Computational Tracking of Mental Health in Youth: Latin American Contributions to a Low-Cost and Effective Solution for Early Psychiatric Diagnosis

The early onset of mental disorders can lead to serious cognitive damage, and timely interventions are needed in order to prevent them. In patients of low socioeconomic status, as is common in Latin America, it can be hard to identify children at risk. Here, we briefly introduce the problem by reviewing the scarce epidemiological data from Latin America regarding the onset of mental disorders, and discussing the difficulties associated with early diagnosis. Then we present computational psychiatry, a new field to which we and other Latin American researchers have contributed methods particularly relevant for the quantitative investigation of psychopathologies manifested during childhood. We focus on new technologies that help to identify mental disease and provide prodromal evaluation, so as to promote early differential diagnosis and intervention. To conclude, we discuss the application of these methods to clinical and educational practice. A comprehensive and quantitative characterization of verbal behavior in children, from hospitals and laboratories to homes and schools, may lead to more effective pedagogical and medical intervention

Periodic nonlinear Fourier transform for fiber-optic communications, Part I:theory and numerical methods

In this work, we introduce the periodic nonlinear Fourier transform (PNFT) method as an alternative and efficacious tool for compensation of the nonlinear transmission effects in optical fiber links. In the Part I, we introduce the algorithmic platform of the technique, describing in details the direct and inverse PNFT operations, also known as the inverse scattering transform for periodic (in time variable) nonlinear Schrödinger equation (NLSE). We pay a special attention to explaining the potential advantages of the PNFT-based processing over the previously studied nonlinear Fourier transform (NFT) based methods. Further, we elucidate the issue of the numerical PNFT computation: we compare the performance of four known numerical methods applicable for the calculation of nonlinear spectral data (the direct PNFT), in particular, taking the main spectrum (utilized further in Part II for the modulation and transmission) associated with some simple example waveforms as the quality indicator for each method. We show that the Ablowitz-Ladik discretization approach for the direct PNFT provides the best performance in terms of the accuracy and computational time consumption.

Application of Numerical Methods to Study Arrangement and Fracture of Lithium-Ion Microstructure

The focus of this work is to develop and employ numerical methods that provide characterization of granular microstructures, dynamic fragmentation of brittle materials, and dynamic fracture of three-dimensional bodies.

We first propose the fabric tensor formalism to describe the structure and evolution of lithium-ion electrode microstructure during the calendaring process. Fabric tensors are directional measures of particulate assemblies based on inter-particle connectivity, relating to the structural and transport properties of the electrode. Applying this technique to X-ray computed tomography of cathode microstructure, we show that fabric tensors capture the evolution of the inter-particle contact distribution and are therefore good measures for the internal state of and electronic transport within the electrode.

We then shift focus to the development and analysis of fracture models within finite element simulations. A difficult problem to characterize in the realm of fracture modeling is that of fragmentation, wherein brittle materials subjected to a uniform tensile loading break apart into a large number of smaller pieces. We explore the effect of numerical precision in the results of dynamic fragmentation simulations using the cohesive element approach on a one-dimensional domain. By introducing random and non-random field variations, we discern that round-off error plays a significant role in establishing a mesh-convergent solution for uniform fragmentation problems. Further, by using differing magnitudes of randomized material properties and mesh discretizations, we find that employing randomness can improve convergence behavior and provide a computational savings.

The Thick Level-Set model is implemented to describe brittle media undergoing dynamic fragmentation as an alternative to the cohesive element approach. This non-local damage model features a level-set function that defines the extent and severity of degradation and uses a length scale to limit the damage gradient. In terms of energy dissipated by fracture and mean fragment size, we find that the proposed model reproduces the rate-dependent observations of analytical approaches, cohesive element simulations, and experimental studies.

Lastly, the Thick Level-Set model is implemented in three dimensions to describe the dynamic failure of brittle media, such as the active material particles in the battery cathode during manufacturing. The proposed model matches expected behavior from physical experiments, analytical approaches, and numerical models, and mesh convergence is established. We find that the use of an asymmetrical damage model to represent tensile damage is important to producing the expected results for brittle fracture problems.

The impact of this work is that designers of lithium-ion battery components can employ the numerical methods presented herein to analyze the evolving electrode microstructure during manufacturing, operational, and extraordinary loadings. This allows for enhanced designs and manufacturing methods that advance the state of battery technology. Further, these numerical tools have applicability in a broad range of fields, from geotechnical analysis to ice-sheet modeling to armor design to hydraulic fracturing.

Point-and-shoot: rapid quantitative detection methods for on-site food fraud analysis – moving out of the laboratory and into the food supply chain

Major food adulteration and contamination events occur with alarming regularity and are known to be episodic, with the question being not if but when another large-scale food safety/integrity incident will occur. Indeed, the challenges of maintaining food security are now internationally recognised. The ever increasing scale and complexity of food supply networks can lead to them becoming significantly more vulnerable to fraud and contamination, and potentially dysfunctional. This can make the task of deciding which analytical methods are more suitable to collect and analyse (bio)chemical data within complex food supply chains, at targeted points of vulnerability, that much more challenging. It is evident that those working within and associated with the food industry are seeking rapid, user-friendly methods to detect food fraud and contamination, and rapid/high-throughput screening methods for the analysis of food in general. In addition to being robust and reproducible, these methods should be portable and ideally handheld and/or remote sensor devices, that can be taken to or be positioned on/at-line at points of vulnerability along complex food supply networks and require a minimum amount of background training to acquire information rich data rapidly (ergo point-and-shoot). Here we briefly discuss a range of spectrometry and spectroscopy based approaches, many of which are commercially available, as well as other methods currently under development. We discuss a future perspective of how this range of detection methods in the growing sensor portfolio, along with developments in computational and information sciences such as predictive computing and the Internet of Things, will together form systems- and technology-based approaches that significantly reduce the areas of vulnerability to food crime within food supply chains. As food fraud is a problem of systems and therefore requires systems level solutions and thinking.

Heating the Early Universe : Numerical Methods and Their Analysis

During the epoch when the first collapsed structures formed (6<z<50) our Universe went through an extended period of changes. Some of the radiation from the first stars and accreting black holes in those structures escaped and changed the state of the Intergalactic Medium (IGM). The era of this global phase change in which the state of the IGM was transformed from cold and neutral to warm and ionized, is called the Epoch of Reionization.In this thesis we focus on numerical methods to calculate the effects of this escaping radiation. We start by considering the performance of the cosmological radiative transfer code C2-Ray. We find that although this code efficiently and accurately solves for the changes in the ionized fractions, it can yield inaccurate results for the temperature changes. We introduce two new elements to improve the code. The first element, an adaptive time step algorithm, quickly determines an optimal time step by only considering the computational cells relevant for this determination. The second element, asynchronous evolution, allows different cells to evolve with different time steps. An important constituent of methods to calculate the effects of ionizing radiation is the transport of photons through the computational domain or ``ray-tracing''. We devise a novel ray tracing method called PYRAMID which uses a new geometry - the pyramidal geometry. This geometry shares properties with both the standard Cartesian and spherical geometries. This makes it on the one hand easy to use in conjunction with a Cartesian grid and on the other hand ideally suited to trace radiation from a radially emitting source. A time-dependent photoionization calculation not only requires tracing the path of photons but also solving the coupled set of photoionization and thermal equations. Several different solvers for these equations are in use in cosmological radiative transfer codes. We conduct a detailed and quantitative comparison of four different standard solvers in which we evaluate how their accuracy depends on the choice of the time step. This comparison shows that their performance can be characterized by two simple parameters and that the C2-Ray generally performs best.

Stochastic Modeling of Reversible Biochemical Reaction-Diffusion Systems and High-Resolution Shock-Capturing Methods for Fluid Interfaces

Thesis (Ph.D.)--University of Washington, 2016-08

Development of a domain decomposition method for computational aeroacoustics

Abstract not available

Computational solid mechanics using a vertex-based finite volume method

A number of research groups are now developing and using finite volume (FV) methods for computational solid mechanics (CSM). These methods are proving to be equivalent and in some cases superior to their finite element (FE) counterparts. In this paper we will describe a vertex-based FV method with arbitrarily structured meshes, for modelling the elasto-plastic deformation of solid materials undergoing small strains in complex geometries. Comparisons with rational FE methods will be given.

Design, modelling, simulation and integration of cyber physical systems: methods and applications

The main drivers for the development and evolution of Cyber Physical Systems (CPS) are the reduction of development costs and time along with the enhancement of the designed products. The aim of this survey paper is to provide an overview of different types of system and the associated transition process from mechatronics to CPS and cloud-based (IoT) systems. It will further consider the requirement that methodologies for CPS-design should be part of a multi-disciplinary development process within which designers should focus not only on the separate physical and computational components, but also on their integration and interaction. Challenges related to CPS-design are therefore considered in the paper from the perspectives of the physical processes, computation and integration respectively. Illustrative case studies are selected from different system levels starting with the description of the overlaying concept of Cyber Physical Production Systems (CPPSs). The analysis and evaluation of the specific properties of a sub-system using a condition monitoring system, important for the maintenance purposes, is then given for a wind turbine.

Characterizing neural tissues with mass spectrometry imaging via enhanced computational approaches

Neuropeptides affect the activity of the myriad of neuronal circuits in the brain. They are under tight spatial and chemical control and the dynamics of their release and catabolism directly modify neuronal network activity. Understanding neuropeptide functioning requires approaches to determine their chemical and spatial heterogeneity within neural tissue, but most imaging techniques do not provide the complete information desired. To provide chemical information, most imaging techniques used to study the nervous system require preselection and labeling of the peptides of interest; however, mass spectrometry imaging (MSI) detects analytes across a broad mass range without the need to target a specific analyte. When used with matrix-assisted laser desorption/ionization (MALDI), MSI detects analytes in the mass range of neuropeptides. MALDI MSI simultaneously provides spatial and chemical information resulting in images that plot the spatial distributions of neuropeptides over the surface of a thin slice of neural tissue. Here a variety of approaches for neuropeptide characterization are developed. Specifically, several computational approaches are combined with MALDI MSI to create improved approaches that provide spatial distributions and neuropeptide characterizations. After successfully validating these MALDI MSI protocols, the methods are applied to characterize both known and unidentified neuropeptides from neural tissues. The methods are further adapted from tissue analysis to be able to perform tandem MS (MS/MS) imaging on neuronal cultures to enable the study of network formation. In addition, MALDI MSI has been carried out over the timecourse of nervous system regeneration in planarian flatworms resulting in the discovery of two novel neuropeptides that may be involved in planarian regeneration. In addition, several bioinformatic tools are developed to predict final neuropeptide structures and associated masses that can be compared to experimental MSI data in order to make assignments of neuropeptide identities. The integration of computational approaches into the experimental design of MALDI MSI has allowed improved instrument automation and enhanced data acquisition and analysis. These tools also make the methods versatile and adaptable to new sample types.

Variational ensemble Kalman filtering applied to data assimilation problems in computational fluid dynamics

One challenge on data assimilation (DA) methods is how the error covariance for the model state is computed. Ensemble methods have been proposed for producing error covariance estimates, as error is propagated in time using the non-linear model. Variational methods, on the other hand, use the concepts of control theory, whereby the state estimate is optimized from both the background and the measurements. Numerical optimization schemes are applied which solve the problem of memory storage and huge matrix inversion needed by classical Kalman filter methods. Variational Ensemble Kalman filter (VEnKF), as a method inspired the Variational Kalman Filter (VKF), enjoys the benefits from both ensemble methods and variational methods. It avoids filter inbreeding problems which emerge when the ensemble spread underestimates the true error covariance. In VEnKF this is tackled by resampling the ensemble every time measurements are available. One advantage of VEnKF over VKF is that it needs neither tangent linear code nor adjoint code. In this thesis, VEnKF has been applied to a two-dimensional shallow water model simulating a dam-break experiment. The model is a public code with water height measurements recorded in seven stations along the 21:2 m long 1:4 m wide flume’s mid-line. Because the data were too sparse to assimilate the 30 171 model state vector, we chose to interpolate the data both in time and in space. The results of the assimilation were compared with that of a pure simulation. We have found that the results revealed by the VEnKF were more realistic, without numerical artifacts present in the pure simulation. Creating a wrapper code for a model and DA scheme might be challenging, especially when the two were designed independently or are poorly documented. In this thesis we have presented a non-intrusive approach of coupling the model and a DA scheme. An external program is used to send and receive information between the model and DA procedure using files. The advantage of this method is that the model code changes needed are minimal, only a few lines which facilitate input and output. Apart from being simple to coupling, the approach can be employed even if the two were written in different programming languages, because the communication is not through code. The non-intrusive approach is made to accommodate parallel computing by just telling the control program to wait until all the processes have ended before the DA procedure is invoked. It is worth mentioning the overhead increase caused by the approach, as at every assimilation cycle both the model and the DA procedure have to be initialized. Nonetheless, the method can be an ideal approach for a benchmark platform in testing DA methods. The non-intrusive VEnKF has been applied to a multi-purpose hydrodynamic model COHERENS to assimilate Total Suspended Matter (TSM) in lake Säkylän Pyhäjärvi. The lake has an area of 154 km2 with an average depth of 5:4 m. Turbidity and chlorophyll-a concentrations from MERIS satellite images for 7 days between May 16 and July 6 2009 were available. The effect of the organic matter has been computationally eliminated to obtain TSM data. Because of computational demands from both COHERENS and VEnKF, we have chosen to use 1 km grid resolution. The results of the VEnKF have been compared with the measurements recorded at an automatic station located at the North-Western part of the lake. However, due to TSM data sparsity in both time and space, it could not be well matched. The use of multiple automatic stations with real time data is important to elude the time sparsity problem. With DA, this will help in better understanding the environmental hazard variables for instance. We have found that using a very high ensemble size does not necessarily improve the results, because there is a limit whereby additional ensemble members add very little to the performance. Successful implementation of the non-intrusive VEnKF and the ensemble size limit for performance leads to an emerging area of Reduced Order Modeling (ROM). To save computational resources, running full-blown model in ROM is avoided. When the ROM is applied with the non-intrusive DA approach, it might result in a cheaper algorithm that will relax computation challenges existing in the field of modelling and DA.

Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems on Anisotropically Refined Meshes

In this paper we consider the a posteriori and a priori error analysis of discontinuous Galerkin interior penalty methods for second-order partial differential equations with nonnegative characteristic form on anisotropically refined computational meshes. In particular, we discuss the question of error estimation for linear target functionals, such as the outflow flux and the local average of the solution. Based on our a posteriori error bound we design and implement the corresponding adaptive algorithm to ensure reliable and efficient control of the error in the prescribed functional to within a given tolerance. This involves exploiting both local isotropic and anisotropic mesh refinement. The theoretical results are illustrated by a series of numerical experiments.

Discontinuous Galerkin Methods on hp-Anisotropic Meshes I: A Priori Error Analysis

We consider the a priori error analysis of hp-version interior penalty discontinuous Galerkin methods for second-order partial differential equations with nonnegative characteristic form under weak assumptions on the mesh design and the local finite element spaces employed. In particular, we prove a priori hp-error bounds for linear target functionals of the solution, on (possibly) anisotropic computational meshes with anisotropic tensor-product polynomial basis functions. The theoretical results are illustrated by a numerical experiment.

Two-Level Schwarz Preconditioners for Super Penalty Discontinuous Galerkin Methods

We extend the construction and analysis of the non-overlapping Schwarz preconditioners proposed in Antonietti et al. [Math. Model. Numer. Anal., 41(1):21-54, 2007] and [Math. Model. Numer. Anal., submitted, 2006] to the (non-consistent) super penalty discontinuos Galerkin methods introduced by Babuska et al. [SIAM J. Numer. Anal., 10:863-875, 1973] and by Brezzi et al. [Numer. Methods Partial Differential Equations, 16(4):365-378, 2000]. We show that the resulting preconditioners are scalable, and we provide the convergence estimates. We also present numerical experiments demonstrating the theoretical results.