+publisher:"King Abdullah University of Science and Technology" +contributor:("Gomes, Diogo A.")

King Abdullah University of Science and Technology

1. Seneci, Tommaso. Displacement Convexity for First-Order Mean-Field Games.

Degree: Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, 2018, King Abdullah University of Science and Technology

URL: http://hdl.handle.net/10754/627746

► In this thesis, we consider the planning problem for first-order mean-field games (MFG). These games degenerate into optimal transport when there is no coupling between… (more)

Subjects/Keywords: analysis of PDE; Mean-field games; Optimal transport; apriori bounds; convexity

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APA (6^th Edition):

Seneci, T. (2018). Displacement Convexity for First-Order Mean-Field Games. (Thesis). King Abdullah University of Science and Technology. Retrieved from http://hdl.handle.net/10754/627746

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Seneci, Tommaso. “Displacement Convexity for First-Order Mean-Field Games.” 2018. Thesis, King Abdullah University of Science and Technology. Accessed April 14, 2021. http://hdl.handle.net/10754/627746.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Seneci, Tommaso. “Displacement Convexity for First-Order Mean-Field Games.” 2018. Web. 14 Apr 2021.

Vancouver:

Seneci T. Displacement Convexity for First-Order Mean-Field Games. [Internet] [Thesis]. King Abdullah University of Science and Technology; 2018. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/10754/627746.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Seneci T. Displacement Convexity for First-Order Mean-Field Games. [Thesis]. King Abdullah University of Science and Technology; 2018. Available from: http://hdl.handle.net/10754/627746

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

King Abdullah University of Science and Technology

2. Yang, Xianjin. A regularized stationary mean-field game.

Degree: Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, 2016, King Abdullah University of Science and Technology

URL: http://hdl.handle.net/10754/607757

► In the thesis, we discuss the existence and numerical approximations of solutions of a regularized mean-field game with a low-order regularization. In the first part,… (more)

Subjects/Keywords: Mean field games; continuation method; monotone flow; energy method; regularity; Stationary

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APA (6^th Edition):

Yang, X. (2016). A regularized stationary mean-field game. (Thesis). King Abdullah University of Science and Technology. Retrieved from http://hdl.handle.net/10754/607757

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Yang, Xianjin. “A regularized stationary mean-field game.” 2016. Thesis, King Abdullah University of Science and Technology. Accessed April 14, 2021. http://hdl.handle.net/10754/607757.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Yang, Xianjin. “A regularized stationary mean-field game.” 2016. Web. 14 Apr 2021.

Vancouver:

Yang X. A regularized stationary mean-field game. [Internet] [Thesis]. King Abdullah University of Science and Technology; 2016. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/10754/607757.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Yang X. A regularized stationary mean-field game. [Thesis]. King Abdullah University of Science and Technology; 2016. Available from: http://hdl.handle.net/10754/607757

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

King Abdullah University of Science and Technology

3. Alghamdi, Moataz. Symbolic Detection of Permutation and Parity Symmetries of Evolution Equations.

Degree: Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, 2017, King Abdullah University of Science and Technology

URL: http://hdl.handle.net/10754/625045

► We introduce a symbolic computational approach to detecting all permutation and parity symmetries in any general evolution equation, and to generating associated invariant polynomials, from… (more)

Subjects/Keywords: symmetry; permutation; evolution; purity

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APA (6^th Edition):

Alghamdi, M. (2017). Symbolic Detection of Permutation and Parity Symmetries of Evolution Equations. (Thesis). King Abdullah University of Science and Technology. Retrieved from http://hdl.handle.net/10754/625045

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Alghamdi, Moataz. “Symbolic Detection of Permutation and Parity Symmetries of Evolution Equations.” 2017. Thesis, King Abdullah University of Science and Technology. Accessed April 14, 2021. http://hdl.handle.net/10754/625045.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Alghamdi, Moataz. “Symbolic Detection of Permutation and Parity Symmetries of Evolution Equations.” 2017. Web. 14 Apr 2021.

Vancouver:

Alghamdi M. Symbolic Detection of Permutation and Parity Symmetries of Evolution Equations. [Internet] [Thesis]. King Abdullah University of Science and Technology; 2017. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/10754/625045.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Alghamdi M. Symbolic Detection of Permutation and Parity Symmetries of Evolution Equations. [Thesis]. King Abdullah University of Science and Technology; 2017. Available from: http://hdl.handle.net/10754/625045

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

King Abdullah University of Science and Technology

4. Duisembay, Serikbolsyn. Convergent Difference Schemes for Hamilton-Jacobi equations.

Degree: Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, 2018, King Abdullah University of Science and Technology

URL: http://hdl.handle.net/10754/627772

► In this thesis, we consider second-order fully nonlinear partial differential equations of elliptic type. Our aim is to develop computational methods using convergent difference schemes… (more)

Subjects/Keywords: Hamilton-Jacobi equations; difference schemes; Viscosity solutions; numerical methods

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APA (6^th Edition):

Duisembay, S. (2018). Convergent Difference Schemes for Hamilton-Jacobi equations. (Thesis). King Abdullah University of Science and Technology. Retrieved from http://hdl.handle.net/10754/627772

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Duisembay, Serikbolsyn. “Convergent Difference Schemes for Hamilton-Jacobi equations.” 2018. Thesis, King Abdullah University of Science and Technology. Accessed April 14, 2021. http://hdl.handle.net/10754/627772.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Duisembay, Serikbolsyn. “Convergent Difference Schemes for Hamilton-Jacobi equations.” 2018. Web. 14 Apr 2021.

Vancouver:

Duisembay S. Convergent Difference Schemes for Hamilton-Jacobi equations. [Internet] [Thesis]. King Abdullah University of Science and Technology; 2018. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/10754/627772.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Duisembay S. Convergent Difference Schemes for Hamilton-Jacobi equations. [Thesis]. King Abdullah University of Science and Technology; 2018. Available from: http://hdl.handle.net/10754/627772

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

King Abdullah University of Science and Technology

5. Berkemeier, Francisco. A Priori Regularity of Parabolic Partial Differential Equations.

Degree: Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, 2018, King Abdullah University of Science and Technology

URL: http://hdl.handle.net/10754/627833

► In this thesis, we consider parabolic partial differential equations such as the heat equation, the Fokker-Planck equation, and the porous media equation. Our aim is… (more)

Subjects/Keywords: PDE; regularity; parabolic; estimates

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Berkemeier, F. (2018). A Priori Regularity of Parabolic Partial Differential Equations. (Thesis). King Abdullah University of Science and Technology. Retrieved from http://hdl.handle.net/10754/627833

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Berkemeier, Francisco. “A Priori Regularity of Parabolic Partial Differential Equations.” 2018. Thesis, King Abdullah University of Science and Technology. Accessed April 14, 2021. http://hdl.handle.net/10754/627833.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Berkemeier, Francisco. “A Priori Regularity of Parabolic Partial Differential Equations.” 2018. Web. 14 Apr 2021.

Vancouver:

Berkemeier F. A Priori Regularity of Parabolic Partial Differential Equations. [Internet] [Thesis]. King Abdullah University of Science and Technology; 2018. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/10754/627833.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Berkemeier F. A Priori Regularity of Parabolic Partial Differential Equations. [Thesis]. King Abdullah University of Science and Technology; 2018. Available from: http://hdl.handle.net/10754/627833

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

King Abdullah University of Science and Technology

6. Evangelista, David. Stationary Mean-Field Games with Congestion.

Degree: Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, 2019, King Abdullah University of Science and Technology

URL: http://hdl.handle.net/10754/655679

► Mean-field games (MFG) are models of large populations of rational agents who seek to optimize an objective function that takes into account their state variables… (more)

▼ Mean-field games (MFG) are models of large populations of rational agents who seek to optimize an objective function that takes into account their state variables and the distribution of the state variable of the remaining agents. MFG with congestion model problems where the agents’ motion is hampered in high-density regions. First, we study radial solutions for first- and second-order stationary MFG with congestion on Rd. The radial case, which is one of the simplest non one-dimensional MFG, is relatively tractable. As we observe, the Fokker-Planck equation is integrable with respect to one of the unknowns. Consequently, we obtain a single equation substituting this solution into the Hamilton-Jacobi equation. For the first-order case, we derive explicit formulas; for the elliptic case, we study a variational formulation of the resulting equation. For the first case, we use our approach to compute numerical approximations to the solutions of the corresponding MFG systems. Next, we consider second-order stationary MFG with congestion and prove the existence of stationary solutions. Because moving in congested areas is difficult, agents prefer to move in non-congested areas. As a consequence, the model becomes singular near the zero density. The existence of stationary solutions was previously obtained for MFG with quadratic Hamiltonians thanks to a very particular identity. Here, we develop robust estimates that give the existence of a solution for general subquadratic Hamiltonians. Additionally, we study first-order stationary MFG with congestion with quadratic or power-like Hamiltonians. Using explicit examples, we illustrate two key difficulties: the lack of classical solutions and the existence of areas with vanishing densities. Our main contribution is a new variational formulation for MFG with congestion. With this formulation, we prove the existence and uniqueness of solutions. Finally, we devise a discretization that is combined with optimization algorithms to numerically solve various MFG with congestion. Advisors/Committee Members: Gomes, Diogo A. (advisor), Tempone, Raul (committee member), Santamarina, Carlos (committee member), Fusco, Nicola (committee member).

Subjects/Keywords: mean-field games; congestion problems; stationary problems; calculus f variations

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APA (6^th Edition):

Evangelista, D. (2019). Stationary Mean-Field Games with Congestion. (Thesis). King Abdullah University of Science and Technology. Retrieved from http://hdl.handle.net/10754/655679

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Evangelista, David. “Stationary Mean-Field Games with Congestion.” 2019. Thesis, King Abdullah University of Science and Technology. Accessed April 14, 2021. http://hdl.handle.net/10754/655679.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Evangelista, David. “Stationary Mean-Field Games with Congestion.” 2019. Web. 14 Apr 2021.

Vancouver:

Evangelista D. Stationary Mean-Field Games with Congestion. [Internet] [Thesis]. King Abdullah University of Science and Technology; 2019. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/10754/655679.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Evangelista D. Stationary Mean-Field Games with Congestion. [Thesis]. King Abdullah University of Science and Technology; 2019. Available from: http://hdl.handle.net/10754/655679

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

7. Vilanova, Pedro. Multilevel Approximations of Markovian Jump Processes with Applications in Communication Networks.

Degree: Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, 2015, King Abdullah University of Science and Technology

URL: http://hdl.handle.net/10754/552664

► This thesis focuses on the development and analysis of efficient simulation and inference techniques for Markovian pure jump processes with a view towards applications in… (more)

▼ This thesis focuses on the development and analysis of efficient simulation and inference techniques for Markovian pure jump processes with a view towards applications in dense communication networks. These techniques are especially relevant for modeling networks of smart devices —tiny, abundant microprocessors with integrated sensors and wireless communication abilities— that form highly complex and diverse communication networks. During 2010, the number of devices connected to the Internet exceeded the number of people on Earth: over 12.5 billion devices. By 2015, Cisco’s Internet Business Solutions Group predicts that this number will exceed 25 billion. The first part of this work proposes novel numerical methods to estimate, in an efficient and accurate way, observables from realizations of Markovian jump processes. In particular, hybrid Monte Carlo type methods are developed that combine the exact and approximate simulation algorithms to exploit their respective advantages. These methods are tailored to keep a global computational error below a prescribed global error tolerance and within a given statistical confidence level. Indeed, the computational work of these methods is similar to the one of an exact method, but with a smaller constant. Finally, the methods are extended to systems with a disparity of time scales. The second part develops novel inference methods to estimate the parameters of Markovian pure jump process. First, an indirect inference approach is presented, which is based on upscaled representations and does not require sampling. This method is simpler than dealing directly with the likelihood of the process, which, in general, cannot be expressed in closed form and whose maximization requires computationally intensive sampling techniques. Second, a forward-reverse Monte Carlo Expectation-Maximization algorithm is provided to approximate a local maximum or saddle point of the likelihood function of the parameters given a set of observations. The third part is devoted to applications in communication networks where also mean field or fluid approximations techniques, to substantially reduce the computational work of simulating large communication networks are explored. These methods aim to capture the global behaviour of systems with large state spaces by using an aggregate approximation, which is often described by means of a non-linear dynamical system. Advisors/Committee Members: Tempone, Raul (advisor), Keyes, David E. (committee member), Gomes, Diogo A. (committee member), Shihada, Basem (committee member), Djehiche, Boualem (committee member).

Subjects/Keywords: inference for continuous-time; Markov Chains; error control; weak approximation; multilevel monte carlo; chernoff tau-leap

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APA (6^th Edition):

Vilanova, P. (2015). Multilevel Approximations of Markovian Jump Processes with Applications in Communication Networks. (Thesis). King Abdullah University of Science and Technology. Retrieved from http://hdl.handle.net/10754/552664

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Vilanova, Pedro. “Multilevel Approximations of Markovian Jump Processes with Applications in Communication Networks.” 2015. Thesis, King Abdullah University of Science and Technology. Accessed April 14, 2021. http://hdl.handle.net/10754/552664.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Vilanova, Pedro. “Multilevel Approximations of Markovian Jump Processes with Applications in Communication Networks.” 2015. Web. 14 Apr 2021.

Vancouver:

Vilanova P. Multilevel Approximations of Markovian Jump Processes with Applications in Communication Networks. [Internet] [Thesis]. King Abdullah University of Science and Technology; 2015. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/10754/552664.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Vilanova P. Multilevel Approximations of Markovian Jump Processes with Applications in Communication Networks. [Thesis]. King Abdullah University of Science and Technology; 2015. Available from: http://hdl.handle.net/10754/552664

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

8. Haji Ali, Abdul Lateef. Efficient Multilevel and Multi-index Sampling Methods in Stochastic Differential Equations.

Degree: Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, 2016, King Abdullah University of Science and Technology

URL: http://hdl.handle.net/10754/610543

► Most problems in engineering and natural sciences involve parametric equations in which the parameters are not known exactly due to measurement errors, lack of measurement… (more)

▼ Most problems in engineering and natural sciences involve parametric equations in which the parameters are not known exactly due to measurement errors, lack of measurement data, or even intrinsic variability. In such problems, one objective is to compute point or aggregate values, called “quantities of interest”. A rapidly growing research area that tries to tackle this problem is Uncertainty Quantification (UQ). As the name suggests, UQ aims to accurately quantify the uncertainty in quantities of interest. To that end, the approach followed in this thesis is to describe the parameters using probabilistic measures and then to employ probability theory to approximate the probabilistic information of the quantities of interest. In this approach, the parametric equations must be accurately solved for multiple values of the parameters to explore the dependence of the quantities of interest on these parameters, using various so-called “sampling methods”. In almost all cases, the parametric equations cannot be solved exactly and suitable numerical discretization methods are required. The high computational complexity of these numerical methods coupled with the fact that the parametric equations must be solved for multiple values of the parameters make UQ problems computationally intensive, particularly when the dimensionality of the underlying problem and/or the parameter space is high. This thesis is concerned with optimizing existing sampling methods and developing new ones. Starting with the Multilevel Monte Carlo (MLMC) estimator, we first prove its normality using the Lindeberg-Feller CLT theorem. We then design the Continuation Multilevel Monte Carlo (CMLMC) algorithm that efficiently approximates the parameters required to run MLMC. We also optimize the hierarchies of one-dimensional discretization parameters that are used in MLMC and analyze the tolerance splitting parameter between the statistical error and the bias constraints. An important contribution of this thesis is the novel Multi-index Monte Carlo (MIMC) method which is an extension of MLMC in high dimensional problems with significant computational savings. Under reasonable assumptions on the weak and variance convergence, which are related to the mixed regularity of the underlying problem and the discretization method, the order of the computational complexity of MIMC is, at worst up to a logarithmic factor, independent of the dimensionality of the underlying parametric equation. We also apply the same multi-index methodology to another sampling method, namely the Stochastic Collocation method. Hence, the novel Multi-index Stochastic Collocation method is proposed and is shown to be more efficient in problems with sufficient mixed regularity than our novel MIMC method and other standard methods. Finally, MIMC is applied to approximate quantities of interest of stochastic particle systems in the mean-field when the number of particles tends to infinity. To approximate these quantities of interest up to an error tolerance, TOL, MIMC has a computational… Advisors/Committee Members: Tempone, Raul (advisor), Gomes, Diogo A. (committee member), Mai, Paul Martin (committee member), Scheichl, Robert (committee member), Giles, Michael B. (committee member).

Subjects/Keywords: stochastic; sampling methods; multilevel; multi-index; Monte Carlo; spare grid

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APA (6^th Edition):

Haji Ali, A. L. (2016). Efficient Multilevel and Multi-index Sampling Methods in Stochastic Differential Equations. (Thesis). King Abdullah University of Science and Technology. Retrieved from http://hdl.handle.net/10754/610543

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Haji Ali, Abdul Lateef. “Efficient Multilevel and Multi-index Sampling Methods in Stochastic Differential Equations.” 2016. Thesis, King Abdullah University of Science and Technology. Accessed April 14, 2021. http://hdl.handle.net/10754/610543.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Haji Ali, Abdul Lateef. “Efficient Multilevel and Multi-index Sampling Methods in Stochastic Differential Equations.” 2016. Web. 14 Apr 2021.

Vancouver:

Haji Ali AL. Efficient Multilevel and Multi-index Sampling Methods in Stochastic Differential Equations. [Internet] [Thesis]. King Abdullah University of Science and Technology; 2016. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/10754/610543.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Haji Ali AL. Efficient Multilevel and Multi-index Sampling Methods in Stochastic Differential Equations. [Thesis]. King Abdullah University of Science and Technology; 2016. Available from: http://hdl.handle.net/10754/610543

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

King Abdullah University of Science and Technology

9. Alzahrani, Hasnaa H. Mixed, Nonsplit, Extended Stability, Stiff Integration of Reaction Diffusion Equations.

Degree: Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, 2016, King Abdullah University of Science and Technology

URL: http://hdl.handle.net/10754/617606

► A tailored integration scheme is developed to treat stiff reaction-diffusion prob- lems. The construction adapts a stiff solver, namely VODE, to treat reaction im- plicitly… (more)

Subjects/Keywords: stiffness; low mach number; numerical integration; runge-kutta-chebyshev; non-split scheme

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APA (6^th Edition):

Alzahrani, H. H. (2016). Mixed, Nonsplit, Extended Stability, Stiff Integration of Reaction Diffusion Equations. (Thesis). King Abdullah University of Science and Technology. Retrieved from http://hdl.handle.net/10754/617606

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Alzahrani, Hasnaa H. “Mixed, Nonsplit, Extended Stability, Stiff Integration of Reaction Diffusion Equations.” 2016. Thesis, King Abdullah University of Science and Technology. Accessed April 14, 2021. http://hdl.handle.net/10754/617606.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Alzahrani, Hasnaa H. “Mixed, Nonsplit, Extended Stability, Stiff Integration of Reaction Diffusion Equations.” 2016. Web. 14 Apr 2021.

Vancouver:

Alzahrani HH. Mixed, Nonsplit, Extended Stability, Stiff Integration of Reaction Diffusion Equations. [Internet] [Thesis]. King Abdullah University of Science and Technology; 2016. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/10754/617606.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Alzahrani HH. Mixed, Nonsplit, Extended Stability, Stiff Integration of Reaction Diffusion Equations. [Thesis]. King Abdullah University of Science and Technology; 2016. Available from: http://hdl.handle.net/10754/617606

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

King Abdullah University of Science and Technology

10. Abdelhamid, Ehab. Scalable Frequent Subgraph Mining.

Degree: Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, 2017, King Abdullah University of Science and Technology

URL: http://hdl.handle.net/10754/625049

► A graph is a data structure that contains a set of nodes and a set of edges connecting these nodes. Nodes represent objects while edges… (more)

▼ A graph is a data structure that contains a set of nodes and a set of edges connecting these nodes. Nodes represent objects while edges model relationships among these objects. Graphs are used in various domains due to their ability to model complex relations among several objects. Given an input graph, the Frequent Subgraph Mining (FSM) task finds all subgraphs with frequencies exceeding a given threshold. FSM is crucial for graph analysis, and it is an essential building block in a variety of applications, such as graph clustering and indexing. FSM is computationally expensive, and its existing solutions are extremely slow. Consequently, these solutions are incapable of mining modern large graphs. This slowness is caused by the underlying approaches of these solutions which require finding and storing an excessive amount of subgraph matches. This dissertation proposes a scalable solution for FSM that avoids the limitations of previous work. This solution is composed of four components. The first component is a single-threaded technique which, for each candidate subgraph, needs to find only a minimal number of matches. The second component is a scalable parallel FSM technique that utilizes a novel two-phase approach. The first phase quickly builds an approximate search space, which is then used by the second phase to optimize and balance the workload of the FSM task. The third component focuses on accelerating frequency evaluation, which is a critical step in FSM. To do so, a machine learning model is employed to predict the type of each graph node, and accordingly, an optimized method is selected to evaluate that node. The fourth component focuses on mining dynamic graphs, such as social networks. To this end, an incremental index is maintained during the dynamic updates. Only this index is processed and updated for the majority of graph updates. Consequently, search space is significantly pruned and efficiency is improved. The empirical evaluation shows that the proposed components significantly outperform existing solutions, scale to a large number of processors and process graphs that previous techniques cannot handle, such as large and dynamic graphs. Advisors/Committee Members: Kalnis, Panos (advisor), Gomes, Diogo A. (committee member), Gao, Xin (committee member), Zaki, Mohammed J. (committee member).

Subjects/Keywords: graph; parallel processing; Frequent subgraph mining; incremental indexing

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APA (6^th Edition):

Abdelhamid, E. (2017). Scalable Frequent Subgraph Mining. (Thesis). King Abdullah University of Science and Technology. Retrieved from http://hdl.handle.net/10754/625049

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Abdelhamid, Ehab. “Scalable Frequent Subgraph Mining.” 2017. Thesis, King Abdullah University of Science and Technology. Accessed April 14, 2021. http://hdl.handle.net/10754/625049.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Abdelhamid, Ehab. “Scalable Frequent Subgraph Mining.” 2017. Web. 14 Apr 2021.

Vancouver:

Abdelhamid E. Scalable Frequent Subgraph Mining. [Internet] [Thesis]. King Abdullah University of Science and Technology; 2017. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/10754/625049.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Abdelhamid E. Scalable Frequent Subgraph Mining. [Thesis]. King Abdullah University of Science and Technology; 2017. Available from: http://hdl.handle.net/10754/625049

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

King Abdullah University of Science and Technology

11. Sierra Nunez, Jesus Alfredo. A Study of Schrödinger–Type Equations Appearing in Bohmian Mechanics and in the Theory of Bose–Einstein Condensates.

Degree: Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, 2018, King Abdullah University of Science and Technology

URL: http://hdl.handle.net/10754/627883

► The Schrödinger equations have had a profound impact on a wide range of fields of modern science, including quantum mechanics, superfluidity, geometrical optics, Bose-Einstein condensates,… (more)

▼ The Schrödinger equations have had a profound impact on a wide range of fields of modern science, including quantum mechanics, superfluidity, geometrical optics, Bose-Einstein condensates, and the analysis of dispersive phenomena in the theory of PDE. The main purpose of this thesis is to explore two Schrödinger-type equations appearing in the so-called Bohmian formulation of quantum mechanics and in the study of exciton-polariton condensates. For the first topic, the linear Schrödinger equation is the starting point in the formulation of a phase-space model proposed in [1] for the Bohmian interpretation of quantum mechanics. We analyze this model, a nonlinear Vlasov-type equation, as a Hamiltonian system defined on an appropriate Poisson manifold built on Wasserstein spaces, the aim being to establish its existence theory. For this purpose, we employ results from the theory of PDE, optimal transportation, differential geometry and algebraic topology. The second topic of the thesis is the study of a nonlinear Schrödinger equation, called the complex Gross-Pitaevskii equation, appearing in the context of Bose-Einstein condensation of exciton-polaritons. This model can be roughly described as a driven-damped Gross-Pitaevskii equation which shares some similarities with the complex Ginzburg-Landau equation. The difficulties in the analysis of this equation stem from the fact that, unlike the complex Ginzburg-Landau equation, the complex Gross-Pitaevskii equation does not include a viscous dissipation term. Our approach to this equation will be in the framework of numerical computations, using two main tools: collocation methods and numerical continuation for the stationary solutions and a time-splitting spectral method for the dynamics. After performing a linear stability analysis on the computed stationary solutions, we are led to postulate the existence of radially symmetric stationary ground state solutions only for certain values of the parameters in the equation; these parameters represent the “strength” of the driving and damping terms. Moreover, numerical continuation allows us to show, for fixed parameters, the ground and some of the excited state solutions of this equation. Finally, for the values of the parameters that do not produce a stable radially symmetric solution, our dynamical computations show the emergence of rotating vortex lattices. Advisors/Committee Members: Markowich, Peter A. (advisor), Gomes, Diogo A. (committee member), Alouini, Mohamed-Slim (committee member), Marcati, Pierangelo (committee member).

Subjects/Keywords: PDE's; Optimal transport; Schrödinger; hamiltonian flow; existence; Bose-Einstein condensates

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APA (6^th Edition):

Sierra Nunez, J. A. (2018). A Study of Schrödinger–Type Equations Appearing in Bohmian Mechanics and in the Theory of Bose–Einstein Condensates. (Thesis). King Abdullah University of Science and Technology. Retrieved from http://hdl.handle.net/10754/627883

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Sierra Nunez, Jesus Alfredo. “A Study of Schrödinger–Type Equations Appearing in Bohmian Mechanics and in the Theory of Bose–Einstein Condensates.” 2018. Thesis, King Abdullah University of Science and Technology. Accessed April 14, 2021. http://hdl.handle.net/10754/627883.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Sierra Nunez, Jesus Alfredo. “A Study of Schrödinger–Type Equations Appearing in Bohmian Mechanics and in the Theory of Bose–Einstein Condensates.” 2018. Web. 14 Apr 2021.

Vancouver:

Sierra Nunez JA. A Study of Schrödinger–Type Equations Appearing in Bohmian Mechanics and in the Theory of Bose–Einstein Condensates. [Internet] [Thesis]. King Abdullah University of Science and Technology; 2018. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/10754/627883.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Sierra Nunez JA. A Study of Schrödinger–Type Equations Appearing in Bohmian Mechanics and in the Theory of Bose–Einstein Condensates. [Thesis]. King Abdullah University of Science and Technology; 2018. Available from: http://hdl.handle.net/10754/627883

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

King Abdullah University of Science and Technology

12. Yang, Xianjin. Two-scale Homogenization and Numerical Methods for Stationary Mean-field Games.

Degree: Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, 2020, King Abdullah University of Science and Technology

URL: http://hdl.handle.net/10754/664089

► Mean-field games (MFGs) study the behavior of rational and indistinguishable agents in a large population. Agents seek to minimize their cost based upon statis- tical… (more)

Subjects/Keywords: Mean-field Games; Homogenization; Effective Hamiltonian; Two-scale convergence; Hessian Riemannian Flow; Mather Measures

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APA (6^th Edition):

Yang, X. (2020). Two-scale Homogenization and Numerical Methods for Stationary Mean-field Games. (Thesis). King Abdullah University of Science and Technology. Retrieved from http://hdl.handle.net/10754/664089

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Yang, Xianjin. “Two-scale Homogenization and Numerical Methods for Stationary Mean-field Games.” 2020. Thesis, King Abdullah University of Science and Technology. Accessed April 14, 2021. http://hdl.handle.net/10754/664089.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Yang, Xianjin. “Two-scale Homogenization and Numerical Methods for Stationary Mean-field Games.” 2020. Web. 14 Apr 2021.

Vancouver:

Yang X. Two-scale Homogenization and Numerical Methods for Stationary Mean-field Games. [Internet] [Thesis]. King Abdullah University of Science and Technology; 2020. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/10754/664089.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Yang X. Two-scale Homogenization and Numerical Methods for Stationary Mean-field Games. [Thesis]. King Abdullah University of Science and Technology; 2020. Available from: http://hdl.handle.net/10754/664089

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

King Abdullah University of Science and Technology

13. Talgat, Anna. Stochastic Geometry-based Analysis of LEO Satellite Communication Systems.

Degree: Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, 2020, King Abdullah University of Science and Technology

URL: http://hdl.handle.net/10754/664342

► Wireless coverage becomes one of the most significant needs of modern society because of its importance in various applications such as health, distance education, industry,… (more)

Subjects/Keywords: Stochastic geometry; binomial point process; distance distribution; coverage probability; LEO satellites

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APA (6^th Edition):

Talgat, A. (2020). Stochastic Geometry-based Analysis of LEO Satellite Communication Systems. (Thesis). King Abdullah University of Science and Technology. Retrieved from http://hdl.handle.net/10754/664342

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Talgat, Anna. “Stochastic Geometry-based Analysis of LEO Satellite Communication Systems.” 2020. Thesis, King Abdullah University of Science and Technology. Accessed April 14, 2021. http://hdl.handle.net/10754/664342.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Talgat, Anna. “Stochastic Geometry-based Analysis of LEO Satellite Communication Systems.” 2020. Web. 14 Apr 2021.

Vancouver:

Talgat A. Stochastic Geometry-based Analysis of LEO Satellite Communication Systems. [Internet] [Thesis]. King Abdullah University of Science and Technology; 2020. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/10754/664342.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Talgat A. Stochastic Geometry-based Analysis of LEO Satellite Communication Systems. [Thesis]. King Abdullah University of Science and Technology; 2020. Available from: http://hdl.handle.net/10754/664342

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

King Abdullah University of Science and Technology

14. Ben Hammouda, Chiheb. Hierarchical Approximation Methods for Option Pricing and Stochastic Reaction Networks.

Degree: Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, 2020, King Abdullah University of Science and Technology

URL: http://hdl.handle.net/10754/664348

► In biochemically reactive systems with small copy numbers of one or more reactant molecules, stochastic effects dominate the dynamics. In the first part of this… (more)

▼ In biochemically reactive systems with small copy numbers of one or more reactant molecules, stochastic effects dominate the dynamics. In the first part of this thesis, we design novel efficient simulation techniques for a reliable and fast estimation of various statistical quantities for stochastic biological and chemical systems under the framework of Stochastic Reaction Networks. In the first work, we propose a novel hybrid multilevel Monte Carlo (MLMC) estimator, for systems characterized by having simultaneously fast and slow timescales. Our hybrid multilevel estimator uses a novel split-step implicit tau-leap scheme at the coarse levels, where the explicit tau-leap method is not applicable due to numerical instability issues. In a second work, we address another challenge present in this context called the high kurtosis phenomenon, observed at the deep levels of the MLMC estimator. We propose a novel approach that combines the MLMC method with a pathwise-dependent importance sampling technique for simulating the coupled paths. Our theoretical estimates and numerical analysis show that our method improves the robustness and complexity of the multilevel estimator, with a negligible additional cost. In the second part of this thesis, we design novel methods for pricing financial derivatives. Option pricing is usually challenging due to: 1) The high dimensionality of the input space, and 2) The low regularity of the integrand on the input parameters. We address these challenges by developing different techniques for smoothing the integrand to uncover the available regularity. Then, we approximate the resulting integrals using hierarchical quadrature methods combined with Brownian bridge construction and Richardson extrapolation. In the first work, we apply our approach to efficiently price options under the rough Bergomi model. This model exhibits several numerical and theoretical challenges, implying classical numerical methods for pricing being either inapplicable or computationally expensive. In a second work, we design a numerical smoothing technique for cases where analytic smoothing is impossible. Our analysis shows that adaptive sparse grids’ quadrature combined with numerical smoothing outperforms the Monte Carlo approach. Furthermore, our numerical smoothing improves the robustness and the complexity of the MLMC estimator, particularly when estimating density functions. Advisors/Committee Members: Tempone, Raul (advisor), Gomes, Diogo A. (committee member), Jasra, Ajay (committee member), Gobet, Emmanuel (committee member), Kebaier, Ahmed (committee member).

Subjects/Keywords: Multilevel Monte Carlo; smoothing techniques; Hierarchical quadrature methods; Continuous-time Markov chains; Option pricing; Stochastic biological/chemical systems

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Ben Hammouda, C. (2020). Hierarchical Approximation Methods for Option Pricing and Stochastic Reaction Networks. (Thesis). King Abdullah University of Science and Technology. Retrieved from http://hdl.handle.net/10754/664348

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Ben Hammouda, Chiheb. “Hierarchical Approximation Methods for Option Pricing and Stochastic Reaction Networks.” 2020. Thesis, King Abdullah University of Science and Technology. Accessed April 14, 2021. http://hdl.handle.net/10754/664348.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Ben Hammouda, Chiheb. “Hierarchical Approximation Methods for Option Pricing and Stochastic Reaction Networks.” 2020. Web. 14 Apr 2021.

Vancouver:

Ben Hammouda C. Hierarchical Approximation Methods for Option Pricing and Stochastic Reaction Networks. [Internet] [Thesis]. King Abdullah University of Science and Technology; 2020. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/10754/664348.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Ben Hammouda C. Hierarchical Approximation Methods for Option Pricing and Stochastic Reaction Networks. [Thesis]. King Abdullah University of Science and Technology; 2020. Available from: http://hdl.handle.net/10754/664348

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

King Abdullah University of Science and Technology

15. Happola, Juho. Efficient Numerical Methods for Stochastic Differential Equations in Computational Finance.

Degree: Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, 2017, King Abdullah University of Science and Technology

URL: http://hdl.handle.net/10754/625924

► Stochastic Differential Equations (SDE) offer a rich framework to model the probabilistic evolution of the state of a system. Numerical approximation methods are typically needed… (more)

Subjects/Keywords: options; Stochastic Differential Equations; Numerical Methods

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APA (6^th Edition):

Happola, J. (2017). Efficient Numerical Methods for Stochastic Differential Equations in Computational Finance. (Thesis). King Abdullah University of Science and Technology. Retrieved from http://hdl.handle.net/10754/625924

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Happola, Juho. “Efficient Numerical Methods for Stochastic Differential Equations in Computational Finance.” 2017. Thesis, King Abdullah University of Science and Technology. Accessed April 14, 2021. http://hdl.handle.net/10754/625924.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Happola, Juho. “Efficient Numerical Methods for Stochastic Differential Equations in Computational Finance.” 2017. Web. 14 Apr 2021.

Vancouver:

Happola J. Efficient Numerical Methods for Stochastic Differential Equations in Computational Finance. [Internet] [Thesis]. King Abdullah University of Science and Technology; 2017. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/10754/625924.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Happola J. Efficient Numerical Methods for Stochastic Differential Equations in Computational Finance. [Thesis]. King Abdullah University of Science and Technology; 2017. Available from: http://hdl.handle.net/10754/625924

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

16. Prazeres, Mariana. Explicit Solutions for One-Dimensional Mean-Field Games.

Degree: Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, 2017, King Abdullah University of Science and Technology

URL: http://hdl.handle.net/10754/623065

► In this thesis, we consider stationary one-dimensional mean-field games (MFGs) with or without congestion. Our aim is to understand the qualitative features of these games… (more)

Subjects/Keywords: PDE's; explicit solutions; Mean-field games

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APA (6^th Edition):

Prazeres, M. (2017). Explicit Solutions for One-Dimensional Mean-Field Games. (Thesis). King Abdullah University of Science and Technology. Retrieved from http://hdl.handle.net/10754/623065

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Prazeres, Mariana. “Explicit Solutions for One-Dimensional Mean-Field Games.” 2017. Thesis, King Abdullah University of Science and Technology. Accessed April 14, 2021. http://hdl.handle.net/10754/623065.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Prazeres, Mariana. “Explicit Solutions for One-Dimensional Mean-Field Games.” 2017. Web. 14 Apr 2021.

Vancouver:

Prazeres M. Explicit Solutions for One-Dimensional Mean-Field Games. [Internet] [Thesis]. King Abdullah University of Science and Technology; 2017. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/10754/623065.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Prazeres M. Explicit Solutions for One-Dimensional Mean-Field Games. [Thesis]. King Abdullah University of Science and Technology; 2017. Available from: http://hdl.handle.net/10754/623065

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

17. Alharbi, Abdulrahman. On the Lp-Integrability of Green’s function for Elliptic Operators.

Degree: Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, 2019, King Abdullah University of Science and Technology

URL: http://hdl.handle.net/10754/655516

► In this thesis, we discuss some of the results that were proven by Fabes and Stroock in 1984. Our main purpose is to give a… (more)

Subjects/Keywords: Green's Functions; non-divergence form; Fabes-Stroock; ABP Estimate; Muckenhoupt Weights

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APA (6^th Edition):

Alharbi, A. (2019). On the Lp-Integrability of Green’s function for Elliptic Operators. (Thesis). King Abdullah University of Science and Technology. Retrieved from http://hdl.handle.net/10754/655516

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Alharbi, Abdulrahman. “On the Lp-Integrability of Green’s function for Elliptic Operators.” 2019. Thesis, King Abdullah University of Science and Technology. Accessed April 14, 2021. http://hdl.handle.net/10754/655516.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Alharbi, Abdulrahman. “On the Lp-Integrability of Green’s function for Elliptic Operators.” 2019. Web. 14 Apr 2021.

Vancouver:

Alharbi A. On the Lp-Integrability of Green’s function for Elliptic Operators. [Internet] [Thesis]. King Abdullah University of Science and Technology; 2019. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/10754/655516.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Alharbi A. On the Lp-Integrability of Green’s function for Elliptic Operators. [Thesis]. King Abdullah University of Science and Technology; 2019. Available from: http://hdl.handle.net/10754/655516

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

18. Machado Velho, Roberto. Finite-State Mean-Field Games, Crowd Motion Problems, and its Numerical Methods.

Degree: Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, 2017, King Abdullah University of Science and Technology

URL: http://hdl.handle.net/10754/625444

► In this dissertation, we present two research projects, namely finite-state mean-field games and the Hughes model for the motion of crowds. In the first part,… (more)

▼ In this dissertation, we present two research projects, namely finite-state mean-field games and the Hughes model for the motion of crowds. In the first part, we describe finite-state mean-field games and some applications to socio-economic sciences. Examples include paradigm shifts in the scientific community and the consumer choice behavior in a free market. The corresponding finite-state mean-field game models are hyperbolic systems of partial differential equations, for which we propose and validate a new numerical method. Next, we consider the dual formulation to two-state mean-field games, and we discuss numerical methods for these problems. We then depict different computational experiments, exhibiting a variety of behaviors, including shock formation, lack of invertibility, and monotonicity loss. We conclude the first part of this dissertation with an investigation of the shock structure for two-state problems. In the second part, we consider a model for the movement of crowds proposed by R. Hughes in [56] and describe a numerical approach to solve it. This model comprises a Fokker-Planck equation coupled with an Eikonal equation with Dirichlet or Neumann data. We first establish a priori estimates for the solutions. Next, we consider radial solutions, and we identify a shock formation mechanism. Subsequently, we illustrate the existence of congestion, the breakdown of the model, and the trend to the equilibrium. We also propose a new numerical method for the solution of Fokker-Planck equations and then to systems of PDEs composed by a Fokker-Planck equation and a potential type equation. Finally, we illustrate the use of the numerical method both to the Hughes model and mean-field games. We also depict cases such as the evacuation of a room and the movement of persons around Kaaba (Saudi Arabia). Advisors/Committee Members: Gomes, Diogo A. (advisor), Tempone, Raul (committee member), Sun, Shuyu (committee member), Falcone, Maurizio (committee member).

Subjects/Keywords: Mean-field games; Crowd motion; Fokker-Planck Equation; Numerical Methods; Hamilton-Jacobi equations

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APA (6^th Edition):

Machado Velho, R. (2017). Finite-State Mean-Field Games, Crowd Motion Problems, and its Numerical Methods. (Thesis). King Abdullah University of Science and Technology. Retrieved from http://hdl.handle.net/10754/625444

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Machado Velho, Roberto. “Finite-State Mean-Field Games, Crowd Motion Problems, and its Numerical Methods.” 2017. Thesis, King Abdullah University of Science and Technology. Accessed April 14, 2021. http://hdl.handle.net/10754/625444.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Machado Velho, Roberto. “Finite-State Mean-Field Games, Crowd Motion Problems, and its Numerical Methods.” 2017. Web. 14 Apr 2021.

Vancouver:

Machado Velho R. Finite-State Mean-Field Games, Crowd Motion Problems, and its Numerical Methods. [Internet] [Thesis]. King Abdullah University of Science and Technology; 2017. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/10754/625444.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Machado Velho R. Finite-State Mean-Field Games, Crowd Motion Problems, and its Numerical Methods. [Thesis]. King Abdullah University of Science and Technology; 2017. Available from: http://hdl.handle.net/10754/625444

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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