A practical approach to computing Lyapunov exponents of renewal and delay equations

We propose a method for computing the Lyapunov exponents of renewal equations (delay equations of Volterra type) and of coupled systems of renewal and delay differential equations. The method consists of the reformulation of the delay equation as an abstract differential equation, the reduction of the latter to a system of ordinary differential equations via pseudospectral collocation and the application of the standard discrete QR method. The effectiveness of the method is shown experimentally and a MATLAB implementation is provided

Hyperpolarized Long-T1 Silicon Nanoparticles for Magnetic Resonance Imaging

Silicon nanoparticles are experimentally investigated as a potential hyperpolarized, targetable MRI imaging agent. Nuclear T_1 times at room temperature for a variety of Si nanoparticles are found to be remarkably long (10^2 to 10^4 s) - roughly consistent with predictions of a core-shell diffusion model - allowing them to be transported, administered and imaged on practical time scales without significant loss of polarization. We also report surface functionalization of Si nanoparticles, comparable to approaches used in other biologically targeted nanoparticle systems.Comment: supporting material here: http://marcuslab.harvard.edu/Aptekar_hyper1_sup.pd

SMCTC : sequential Monte Carlo in C++

Sequential Monte Carlo methods are a very general class of Monte Carlo methods for sampling from sequences of distributions. Simple examples of these algorithms are used very widely in the tracking and signal processing literature. Recent developments illustrate that these techniques have much more general applicability, and can be applied very effectively to statistical inference problems. Unfortunately, these methods are often perceived as being computationally expensive and difficult to implement. This article seeks to address both of these problems. A C++ template class library for the efficient and convenient implementation of very general Sequential Monte Carlo algorithms is presented. Two example applications are provided: a simple particle filter for illustrative purposes and a state-of-the-art algorithm for rare event estimation

Retrieval of Snow Water Equivalent by the Precipitation Imaging Package (PIP) in the Northern Great Lakes

Performance of the Precipitation Imaging Package (PIP) for estimating the snow water equivalent (SWE) is evaluated through a comparative study with the collocated National Oceanic and Atmospheric Administration National Weather Service snow stake field measurements. The PIP together with a vertically pointing radar, a weighing bucket gauge, and a laser-optical disdrometer was deployed at the NWS Marquette, Michigan, office building for a long-term field study supported by the National Aeronautics and Space Administration's Global Precipitation Measurement mission Ground Validation program. The site was also equipped with a weather station. During the 2017/18 winter, the PIP functioned nearly uninterrupted at frigid temperatures accumulating 2345.8 mm of geometric snow depth over a total of 499 h. This long record consists of 30 events, and the PIP-retrieved and snow stake field measured SWE differed less than 15% in every event. Two of the major events with the longest duration and the highest accumulation are examined in detail. The particle mass with a given diameter was much lower during a shallow, colder, uniform lake-effect event than in the deep, less cold, and variable synoptic event. This study demonstrated that the PIP is a robust instrument for operational use, and is reliable for deriving the bulk properties of falling snow.Peer reviewe

Proportional Odds Models with High-dimensional Data Structure

The proportional odds model (POM) is the most widely used model when the response has ordered categories. In the case of high-dimensional predictor structure the common maximum likelihood approach typically fails when all predictors are included. A boosting technique pomBoost is proposed that fits the model by implicitly selecting the influential predictors. The approach distinguishes between metric and categorical predictors. In the case of categorical predictors, where each predictor relates to a set of parameters, the objective is to select simultaneously all the associated parameters. In addition the approach distinguishes between nominal and ordinal predictors. In the case of ordinal predictors, the proposed technique uses the ordering of the ordinal predictors by penalizing the difference between the parameters of adjacent categories. The technique has also a provision to consider some mandatory predictors (if any) which must be part of the final sparse model. The performance of the proposed boosting algorithm is evaluated in a simulation study and applications with respect to mean squared error and prediction error. Hit rates and false alarm rates are used to judge the performance of pomBoost for selection of the relevant predictors

Applicability of climate-based daylight modelling

This PhD thesis evaluated the applicability of Climate-Based Daylight Modelling (CBDM) as it is presently done. The objectives stated in this thesis aimed at broadly assessing applicability by looking at multiple aspects: (i) the way CBDM is used by expert researchers and practitioners; (ii) how state-of-the-art simulation techniques compare to each other and how they are affected by uncertainty in input factors; (iii) how the simulated results compare with data measured in real occupied spaces. The answers obtained from a web-based questionnaire portrayed a variety of workflows used by different people to perform similar, if not the same, evaluations. At the same time, the inter-model comparison performed to compare the existing simulation techniques revealed significant differences in the way the sky and the sun are recreated by each technique. The results also demonstrated that some of the annual daylight metrics commonly required in building guidelines are sensitive to the choice of simulation tool, as well as other input parameters, such as climate data, orientation and material optical properties. All the analyses were carried out on four case study spaces, remodelled from existing classrooms that were the subject of a concurrent research study that monitored their interior luminous conditions. A large database of High Dynamic Range images was collected for that study, and the luminance data derived from these images could be used in this work to explore a new methodology to calibrate climate-based daylight models. The results collected and presented in this dissertation illustrate how, at the time of writing, there is not a single established common framework to follow when performing CBDM evaluations. Several different techniques coexist but each of them is characterised by a specific domain of applicability