Basis Expansions for Functional Snippets

Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate both the mean and covariance functions. In this paper, we investigate mean and covariance estimation for functional snippets in which observations from a subject are available only in an interval of length strictly (and often much) shorter than the length of the whole interval of interest. For such a sampling plan, no data is available for direct estimation of the off-diagonal region of the covariance function. We tackle this challenge via a basis representation of the covariance function. The proposed approach allows one to consistently estimate an infinite-rank covariance function from functional snippets. We establish the convergence rates for the proposed estimators and illustrate their finite-sample performance via simulation studies and two data applications.Comment: 51 pages, 10 figure

Scheduling real-time, periodic jobs using imprecise results

A process is called a monotone process if the accuracy of its intermediate results is non-decreasing as more time is spent to obtain the result. The result produced by a monotone process upon its normal termination is the desired result; the error in this result is zero. External events such as timeouts or crashes may cause the process to terminate prematurely. If the intermediate result produced by the process upon its premature termination is saved and made available, the application may still find the result unusable and, hence, acceptable; such a result is said to be an imprecise one. The error in an imprecise result is nonzero. The problem of scheduling periodic jobs to meet deadlines on a system that provides the necessary programming language primitives and run-time support for processes to return imprecise results is discussed. This problem differs from the traditional scheduling problems since the scheduler may choose to terminate a task before it is completed, causing it to produce an acceptable but imprecise result. Consequently, the amounts of processor time assigned to tasks in a valid schedule can be less than the amounts of time required to complete the tasks. A meaningful formulation of this problem taking into account the quality of the overall result is discussed. Three algorithms for scheduling jobs for which the effects of errors in results produced in different periods are not cumulative are described, and their relative merits are evaluated

Imprecise results: Utilizing partial computations in real-time systems

In real-time systems, a computation may not have time to complete its execution because of deadline requirements. In such cases, no result except the approximate results produced by the computations up to that point will be available. It is desirable to utilize these imprecise results if possible. Two approaches are proposed to enable computations to return imprecise results when executions cannot be completed normally. The milestone approach records results periodically, and if a deadline is reached, returns the last recorded result. The sieve approach demarcates sections of code which can be skipped if the time available is insufficient. By using these approaches, the system is able to produce imprecise results when deadlines are reached. The design of the Concord project is described which supports imprecise computations using these techniques. Also presented is a general model of imprecise computations using these techniques, as well as one which takes into account the influence of the environment, showing where the latter approach fits into this model

Scheduling periodic jobs using imprecise results

One approach to avoid timing faults in hard, real-time systems is to make available intermediate, imprecise results produced by real-time processes. When a result of the desired quality cannot be produced in time, an imprecise result of acceptable quality produced before the deadline can be used. The problem of scheduling periodic jobs to meet deadlines on a system that provides the necessary programming language primitives and run-time support for processes to return imprecise results is discussed. Since the scheduler may choose to terminate a task before it is completed, causing it to produce an acceptable but imprecise result, the amount of processor time assigned to any task in a valid schedule can be less than the amount of time required to complete the task. A meaningful formulation of the scheduling problem must take into account the overall quality of the results. Depending on the different types of undesirable effects caused by errors, jobs are classified as type N or type C. For type N jobs, the effects of errors in results produced in different periods are not cumulative. A reasonable performance measure is the average error over all jobs. Three heuristic algorithms that lead to feasible schedules with small average errors are described. For type C jobs, the undesirable effects of errors produced in different periods are cumulative. Schedulability criteria of type C jobs are discussed

Starch Structures and Physicochemical Properties of a Novel β-glucan enriched Oat Hydrocolloid Product with and without Supercritical Carbon Dioxide Extraction

Starch structures and physicochemical properties of C-trim30, a β-glucan-enriched oat product (32% β-glucan), with or without supercritical carbon dioxide extraction (SCD) were studied to evaluate suitability for commercial applications and potential to degrade starch to increase β-glucan concentration. Scanning electron micrographs showed C-trim30 was composed of 200-300 μm long, porous particles. HPSEC equipped with MALLS and RI detectors showed C-trim30 had three peaks, corresponding to amylopectin with weight-average molecular weight (Mw) of 1.0x108, breakdown amylopectin product (Mw 1.1x107) and amylose (Mw 1.7x106). β-glucans were not observed due to HPSEC column absorption. C-trim30 amylopectin Mw and gyration radii increased after SCD suggesting aggregation of molecules occurred. No thermal transitions were observed for C-trim30 heated 0-150°C. C-trim30 pasting properties, measured using Rapid ViscoAnalyser, showed high peak viscosity (291 RVU) at 30°C, high breakdown (200 RVU), final (273 RVU) and setback (183 RVU) viscosity after heated to 95°C while stirred. SCD increased peak (423 RVU) and breakdown (318 RVU) viscosity. C-trim30 heated from 15 to 110°C showed higher water-holding capacity occurred without SCD. SCD oil fatty acid composition of 82% unsaturated was apposite for health-food applications. Study suggests C-trim30 with and without SCD could function as fat substitutes

PERTS: A Prototyping Environment for Real-Time Systems

PERTS is a prototyping environment for real-time systems. It is being built incrementally and will contain basic building blocks of operating systems for time-critical applications, tools, and performance models for the analysis, evaluation and measurement of real-time systems and a simulation/emulation environment. It is designed to support the use and evaluation of new design approaches, experimentations with alternative system building blocks, and the analysis and performance profiling of prototype real-time systems

A look into the United States' Underfunded Pension System

The public pension crisis has come under increasing scrutiny over the past decade as shifting demographic trends, harsh economic conditions and the very nature of pension funds have changed, and not for the better. Pension funds create valuable saving and investment tools for an individual's retirement. They make what seems like the impossible daunting task of saving sufficient funds for retirement completely feasible. All indications lead to these trends continuing, therefore pension plans need to adapt and reform. This paper is to address the pension crisis in the U.S. and intends to provide some recommendations for policy makers. This paper used the U.S. Census Bureau pension data for the fiscal years 2005-2014 to select a sample of 15 states. The time series data will be analyzed using the MDA (Multiple Discriminant Analysis) methodology to assess if a pension plan is bound to fail. MDA is used in the banking industry as a method to predict financial distress or default of bank loans. Once the regression line is determined, it can be utilized to estimate the probability of default. This methodology will be used to determine financial health of public pensions selected in the sample. The Multiple Discriminant Analysis model can be utilized to run a stress test on the public pension plans of those states selected in the sample. The Multiple Discriminant Analysis will enable public pensions and policy makers to somewhat predict the viability of their pensions. The contribution of this paper will be providing pre-warning signals and some policy recommendations for local governments to sustain their pension systems