Quantitative equidistribution for certain quadruples in quasi-random groups

In a recent paper (arXiv:1211.6372), Bergelson and Tao proved that if $G$ is a $D$-quasi-random group, and $x$,$g$ are drawn uniformly and independently from $G$, then the quadruple $(g,x,gx,xg)$ is roughly equidistributed in the subset of $G^4$ defined by the constraint that the last two coordinates lie in the same conjugacy class. Their proof gives only a qualitative version of this result. The present notes gives a rather more elementary proof which improves this to an explicit polynomial bound in $D^{-1}$.Comment: 5 pages; [TDA Jun 6, 2014] Updated with reference to arxiv:1405.5629 [v3:] This preprint has been re-written to correct to a mistake in the proof of Corollary 3. The journal published that correction in a separate erratu

Parsing the Plagiary Scandals in History and Law

[Excerpt] “In 2002 the history of History was scandal. The narrative started when a Pulitzer Prize winning professor was caught foisting bogus Vietnam War exploits as background for classroom discussion. His fantasy lapse prefaced a more serious irregularity—the author of the Bancroft Prize book award was accused of falsifying key research documents. The award was rescinded. The year reached a crescendo with two plagiarism cases “that shook the history profession to its core.” Stephen Ambrose and Doris Kearns Goodwin were “crossover” celebrities: esteemed academics—Pulitzer winners—with careers embellished by a public intellectual reputation. The media nurtured a Greek Tragedy —two superstars entangled in the labyrinth of the worst case academic curse—accusations that they copied without attribution. Their careers dangled on the idiosyncratic slope of paraphrasing with its reefs of echoes, mirroring, recycling, borrowing, etc. As the Ambrose-Kearns Goodwin imbroglio ignited critique from the History community, a sequel engulfed Harvard Law School. Alan Dershowitz, Charles Ogletree, and Laurence Tribe were implicated in plagiarism allegations; the latter two ensnared on the paraphrase slope. The New York Times headline anticipated a new media frenzy: When Plagiarism’s Shadow Falls on Admired Scholars. Questioned after the first two incidents, the President of Harvard said: “If you had a third one then I would have said, ‘Okay, you get to say this is a special thing, a focused problem at the Law School.’” There was no follow up comment after the Tribe accusation. The occurrence of similar plagiarism packages in two disciplines within an overlapping time frame justifies an inquiry. The following case studies of six accusation narratives identify a congeries of shared issues, subsuming a crossfire of contention over definition, culpability, and sanction. While the survey connects core History-Law commonalities, each case is defined by its own distinctive cluster of signifiers. The primary source for the explication of each signifier cluster is the media of newspaper, trade journal, television, and internet. The media presence is the Article’s motif—each case study summarizes a media construct of a slice of the plagiarism debate. By author’s decree the debate is restricted to “pure” plagiarism: the appropriation of another’s text without attribution. The survey is conducted according to chronological order, beginning with History. Ward Churchill’s sui generis smutch from plagiarism continues to agitate media coverage. His argument that a dismissal by the University of Colorado for academic misconduct would constitute a cover for a First Amendment protected essay on 9/11 adds more challenge to the plagiary abyss. This Article concludes with up-to-date coverage of the Churchill narrative.

Behaviour of entropy under bounded and integrable orbit equivalence

Let $G$ and $H$ be infinite finitely generated amenable groups. This paper studies two notions of equivalence between actions of such groups on standard Borel probability spaces. They are defined as stable orbit equivalences in which the associated cocycles satisfy certain tail bounds. In `integrable stable orbit equivalence', the length in $H$ of the cocycle-image of an element of $G$ must have finite integral over its domain (a subset of the $G$-system), and similarly for the reverse cocycle. In `bounded stable orbit equivalence', these functions must be essentially bounded in terms of the length in $G$. `Integrable' stable orbit equivalence arises naturally in the study of integrable measure equivalence of groups themselves, as introduced recently by Bader, Furman and Sauer. The main result is a formula relating the Kolmogorov--Sinai entropies of two actions which are equivalent in one of these ways. Under either of these tail assumptions, the entropies stand in a proportion given by the compression constant of the stable orbit equivalence. In particular, in the case of full orbit equivalence subject to such a tail bound, entropy is an invariant. This contrasts with the case of unrestricted orbit equivalence, under which all free ergodic actions of countable amenable groups are equivalent. The proof uses an entropy-bound based on graphings for orbit equivalence relations, and in particular on a new notion of cost which is weighted by the word lengths of group elements.Comment: 53 pages [v2:] Reference added, and several small corrections [v3:] Small fixes and improvements following referee repor

The Greatest Basketball Player of All Time: LeBron vs. Jordan

LeBron James is one of the greatest athletes of this generation. I am seeking to determine what he needs to do to surpass Michael Jordan as the greatest of all time. Considering individual statistics, team success, and personal achievements as well as factors such as political and racial activism and involvement, media coverage (including social media), and generational difference, I am hoping to show what is left to accomplish for LeBron to reach and surpass Jordan

The Role of Indexing in Subject Retrieval

On first reading the list of speakers proposed for this institute, I became aware of being rather the "odd man out" for two reasons. Firstly, I was asked to present a paper on PRECIS which is very much a verbal indexing system-at a conference dominated by contributions on classification schemes with a natural bias, as the centenary year approaches, toward the Dewey Decimal Classification (DDC). Secondly, I feared (quite wrongly, as it happens) that I might be at variance with one or two of my fellow speakers, who would possibly like to assure us, in an age when we can no longer ignore the computer, that traditional library schemes such as DDC and Library of Congress Classification (LCC) are capable of maintaining their original function of organizing collections of documents, and at the same time are also well suited to the retrieval of relevant citations from machine-held files. In this context, I am reminded of a review of a general collection of essays on classification schemes which appeared in the Journal of Documentation in 1972. Norman Roberts, reviewing the papers which dealt specifically with the well established schemes, deduced that "all the writers project their particular schemes into the future with an optimism that springs, perhaps, as much from a sense of emotional involvement as from concrete evidence." Since I do not believe that these general schemes can play any significant part in the retrieval of items from mechanized files, it appeared that I had been cast in the role of devil's advocate.published or submitted for publicatio

The Doomsday Argument in Many Worlds

You and I are highly unlikely to exist in a civilization that has produced only 70 billion people, yet we find ourselves in just such a civilization. Our circumstance, which seems difficult to explain, is easily accounted for if (1) many other civilizations exist and if (2) nearly all of these civilizations (including our own) die out sooner than usually thought, i.e., before trillions of people are produced. Because the combination of (1) and (2) make our situation likely and alternatives do not, we should drastically increase our belief that (1) and (2) are true. These results follow immediately when considering a many worlds version of the "Doomsday Argument" and are immune to the main criticism of the original Doomsday Argument.Comment: 18 page

Collection of Cryptocurrency Customer-Information: Tax Enforcement Mechanism or Invasion of Privacy?

After granting permission to the Internal Revenue Service to serve a digital exchange company a summons for user information, the Federal District Court for the Northern District of California created some uncertainty regarding the privacy of cryptocurrencies. The IRS views this information gathering as necessary for monitoring compliance with Notice 2014-21, which classifies cryptocurrencies as property for tax purposes. Cryptocurrency users, however, view the attempt for information as an infringement on their privacy rights and are seeking legal protection. This Issue Brief investigates the future tax implications of Notice 2014-21 and considers possible routes the cryptocurrency market can take to avoid the burden of capital gains taxes. Further, this Issue Brief attempts to uncover the validity of the privacy claims made against the customer information summons and will recommend alternative actions for the IRS to take regardless of whether it succeeds in obtaining the information

Benefits of thoracic epidural analgesia in patients undergoing an open posterior component separation for abdominal herniorrhaphy

INTRODUCTION: The implementation of open posterior component separation (PCS) surgery has led to improved outcomes for complex hernias. While the PCS technique has been shown to decrease recurrence rates, and provide a feasible option to repair hernias in nontraditional locations, there is still significant postoperative pain associated with the laparotomy and extensive abdominal wall manipulation. Systemic opioids and thoracic epidural analgesia (TEA) are both commonly utilized, either together or independently, as postoperative analgesic regimens. The benefits of TEA have been studied following a variety of surgeries, however to date no study has been performed to investigate its efficacy in this particular surgery. The aim of this study is to evaluate the benefits of TEA following open PCS. We hypothesized that the incorporation of TEA in a patients postoperative analgesic regimen would show an advantage in time to bowel recovery. METHODS: An electronic medical record query was done to identify patients who had undergone an open PCS. Once this list was compiled, a retrospective chart review was performed and patients receiving TEA (either alone or combined with systemic opioids) were compared to patients receiving only systemic opioids. The primary endpoint compared time to resumption of a full diet, given by the patients postoperative day (POD). Secondarily, time to resumption of a liquid diet, postoperative length of stay (LOS), intensive care unit (ICU) admission rate, ICU LOS, and rates of several postoperative complications were all recorded and compared. A post-hoc analysis was also performed using the same endpoints. This analysis compared cohorts of patients receiving TEA and avoiding all systemic opioids, to patients who received systemic opioids (whether alone or combined with TEA). RESULTS: Based on inclusion parameters, 101 patients met criteria for analysis. In the initial analysis, 62 patients received TEA with or without systemic opioids, and 39 patients received only systemic opioids. In comparing these groups, there was no statistically significant difference in time to full diet (TEA 2.6 ± 1.7 vs Systemic opioids 3.1 ± 2.1 [mean POD ± SD]; P=0.21). In addition, no differences were found in the secondary outcomes of time to liquid diet, ICU admission, ICU LOS, or postoperative complications. In the post-hoc analysis, the 37 patients that received only TEA, were compared against 64 patients that received systemic opioids (either with or without TEA). In this comparison, the group receiving only TEA was found to have a statically shorter time to bowel recovery compared to patients receiving systemic opioids (TEA alone 2.2 ± 1.0 vs Systemic opioids 3.2 ± 2.2, P=0.0033). This subgroup (TEA only) also showed statically shorter time to liquid diet and a decreased postoperative LOS. CONCLUSION: For patients undergoing an open PCS, the inclusion of TEA in the postoperative analgesic regimen did not shorten return of bowel function. However, when TEA was utilized and systemic opioids were avoided, time to bowel recovery and hospital LOS were both significantly shortened