Fast Fourier Transforms for the Rook Monoid

We define the notion of the Fourier transform for the rook monoid (also called the symmetric inverse semigroup) and provide two efficient divide-and-conquer algorithms (fast Fourier transforms, or FFTs) for computing it. This paper marks the first extension of group FFTs to non-group semigroups

Generating and Searching Families of FFT Algorithms

A fundamental question of longstanding theoretical interest is to prove the lowest exact count of real additions and multiplications required to compute a power-of-two discrete Fourier transform (DFT). For 35 years the split-radix algorithm held the record by requiring just 4n log n - 6n + 8 arithmetic operations on real numbers for a size-n DFT, and was widely believed to be the best possible. Recent work by Van Buskirk et al. demonstrated improvements to the split-radix operation count by using multiplier coefficients or "twiddle factors" that are not n-th roots of unity for a size-n DFT. This paper presents a Boolean Satisfiability-based proof of the lowest operation count for certain classes of DFT algorithms. First, we present a novel way to choose new yet valid twiddle factors for the nodes in flowgraphs generated by common power-of-two fast Fourier transform algorithms, FFTs. With this new technique, we can generate a large family of FFTs realizable by a fixed flowgraph. This solution space of FFTs is cast as a Boolean Satisfiability problem, and a modern Satisfiability Modulo Theory solver is applied to search for FFTs requiring the fewest arithmetic operations. Surprisingly, we find that there are FFTs requiring fewer operations than the split-radix even when all twiddle factors are n-th roots of unity.Comment: Preprint submitted on March 28, 2011, to the Journal on Satisfiability, Boolean Modeling and Computatio

Endoscopic placental laser coagulation in dichorionic and monochorionic triplet pregnancies

Objective: To report outcome of monochorionic (MC) and dichorionic (DC) triamniotic (TA) triplet pregnancies treated with endoscopic laser coagulation of communicating placental vessels for severe fetofetal transfusion syndrome (FFTS) and selective fetal growth restriction (sFGR). Methods: Laser surgery was performed at 18 (15-24) weeks gestation in 11 MCTA and 33 DCTA pregnancies complicated by FFTS and 14 DCTA pregnancies complicated by sFGR. Data from our study and previous reports were pooled using meta-analytic techniques. Results: Survival of at least one baby and survival among all fetuses was 97.0% and 72.7% in DCTA pregnancies with FFTS, 78.6% and 52.4% in DCTA pregnancies with sFGR and 81.8% and 39.4% in MCTA pregnancies with FFTS. In the combined data from our study and previous reports, the pooled survival rates in 132 DCTA pregnancies with FFTS were 94.4% and 76.1% and in 29 MCTA pregnancies with FFTS were 80.6% and 57.5%. Conclusions: Survival after laser surgery is higher in DC triplets with FFTS than those with sFGR and in DC than MC triplets with FFTS

FFTrees: A toolbox to create, visualize, and evaluate fast-and-frugal decision trees

Fast-and-frugal trees (FFTs) are simple algorithms that facilitate efficient and accurate decisions based on limited information. But despite their successful use in many applied domains, there is no widely available toolbox that allows anyone to easily create, visualize, and evaluate FFTs. We fill this gap by introducing the R package FFTrees. In this paper, we explain how FFTs work, introduce a new class of algorithms called fan for constructing FFTs, and provide a tutorial for using the FFTrees package. We then conduct a simulation across ten real-world datasets to test how well FFTs created by FFTrees can predict data. Simulation results show that FFTs created by FFTrees can predict data as well as popular classification algorithms such as regression and random forests, while remaining simple enough for anyone to understand and use

Application of graphics processing units to search pipelines for gravitational waves from coalescing binaries of compact objects

We report a novel application of a graphics processing unit (GPU) for the purpose of accelerating the search pipelines for gravitational waves from coalescing binaries of compact objects. A speed-up of 16-fold in total has been achieved with an NVIDIA GeForce 8800 Ultra GPU card compared with one core of a 2.5 GHz Intel Q9300 central processing unit (CPU). We show that substantial improvements are possible and discuss the reduction in CPU count required for the detection of inspiral sources afforded by the use of GPUs