Universal countable Borel quasi-orders

In recent years, much work in descriptive set theory has been focused on the Borel complexity of naturally occurring classification problems, in particular, the study of countable Borel equivalence relations and their structure under the quasi-order of Borel reducibility. Following the approach of Louveau and Rosendal for the study of analytic equivalence relations, we study countable Borel quasi-orders. In this paper we are concerned with universal countable Borel quasi-orders, i.e. countable Borel quasi-orders above all other countable Borel quasi-orders with regard to Borel reducibility. We first establish that there is a universal countable Borel quasi-order, and then establish that several countable Borel quasi-orders are universal. An important example is an embeddability relation on descriptive set theoretic trees. Our main result states that embeddability of finitely generated groups is a universal countable Borel quasi-order, answering a question of Louveau and Rosendal. This immediately implies that biembeddability of finitely generated groups is a universal countable Borel equivalence relation. The same techniques are also used to show that embeddability of countable groups is a universal analytic quasi-order. Finally, we show that, up to Borel bireducibility, there are continuum-many distinct countable Borel quasi-orders which symmetrize to a universal countable Borel equivalence relation

A Methodology for Discovering how to Adaptively Personalize to Users using Experimental Comparisons

We explain and provide examples of a formalism that supports the methodology of discovering how to adapt and personalize technology by combining randomized experiments with variables associated with user models. We characterize a formal relationship between the use of technology to conduct A/B experiments and use of technology for adaptive personalization. The MOOClet Formalism [11] captures the equivalence between experimentation and personalization in its conceptualization of modular components of a technology. This motivates a unified software design pattern that enables technology components that can be compared in an experiment to also be adapted based on contextual data, or personalized based on user characteristics. With the aid of a concrete use case, we illustrate the potential of the MOOClet formalism for a methodology that uses randomized experiments of alternative micro-designs to discover how to adapt technology based on user characteristics, and then dynamically implements these personalized improvements in real time

Dissimilar metal joining of stainless steel and titanium using copper as transition metal

Joining of stainless steel and titanium dissimilar metal combination has a specific interest in the nuclear industry. Due to the metallurgical incompatibility, it has been very difficult to produce reliable joints between these metals due to the formation of FeTi and Fe2Ti types of intermetallic compounds. The metallurgical incompatibility between both materials is enhanced by the time–temperature profile of the welding process used. Brittle intermetallics (IMCs) are formed during Fe–Ti welding (FeTi and Fe2Ti). The present study uses the low thermal heat input process cold metal transfer (CMT), when compared with conventional GMAW, to deposit a copper (Cu) bead between Ti and stainless steel. Cu is compatible with Fe, and it has a lower melting point than the two base materials. The welds were produced between AMS 4911L (Ti-6Al-4V) and AISI 316L stainless steel using a CuSi-3 welding wire. The joints produced revealed two IM layers located near the parent metals/weld interfaces. The hardness of these layers is higher than the remainder of the weld bead. Tensile tests were carried out with a maximum strength of 200 MPa, but the interfacial failure could not be avoided. Ti atomic migration was observed during experimental trials; however, the IMC formed are less brittle than FeTi, inducing higher mechanical properties.EPSR

2006 Homicide Report: An Analysis of Homicides in Oakland from January through December, 2006

Urban Strategies Council has produced quarterly reports on homicides in Oakland throughout 2006. Through the cooperation of the Oakland Police Department Homicide Section, we have obtained detailed information on the homicides occurring during 2006. From these data we have created this report on the characteristics of the 148 homicides that occurred in Oakland from January 1 through December 31, 2006. This report presents annual data from 2006 and shows how characteristics of homicides in Oakland changed from 2005 to 2006 and how 2006 homicides compare with the five -- year averages from 2001-2005.This report summarizes available information such as victim and/or suspect demographic characteristics, locations and times of the incidents. Comparing 2006 data to a five-year average of homicides helps to provide a context for understanding whether there are emerging patterns that differ substantially from the patterns in prior years

Chain conditions, elementary amenable groups, and descriptive set theory

We first consider three well-known chain conditions in the space of marked groups: the minimal condition on centralizers, the maximal condition on subgroups, and the maximal condition on normal subgroups. For each condition, we produce a characterization in terms of well-founded descriptive-set-theoretic trees. Using these characterizations, we demonstrate that the sets given by these conditions are co-analytic and not Borel in the space of marked groups. We then adapt our techniques to show elementary amenable marked groups may be characterized by well-founded descriptive-set-theoretic trees, and therefore, elementary amenability is equivalent to a chain condition. Our characterization again implies the set of elementary amenable groups is co-analytic and non-Borel. As corollary, we obtain a new, non-constructive, proof of the existence of finitely generated amenable groups that are not elementary amenable

The bi-embeddability relation for finitely generated groups II

We study the isomorphism and bi-embeddability relations on the spaces of Kazhdan groups and finitely generated simple groups

How Do We Get These Kids Reading? Supporting Readerly Identity in Secondary English Classrooms

In this article, we aim to clarify the specialized purposes for reading in secondary English language arts (ELA) classes. We will suggest ways ELA teachers can help build (or repair) students’ readerly identities while also ensuring they graduate with the necessary skill sets to transfer their knowledge into further studies, careers, and lifelong pleasure reading

The Footnote, in Theory

And, so, when Richard Stern published his private dialogue with himself about the physical appearance of certain writers at the 1986 International PEN conference, Joyce Carol Oates insisted on not only an angry rebuttal-punctuated by constant page referencing to Stern\u27s pig-souled sexism -but photographic evidence-a kind of footnote in itself-dismissing his physical characterization of her. When Susan Gubar published What Ails Feminist Criticism? her essay provoked an immediate, critical, and heavily documented response from Robyn Weigman, several letters to the editor, and Gubar\u27s own footnoted rejoinder. Jane Gallop\u27s defense of a sexual act she engaged in with one of her students and Paul de Man\u27s controversial writings in a Belgian newspaper in the thirties (which, incidentally, resulted in a marked decline in the number of times he was cited in our pages) generated similar feelings of anger, disgust, and betrayal, all accompanied by footnotes. This journal, in fact, argues that passion is not diminished when it is superscripted. In point of fact this apparent function may nearly always be associated with such diverse functions as the manifestation of relations of allegiance or dependence, of strategies of affiliation, of annexation or of defence (this is the role, for example, of guarantee references, ostentatious references or alibi-references)