Thursday, November 19, 2020, 12:00
- 13:00
https://kaust.zoom.us/j/95474758108?pwd=WkwrdiszTE1uYTdmR3JRK09LVDErZz09
Contact Person
In this talk we consider the problem of estimating the score function (or gradient of the log-likelihood) associated to a class of partially observed diffusion processes, with discretely observed, fixed length, data and finite dimensional parameters. We construct an estimator that is unbiased with no time-discretization bias. Using a simple Girsanov change of measure method to represent the score function, our methodology can be used for a wide class of diffusion processes and requires only access to a time-discretization method such as Euler-Maruyama. Our approach is based upon a novel adaptation of the randomization schemes developed by Glynn and co-authors along with a new coupled Markov chain simulation scheme. The latter methodology is an original type of coupling of the coupled conditional particle filter. We prove that our estimator is unbiased and of finite variance. We then illustrate our methodology on several challenging statistical examples. This is a joint work with Jeremy Heng (ESSEC, Singapore) and Jeremie Houssineau (Warwick, UK)
Jose Urbano, Professor of Mathematics at the University of Coimbra, Portugal
Thursday, November 12, 2020, 16:00
- 17:30
https://kaust.zoom.us/j/95491279304
Contact Person
The mini-course is an introduction to intrinsic scaling, a powerful method in the analysis of degenerate and singular parabolic PDEs. The local Hölder continuity of bounded weak solutions will be derived from scratch for the model case of the degenerate p-Laplace equation. Our approach is entirely self-contained and focused on the essence of the method, leaving aside technical refinements needed to deal with more general equations.
Thursday, November 12, 2020, 12:00
- 13:00
https://kaust.zoom.us/j/96516742266
In this talk, we start by introducing optimization and interesting optimization applications. We review some optimization formulations and focus on applications studied in our research, such as energy systems, and trajectory planning of autonomous underwater vehicles. After the introduction, we address the self-scheduling and market involvement of a virtual power plant using adaptive robust optimization under uncertainty in the wind speed and electricity prices. Two types of uncertainty sets are considered to represent uncertainty: discrete and continuous. We perform a thorough comparison between the power generation schedule and market involvement of the VPP with the two alternative uncertainty sets. Also, we analyze the worst output of the electricity prices obtained from both uncertainty sets. We conclude with a risk management analysis made using a verification step of a sample average approximation methodology. Ricardo M. Lima is a Research Scientist in Professor Omar Knio’s research group in CEMSE. He is also the co-founder of the KAUST/Saudi startup Decision Science Technologies. Ricardo joined KAUST in 2014. He received the Ph.D. degree in 2006 in Chemical Engineering from the Faculty of Engineering, University of Porto, Portugal. In 2006, he became a Post-doc fellow in the Department of Chemical Engineering at the Carnegie Mellon University, Pittsburgh, PA, USA. From 2008 to 2011, he was an invited researcher in PPG Industries, USA. He was a Marie Curie Fellow in the National Laboratory of Energy and Geology (LNEG) in Lisbon, Portugal from 2011 to 2014. His research interests include modeling and optimization of complex problems related to chemical, processing industries, and energy systems. Target applications include integration, planning and scheduling of renewable energy systems, process synthesis, planning and scheduling of chemical engineering systems, and trajectory planning of autonomous underwater vehicles. In terms of methodologies, Ricardo focus on the development of mathematical programming methodologies, namely combinatorial optimization models, continuous optimization models, deterministic global optimization solution approaches, stochastic programming models, and decomposition algorithms to solve large-scale problems.
Jose Urbano, Professor of Mathematics at the University of Coimbra, Portugal
Tuesday, November 10, 2020, 16:00
- 17:30
https://kaust.zoom.us/j/94457711238
Contact Person
The mini-course is an introduction to intrinsic scaling, a powerful method in the analysis of degenerate and singular parabolic PDEs. The local Hölder continuity of bounded weak solutions will be derived from scratch for the model case of the degenerate p-Laplace equation. Our approach is entirely self-contained and focused on the essence of the method, leaving aside technical refinements needed to deal with more general equations.
Jose Urbano, Professor of Mathematics at the University of Coimbra, Portugal
Thursday, November 05, 2020, 16:00
- 17:30
https://kaust.zoom.us/j/92224259958
Contact Person
The mini-course is an introduction to intrinsic scaling, a powerful method in the analysis of degenerate and singular parabolic PDEs. The local Hölder continuity of bounded weak solutions will be derived from scratch for the model case of the degenerate p-Laplace equation. Our approach is entirely self-contained and focused on the essence of the method, leaving aside technical refinements needed to deal with more general equations.
Thursday, November 05, 2020, 12:00
- 13:00
https://kaust.zoom.us/j/95474758108?pwd=WkwrdiszTE1uYTdmR3JRK09LVDErZz09
Contact Person
Advances in imaging technology have given neuroscientists unprecedented access to examine various facets of how the brain “works”. Brain activity is complex. A full understanding of brain activity requires careful study of its multi-scale spatial-temporal organization (from neurons to regions of interest; and from transient events to long-term temporal dynamics). Motivated by these challenges, we will explore some characterizations of dependence between components of a multivariate time series and then apply these to the study of brain functional connectivity. This is potentially interesting for brain scientists because functional brain networks are associated with cognitive function and mental and neurological diseases. There is no single measure of dependence that can capture all facets of brain connectivity. In this talk, we shall present some new models for exploring potential non-linear cross-frequency interactions. These interactions include the impact of phase of one oscillatory activity in one component on the amplitude of another oscillation. The proposed approach captures lead-lag relationships and hence can be used as a general framework for spectral causality. This is joint work with Marco Pinto (KAUST and Oslo Metropolitan University)
Jose Urbano, Professor of Mathematics at the University of Coimbra, Portugal
Tuesday, November 03, 2020, 16:00
- 17:30
https://kaust.zoom.us/j/94380127179
Contact Person
The mini-course is an introduction to intrinsic scaling, a powerful method in the analysis of degenerate and singular parabolic PDEs. The local Hölder continuity of bounded weak solutions will be derived from scratch for the model case of the degenerate p-Laplace equation. Our approach is entirely self-contained and focused on the essence of the method, leaving aside technical refinements needed to deal with more general equations.
Thursday, October 29, 2020, 12:00
- 13:00
https://kaust.zoom.us/j/98958184866
Contact Person
Eigenvalue problems associated with partial differential equations are key ingredients for the modeling and simulation of a variety of real world applications, ranging from fluid-dynamics, structural mechanics, acoustics, to electromagnetism and medical problems. We review some properties related to the approximation of eigenvalue problems. Starting from matrix algebraic problems, we present a series of examples and counterexamples showing that even extremely simple situations can produce unexpected results.
Thursday, October 22, 2020, 12:00
- 13:00
https://kaust.zoom.us/j/95474758108?pwd=WkwrdiszTE1uYTdmR3JRK09LVDErZz09
Contact Person
Our suggested criteria are more useful for the determination of tuning parameters for sophisticated approximation methods of spatial model fitting. To illustrate this, we investigate the trade-off between the execution time, estimation accuracy, and prediction efficiency for the TLR method with intensive simulation studies and suggest proper settings of the TLR tuning parameters.
Prof. José Miguel Urbano, Department of Mathematics, University of Coimbra, Portugal
Thursday, October 15, 2020, 16:00
- 17:30
https://kaust.zoom.us/j/92922071557
Contact Person
The mini-course is an introduction to the analysis of infinity-harmonic functions. We detail the proof of the equivalence between enjoying comparison with cones and solving the infinity-Laplace equation in the viscosity sense, thus making a seamless connection with the previous mini-course. Further material includes the existence of infinity-harmonic functions in the case of an unbounded domain and an easy and self-contained proof, due to Armstrong and Smart, of the celebrated uniqueness theorem of Jensen.
Thursday, October 15, 2020, 12:00
- 13:00
https://kaust.zoom.us/j/95474758108?pwd=WkwrdiszTE1uYTdmR3JRK09LVDErZz09
Contact Person
Compartmental epidemiological models are one of the simplest models for the spread of a disease.  They are based on statistical models of interactions in large populations and can be effective in the appropriate circumstances.  Their application historically and in the present pandemic has sometimes been successful and sometimes spectacularly wrong.  In this talk I will review some of these models and their application.  I will also discuss the behavior of the corresponding dynamical systems, and discuss how the theory of optimal control can be applied to them.  I will describe some of the challenges in using such a theory to make decisions about public policy.
Tuesday, October 13, 2020, 16:15
- 17:00
https://kaust.zoom.us/my/phddissertation
Contact Person
This dissertation presents our efforts to build an operational ensemble forecasting system for the Red Sea, based on the Data Research Testbed (DART) package for ensemble data assimilation and the Massachusetts Institute of Technology general circulation ocean model (MITgcm) for forecasting. The Red Sea DART-MITgcm system efficiently integrates all the ensemble members in parallel, while accommodating different ensemble assimilation schemes. The promising ensemble adjustment Kalman filter (EAKF), designed to avoid manipulating the gigantic covariance matrices involved in the ensemble assimilation process, possesses relevant features required for an operational setting. We developed new schemes aiming at lowering the computational burden while preserving reliable assimilation results. The ensemble data assimilation system is implemented and tested on Shaheen, our world-class supercomputer, and will form the basis of the first ever operational Red Sea forecasting system that is currently being implemented to support Saudi Aramco operations in this basin.
Prof. José Miguel Urbano, Department of Mathematics, University of Coimbra, Portugal
Tuesday, October 13, 2020, 16:00
- 17:30
https://kaust.zoom.us/j/94098462169
Contact Person
The mini-course is an introduction to the analysis of infinity-harmonic functions. We detail the proof of the equivalence between enjoying comparison with cones and solving the infinity-Laplace equation in the viscosity sense, thus making a seamless connection with the previous mini-course. Further material includes the existence of infinity-harmonic functions in the case of an unbounded domain and an easy and self-contained proof, due to Armstrong and Smart, of the celebrated uniqueness theorem of Jensen.
Prof. José Miguel Urbano, Department of Mathematics, University of Coimbra, Portugal
Thursday, October 08, 2020, 16:00
- 17:30
https://kaust.zoom.us/j/92438998828
Contact Person
The mini-course is an introduction to the analysis of infinity-harmonic functions. We detail the proof of the equivalence between enjoying comparison with cones and solving the infinity-Laplace equation in the viscosity sense, thus making a seamless connection with the previous mini-course. Further material includes the existence of infinity-harmonic functions in the case of an unbounded domain and an easy and self-contained proof, due to Armstrong and Smart, of the celebrated uniqueness theorem of Jensen.
Thursday, October 08, 2020, 12:00
- 13:00
https://kaust.zoom.us/j/95474758108?pwd=WkwrdiszTE1uYTdmR3JRK09LVDErZz09
Contact Person
We present Exascale GeoStatistics (ExaGeoStat) software, a high-performance library implemented on a wide variety of contemporary hybrid distributed-shared supercomputers whose primary target is climate and environmental prediction applications.
Prof. José Miguel Urbano, Department of Mathematics, University of Coimbra, Portugal
Tuesday, October 06, 2020, 16:00
- 17:30
https://kaust.zoom.us/j/99953233644
Contact Person
The mini-course is an introduction to the analysis of infinity-harmonic functions. We detail the proof of the equivalence between enjoying comparison with cones and solving the infinity-Laplace equation in the viscosity sense, thus making a seamless connection with the previous mini-course. Further material includes the existence of infinity-harmonic functions in the case of an unbounded domain and an easy and self-contained proof, due to Armstrong and Smart, of the celebrated uniqueness theorem of Jensen.
Jan Haskovec, AMCS, KAUST
Thursday, October 01, 2020, 12:00
- 13:00
https://kaust.zoom.us/j/95474758108?pwd=WkwrdiszTE1uYTdmR3JRK09LVDErZz09
Contact Person
Individual-based models of collective behavior represent a very active research field with applications in physics (spontaneous magnetization), biology (flocking and swarming) and social sciences (opinion formation). They are also a hot topic engineering (swarm robotics). A particularly interesting aspect of the dynamics of multi-agent systems is the emergence of global self-organized patterns, while individuals typically interact only on short scales. In this talk I shall discuss the impact of delay on asymptotic consensus formation in Hegselmann-Krause-type models, where agents adapt their „opinions“ (in broad sense) to the ones of their close neighbors. We shall understand the two principial types/sources of delay - information propagation and processing - and explain their qualitatively different impacts on the consensus dynamics. We then discuss various mathematical methods that provide asymptotic consensus results in the respective settings: Lyapunov functional-type approach, direct estimates, convexity arguments and forward-backward estimates.
Dr. Dimitrios Mitsotakis, Senior Lecturer, Victoria University of Wellington
Wednesday, September 30, 2020, 12:00
- 13:00
https://kaust.zoom.us/j/91364870078
Contact Person
The study of waves in fluids is one of the most significant branches of fluid mechanics. Part of this study is the theory of nonlinear and dispersive waves which has recently emerged and is still under development. Nonlinear and dispersive waves appear in fluids of any form and have significant role in the fields of oceanic waves (surface and internal), atmospheric modelling, electromagnetism, nonlinear optics, ultra-cold matter and even in blood flow problems. In this presentation we will review relevant applications, such as tsunami waves, the El Nino southern oscillation, blood flow in arteries and solitons propagating in optical fibres. Mathematical modelling techniques for deriving equations that describe such phenomena will be introduced in the context of surface water waves. We will also review the minimum required theoretical background in order to proceed with safe numerical simulations. Finally, we will discuss the numerical modelling of such problems where methods such as standard and mixed Galerkin / Finite element methods are of central focus. We close this presentation by showcasing a topic of much current interest, namely, the development of modern mathematical models for nonlinear and dispersive waves by combining machine learning techniques with classical methodologies.
Prof. José Miguel Urbano, Department of Mathematics, University of Coimbra, Portugal
Thursday, September 17, 2020, 16:00
- 17:30
https://kaust.zoom.us/j/97005661538
Contact Person
We will discuss the Lipschitz extension problem, its solution via MacShane-Whitney extensions, and its several drawbacks, leading to the notion of AMLE (Absolutely Minimizing Lipschitz Extension). We then present a rigorous and detailed analysis of the equivalence between being absolutely minimizing Lipschitz and enjoying comparison with cones. Finally, we explore some consequences of this geometric notion, chiefly the derivation of a Harnack inequality.
Thursday, September 17, 2020, 12:00
- 13:00
https://kaust.zoom.us/j/95474758108?pwd=WkwrdiszTE1uYTdmR3JRK09LVDErZz09
Contact Person
In this work, we estimate extreme sea surface temperature (SST) hotspots, i.e., high threshold exceedance regions, for the Red Sea, a vital region of high biodiversity. We analyze high-resolution satellite-derived SST data comprising daily measurements at 16703 grid cells across the Red Sea over the period 1985–2015. We propose a semiparametric Bayesian spatial mixed-effects linear model with a flexible mean structure to capture spatially-varying trend and seasonality, while the residual spatial variability is modeled through a Dirichlet process mixture (DPM) of low-rank spatial Student-t processes (LTPs). By specifying cluster-specific parameters for each LTP mixture component, the bulk of the SST residuals influence tail inference and hotspot estimation only moderately. Our proposed model has a nonstationary mean, covariance and tail dependence, and posterior inference can be drawn efficiently through Gibbs sampling. In our application, we show that the proposed method outperforms some natural parametric and semiparametric alternatives.
Prof. José Miguel Urbano, Department of Mathematics, University of Coimbra, Portugal
Tuesday, September 15, 2020, 16:00
- 17:30
https://kaust.zoom.us/j/92903118164
Contact Person
We will discuss the Lipschitz extension problem, its solution via MacShane-Whitney extensions, and its several drawbacks, leading to the notion of AMLE (Absolutely Minimizing Lipschitz Extension). We then present a rigorous and detailed analysis of the equivalence between being absolutely minimizing Lipschitz and enjoying comparison with cones. Finally, we explore some consequences of this geometric notion, chiefly the derivation of a Harnack inequality.
Prof. José Miguel Urbano, Department of Mathematics, University of Coimbra, Portugal
Thursday, September 10, 2020, 16:00
- 17:30
https://kaust.zoom.us/j/96237974283
Contact Person
We will discuss the Lipschitz extension problem, its solution via MacShane-Whitney extensions, and its several drawbacks, leading to the notion of AMLE (Absolutely Minimizing Lipschitz Extension). We then present a rigorous and detailed analysis of the equivalence between being absolutely minimizing Lipschitz and enjoying comparison with cones. Finally, we explore some consequences of this geometric notion, chiefly the derivation of a Harnack inequality.
Thursday, September 10, 2020, 12:00
- 13:00
https://kaust.zoom.us/j/95474758108?pwd=WkwrdiszTE1uYTdmR3JRK09LVDErZz09
Contact Person
When constructing high-order schemes for solving hyperbolic conservation laws with multi-dimensional finite volume schemes, the corresponding high-order reconstructions are commonly performed in characteristic spaces to eliminate spurious oscillations as much as possible. For multi-dimensional finite volume schemes, we need to perform the characteristic decomposition several times in different normal directions of the target cell, which is very time-consuming. We propose a rotated characteristic decomposition technique that requires only one-time decomposition for multi-dimensional reconstructions. This technique not only reduces the computational cost remarkably, but also controls spurious oscillations effectively. We take a third-order weighted essentially non-oscillatory finite volume scheme for solving the Euler equations as an example to demonstrate the efficiency of the proposed technique. We apply the new methodology to the simulation of instabilities in direct initiation of gaseous detonations in free space.
Prof. José Miguel Urbano, Department of Mathematics, University of Coimbra, Portugal
Tuesday, September 08, 2020, 16:00
- 17:30
https://kaust.zoom.us/j/94899630384
Contact Person
We will discuss the Lipschitz extension problem, its solution via MacShane-Whitney extensions, and its several drawbacks, leading to the notion of AMLE (Absolutely Minimizing Lipschitz Extension). We then present a rigorous and detailed analysis of the equivalence between being absolutely minimizing Lipschitz and enjoying comparison with cones. Finally, we explore some consequences of this geometric notion, chiefly the derivation of a Harnack inequality.
Thursday, September 03, 2020, 12:00
- 13:00
https://kaust.zoom.us/j/95474758108?pwd=WkwrdiszTE1uYTdmR3JRK09LVDErZz09
Contact Person
Discussing the concept of correlation and how to interpret it alone (marginally) or within a more complex environment (conditionally). This rather simple observation is the key observation behind a lot of exciting developments and connections in statistics that can be leveraged for improved computations and better motivated statistical models.