The Elliptic Curve Discrete Logarithm and Functional Graphs

The discrete logarithm problem, and its adaptation to elliptic curves, called the elliptic curve discrete logarithm problem (ECDLP) is an open problem in the field of number theory, and its applications to modern cryptographic algorithms are numerous. This paper focuses on a statistical analysis of a modification to the ECDLP, called the x-ECDLP, where one is only given the xcoordinate of a point, instead of the entire point. Focusing only on elliptic curves whose field of definition is smaller than the number of points, this paper attempts to find a statistical indication of underlying structure (or lack thereof) in the ECDLP. Using functional graphs, this translates into discovering certain structure in the functional graphs induced by the ECDLP on a wide range of elliptic curves, and comparing these statistics to what would be expected of a random functional graph. A lack of randomness may translate into an exploitable structure in the ECDLP that would undermine the security of cryptographic algorithms based on this problem. In addition to providing an extensive list of data for small primes, this paper details a generating function for the number of elliptic curve functional graphs (ECFGs)

Distributional Equivalence and Structure Learning for Bow-free Acyclic Path Diagrams

We consider the problem of structure learning for bow-free acyclic path diagrams (BAPs). BAPs can be viewed as a generalization of linear Gaussian DAG models that allow for certain hidden variables. We present a first method for this problem using a greedy score-based search algorithm. We also prove some necessary and some sufficient conditions for distributional equivalence of BAPs which are used in an algorithmic ap- proach to compute (nearly) equivalent model structures. This allows us to infer lower bounds of causal effects. We also present applications to real and simulated datasets using our publicly available R-package

Money, sticky wages, and the Great Depression

This paper examines the ability of a simple stylized general equilibrium model that incorporates nominal wage rigidity to explain the magnitude and persistence of the Great Depression in the United States. The impulses to our analysis are money supply shocks. The Taylor contracts model is surprisingly successful in accounting for the behavior of major macroaggregates and real wages during the downturn phase of the Depression, i.e., from 1929:3 through mid-1933. Our analysis provides support for the hypothesis that a monetary contraction operating through a sticky wage channel played a significant role in accounting for the downturn, and also provides an interesting refinement to this explanation. In particular, both the absolute severity of the Depression's downturn and its relative severity compared to the 1920-21 recession are likely attributable to the price decline having a much larger unanticipated component during the Depression, as well as less flexible wage-setting practices during this latter period. Another finding casts doubt on explanations for the 1933-36 recovery that rely heavily on the substantial remonetization that began in 1933.Money supply ; Wages ; Depressions

Data Collection Methods in Prospective Economic Evaluations: How Accurate Are the Results?

AbstractObjectivesOften in economic evaluations a division is made between those studies that have a high level of accuracy versus those that are easily generalized. This interstudy dichotomy is often translated into prospective, randomized controlled trials with high internal validity and observational and modeling studies with a high level of external validity. This article challenges this conventional view and examines intrastudy effects on validity.MethodA review and summary of the literature was conducted in order to assess the impact that data collection strategies will have on internal validity. Two scenario models were created in order to gain a preliminary understanding of the magnitude of the problem.ResultsData collection strategies have an impact on the level of internal validity found in an economic evaluation. Comparisons of studies that are prospective in nature is misleading as data collection strategy can lead to different resource and cost estimates even when all other relevant factors are similar. It is possible to shift and improve the level of validity by combining different collection methods.ConclusionInstead of viewing internal and external validity as polar opposites, validity should be considered in terms of a continuum within a particular study. The use of proxies to collect resource utilization estimates, the reliance on patient self-reported data, and the method of collecting this type of data all impact the validity of study results. National guidelines for the economic evaluation of agents and devices should consider this issue in more depth, and existing evidence rankings should be adapted to be more appropriate to pharmacoeconomic studies

A Dark Matter Hurricane: Measuring the S1 Stream with Dark Matter Detectors

The recently discovered S1 stream passes through the Solar neighbourhood on a low inclination, counter-rotating orbit. The progenitor of S1 is a dwarf galaxy with a total mass comparable to the present-day Fornax dwarf spheroidal, so the stream is expected to have a significant DM component. We compute the effects of the S1 stream on WIMP and axion detectors as a function of the density of its unmeasured dark component. In WIMP detectors the S1 stream supplies more high energy nuclear recoils so will marginally improve DM detection prospects. We find that even if S1 comprises less than 10% of the local density, multi-ton xenon WIMP detectors can distinguish the S1 stream from the bulk halo in the relatively narrow mass range between 5 and 25 GeV. In directional WIMP detectors such as CYGNUS, S1 increases DM detection prospects more substantially since it enhances the anisotropy of the WIMP signal. Finally, we show that axion haloscopes possess by far the greatest potential sensitivity to the S1 stream. Once the axion mass has been discovered, the distinctive velocity distribution of S1 can easily be extracted from the axion power spectrum.Comment: 21 pages, 11 figure

Principles of Pituitary Surgery

Key Points 1. Understand the principles of pituitary surgery including the key-elements of surgical planning and decision-making 2. Identify the technical nuances distinguishing the endoscopic from the microscopic transsphenoidal approach 3. Understand the strategies utilized during the nasal, sphenoidal, and sellar stages of surgery that maximize tumor resection while minimizing complications and preserving sino- nasal anatomy/functio