PDE Backstepping Boundary Control of Parabolic PDEs Partial Differential Equations (PDEs) are often used to model various complex physical systems. Representative engineering applications such as heat exchangers, transmission lines, oil wells, road traffic, multiphase flow, melting phenomena, supply chains, collective dynamics, and even chemical processes governing the state of charge of Lithium-ion battery, extrusion, reactors to mention a few. This course will explore the boundary control of a class of parabolic PDE via the well-known backstepping method.

Due essentially to the difficulties associated with obtaining explicit forms of stationary marginal distributions of non-linear stationary processes, appropriate characterizations of such processes are worked upon little. After discussing an elaborate motivation behind this thesis and presenting preliminaries in Chapter 1, we characterize, in Chapter 2, the stationary marginal distributions of certain non-linear multivariate stationary processes. To do so, we show that the stationary marginal distributions of these processes belong to specific skew-distribution families, and for a given skew-distribution from the corresponding family, a process, with stationary marginal distribution identical to that given skew-distribution, can be found.

Partial Differential Equations (PDEs) are often used to model various complex physical systems. Representative engineering applications such as heat exchangers, transmission lines, oil wells, road traffic, multiphase flow, melting phenomena, supply chains, collective dynamics, and even chemical processes governing the state of charge of Lithium-ion battery, extrusion, reactors to mention a few. This course will explore the boundary control of a class of parabolic PDE via the well-known backstepping method.

The modeling of spatio-temporal and multivariate spatial random fields has been an important and growing area of research due to the increasing availability of space-time-referenced data in a large number of scientific applications. In geostatistics, the covariance function plays a crucial role in describing the spatio-temporal dependence in the data and is key to statistical modeling, inference, stochastic simulation, and prediction. Therefore, the development of flexible covariance models, which can accommodate the inherent variability of the real data, is necessary for advantageous modeling of random fields. This thesis is composed of four significant contributions in the development and applications of new covariance models for stationary multivariate spatial processes, and nonstationary spatial and spatio-temporal processes. Firstly, this thesis proposes a semiparametric approach for multivariate covariance function estimation with flexible specification of the cross-covariance functions via their spectral representations. The flexibility in the proposed cross-covariance function arises due to B-spline based specification of the underlying coherence functions, which in turn allows for capturing non-trivial cross-spectral features. The proposed method is applied to model and predict the bivariate data of particulate matter concentration and wind speed in the United States. Secondly, this thesis introduces a parametric class of multivariate covariance functions with asymmetric cross-covariance functions. The proposed covariance model is applied to analyze the asymmetry and perform prediction in a trivariate data of particulate matter concentration, wind speed and relative humidity in the United States.
 Thirdly, the thesis presents a space deformation method which imparts nonstationarity to any stationary covariance function. The proposed method utilizes the functional data registration algorithm and classical multidimensional scaling to estimate the spatial deformation. The application of the proposed method is demonstrated on precipitation data from Colorado, United States. Finally, this thesis proposes a parametric class of time-varying spatio-temporal covariance functions, which are stationary in space but nonstationary in time. The proposed time-varying spatio-temporal covariance model is applied to study the seasonality effect and perform space-time predictions in the daily particulate matter concentration data from Oregon, United States.

Wavefront sensing is a fundamental problem in applied optics. Wavefront sensors that work in a deterministic manner are of particular interest. Initialized with a unified theory for classical wavefront sensors, this dissertation discusses relevant properties of wavefront sensor designs. Based on which, a new wavefront sensor, termed Coded Wavefront Sensor, is proposed to leverage the advantages of the analysis, especially the lateral wavefront resolution. A prototype was built to demonstrate this new wavefront sensor.

We recall the state of the art and the role of polyconvexity in the calculus of variations. Then we keep our focus on a particular polyconvex function, applicable to the study of Euler incompressible fluids. We prove the existence, uniqueness, and regularity of minimizers of a polyconvex functional which corresponds to the H1-projection of measure-preserving maps. Our result introduces a new criteria on the uniqueness of the minimizer, based on the smallness of the Lagrange multiplier. No estimate on the second derivatives of the pressure is needed to get a unique global minimizer. We introduce a minimizing movement scheme to construct Lr-solutions of the Navier-Stokes equation (NSE) for a short time interval. Our scheme is an improved version of the split scheme introduced in Ebin–Marsden in 1970, and allows us to solve the equation with less regular initial data as opposed to more regular initial data requirement in the 1970 Ebin–Marsden’s work. (Most of the material of these lectures is based on a joint work with M. Jacobs and I. Kim).

Fifth generation (5G) wireless communication networks are being deployed worldwide and more capabilities are in the process of being standardized, such as massive connectivity, ultra-reliability, and low latency. However, 5G will not meet all requirements of the future, and sixth generation (6G) wireless networks are expected to provide global coverage, enhanced spectral/energy/cost efficiency, greater intelligence and security, etc. To meet these requirements, 6G networks will rely on new enabling technologies, i.e., air interface and transmission technologies and novel network architectures, such as waveform design, multiple access, channel coding schemes, multi-antenna technologies, network slicing, cell-free architecture, and cloud/fog/edge computing. One vision on 6G is that it will have four new paradigm shifts. First, to satisfy the requirement of global coverage, 6G will not be limited to terrestrial communication networks, which will need to be complemented with non-terrestrial networks such as satellite and unmanned aerial vehicle (UAV) communication networks, thus achieving a space-air-ground-sea integrated communication networks. Multiple spectra will be exploited to further increase data rates and connection density, including the sub-6 GHz, millimeter wave (mmWave), terahertz (THz), and optical frequency bands. Third, facing the very large datasets generated by heterogeneous networks, diverse communication scenarios, large numbers of antennas, wide bandwidths, and new service requirements, 6G networks will enable a new range of smart applications with the aid of AI-related technologies. And, fourth, network security will have to be strengthened when developing 6G networks. This talk will review recent advances and future trends in these four aspects.

We recall the state of the art and the role of polyconvexity in the calculus of variations. Then we keep our focus on a particular polyconvex function, applicable to the study of Euler incompressible fluids. We prove the existence, uniqueness, and regularity of minimizers of a polyconvex functional which corresponds to the H1-projection of measure-preserving maps. Our result introduces a new criteria on the uniqueness of the minimizer, based on the smallness of the Lagrange multiplier. No estimate on the second derivatives of the pressure is needed to get a unique global minimizer. We introduce a minimizing movement scheme to construct Lr-solutions of the Navier-Stokes equation (NSE) for a short time interval. Our scheme is an improved version of the split scheme introduced in Ebin–Marsden in 1970, and allows us to solve the equation with less regular initial data as opposed to more regular initial data requirement in the 1970 Ebin–Marsden’s work. (Most of the material of these lectures is based on a joint work with M. Jacobs and I. Kim).

Abstract

As simulation and analytics enter the exascale era, numerical algorithms must span a wide

We recall the state of the art and the role of polyconvexity in the calculus of variations. Then we keep our focus on a particular polyconvex function, applicable to the study of Euler incompressible fluids. We prove the existence, uniqueness, and regularity of minimizers of a polyconvex functional which corresponds to the H1-projection of measure-preserving maps. Our result introduces a new criteria on the uniqueness of the minimizer, based on the smallness of the Lagrange multiplier. No estimate on the second derivatives of the pressure is needed to get a unique global minimizer. We introduce a minimizing movement scheme to construct Lr-solutions of the Navier-Stokes equation (NSE) for a short time interval. Our scheme is an improved version of the split scheme introduced in Ebin–Marsden in 1970, and allows us to solve the equation with less regular initial data as opposed to more regular initial data requirement in the 1970 Ebin–Marsden’s work. (Most of the material of these lectures is based on a joint work with M. Jacobs and I. Kim)

The 2016 DREAM Disease Module Identification Challenge was developed to systematically assess the state of computational module identification methods on a diverse collection of molecular networks. Six different anonymized networks were presented with the gene names anonymized. The goal was to partition the genes into non-overlapping modules of from 3-100 genes each, based soley on the patterns of network connectivity.

Electromechanical switches were the core elements of the very first digital computers in early 20th century. While these switches were later replaced by the smaller, faster and more reliable "transistor" technology, they found a new life following the development of nanofabrication tools and Micro-electromechannical Systems (MEMS). In this seminar we will explore the most recent advances in the field of MEMS-based digital circuit and sensor design. We also examine the application of MEMS switches and resonators in building the most important blocks of a digital system, namely adders, multipliers, data converters, sequential and combinational complex logic, and discuss the future of this technology in the beyond-CMOS era.

Explosive volcanic eruptions are magnificent events that in many ways affect the Earth’s natural processes and climate. They cause sporadic perturbations of the planet’s energy balance, activating complex climate feedbacks and providing unique opportunities to better quantify those processes. We know that explosive eruptions cause cooling in the atmosphere for a few years, but we have just recently realized that they affect the major climate variability modes and volcanic signals can be seen in the subsurface ocean for decades. The volcanic forcing of the previous two centuries offsets the ocean heat uptake and diminishes global warming by about 30%. In the future, explosive volcanism could slightly delay the pace of global warming and has to be accounted for in long-term climate predictions. The recent interest in dynamic, microphysical, chemical and climate impacts of volcanic eruptions is also excited by the fact these impacts provide a natural analog for climate geoengineering schemes involving the deliberate development of an artificial aerosol layer in the lower stratosphere to counteract global warming. In this talk, I will discuss these recently discovered volcanic effects and specifically pay attention to how we can learn about the hidden Earth-system mechanisms activated by explosive volcanic eruptions.

In low-resource settings, disease registries do not exist, and prevalence mapping relies on data collected form surveys of disease prevalence taken in a sample of the communities at risk within the region of interest, possibly supplemented by remotely sensed images that can act as proxies for environmental risk factors. A standard geostatistical model for data of this kind is a generalized linear mixed model, Yᵢ ~ Binomial(mᵢ; P(xᵢ)) log [P(x)/{(1- P(xᵢ)}] = d(x)β + S(x), where Yᵢ is the number of positives in a sample of mi individuals at location xᵢ, d(x) is a vector of spatially referenced explanatory variables available at any location x within the region of interest, and S(x) is a Gaussian process.

In this talk, I will first review statistical methods and software associated with this standard model, then consider several methodological extensions and their applications to some Africa-wide control programmes for Neglected Tropical Diseases to demonstrate the very substantial gains in efficiency that can be obtained by comparison with currently used methods.