In this talk, I will present the recent developments in the topic of the existence of solutions to the two-fluid systems. The compensated compactness technique of P.-L. Lions and E. Feireisl for single-component fluids has certain limitations, distinctly in the context of multi-component flow models. A particular example of such a model is the two-fluids Stokes system with a single velocity field and two densities, and with an algebraic pressure law closure. The first result that I will present is the existence of weak solutions for such a system, using the compactness criterion introduced recently by D. Bresch and P.-E. Jabin. I will also outline an innovative construction of solutions relying on the G. Crippa and C. DeLellis stability estimates for the transport equation. In the last part of my talk, I will relate to a couple of more recent results: the existence of solutions to the one-dimensional system, non-uniqueness of solutions to the inviscid system, and I will comment on issues around weak-strong uniqueness.

Abstract

The outstanding performance of deep neural networks (DNNs), for visual recognition tasks

Machine learning has been widely applied to diverse problems of forwarding prediction and backward design. The former problem of forwarding prediction is to predict the reaction of a system given the input x, i.e., y=f(x). This talk will introduce several groups of algorithms for learning the prediction function f. The backward design is an inverse problem, predicting the input x according to the system reaction y, i.e., x=g(y). This is an important problem for the design of chemical material and optical devices. This talk will introduce several successful application examples of machine learning algorithms on the backward design problems.

Droughts, high temperatures and strong winds are key causes of the recent bushfires that have touched a major part of the Australian territory. Such extreme events seem to appear with increasing frequency, creating an urgent need to better understand the behavior of extreme environmental phenomena.

In this talk, we begin by a brief introduction to proper scoring rules and their use in statistics. Then, we discuss an often overlooked problem: the up-weighting of observations with large uncertainty, which can lead to unintuitive rankings of models, by some of the most popular proper scoring rules, such as the continuously ranked probability score (CRPS), the MAE, and the MSE.

A healthy ecosystem is essential to our well being and to ensure that we need a better understanding of the life or biodiversity around us. In the first part of this talk, I will introduce how modern technology is being used to collect data on biodiversity across space and time. These data come in complex forms such as DNA sequences, high-dimensional binary vectors, sound signals, etc. I will briefly touch upon the statistical challenges involved in making sense of these data.   In the second part, I will elaborate on a project motivated by studying temporal patterns in bird vocalizations. I will introduce a new class of semiparametric latent variable models for long memory discretized event data. The proposed class of FRActional Probit (FRAP) models are based on the thresholding of a latent process consisting of an additive expansion of a smooth Gaussian process with a fractional Brownian motion. I will describe a Bayesian approach to inference using Markov chain Monte Carlo. Results from applying the model on Amazon bird vocalization data will be presented which provide substantial evidence for self-similarity and non-Markovian/Poisson dynamics. A hierarchical extension of the proposed model to accommodate vocalizations of multiple birds at the same time will also be discussed.

This session will help you to improve the efficiency of your literature searches. You will learn basic search techniques – using Boolean operators, keyword search, concept search, truncation, etc. Two major interdisciplinary scientific databases – Web of Science and Scopus, as well as CEMSE specific resources in KAUST library collections will be presented.

Computational mathematics has a millennium long history but its modern incarnation started after the advent of electronic computers about 80 years ago. Scientifically, it lies in the intersection between mathematics, a subject with a long history, and computer sciences, a relatively new discipline. Its motivations, approaches and practitioners have derived from different fields, and it has also had to evolve and adapt to new tools and opportunities. My own scientific career overlaps quite a bit with the field’s modern evolution and in this talk, I’ll give a personal, as well as a “historical” view of the field.

Geospatial health data are essential to inform public health and policy. These data can be used to quantify disease burden, understand geographic and temporal patterns, identify risk factors, and measure inequalities. In this talk, I will give an overview of my research which focuses on the development of geospatial methods and interactive visualization applications for health surveillance. I will present disease risk models where environmental, demographic and climatic data are used to predict the risk and identify targets for intervention of lymphatic filariasis in sub-Saharan Africa, and leptospirosis in a Brazilian urban slum. I will also show the R packages epiflows for risk assessment of travel-related spread of disease, and SpatialEpiApp for disease mapping and the detection of clusters. Finally, I will describe my future research and how it can inform better surveillance and improve population health globally.

Biological systems are distinguished by their enormous complexity and variability. That is why mathematical modeling and computational simulation of those systems is very difficult, in particular thinking of detailed models which are based on first principles. The difficulties start with geometric modeling which needs to extract basic structures from highly complex and variable phenotypes, on the other hand also has to take the statistic variability into account. Moreover, the models of the processes running on these geometries are not yet well established, since these are equally complex and often couple many scales in space and time. Thus, simulating such systems always means to put the whole frame to test, from modelling to the numerical methods and software tools used for simulation. These need to be advanced in connection with validating simulation results by comparing them to experiments.

The past few decades have witnessed rapid and unprecedented theoretical progress in the science of causal inference, ranging from the “credibility revolution” with the popularization of quasi-experimental designs, to the development of a complete solution to non-parametric identification with causal graphical models. Most of these theoretical progress, however, relies on strong, exact assumptions, such as the absence of unobserved common causes, or the absence of certain direct effects. Unfortunately, more often than not these assumptions are very hard to defend in practice. This leads to two undesirable consequences for applied quantitative work in the data-intensive sciences: (i) important research questions may be neglected, simply because they do not exactly match the requirements of current methods; or, (ii) researchers may succumb to making the required “identification assumptions” simply to justify the use of available methods, but not because these assumptions are truly believed (or understood).  In this talk, I will discuss new theories, methods, and software for permitting causal inferences under more flexible and realistic settings. These tools empower scientists, and policymakers to both examine the sensitivity of causal inferences to violations of its underlying assumptions, and also to draw robust and trustworthy conclusions from settings in which traditional methods fail.  

Intrinsic connectivity networks (ICNs) refer to brain functional networks that are consistently found under various conditions, during tasks or at rest. Some studies demonstrated that while some stimuli do not impact intrinsic connectivity, other stimuli actually activate intrinsic connectivity through suppression, excitation, moderation or modification. Most analyses of fMRI data use ad-hoc methods to estimate the latent structure of ICNs. Modeling the effects on ICNs has also not been fully investigated. We propose a Bayesian Intrinsic Connectivity Network (BICNet) model, an extended Bayesian dynamic sparse latent factor model, to identify the ICNs and quantify task-related effects on the ICNs. BICNet has the following advantages: (1) It simultaneously identifies the individual and group-level ICNs; (2) It robustly identifies ICNs by jointly modeling rfMRI and tfMRI; (3) Compared to ICA-based methods, it can quantify the difference of ICN amplitudes across different states; (4) The sparsity of ICNs automatically performs feature selection, instead of ad-hoc thresholding. We apply BICNet to the rfMRI and language tfMRI data from the HCP and identify several ICNs related to distinct language processing functions.

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)

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.

This thesis presents a set of quantile analysis methods for multivariate data and multivariate functional data, with an emphasis on environmental applications, and consists of four significant contributions.

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.

Environmental statistics plays an important role in many related applications, such as weather-related risk assessment for urban design and crop growth. However, modeling the spatio-temporal dynamics of environmental data is challenging due to their inherent high variability and nonstationarity. This dissertation focuses on the modeling, simulation, and prediction of spatio-temporal processes using statistical techniques and machine learning algorithms, especially for nonstationary processes.

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.

In this thesis, I firstly provide a comprehensive assessment of wind energy resources and associated spatio-temporal patterns over Saudi Arabia in both current and future climate conditions, based on a Regional Climate Model output. A high wind energy potential exists and is likely to persist at least until 2050 over a vast area of Western Saudi Arabia, particularly in the region between Medina and the Red Sea coast and during Summer months. Since an accurate assessment of wind extremes is crucial for risk management purposes, I then present the first high-resolution risk assessment of wind extremes over Saudi Arabia.

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.

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.

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.

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.

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.