Optoelectronics in the deep-ultraviolet (DUV) regime is still a growing research field that requires significant effort to understand the material properties and optimize the device structures to realize highly efficient DUV devices. Of all the wide bandgap materials, AlGaN is perhaps the most studied semiconductor to replace the environmentally hazardous mercury lamps; however, the external quantum efficiency (EQE) of AlGaN based DUV devices is insufficient to replace the existing old-fashioned mercury UV lamps.

Bayesian inference for nonlinear diffusions, observed at discrete times,is a challenging task that has prompted the development of a number of algorithms, mainly within the computational statistics community. We propose a new direction, and accompanying methodology - borrowing ideas from statistical physics and computational chemistry - for inferring the posterior distribution of latent diffusion paths and model parameters, given observations of the process

The limited overcrowded radio frequency spectrum compelled researchers to explore higher frequency ranges for wireless transmission such as optical frequency bands. In recent decades, visible light communications (VLC) have gained lots of research attention thanks to the abundant bandwidth they offer and the existing lighting infrastructure they utilize that consequently reduces deployment costs.

We consider two sets of new priors for Bayesian inversion and machine learning: The first one is based on mixture of experts models with Gaussian processes. The target is to estimate the number of experts and their parameters, and to make state estimation. For sampling, we use SMC^2. For non-Gaussian priors, we discuss Cauchy priors and the generalisation to high-order Cauchy fields and further generalisation to alpha-stable fields. For sampling, we use a selection of modern MCMC tools. Finally, we apply some of the methods and models to an industrial tomography problem on estimating log internal structure, measured at sawmills, based on X-ray, RGB camera and laser scanning.

Constructing functional representations of the key quantities of interest (QoIs), the ignition delay time (_ign), of an uncertain ignition reaction in high dimension is our main goal. First, attention is focused on the ignition delay time of an iso-octane air mixture, using a detailed chemical mechanism with 3,811 elementary reactions. Uncertainty in all reaction rates is directly accounted for using associated uncertainty factors, assuming independent log uniform priors. A Latin hypercube sample (LHS) of the ignition delay times was first generated, and the resulting database was then exploited to assess the possibility of constructing polynomial chaos (PC) representations in terms of the canonical random variables parameterizing the uncertain rates.

Semiconductor devices based on wide-bandgap materials exhibit a higher breakdown voltage, temperature tolerance, and device stability, and lower energy loss than devices based on low-bandgap materials. Several limitations challenge the use of III-nitrides and transition metal oxides as wide-bandgap materials. This thesis proposes novel methods to surmount these issues. 

The natural sciences such as biology, medicine, and chemistry are currently in a transformative stage. Progress in technologies for measuring and collecting data (sequences, images, and molecules) has exploded since the human genome project. In parallel, we have witnessed stunning advances in what can broadly be referred to as computational techniques. This includes data-driven analysis of data such as Machine learning and Artificial Intelligence. From an ML/AI standpoint, there is a renewed interest in classical” equation-based modeling, causal analysis, and generative probabilistic modeling techniques. BioAI refers to this “perfect storm” between Bio and AI.

The statistical analysis based on the quantile method is more comprehensive, flexible, and not sensitive against outliers compared to the mean methods. The study of the joint disease mapping focuses on the mean regression. This means they study the correlation or the dependence between the means of the diseases by using standard regression. However, sometimes one disease limits the occurrence of another disease. In this case, the dependence between the two diseases will not be in the means but in the different quantiles; thus, the analyzes will consider a joint disease mapping of high quantile for one disease with low quantile of the other disease.

Lyapunov's stability theory, which was formulated around 1892, presents itself as a watershed event in the study of dynamical systems.

his talk reviews some fundamental and practical issues related to the formulation and analysis of joint models of mixed types of outcomes with latent variables, with particular emphasis on both several case-studies in applied statistics and their computational implementation

Fluid dynamics models are ubiquitous in a multitude of applications. One of the most important applications of fluid dynamics models is numerical weather prediction. Modern numerical weather prediction combines sophisticated nonlinear fluid dynamics models with increasingly accurate high-dimensional data.  This process is called data assimilation and it is performed every day at all major operational weather centers across the world. Data assimilation  (DA) requires massive computing capabilities as realistic atmosphere-ocean models typically have billions of degrees of freedom. I will give a short overview of the ongoing research that aims to drastically decrease the required DA computational effort by reducing the dimension of the models involved and using stochastic perturbations to account for the unresolved scales. The incorporation of observation data is done by using particle approximations suitably adapted to solve high-dimensional problems.

Human knowledge can facilitate the evolution of artificial intelligence towards learning the capability of planning and reasoning and has been the critical element for developing the next-generation artificial intelligence. Although knowledge collection and organization have achieved significant progress, it is still non-trivial to construct a comprehensive knowledge graph for downstream applications. The difficulty motivates the study of knowledge association to resolve the problem, yet current solutions suffer from two primary shortages, i.e., generalization and robustness. Specifically, most existing methods require a sufficient number of labeled data and ignore the effective utilization of complex relationships between entities, limiting the generalization ability of knowledge association approaches. Moreover, prevailing approaches severely rely on clean labeled data, making the model vulnerable to noises in the given labeled data. These shortages motivate the research on generalization and robustness of knowledge association in this dissertation. 

Partial differential equations (PDEs) are used to describe multi-dimensional physical phenomena. However, some of these phenomena are described by a more general class of systems called fractional systems (FS). 

Error feedback (EF), also known as error compensation, is an immensely popular convergence stabilization mechanism in the context of distributed training of supervised machine learning models enhanced by the use of contractive communication compression mechanisms, such as Top-k. First proposed by Seide et al (2014) as a heuristic, EF resisted any theoretical understanding until recently [Stich et al., 2018, Alistarh et al., 2018].

Semi-implicit schemes for evolutionary partial differential equations. Topic 3 - construction of more general schemes for evolutionary partial differential equations, in which the stiffness may be of a different type than the one previously considered. Several examples will be given illustrating the general procedure.

Robot navigation typically comprises of decision making at two different levels - global planning to compute a viable trajectory to the robot's destination and strategic (local) interaction to elicit cooperation and resolve any conflicts with other robots/pedestrians that would arise while navigating along the trajectory. Robot navigation in crowded environments is particularly challenging as the robot needs to exhibit navigation behaviors that are conceived as socially compliant by human pedestrians or vehicles they maneuver at both of the levels. In this presentation, I will introduce some of relevant works from my research group.

Optical wireless communication, taking advantage of the unlicensed ultraviolet-to-visible wavelength region of the electromagnetic spectrum, had been coined as the next-generation wireless communication technology and holds promises to deliver a boundless, high-speed, reliable and secured broadband experience.

The qualitative study of PDEs often relies on integral identities and inequalities. For example, for time-dependent  PDEs, conserved integral quantities or quantities that are dissipated play an important role. In particular, if these integral quantities have a definite sign, they are of great interest as they may provide control on the solutions to establish well-posedness.

Implicit-Explicit schemes for hyperbolic systems with stiff relaxation. Topic 2 - hyperbolic relaxation models and to the methods for their numerical solution. After introduction of hyperbolic-hyperbolic and hyperbolic-parabolic type relaxation problem, conservative finite difference space discretization will be introduced.

Construction of high order finite volume and finite difference shock-capturing schemes for conservation laws. Topic 1 - illustrating how to construct shock capturing schemes for conservation laws. We focus on semi-discrete schemes based on the method of lines.

The numerical solution of multi-physics problems relying on the Navier-Stokes equations has kept multiple generations of supercomputers busy. For fundamental problems, computational fluid dynamic aims to resolve all relevant time and length scales, which is then known as direct numerical simulation (DNS).

During my Ph.D. program, we have studied mean-field games (MFGs). MFGs model games with large populations of rational agents. The agents search for their optimal strategies and trajectories to minimize an individual cost, which depends on the statistical distribution of the population. Although it is quite hard to consider the systems of large populations in the numerical analysis, we can expect to consider the average effect given by the populations because the influence of each agent should be small.

The human race is facing what may turn out to be an existential threat due to entrenched practices that are contributing to climate change. This talk addresses the impact of information technology (IT) in this regard.

Singular and degenerate partial differential equations are unavoidable in the modelling of several phenomena, from phase transitions to flows in porous media or chemotaxis. They encompass a crucial issue in the analysis of pdes, namely wether we can still derive analytical estimates when the crucial algebraic assumption of ellipticity collapses.

We live in the age of information where electronics play a critical role in our daily life. Moore’s Law: performance over cost has inspired innovation in complementary metal oxide semiconductor (CMOS) technology and enabled high performance, ultra-scaled CMOS electronics.