Principal components analysis in the space of phylogenetic trees

Phylogenetic analysis of DNA or other data commonly gives rise to a collection or sample of inferred evolutionary trees. Principal Components Analysis (PCA) cannot be applied directly to collections of trees since the space of evolutionary trees on a fixed set of taxa is not a vector space. This paper describes a novel geometrical approach to PCA in tree-space that constructs the first principal path in an analogous way to standard linear Euclidean PCA. Given a data set of phylogenetic trees, a geodesic principal path is sought that maximizes the variance of the data under a form of projection onto the path. Due to the high dimensionality of tree-space and the nonlinear nature of this problem, the computational complexity is potentially very high, so approximate optimization algorithms are used to search for the optimal path. Principal paths identified in this way reveal and quantify the main sources of variation in the original collection of trees in terms of both topology and branch lengths. The approach is illustrated by application to simulated sets of trees and to a set of gene trees from metazoan (animal) species.Comment: Published in at http://dx.doi.org/10.1214/11-AOS915 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Competitive Advocacy Opportunity: Zeroing in U.S. Antidumping Enforcement

Almost all countries have antidumping laws which regulate their imports. The United States and other countries enforce these laws within the terms of the World Trade Organization ("WTO"). There is a difference between U.S. enforcement and the enforcement approach of other countries, however. The United States­but not other countries of which I am aware--now uses 'zeroing' in its determination of whether imports are dumped. The use of 'zeroing' will almost always increase the level of any antidumping duty, and will sometimes create a duty where none would have been imposed, had the methodology not been used. All countries test for dumping by attempting to determine whether imports are being sold at less than 'normal' value. Other countries generally do this by directly comparing the average price at which the product is sold in the country of production with the average price at which the same product are sold in the importing market. If the average of the observed prices in the importing country is lower than the average price in the country of production (the 'normal' value), then the foreign firm is said to be dumping. Using zeroing, however, the U.S. treats import price observations above the 'normal' value as if they occurred at the 'normal' value (rather than at their observed level). Transactions at prices below the normal value are treated at their observed levels. The result of zeroing has been to make the U.S. antidumping laws more restrictive than they might appear, with a positive antidumping margin potentially being found if any single transaction occurs below 'normal' value, even if the average of the import prices in the U.S. is much higher than the 'normal' value. The U.S. practice of zeroing has recently been challenged at least six times before the World Trade Organization (WTO), and has generally been found to be inconsistent with the obligations of the United States under the WTO. Many economists feel that the antidumping laws of the U.S., or of any other country, are misguided. Antidumping regulations seem ill suited to play the most likely roles according to which import restrictions might be beneficial: addressing the possibility of predation or strategic trade by foreign firms, or serving as an 'optimal tariff'. Zeroing, therefore, may increase the cost to the U.S. of import protection without any corresponding benefit. The net impact of the zeroing methodology on the United States (compared to antidumping enforcement without zeroing) depends inter alia on the dispersion of the U.S. prices obtained by foreign exporters under dumping investigation by U.S. authorities. One estimate is that the cost of zeroing to the U.S. could be in the range of $46-112 million/year, with the higher end of the range being more likely.Trade, Dumping, Import, Zeroing, United States, WTO

The Implications of ‘Zeroing' on Enforcement of U.S. Antidumping Law

The United States and other countries enforce their antidumping regulations in roughly the same way. There is a difference, however. The United States–but not other countries--now uses ‘zeroing’ in its determination of whether imports are dumped. The use of ‘zeroing’ will almost always increase the level of any antidumping duty, and will sometimes create a duty where none would have been imposed, had the methodology not been used. All countries test for dumping by attempting to determine whether imports are being sold at less than ‘normal’ value. Other countries do this by simply comparing the average price at which the product is sold in the country of production with the average price at which the same product is sold in the importing market. If the average of the observed prices in the importing country is lower than the average price in the country of production (the ‘normal’ value), then the foreign firm is said to be dumping. Using zeroing, however, the U.S. treats import price observations above the ‘normal’ value as if they occurred at the ‘normal’ value (rather than at their observed level). Transactions at prices below the normal value are treated at their observed levels. The result of zeroing has been to make the U.S. antidumping laws more restrictive than they might appear, with a positive antidumping margin potentially being found if any single transaction occurs below ‘normal’ value, even if the average of the import prices in the U.S. is much higher than the ‘normal’ value. The U.S. practice of zeroing has recently been challenged at least six times before the World Trade Organization (WTO), and has generally been found to be inconsistent with the WTO obligations of the United States. The net impact of the zeroing methodology on the United States (compared to antidumping enforcement without zeroing) depends inter alia on the dispersion of the U.S. prices obtained by foreign exporters under dumping investigation. No real estimates of this dispersion exist, but the paper discusses some related evidence which may permit an inference. This evidence is itself quite dispersed, and, therefore, an estimate of the impact and cost of zeroing to the United States has a broad range of uncertainty. But it is plausible that zeroing could add perhaps 3-4 % to the typical U.S. antidumping duty with a cost to the U.S. of around $150 million per year when all existing U.S. antidumping orders were determined by zeroing.Trade, Dumping, Import, Zeroing, United States, WTO

What is the Effect of U.S. Antidumping Duties on Imports? Some Evidence from the Sunset Review Process

The voluminous literature on the U.S. antidumping laws has a curious lacuna. There is little in this literature about the effects of antidumping duties on the volume of subject imports. One reason this key question has not frequently been investigated is the lack of data. U.S. antidumping duties are firm specific, while information about U.S. imports is collected by commodity and country, but not by firm. This paper avoids this problem by examining a sample of U.S. antidumping orders for which the duties were the same for all firms from a given country, or for which there was only one foreign firm exporting the product from the foreign country in question. Using this sample, the present paper is the first study of which the author is aware that investigates the relation between antidumping duties and subject imports using accurate information about the level of antidumping duties. The paper is also unique in accurately measuring the quantity of imports affected by the antidumping duties. The study uses import quantity data reported by the USITC in its Sunset Review reports, rather than using ten-digit HTUSA categories, which sometimes do not match antidumping product definitions precisely. The price of using this unique dataset is that the current study is restricted to a sample of only 32 of the approximately 350 antidumping orders originating during the relevant years, of which about 188 are still in effect. Some evidence is presented suggesting that the sample of orders used may be representative of the larger universe. For the sample examined, the paper finds an elasticity of subject imports with respect to U.S. antidumping duties of roughly 0.9. The paper also finds some evidence that age of the antidumping order may be a factor in explaining reduction in volume of subject imports. Study of this effect may be complicated by the fact that the initial level of all U.S. antidumping duties was lower during the early 1980s than in the early 1990s; so older orders tend to have lower duties. The study finds inconclusive evidence about the effect of antidumping orders on the price received by the foreign suppliers of subject imports.

An L^2-Index Theorem for Dirac Operators on S^1 * R^3

An expression is found for the $L^2$-index of a Dirac operator coupled to a connection on a $U_n$ vector bundle over $S^1\times{\mathbb R}^3$. Boundary conditions for the connection are given which ensure the coupled Dirac operator is Fredholm. Callias' index theorem is used to calculate the index when the connection is independent of the coordinate on $S^1$. An excision theorem due to Gromov, Lawson, and Anghel reduces the index theorem to this special case. The index formula can be expressed using the adiabatic limit of the $\eta$-invariant of a Dirac operator canonically associated to the boundary. An application of the theorem is to count the zero modes of the Dirac operator in the background of a caloron (periodic instanton).Comment: 14 pages, Latex, to appear in the Journal of Functional Analysi

Harmonic drive gear error: Characterization and compensation for precision pointing and tracking

Imperfections and geometry effects in harmonic drive gear reducers cause a cyclic gear error, which at a systems level, results in high frequency torque fluctuations. To address this problem, gear error testing was performed on a wide variety of sizes and types of harmonic drives. It was found that although all harmonic drives exhibit a significant first harmonic, higher harmonics varied greatly with each unit. From life tests, small changes were found in harmonic content, phase shift, and error magnitude (on the order of .008 deg peak-to-peak maximum) occurred for drives with many millions of degrees of output travel. Temperature variations also influenced gear error. Over a spread of approximately 56 C (100 F), the error varied in magnitude approximately 20 percent but changes in a repeatable and predictable manner. Concentricity and parallelness tests of harmonic drive parts resulted in showing alignment influence gear error amplitude. Tests on dedoidaled harmonic drives showed little effect on gear error; surprisingly, in one case for a small drive, gear error actually improved. Electronic compensation of gear error in harmonic drives was shown to be substantially effective for units that are first harmonic dominant

Sensory aids for the blind: A challenging problem with lessons for the future

The two major objectives of sensory aids for the blind are to permit access to printed matter and to permit safe travel through the environment. The difficulties of designing technological means to achieve these objectives are in many respects unrelated to the concerns of the engineering laboratory. Social, economic, political, and logistic considerations all play a role. The "blind population" in the United States includes both the totally blind and those with a wide range of visual impairment. This population totals about 400 000 people in which the aged, the multiply handicapped, and those with significant residual vision predominate. Singly handicapped, working-aged people are the initial targets of the current sensory aids. Expansion of their range of usefulness to larger fractions of the blind population is expected to come later. About 800 agencies serve the blind population in the United States, and in 1967 they were responsible for an annual expenditure of 1 million. Nevertheless, several potentially useful prototype devices have been developed and are about to be evaluated in this country; at least one is of foreign origin. But if these devices are ever to have the opportunity of reaching the blind public, then mechanisms for evaluation, field trials, manufacture, and deployment must be set up. The field of currently active sensory-aids research programs is reviewed. Several programs are concerned with increasing the convenience and accessibility of braille by the application of computer technology. Nevertheless, despite the unquestionable value of these developments, the usefulness of braille is limited by its bulk, its cost, and the transcription time. To provide direct access to printed documents several devices are being developed that transform optical images from a printed page into auditory or tactile displays requiring motivation and training for effective use. These machines are termed "direct-translation" units and are designed for simplicity and low cost. Other systems utilize print recognition techniques to create a reading machine providing braille or speech as an output. These machines offer potentially faster reading rates and their use promises to be easier to learn than direct-translation machines, but at the penalty of complexity and high cost. Several mobility aids designed to augment the cane or guide dog have recently been developed. These are also described. The prospects of achieving direct input to the visual cortex are discussed. It is apparent that the cost of this research is likely to be extremely high in relation to the size of the blind population which might ultimately benefit. Somewhat more easily realizable is a visual substitution system involving stimulation of an area of the skin. Several systems are being developed but all suffer from limitations in image resolution. Finally, an examination of the organization of research and funding reveals that the U.S. program is small, poorly coordinated, and contains some seemingly unnecessary duplication of effort. Several obvious lessons emerge which, if heeded, could greatly improve the effectiveness of sensory-aids research by providing development, manufacture, evaluation, and deployment services within an integrated program

Polarization of tightly focused laser beams

The polarization properties of monochromatic light beams are studied. In contrast to the idealization of an electromagnetic plane wave, finite beams which are everywhere linearly polarized in the same direction do not exist. Neither do beams which are everywhere circularly polarized in a fixed plane. It is also shown that transversely finite beams cannot be purely transverse in both their electric and magnetic vectors, and that their electromagnetic energy travels at less than c. The electric and magnetic fields in an electromagnetic beam have different polarization properties in general, but there exists a class of steady beams in which the electric and magnetic polarizations are the same (and in which energy density and energy flux are independent of time). Examples are given of exactly and approximately linearly polarized beams, and of approximately circularly polarized beams.Comment: 9 pages, 6 figure