Clemson University

About: Clemson University is a education organization based out in Clemson, South Carolina, United States. It is known for research contribution in the topics: Population & Control theory. The organization has 20556 authors who have published 42518 publications receiving 1170779 citations. The organization is also known as: Clemson Agricultural College of South Carolina.

Fast fourier transform algorithms with applications

Abstract: This manuscript describes a number of algorithms that can be used to quickly evaluate a polynomial over a collection of points and interpolate these evaluations back into a polynomial. Engineers define the “Fast Fourier Transform” as a method of solving the interpolation problem where the coefficient ring used to construct the polynomials has a special multiplicative structure. Mathematicians define the “Fast Fourier Transform” as a method of solving the evaluation problem. One purpose of the document is to provide a mathematical treatment of the topic of the “Fast Fourier Transform” that can also be understood by someone who has an understanding of the topic from the engineering perspective. The manuscript will also introduce several new algorithms that solve the fast multipoint evaluation problem over certain finite fields and require fewer finite field operations than existing techniques. The document will also demonstrate that these new algorithms can be used to multiply polynomials with finite field coefficients with fewer operations than Schonhage's algorithm in most circumstances. A third objective of this document is to provide a mathematical perspective of several algorithms which can be used to multiply polynomials of size which is not a power of two. Several improvements to these algorithms will also be discussed. Finally, the document will describe several applications of the “Fast Fourier Transform” algorithms presented and will introduce improvements in several of these applications. In addition to polynomial multiplication, the applications of polynomial division with remainder, the greatest common divisor, decoding of Reed-Solomon error-correcting codes, and the computation of the coefficients of a discrete Fourier Series will be addressed.

Analysis of the impact of early surgery on in-hospital mortality of native valve endocarditis: use of propensity score and instrumental variable methods to adjust for treatment-selection bias.

Abstract: Background—The impact of early surgery on mortality in patients with native valve endocarditis (NVE) is unresolved. This study sought to evaluate valve surgery compared with medical therapy for NVE and to identify characteristics of patients who are most likely to benefit from early surgery. Methods and Results—Using a prospective, multinational cohort of patients with definite NVE, the effect of early surgery on in-hospital mortality was assessed by propensity-based matching adjustment for survivor bias and by instrumental variable analysis. Patients were stratified by propensity quintile, paravalvular complications, valve perforation, systemic embolization, stroke, Staphylococcus aureus infection, and congestive heart failure. Of the 1552 patients with NVE, 720 (46%) underwent early surgery and 832 (54%) were treated with medical therapy. Compared with medical therapy, early surgery was associated with a significant reduction in mortality in the overall cohort (12.1% [87/720] versus 20.7% [172/832]) and after propensity-based matching and adjustment for survivor bias (absolute risk reduction [ARR] 5.9%, P0.001). With a combined instrument, the instrumental-variable–adjusted ARR in mortality associated with early surgery was 11.2% (P0.001). In subgroup analysis, surgery was found to confer a survival benefit compared with medical therapy among patients with a higher propensity for surgery (ARR 10.9% for quintiles 4 and 5, P0.002) and those with paravalvular complications (ARR 17.3%, P0.001), systemic embolization (ARR 12.9%, P0.002), S aureus NVE (ARR 20.1%, P0.001), and stroke (ARR 13%, P0.02) but not those with valve perforation or congestive heart failure. Conclusions—Early surgery for NVE is associated with an in-hospital mortality benefit compared with medical therapy alone. (Circulation. 2010;121:1005-1013.)

Challenges with fats and fatty acid methods.

Abstract: The content and chemical nature of lipids in feedstuffs is heterogeneous. It has long been known that ether extraction by the Weende procedure inadequately characterizes the fat content of feedstuffs, yet it remains the official method. Diethyl ether (or hexanes that are often used) extracts significant amounts of nonnutritive, nonsaponifiable lipids from forages, and often incompletely extracts lipids of nutritional value, especially fatty acids present as salts of divalent cations. Preextraction hydrolysis of insoluble fatty acid salts with acid releases these fatty acids, and this step is included in the official procedure for certain feedstuffs in the United Kingdom; however, acid hydrolysis increases analysis time and decreases precision. Acid hydrolysis also causes confusion as to the proper definition of the fat content of feedstuffs. A preferred method of fat analysis determines the total fatty acid concentration in feed samples by converting fatty acid salts, as well as the acyl components in all lipid classes, such as triacylglycerols, phospholipids, and sphingolipids, to methyl esters using a simple, direct one-step esterification procedure. Fatty acid methyl esters are then quantified by GLC, which provides information on both fatty acid quantity and profile in a single analysis. Adjustments in conditions and reagents may be necessary to overcome difficulty in quantitatively preparing esters from certain types of fatty acids and their derivatives in commercial fat supplements. After correction for glycerol content, analysis of oils by this procedure provides information on the content of nonsaponifiable material, such as chlorophyll, waxes, and indigestible polymers formed from heat- or oxidatively damaged fats. The correct description of feedstuffs for energy value of fats is the content of total fatty acids.