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

Preparation and characteristics of enzyme-resistant pyrodextrins from corn s

Corn starch was modified by pyroconversion at 130°C in the presence of acid catalyst in a sealed container to produce non-digestible pyrodextrins. The effect of reaction time on the dextrinization process was investigated. Physicochemical properties of the pyrodextrins were analyzed, and the effect of the structure of pyrodextrins on the digestibility was evaluated. The pyrodextrin, prepared by heating corn starch with hydrochloric acid (0.1%, dry starch basis) at 130°C for 180 min, was well-soluble (97% at 25°C) and contained only one fraction of average molecular weight of 2.2 x 104 g/mol. The enzyme resistance of pyrodextrin, measured according to AOAC method 991.43 for Total Dietary Fiber, reached 42%

Cereal grain-based biodegradable thermoplastic compositions

The present invention provides a biodegradable thermoplastic composition made of a cereal grain that is treated with an organic solvent, and optionally a cross-linking agent such as an aldehyde, an acid anhydride or an epoxide, to link together the starch and protein of the cereal grain. The compositions may be used to make extruded or molded articles that are biodegradable, water-resistant, and have a high level of physical strength

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

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

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