deposit.ddb.de/cgi-bin/dokserv?idn=983583951.
Pełny tekst źródłaGómez, Cortés Verónica. "Sequential injection analysis using second-order calibration for the development of analytical methods". Doctoral thesis, Universitat Rovira i Virgili, 2007. http://hdl.handle.net/10803/9019.
Pełny tekst źródłaLos avances en el campo del análisis medioambiental se han dirigido al desarrollo de nuevas técnicas que sean de fácil uso, que permitan minimizar la manipulación de la muestra, los costes y el tiempo de análisis, que no precisen del uso de disolventes orgánicos, que puedan ser fácilmente automatizadas y que sean rápidas. Entre las técnicas analíticas que presentan las características citadas se encuentran las técnicas de inyección de flujo.
La instrumentación analítica actual permite generar datos de diferente dimensionalidad: los denominados datos de orden cero, cuando la señal obtenida por el detector para cada muestra es un escalar y este valor se relaciona con la concentración mediante un calibrado univariante; los datos de primer orden son aquellos que corresponden a un vector por muestra, y se relacionan con la concentración mediante una calibración multivariante o de primer orden; y datos de segundo orden, que son aquellos que corresponden a una matriz por muestra y aplican una calibración de segundo orden para relacionar la señal con la concentración de los analitos de interés. Los datos de orden cero son útiles en los casos en los que se tiene una respuesta única y específica para el analito de interés, mientras que los datos de primer orden permiten determinar la concentración de un analito en presencia de interferentes siempre que éstos estén contemplados en las muestras de calibrado. En el caso de tener interferentes no definidos o que éstos no se puedan reproducir en las muestras de calibrado, se emplean datos de segundo orden y calibraciones de segundo orden.
Esta Tesis Doctoral se ha enmarcado en el desarrollo de nuevas metodologías analíticas para la determinación de subproductos de la industria de curtidos de pieles mediante un sistema de inyección de flujo, Análisis por inyección secuencial (SIA) y calibración de datos de segundo orden.
SIA, Sequential Injection Analysis, es un sistema de inyección de flujo, introducido por el profesor Jaromir Ruzicka el 1990, en el que la muestra y los reactivos son aspirados de forma secuencial, se mezclan por difusión en el reactor y se transportan mediante un flujo hacia el detector.
Un sistema SIA acoplado con un detector espectrofotométrico de diodos en fila (DAD) permite obtener datos de segundo orden, de forma que se recoge el espectro completo en un intervalo de longitudes de onda, a diferentes tiempos durante la elución del pico SIA. De esta forma se obtiene una matriz de datos (m x n), donde m son los diferentes tiempos y n las longitudes de onda de medida, para el análisis de cada una de las muestras.
En este trabajo, se presentan diferentes aplicaciones mediante análisis por inyección secuencial y calibración de datos de segundo orden con resolución de curvas multivariante con mínimos cuadrados alternados (MCR-ALS) para la determinación y especiación de cromo y para la determinación de tres colorantes simultáneamente. También se presentan dos revisiones bibliográficas críticas acerca de la determinación de cromo y del análisis multicomponente en sistemas de flujo. Además se desarrolló una aplicación de Cromatografía por Inyección Secuencial (SIC) con resolución de curvas multivariante con mínimos cuadrados alternados para la determinación de fenoles.
El cromo es un elemento ampliamente usado en esta industria. Su determinación tiene gran importancia medioambiental debido a la gran toxicidad de la especie de Cr(VI) como agente cancerígeno, mientras que el Cr(III) es un elemento esencial. En esta Tesis se presentan cuatro trabajos referidos a la determinación de cromo. En el primero, Use of multivariate curve resolution for determination of chromium in tanning samples using sequential injection analysis, Analytical and Bioanalytical Chemistry 382 (2005) 328-334 se basa en los fundamentos para permitir la determinación de cromo con el sistema SIA-MCR-ALS. Dependiendo de la capacidad de reacción del Cr(III) se puede diseñar una secuencia analítica en el sistema SIA de modo que se obtenga un sistema en evolución para obtener una matriz de datos como señal analítica. Cr(III) fue oxidado a Cr(VI) fuera del sistema SIA para aumentar la sensibilidad del Cr(III). De este modo, en el sistema SIA se produjo un gradiente de pH para provocar una conversión entre dos especies de Cr(VI), cromato y dicromato. El segundo artículo, Factorial design for optimizing chromium determination in tanning wastewater, Microchemical Journal 83 (2006) 98-104 consiste, tal y como el título sugiere, en la optimización del método desarrollado previamente para incorporar en una única etapa las dos etapas principales (oxidación de Cr(III) y evolución del Cr(VI)). El tercer trabajo, Chromium speciation using sequential injection analysis and multivariate curve resolution, Analytica Chimica Acta 571 (2006) 129-135 consiste en la determinación simultánea de Cr(III) y Cr(VI) debido a que la especiación de cromo es de gran interés, sobretodo en el campo medioambiental. Se llevó a cabo una derivatización previa de Cr(III), formando un complejo con ácido etilendiaminotetraacético (EDTA) para aumentar la sensibilidad del Cr(III). El sistema en evolución en el sistema SIA se generó mediante un gradiente de pH. El cuarto trabajo, Chromium determination and speciation since 2000, Trends in Analytical Chemistry, 25 (2006) 1006-1015 consiste en un trabajo bibliográfico que describe las posibilidades de determinación y especiación de cromo.
Otros analitos de interés en este ámbito son los colorantes de los baños residuales, debido a su elevada toxicidad y a su baja biodegradabilidad. Por tanto, tiene gran relevancia el estudio de la proporción de colorantes en las muestras y su efecto al largo del tiempo. Tanto el cromo como los colorantes son compuestos de interés en otros ámbitos como por ejemplo, alimentos, artes gráficas, etc. Se presentan cuatro trabajos científicos en este ámbito con dos objetivos prácticos. Por un lado, controlar la cantidad de colorante que permanece en solución después del proceso de teñido, de modo que se puedan optimizar algunas de las etapas del proceso, y por otro lado, estudiar diferentes estrategias para reducir el porcentaje de colorantes en aguas residuales. El primer trabajo Sequential injection analysis with second-order treatment for the determination of dyes in the exhaustion process of tanning effluents, Talanta 71 (2007) 1393-1398 consiste en el desarrollo de un método analítico basado en SIA y calibración de datos de segundo orden (MCR-ALS) para determinar simultáneamente tres colorantes en muestras de deshecho de la industria de curtidos. Este método se aplicó a muestras curtidas con sales de cromo o con especies vegetales. El segundo trabajo Matrix effect in second-order data. Determination of dyes in a tanning process using vegetable tanning agents, Analytica Chimica Acta 600 (2007) 233-239 conlleva la aplicación del método a muestras curtidas con especies vegetales, ya que éstas son especies altamente absorbentes y provocan el conocido efecto matriz, por lo que se propusieron estrategias para tratar de corregir estos efectos. Para alcanzar el segundo objetivo se consideró la adsorción de colorantes en carbón activo como una estrategia atractiva para eliminar los colorantes. El tercer trabajo, Kinetic and adsorption study of acid dye removal using activated carbon, Chemosphere 69 (2007) 1151-1158 estudia la adsorción y los parámetros cinéticos, tanto para los colorantes individuales como para las mezclas. El cuarto trabajo, Experimental designs for optimizing and fitting the adsorption of dyes onto activated carbon, submitted, pretende obtener una superficie de respuesta de forma que, dependiendo de las concentraciones de colorantes, se puedan establecer las condiciones experimentales para obtener una predeterminada adsorción de colorantes en carbón activo.
En la última etapa de la Tesis se exploraron diferentes posibilidades para aumentar la capacidad de los análisis simultáneos mediante sistemas de flujo y métodos de calibración de segundo orden. De este estudio se obtuvieron dos trabajos. El primero, Multicomponent analysis in flow systems, Trends in Analytical Chemistry, 26 (2007) 767-774 muestra una visión general de las determinaciones de múltiples analitos en sistemas de flujo. El segundo trabajo, Coupling of sequential injection chromatography with multivariate curve resolution alternating least squares for enhancement of peak capacity, Analytical Chemistry, 10.1021/ac071202h es el resultado de la combinación de dos estrategias propuestas para el análisis multicomponente, la cromatografía de inyección secuencial (SIC) y la calibración de datos de segundo orden con MCR-ALS. Este estudio se llevó a cabo en colaboración con el Grupo de Química Analítica, Automatización y Medioambiente de la Universidad de las Islas Baleares (UIB), en donde se realizó la parte experimental.
Environmental analysis is a field with high interest in the analytical chemistry community. It is very important to assure and maintain the quality, from air as well as from water, to avoid that its composition cause any risk for the living organisms. Different industrial processes have contributed to improve health quality, but they can produce intermediates that if are introduced direct or indirectly to the waters can cause important problems of pollution. In that way, it is necessary to treat a big amount of industrial wastes, which should be continuously minimized.
Advances in the environmental field have been focusing on the development of new techniques of easy use, with low sample manipulation, low costs and short analysis times that could be easily automatised and fast. Flow analysis techniques can be found in this classification.
The current analytical instruments can generate data with different dimensionality. The analytical signal can be a scalar (a single absorbance measure), a vector (single absorbance measurement along time), or a data matrix (spectrum recorded along time) per each analysed sample. These data have been classified, as zero-order data when the signal is a scalar, first-order data when is a vector, and second-order data when the signal is a matrix. Zero-order data are useful for cases in which we have a unique and specific response for the analyte of interest, meanwhile first-order data allow quantification of an analyte in the presence of interferents but they should be contained in the calibration samples. When the interferents are not known and they could not be present in the calibration samples, second-order data and second-order calibrations are used.
This doctoral thesis has been carried out for developing new analytical methodologies for determining subproducts of the tanning industry using sequential injection analysis (SIA) and second-order calibration.
SIA, Sequential Injection Analysis, is a flow injection system introduced in 1990 by Professor Jaromir Ruzicka, where the sample and reagents are introduced sequentially into the system, are mixed by diffusion process in the reactor and then they are pumped through the detector.
A SIA system using a diode array spectrophotometer can generate second-order data, it means that the analytical signal is a data matrix for each sample on which we have absorbances in a wavelength interval in one axis and in a time interval in the other axis.
In this project, we present different practical applications using sequential injection analysis and second-order calibration using multivariate curve resolution alternating least squares (MCR-ALS) for determining and speciating chromium and for determining three acid dyes simultaneously. Furthermore we present two bibliographic overviews about chromium determination and multicomponent analysis in flow systems. We also developed an application of sequential injection chromatography (SIC) using multivariate curve resolution alternating least squares (MCR-ALS) for determining phenolic derivatives.
Chromium is an element widely used in the industry. Its determination presents high environmental interest because the toxicity of the Cr(VI) species as a carcinogenic agent, meanwhile Cr(III) is an essential element. In this Thesis we present four papers relative to chromium determination. The first paper Use of multivariate curve resolution for determination of chromium in tanning samples using sequential injection analysis, Analytical and Bioanalytical Chemistry 382 (2005) 328-334 is based on the basis to permit quantification of chromium with the system SIA-MCR-ALS. Depending on the capacity of reaction of Cr(III), different analytical sequences in the SIA system can be designed. Cr(III) was oxidized into Cr(VI) outside of the SIA system to increase Cr(III) sensibility. In that way, in the SIA system we induced a pH gradient to see the conversion of the two species of Cr(VI), chromate and dichromate. The second paper Factorial design for optimizing chromium determination in tanning wastewater, Microchemical Journal 83 (2006) 98-104 presents an automatic system for total chromium determination using different experimental designs to optimize the overall process. The third paper, Chromium speciation using sequential injection analysis and multivariate curve resolution, Analytica Chimica Acta 571 (2006) 129-135 is a paper in which the two main species of chromium, Cr(III) and Cr(VI), are determined simultaneously in a single analysis in the presence of interferents. The fourth paper, Chromium determinations and speciation since 2000, Trends in Analytical Chemistry, 25 (2006) 1006-1015 is a bibliographic study that describes the possibilities available for chromium determination and speciation.
Other analytes of interest in this field are dyes from wastewater due to its high toxicity and its low biodegradability. That is why studying the proportion of dyes in samples and its effect through time presents high relevance. Chromium and dyes are compounds of high interest in other application fields, such as, foods, printing and graphic design, etc. We present four scientific papers in this field with two practical objectives. On the one hand, control the amount of dyes that remains in solution after the dyeing process has been done. On the other hand, study different strategies to reduce the percentage of dyes in wastewater. The first paper, Sequential injection analysis with second-order treatment for the determination of dyes in the exhaustion process of tanning effluents Talanta 71 (2007) 1393-1398, describes the developed method for determining three acid dyes in a single step. This method was applied to water samples of leathers tanned with chromium salts and with vegetal agents. The second paper Matrix effect in second-order data. Determination of dyes in a tanning process using vegetable tanning agents Analytica Chimica Acta 600 (2007) 233-239 presents strategies to use when a sample presents matrix effects using second-order data. To solve the second objective, we studied the behaviour of dyes on activated carbon and present the results in the third paper Kinetic and adsorption study of acid dye removal using activated carbon Chemosphere 69 (2007) 1151-1158 where we studied the adsorption and the kinetic parameters of dyes being alone in solution or in a mixture of them. The fourth paper, Experimental designs for optimizing and fitting the adsorption of dyes onto activated carbon Submitted, we described a sequential methodology to obtain a response surface and optimize the adsorption process as a way of eliminating dyes in wastewater samples from the tanning industry.
In the last period of the Thesis, we explored different strategies to increase the capacity of simultaneous analysis using flow systems and second-order calibration. From this study, we obtained two papers. The first, Multicomponent analysis in flow systems, Trends in Analytical Chemistry, 26 (2007) 767-774, shows a general vision of multiple determinations in flow systems. The second paper, Coupling of sequential injection chromatography with multivariate curve resolution alternating least squares for enhancement of peak capacity, Analytical Chemistry 79 (2007) 7767-7774 shows a combination of two strategies proposed for multicomponent analysis, sequential injection chromatography (SIC) and second-order calibration with MCR-ALS. This study was carried out in collaboration with the Analytical Chemistry, Automation and Environment group of the University of the Balearic Islands.
Kim, Taejong. "Mesh independent convergence of modified inexact Newton methods for second order nonlinear problems". Texas A&M University, 2003. http://hdl.handle.net/1969.1/3870.
Pełny tekst źródłaDenkl, Stephan [Verfasser]. "Second-order approximations to pricing and hedging in presence of jumps and stochastic volatility / Stephan Denkl". Kiel : Universitätsbibliothek Kiel, 2013. http://d-nb.info/1035182157/34.
Pełny tekst źródłaKelome, Djivèdé Armel. "Viscosity solutions of second order equations in a separable Hilbert space and applications to stochastic optimal control". Diss., Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/29159.
Pełny tekst źródłaBooth, Andrew S. "Collocation methods for a class of second order initial value problems with oscillatory solutions". Thesis, Durham University, 1993. http://etheses.dur.ac.uk/5664/.
Pełny tekst źródłaEsposito, Elena. "Numerical treatment of special second order ordinary differential equations: general and exponentially fitted methods". Doctoral thesis, Universita degli studi di Salerno, 2012. http://hdl.handle.net/10556/292.
Pełny tekst źródłaThe aim of this research is the construction and the analysis of new families of numerical methods for the integration of special second order Ordinary Differential Equations (ODEs). The modeling of continuous time dynamical systems using second order ODEs is widely used in many elds of applications, as celestial mechanics, seismology, molecular dynamics, or in the semidiscretisation of partial differential equations (which leads to high dimensional systems and stiffness). Although the numerical treatment of this problem has been widely discussed in the literature, the interest in this area is still vivid, because such equations generally exhibit typical problems (e.g. stiffness, metastability, periodicity, high oscillations), which must efficiently be overcome by using suitable numerical integrators. The purpose of this research is twofold: on the one hand to construct a general family of numerical methods for special second order ODEs of the type y00 = f(y(t)), in order to provide an unifying approach for the analysis of the properties of consistency, zero-stability and convergence; on the other hand to derive special purpose methods, that follow the oscillatory or periodic behaviour of the solution of the problem...[edited by author]
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Shepherd, Adrian John. "Novel second-order techniques and global optimisation methods for supervised training of multi-layer perceptrons". Thesis, University College London (University of London), 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.321662.
Pełny tekst źródłaSternberg, Julia. "Memory efficient approaches of second order for optimal control problems". Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2005. http://nbn-resolving.de/urn:nbn:de:swb:14-1135250699292-11488.
Pełny tekst źródłaEs wird ein Problem der optimalen Steuerung betrachtet. Die dazugehoerigen Zustandsgleichungen sind mit einer Anfangswertaufgabe definiert. Es existieren zahlreiche numerische Methoden, um Probleme der optimalen Steuerung zu loesen. Der so genannte indirekte Ansatz wird in diesen Thesen detailliert betrachtet. Die indirekten Methoden loesen das aus den Notwendigkeitsbedingungen resultierende Randwertproblem. Das so genannte Pantoja Verfahren beschreibt eine zeiteffiziente schrittweise Berechnung der Newton Richtung fuer diskrete Probleme der optimalen Steuerung. Es gibt mehrere Beziehungen zwischen den unterschiedlichen Mehrzielmethoden und dem Pantoja Verfahren, die in diesen Thesen detailliert zu untersuchen sind. In diesem Zusammenhang wird die aequivalence zwischen dem Pantoja Verfahren und der Mehrzielmethode vom Riccati Typ gezeigt. Ausserdem wird das herkoemlige Pantoja Verfahren dahingehend erweitert, dass die Zustandsgleichungen mit Hilfe einer impliziten numerischen Methode diskretisiert sind. Weiterhin wird das Symplektische Konzept eingefuehrt. In diesem Zusammenhang wird eine geeignete numerische Methode praesentiert, die fuer ein unrestringiertes Problem der optimalen Steuerung angewendet werden kann. In diesen Thesen wird bewiesen, dass diese Methode symplectisch ist. Das iterative Loesen eines Problems der optimalen Steuerung in gewoenlichen Differentialgleichungen mit Hilfe von Pantoja oder Riccati aequivalenten Verfahren fuehrt auf eine Aufeinanderfolge der Durchlaeufetripeln in einem diskretisierten Zeitintervall. Der zweite (adjungierte) Lauf haengt von der Information des ersten (primalen) Laufes, und der dritte (finale) Lauf haeng von den beiden vorherigen ab. Ueblicherweise beinhalten Schritte und Zustaende des adjungierten Laufes wesentlich mehr Operationen und benoetigen auch wesentlich mehr Speicherplatzkapazitaet als Schritte und Zustaende der anderen zwei Durchlaeufe. Das Grundproblem besteht in einer enormen Speicherplatzkapazitaet, die fuer die Implementierung dieser Methoden benutzt wird, falls alle Zustaende des primalen und des adjungierten Durchlaufes zu speichern sind. Ein Ziel dieser Thesen besteht darin, Checkpointing Strategien zu praesentieren, um diese Methoden speichereffizient zu implementieren. Diese geschachtelten Umkehrschemata sind so konstruiert, dass fuer einen gegebenen Speicherplatz die gesamte Laufzeit zur Abarbeitung des Umkehrschemas minimiert wird. Die aufgestellten Umkehrschemata wurden fuer eine speichereffiziente Implementierung von Problemen der optimalen Steuerung angewendet. Insbesondere betrifft dies das Problem einer Oberflaechenabhaertung mit Laserbehandlung
Kröner, Axel W. H. [Verfasser], Boris [Akademischer Betreuer] Vexler, Michael [Akademischer Betreuer] Ulbrich i Karl [Akademischer Betreuer] Kunisch. "Numerical Methods for Control of Second Order Hyperbolic Equations / Axel Kröner. Gutachter: Michael Ulbrich ; Karl Kunisch. Betreuer: Boris Vexler". München : Universitätsbibliothek der TU München, 2011. http://d-nb.info/1019587903/34.
Pełny tekst źródłaAl-Shanfari, Fatima. "High-order in time discontinuous Galerkin finite element methods for linear wave equations". Thesis, Brunel University, 2017. http://bura.brunel.ac.uk/handle/2438/15332.
Pełny tekst źródłaHuré, Come. "Numerical methods and deep learning for stochastic control problems and partial differential equations". Thesis, Sorbonne Paris Cité, 2019. http://www.theses.fr/2019USPCC052.
Pełny tekst źródłaThe present thesis deals with numerical schemes to solve Markov Decision Problems (MDPs), partial differential equations (PDEs), quasi-variational inequalities (QVIs), backward stochastic differential equations (BSDEs) and reflected backward stochastic differential equations (RBSDEs). The thesis is divided into three parts.The first part focuses on methods based on quantization, local regression and global regression to solve MDPs. Firstly, we present a new algorithm, named Qknn, and study its consistency. A time-continuous control problem of market-making is then presented, which is theoretically solved by reducing the problem to a MDP, and whose optimal control is accurately approximated by Qknn. Then, a method based on Markovian embedding is presented to reduce McKean-Vlasov control prob- lem with partial information to standard MDP. This method is applied to three different McKean- Vlasov control problems with partial information. The method and high accuracy of Qknn is validated by comparing the performance of the latter with some finite difference-based algorithms and some global regression-based algorithm such as regress-now and regress-later.In the second part of the thesis, we propose new algorithms to solve MDPs in high-dimension. Neural networks, combined with gradient-descent methods, have been empirically proved to be the best at learning complex functions in high-dimension, thus, leading us to base our new algorithms on them. We derived the theoretical rates of convergence of the proposed new algorithms, and tested them on several relevant applications.In the third part of the thesis, we propose a numerical scheme for PDEs, QVIs, BSDEs, and RBSDEs. We analyze the performance of our new algorithms, and compare them to other ones available in the literature (including the recent one proposed in [EHJ17]) on several tests, which illustrates the efficiency of our methods to estimate complex solutions in high-dimension.Keywords: Deep learning, neural networks, Stochastic control, Markov Decision Process, non- linear PDEs, QVIs, optimal stopping problem BSDEs, RBSDEs, McKean-Vlasov control, perfor- mance iteration, value iteration, hybrid iteration, global regression, local regression, regress-later, quantization, limit order book, pure-jump controlled process, algorithmic-trading, market-making, high-dimension
Nattermann, Max [Verfasser], i Ekaterina [Akademischer Betreuer] Kostina. "Numerical Methods of Optimum Experimental Design Based on a Second-Order Approximation of Confidence Regions / Max Nattermann. Betreuer: Ekaterina Kostina". Marburg : Philipps-Universität Marburg, 2015. http://d-nb.info/1068315083/34.
Pełny tekst źródłaMaurer, Marina [Verfasser], i Christian [Akademischer Betreuer] Ochsenfeld. "Efficient quantum-chemical methods for calculating NMR shieldings in second-order Møller-Plesset perturbation theory / Marina Maurer ; Betreuer: Christian Ochsenfeld". München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2014. http://d-nb.info/1125883987/34.
Pełny tekst źródłaLan, Guanghui. "Convex optimization under inexact first-order information". Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29732.
Pełny tekst źródłaCommittee Chair: Arkadi Nemirovski; Committee Co-Chair: Alexander Shapiro; Committee Co-Chair: Renato D. C. Monteiro; Committee Member: Anatoli Jouditski; Committee Member: Shabbir Ahmed. Part of the SMARTech Electronic Thesis and Dissertation Collection.
He, Niao. "Saddle point techniques in convex composite and error-in-measurement optimization". Diss., Georgia Institute of Technology, 2015. http://hdl.handle.net/1853/54400.
Pełny tekst źródłaAlwohaibi, Maram. "Modelling the risk of underfunding in ALM models". Thesis, Brunel University, 2017. http://bura.brunel.ac.uk/handle/2438/16337.
Pełny tekst źródłaMilzarek, Andre [Verfasser], Michael [Akademischer Betreuer] [Gutachter] Ulbrich, Christian [Gutachter] Kanzow i Defeng [Gutachter] Sun. "Numerical methods and second order theory for nonsmooth problems / Andre Milzarek ; Gutachter: Christian Kanzow, Defeng Sun, Michael Ulbrich ; Betreuer: Michael Ulbrich". München : Universitätsbibliothek der TU München, 2016. http://d-nb.info/1120013720/34.
Pełny tekst źródłaWagner, Lisa [Verfasser], Jens [Akademischer Betreuer] Lang, Gerd [Akademischer Betreuer] Steinebach i Winnifried [Akademischer Betreuer] Wollner. "Second-Order Implicit Methods for Conservation Laws with Applications in Water Supply Networks / Lisa Wagner ; Jens Lang, Gerd Steinebach, Winnifried Wollner". Darmstadt : Universitäts- und Landesbibliothek Darmstadt, 2018. http://d-nb.info/1154932036/34.
Pełny tekst źródłaD'ANGELO, Nicoletta. "Local methods for complex spatio-temporal point processes". Doctoral thesis, Università degli Studi di Palermo, 2022. https://hdl.handle.net/10447/574349.
Pełny tekst źródłaBARBARINO, ANDREA. "Numerical Methods for Neutron Transport Calculations of Nuclear Reactors". Doctoral thesis, Politecnico di Torino, 2014. http://hdl.handle.net/11583/2561774.
Pełny tekst źródłaAit, El Faqir Marouane. "Prédiction de la structure de contrôle de bactéries par optimisation sous incertitude". Thesis, Lyon, 2016. http://www.theses.fr/2016LYSEC036/document.
Pełny tekst źródłaIn order to understand the global functioning principals of biological systems, system bio- logy approach aims to integrate the methodologies used in the conception and the analysis of complex technological systems, within the biology. This PhD thesis fits into the system biology framework and in particular the extension of the already existing method Resource Balance Analysis (RBA). We aim in this PhD thesis to improve the predictive power of this method by introducing more complex model. However, this new model should respect a good trade-off between the representativity of the model and its efficient numerical computation. This PhD thesis is decomposed into two major parts. The first part aims the integration of the metabolic network inherent thermodynamical and kinetic aspects. The second part aims the comprehension of the impact of enzyme production stochastic aspect on the bacteria growth. Numerical methods are elaborated to solve the obtained models in both deterministic and stochastic cases
Szekely, Tamas. "Stochastic modelling and simulation in cell biology". Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:f9b8dbe6-d96d-414c-ac06-909cff639f8c.
Pełny tekst źródłaHejazi, Hala Ahmad. "Finite volume methods for simulating anomalous transport". Thesis, Queensland University of Technology, 2015. https://eprints.qut.edu.au/81751/1/Hala%20Ahmad_Hejazi_Thesis.pdf.
Pełny tekst źródłaMaad, 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/.
Pełny tekst źródłaCarneiro, Renato Lajarim. "Algoritimos geneticos para seleção de variaveis em metodos de calibração de segunda ordem". [s.n.], 2007. http://repositorio.unicamp.br/jspui/handle/REPOSIP/249308.
Pełny tekst źródłaDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Quimica
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Resumo: Esse trabalho teve por objetivo desenvolver um programa em MatLab baseado no Algoritmo Genético (GA) para aplicar e verificar as principais vantagens deste na seleção de variáveis para métodos de calibração de segunda ordem (BLLS-RBL, PARAFAC e N-PLS). Para esta finalidade foram utilizados três conjuntos de dados: 1. Determinação de pesticidas e um metabólito em vinho tinto por HPLC-DAD em três situações distintas. Nestas três situações foram observadas sobreposições dos interferentes sobre os compostos de interesse. Estes compostos eram os pesticidas carbaril (CBL), tiofanato metílico (TIO), simazina (SIM) e dimetoato (DMT) e o metabólito ftalimida (PTA). 2. Quantificação das vitaminas B2 (riboflavina) e B6 (piridoxina) por espectrofluorimetria de excitação/emissão em formulações infantis comerciais, sendo três leites em pó e dois suplementos alimentares. 3. Análise dos fármacos ácido ascórbico (AA) e ácido acetilsalicílico (AAS) em formulações farmacêuticas por FIA com gradiente de pH e detecção por arranjo de diodos, onde a variação de pH causa alteração na estrutura das moléculas dos fármacos mudando seus espectros na região do ultravioleta. A performance dos modelos, com e sem seleção de variáveis, foi comparada através de seus erros, expressados como a raiz quadrada da média dos quadrados dos erros de previsão (RMSEP), e os erros relativos de previsão (REP). Resultados melhores foram claramente observados quando o GA foi utilizado para a seleção de variáveis nos métodos de calibração de segunda ordem.
Abstract: The aim of this work was to develop a program in MatLab using Genetic Algorithm (GA) to apply and to verify the main advantages of variables selection for second-order calibration methods (BLLS-RBL, PARAFAC and N-PLS). For this purpose three data sets had been used: 1. Determination of pesticides and a metabolite in red wines using HPLC-DAD in three distinct situations, where overlappings of the interferentes on interest compounds are observed. These composites were the pesticides carbaryl (CBL), methyl thiophanate (TIO), simazine (SIM) and dimethoate (DMT) and the metabolite phthalimide (PTA). 2. Quantification of the B2 (riboflavine) and (pyridoxine) B6 vitamins for spectrofluorimetry of excitation-emission in commercial infantile products, being three powder milk and two supplement foods. 3. Analysis of ascorbic acid (AA) and acetylsalicylic acid (AAS) in pharmaceutical tablets by FIA with pH gradient and detection for diode array, where the variation of pH causes alterations in the structure of molecules of analites shifting its spectra in the region of the ultraviolet. The performance of the models, with and without selection of variable, was compared through its errors, expressed as the root mean square error of prediction (RMSEP), and the relative errors of prediction (REP). The best results were obtained when the GA was used for the selection of variable in second-order calibration methods.
Mestrado
Quimica Analitica
Mestre em Química
Yamaguti, Lucas do Carmo. "Despacho ótimo de geração e controle de potência reativa no sistema elétrico de potência /". Ilha Solteira, 2019. http://hdl.handle.net/11449/183534.
Pełny tekst źródłaResumo: Neste trabalho são propostos modelos matemáticos determinístico e estocástico de programação cônica de segunda ordem em coordenadas retangulares para o problema de fluxo de potência ótimo de geração e controle de potência reativa no sistemas elétricos de potência, considerando as minimização dos custos de geração de energia, perdas ativas da rede e emissão de poluentes no meio ambiente. Os modelos contemplam as principais características físicas e econômicas do problema estudado, assim como os limites operacionais do sistema elétrico. Os modelos são programados em linguagem AMPL e suas soluções são obtidas através do solver comercial CPLEX. Os sistemas testes IEEE30, IEEE118 e ACTIVSg200 são utilizados nas simulações computacionais dos modelos propostos. Os resultados obtidos pelo modelo determinístico desenvolvido são validados através de comparações com os resultados fornecidos pelo software MATPOWER , onde ambos consideram apenas a existência de gerações termoelétricas. No modelo estocástico utiliza-se a técnica de geração de cenários e considera-se um período de um ano (8760 horas), e geradores que utilizam fontes de geração renováveis e não renováveis.
Abstract: In this work we propose deterministic and stochastic mathematical models of second order conical programming in rectangular coordinates for the optimal power flow problem of reactive power generation and control in electric power systems, considering the minimization of energy generation costs, losses networks and emission of pollutants into the environment. The models contemplate the main physical and economic characteristics of the studied problem, as well as the operational limits of the electric system. The models are programmed in AMPL language and their solutions are obtained through the commercial solver CPLEX. The IEEE30, IEEE118 and ACTIVSg200 test systems are used in the computer simulations of the proposed models. The results obtained by the deterministic model developed are validated through comparisons with the results provided by the software MATPOWERR , where both consider only the existence of thermoelectric generations. The stochastic model uses the scenario generation technique and considers a period of one year (8760 hours), and generators using renewable and non-renewable generation sources.
Mestre
Piozin, Lambert. "Quelques résultats sur les équations rétrogrades et équations aux dérivées partielles stochastiques avec singularités". Thesis, Le Mans, 2015. http://www.theses.fr/2015LEMA1004/document.
Pełny tekst źródłaThis thesis is devoted to the study of some problems in the field of backward stochastic differential equations (BSDE), and their applications to partial differential equations.In the first chapter, we introduce the notion of backward doubly stochastic differential equations (BDSDE) with singular terminal condition. A first work consists to study the case of BDSDE with monotone generator. We then obtain existing result by an approximating scheme built considering a truncation of the terminal condition. The last part of this chapter aim to establish the link with stochastic partial differential equations, using a weak solution approach developed by Bally, Matoussi in 2001.The second chapter is devoted to the BSDEs with singular terminal conditions and jumps. As in the previous chapter the tricky part will be to prove continuity in T. We formulate sufficient conditions on the jumps in order to obtain it. A section is then dedicated to establish a link between a minimal solution of our BSDE and partial integro-differential equations.The last chapter is dedicated to doubly reflected second order backward stochastic differential equations (2DRBSDE). We have been looking to establish existence and uniqueness for such equations. In order to obtain this, we had to focus first on the upper reflection problem for 2BSDEs. We combined then these results to those already existing to give a well-posedness context to 2DRBSDE. Uniqueness is established as a straight consequence of a representation property. Existence is obtained using shifted spaces, and regular conditional probability distributions. A last part is then consecrated to the link with some Dynkin games and Israeli options
Eng, Catherine. "Développement de méthodes de fouille de données basées sur les modèles de Markov cachés du second ordre pour l'identification d'hétérogénéités dans les génomes bactériens". Thesis, Nancy 1, 2010. http://www.theses.fr/2010NAN10041/document.
Pełny tekst źródłaSecond-order Hidden Markov Models (HMM2) are stochastic processes with a high efficiency in exploring bacterial genome sequences. Different types of HMM2 (M1M2, M2M2, M2M0) combined to combinatorial methods were developed in a new approach to discriminate genomic regions without a priori knowledge on their genetic content. This approach was applied on two bacterial models in order to validate its achievements: Streptomyces coelicolor and Streptococcus thermophilus. These bacterial species exhibit distinct genomic traits (base composition, global genome size) in relation with their ecological niche: soil for S. coelicolor and dairy products for S. thermophilus. In S. coelicolor, a first HMM2 architecture allowed the detection of short discrete DNA heterogeneities (5-16 nucleotides in size), mostly localized in intergenic regions. The application of the method on a biologically known gene set, the SigR regulon (involved in oxidative stress response), proved the efficiency in identifying bacterial promoters. S. coelicolor shows a complex regulatory network (up to 12% of the genes may be involved in gene regulation) with more than 60 sigma factors, involved in initiation of transcription. A classification method coupled to a searching algorithm (i.e. R’MES) was developed to automatically extract the box1-spacer-box2 composite DNA motifs, structure corresponding to the typical bacterial promoter -35/-10 boxes. Among the 814 DNA motifs described for the whole S. coelicolor genome, those of sigma factors (B, WhiG) could be retrieved from the crude data. We could show that this method could be generalized by applying it successfully in a preliminary attempt to the genome of Bacillus subtilis
Lin, Yiqing. "Équations différentielles stochastiques sous les espérances mathématiques non-linéaires et applications". Thesis, Rennes 1, 2013. http://www.theses.fr/2013REN1S012/document.
Pełny tekst źródłaThis thesis consists of two relatively independent parts : the first part concerns stochastic differential equations in the framework of the G-expectation, while the second part deals with a class of second order backward stochastic differential equations. In the first part, we first consider stochastic integrals with respect to an increasing process and give an extension of Itô's formula in the G-framework. Then, we study a class of scalar valued reflected stochastic differential equations driven by G-Brownian motion. Subsequently, we prove the existence and the uniqueness of solutions for some locally Lipschitz stochastic differential equations driven by G-Brownian motion. At the end of this part, we consider multidimensional reflected problems in the G-framework, and some convergence results are obtained. In the second part, we study the wellposedness of a class of second order backward stochastic differential equations (2BSDEs) under a quadratic growth condition on their coefficients. The aim of this part is to generalize a wellposedness result for quadratic 2BSDEs by Possamaï and Zhou in 2012. In this thesis, we work under some usual assumptions and deduce the existence and uniqueness theorem as well. Moreover, this theoretical result for quadratic 2BSDEs is applied to solve some robust utility maximization problems in finance
Home, Ortiz Juan Manuel. "Análise comparativa de um modelo de programação convexa e meta-heurística para o planejamento de redes de distribuição de energia elétrica com fontes de geração distribuída renováveis e não renováveis /". Ilha Solteira, 2019. http://hdl.handle.net/11449/180928.
Pełny tekst źródłaResumo: Neste trabalho propõem-se formulações matemáticas e metodologias para resolver o problema de planejamento da expansão e operação de sistemas de distribuição de energia elétrica de longo prazo com instalação de geração distribuída despachável, renovável e dispositivos armazenadores de energia, considerando as incertezas nos parâmetros e variáveis envolvidas no comportamento do sistema. No modelo de otimização desenvolvido considera- se uma formulação com espaço de busca convexo como um problema de programação cônica inteira de segunda ordem. Como primeira metodologia de solução para o modelo matemático proposto, usam-se solvers de otimização comerciais através de linguagem de programação matemática. Em segundo lugar é proposta a técnica de otimização meta-heurística VND combinada com um solver de otimização para resolver o modelo de otimização desenvolvido. Os algoritmos e modelos matemáticos de otimização usados para resolver o planejamento de sistemas de distribuição são implementados em AMPL e testados em sistemas presentes na literatura. Finalmente são comparadas as metodologias segundo a solução obtida e desempenho em tempo computacional.
Abstract: This work proposes mathematical formulations and methodologies to solve the long-term electric power distribution system operation and expansion planning with distributed renewable energy sources and energy storage devices, considering the uncertainties in the involved parameters and variables in the system behavior. In the developed optimization model, a convex formulation is considered as integer second-order conic programming problem. The first solution methodology for the proposed mathematical model, the commercial optimization solvers that uses mathematical modelling language is used. In the second way, the VND meta-heuristic optimization technique is proposed combined with the optimization solver to analyze the obtained solutions of the search through optimal neighborhoods. The mathematical optimization model and the proposed algorithm used to solver the planning of distribution systems are implemented in AMPL and tested in literature’s systems. Finally, the methodologies according to the obtained solution and computational time performance are compared.
Doutor