Geometry of the sample frequency spectrum and the perils of demographic inference

The sample frequency spectrum (SFS), which describes the distribution of mutant alleles in a sample of DNA sequences, is a widely used summary statistic in population genetics. The expected SFS has a strong dependence on the historical population demography and this property is exploited by popular statistical methods to infer complex demographic histories from DNA sequence data. Most, if not all, of these inference methods exhibit pathological behavior, however. Specifically, they often display runaway behavior in optimization, where the inferred population sizes and epoch durations can degenerate to 0 or diverge to infinity, and show undesirable sensitivity of the inferred demography to perturbations in the data. The goal of this paper is to provide theoretical insights into why such problems arise. To this end, we characterize the geometry of the expected SFS for piecewise-constant demographic histories and use our results to show that the aforementioned pathological behavior of popular inference methods is intrinsic to the geometry of the expected SFS. We provide explicit descriptions and visualizations for a toy model with sample size 4, and generalize our intuition to arbitrary sample sizes n using tools from convex and algebraic geometry. We also develop a universal characterization result which shows that the expected SFS of a sample of size n under an arbitrary population history can be recapitulated by a piecewise-constant demography with only k(n) epochs, where k(n) is between n/2 and 2n-1. The set of expected SFS for piecewise-constant demographies with fewer than k(n) epochs is open and non-convex, which causes the above phenomena for inference from data.Comment: 21 pages, 5 figure

Transaction services, inflation, and welfare

This paper is motivated by empirical observations on the comovements of currency velocity, inflation, and the relative size of the credit services sector. We document these comovements and incorporate into a monetary growth model a credit services sector that provides services that help people economize on money. Our model makes two new contributions. First, we show that direct evidence on the appropriately defined credit service sector for the United States is consistent with the welfare cost measured using an estimated money demand schedule. Second, we provide welfare cost of inflation estimates that have some new features.Inflation (Finance) ; Welfare

The Twilight of the Opera Pirates: A Prehistory of the Exclusive Right of Public Performance for Musical Compositions

The exclusive right of public performance of a musical composition now brings to composers and songwriters revenue of approximately one billion dollars a year in the US alone. However, this right was not firmly established until a century after America’s first copyright statute, relying until then on the common-law principles that protected unpublished works. The first effort to create this right by statute was the Ingersoll Copyright Bill, an omnibus revision in 1844 which died quickly in committee. After that 50 years passed, and in the final quarter of the nineteenth century the need for statutory protection for public performance became more and more obvious as a result of litigation, especially that surrounding the Gilbert and Sullivan operetta The Mikado. In the mid-1890s the right was once again proposed in an omnibus revision that died in committee, the Treloar Copyright Bill. Simultaneously though, this right went through Congress and was passed as part of an amendatory act which also increased penalties for all unlawful public performances (including drama). This article traces the history of these acts and the litigation in the later nineteenth century, telling a story that has heretofore not been told – the prehistory of the right of public of public performance for musical compositions

How Perris v. Hexamer Was Lost in the Shadow of Baker v. Selden

Perris v. Hexamer stands out as case that is equal parts important and forgotten. It is obviously important – it is one of a preciously small number of Supreme Court decisions on the idea/expression dichotomy, but it is mostly forgotten in favor of the Court’s decision the following year in Baker v. Selden. It is equally obscure – Westlaw counts 2,703 citations of Baker v. Selden, and 81 of Perris v. Hexamer. Yet the subject matter of both decisions is surprisingly similar, and these cases tell us far more when considered in tandem than when either one is considered on its own. This piece will seek to tell the story of Perris v. Hexamer – in terms of both the background of the controversy and the procedural background that led to the lawsuit, as well as discussing the decision itself. Following this, two questions will be addressed – firstly why Perris was largely forgotten as a decision about the idea/expression dichotomy, and secondly why the vote among the Justices was different in Perris than in Baker v. Selden

Power assignment problems in wireless communication

A fundamental class of problems in wireless communication is concerned with the assignment of suitable transmission powers to wireless devices/stations such that the resulting communication graph satisfies certain desired properties and the overall energy consumed is minimized. Many concrete communication tasks in a wireless network like broadcast, multicast, point-to-point routing, creation of a communication backbone, etc. can be regarded as such a power assignment problem. This paper considers several problems of that kind; for example one problem studied before in (Vittorio Bil{\`o} et al: Geometric Clustering to Minimize the Sum of Cluster Sizes, ESA 2005) and (Helmut Alt et al.: Minimum-cost coverage of point sets by disks, SCG 2006) aims to select and assign powers to $k$ of the stations such that all other stations are within reach of at least one of the selected stations. We improve the running time for obtaining a $(1+\epsilon)$-approximate solution for this problem from $n^{((\alpha/\epsilon)^{O(d)})}$ as reported by Bil{\`o} et al. (see Vittorio Bil{\`o} et al: Geometric Clustering to Minimize the Sum of Cluster Sizes, ESA 2005) to $O\left( n+ {\left(\frac{k^{2d+1}}{\epsilon^d}\right)}^{ \min{\{\; 2k,\;\; (\alpha/\epsilon)^{O(d)} \;\}} } \right)$ that is, we obtain a running time that is \emph{linear} in the network size. Further results include a constant approximation algorithm for the TSP problem under squared (non-metric!) edge costs, which can be employed to implement a novel data aggregation protocol, as well as efficient schemes to perform $k$-hop multicasts

Review of Linac-Ring Type Collider Proposals

There are three possibly types of particle colliders schemes: familiar (well known) ring-ring colliders, less familiar however sufficiently advanced linear colliders and less familiar and less advanced linac-ring type colliders. The aim of this paper is two-fold: to present possibly complete list of papers on linac-ring type collider proposals and to emphasize the role of linac-ring type machines for future HEP research.Comment: quality of figures is improved, some misprints are correcte