A Classification of Minimal Sets of Torus Homeomorphisms

We provide a classification of minimal sets of homeomorphisms of the two-torus, in terms of the structure of their complement. We show that this structure is exactly one of the following types: (1) a disjoint union of topological disks, or (2) a disjoint union of essential annuli and topological disks, or (3) a disjoint union of one doubly essential component and bounded topological disks. Periodic bounded disks can only occur in type 3. This result provides a framework for more detailed investigations, and additional information on the torus homeomorphism allows to draw further conclusions. In the non-wandering case, the classification can be significantly strengthened and we obtain that a minimal set other than the whole torus is either a periodic orbit, or the orbit of a periodic circloid, or the extension of a Cantor set. Further special cases are given by torus homeomorphisms homotopic to an Anosov, in which types 1 and 2 cannot occur, and the same holds for homeomorphisms homotopic to the identity with a rotation set which has non-empty interior. If a non-wandering torus homeomorphism has a unique and totally irrational rotation vector, then any minimal set other than the whole torus has to be the extension of a Cantor set.Comment: Published in Mathematische Zeitschrift, June 2013, Volume 274, Issue 1-2, pp 405-42

Efficient algorithms for tensor scaling, quantum marginals and moment polytopes

We present a polynomial time algorithm to approximately scale tensors of any format to arbitrary prescribed marginals (whenever possible). This unifies and generalizes a sequence of past works on matrix, operator and tensor scaling. Our algorithm provides an efficient weak membership oracle for the associated moment polytopes, an important family of implicitly-defined convex polytopes with exponentially many facets and a wide range of applications. These include the entanglement polytopes from quantum information theory (in particular, we obtain an efficient solution to the notorious one-body quantum marginal problem) and the Kronecker polytopes from representation theory (which capture the asymptotic support of Kronecker coefficients). Our algorithm can be applied to succinct descriptions of the input tensor whenever the marginals can be efficiently computed, as in the important case of matrix product states or tensor-train decompositions, widely used in computational physics and numerical mathematics. We strengthen and generalize the alternating minimization approach of previous papers by introducing the theory of highest weight vectors from representation theory into the numerical optimization framework. We show that highest weight vectors are natural potential functions for scaling algorithms and prove new bounds on their evaluations to obtain polynomial-time convergence. Our techniques are general and we believe that they will be instrumental to obtain efficient algorithms for moment polytopes beyond the ones consider here, and more broadly, for other optimization problems possessing natural symmetries

Introducing Learning Commons Functionality into a Traditional Reference Setting

Abstract For the past decade the University Libraries at The University of Akron has been modifying and enhancing its services in response to changing technologies and user needs, as well as evolving campus strategies. Library efforts centered on service excellence and student success have played a leading role in the inclusion of a planned learning commons as one of the key strategic initiatives of the University. At this time the learning commons concept has been fully developed, while the proposed building renovation plan is underway. The Library, however, is utilizing key opportunities in the present to integrate learning commons functionality into its existing reference service. This article is intended as a resource to other reference departments also in the midst of planned learning commons or that are aspiring to incorporate some aspects of commons service models into their existing services

Introduction: Education and Teacher Preparation During the COVID-19 Pandemic: Coping, Adaptation, and Innovation

This is an introduction to the special issue of the Journal of Curriculum, Teaching, Learning and Leadership in Education on education during the COVID-10 pandemic. Each article in the issue is described, with commentary from the Editor of the special issue

Differentiated Anti-Predation Responses in a Superorganism

Insect societies are complex systems, displaying emergent properties much greater than the sum of their individual parts. As such, the concept of these societies as single 'superorganisms' is widely applied to describe their organisation and biology. Here, we test the applicability of this concept to the response of social insect colonies to predation during a vulnerable period of their life history. We used the model system of house-hunting behaviour in the ant Temnothorax albipennis. We show that removing individuals from directly within the nest causes an evacuation response, while removing ants at the periphery of scouting activity causes the colony to withdraw back into the nest. This suggests that colonies react differentially, but in a coordinated fashion, to these differing types of predation. Our findings lend support to the superorganism concept, as the whole society reacts much like a single organism would in response to attacks on different parts of its body. The implication of this is that a collective reaction to the location of worker loss within insect colonies is key to avoiding further harm, much in the same way that the nervous systems of individuals facilitate the avoidance of localised damage

Development of the Concept of Inferential Validity

An argument is valid if its conclusion necessarily follows from its premises, regardless of whether the premises and conclusion are empirically true or false. This research tested the hypothesis that understanding validity of inference (including its differentiation from empirical truth) is a relatively late development. Students in Experiment 1 were asked to sort sets of deductive arguments. None of the fourth graders used validity as a basis for distinguishing arguments, while 45% of the seventh graders and 85% of the college students did so. Experiments 2 and 3 explored whether the dramatic age difference could be narrowed by (a) varying the types of arguments used, (b) explaining the concept of validity and instructing students to use it, and/or (c) providing feedback after each trial. Fourth-grade performance remained poor, while seventh-grade performance increased to nearly the level of the college students. It was concluded that the concept of validity typically develops between ages 10 and 12 but that application of that competence continues to increase over a much longer age span. Students not understanding validity commonly evaluated arguments on the basis of empirical truth of component propositions, though even fourth graders revealed an implicit awareness of logical form

The Individual and Collective Effects of Exact Exchange and Dispersion Interactions on the Ab Initio Structure of Liquid Water

In this work, we report the results of a series of density functional theory (DFT) based ab initio molecular dynamics (AIMD) simulations of ambient liquid water using a hierarchy of exchange-correlation (XC) functionals to investigate the individual and collective effects of exact exchange (Exx), via the PBE0 hybrid functional, non-local vdW/dispersion interactions, via a fully self-consistent density-dependent dispersion correction, and approximate nuclear quantum effects (aNQE), via a 30 K increase in the simulation temperature, on the microscopic structure of liquid water. Based on these AIMD simulations, we found that the collective inclusion of Exx, vdW, and aNQE as resulting from a large-scale AIMD simulation of (H$_2$O)$_{128}$ at the PBE0+vdW level of theory, significantly softens the structure of ambient liquid water and yields an oxygen-oxygen structure factor, $S_{\rm OO}(Q)$, and corresponding oxygen-oxygen radial distribution function, $g_{\rm OO}(r)$, that are now in quantitative agreement with the best available experimental data. This level of agreement between simulation and experiment as demonstrated herein originates from an increase in the relative population of water molecules in the interstitial region between the first and second coordination shells, a collective reorganization in the liquid phase which is facilitated by a weakening of the hydrogen bond strength by the use of the PBE0 hybrid XC functional, coupled with a relative stabilization of the resultant disordered liquid water configurations by the inclusion of non-local vdW/dispersion interactions

The Redirect Behavior Model and the Effects on Pre-service Teachers\u27 Self-Efficacy

The ability for a novice teacher to confidently address inappropriate behavior has a substantial impact on student achievement, teacher attrition, and the reduction of bullying instances (Allen, 2010; Marzano, 2003). Classroom management plays a critical role in the success of the student as well as the teacher. The authors propose an intervention that potentially may have considerable impact on a novice teachers’ confidence regarding classroom management. The idea of providing guidelines for novice teachers to implement while redirecting student behavior could perhaps impact self-efficacy with classroom management. This paper describes the implementation of the Redirect Behavior Model with pre-service teachers during a five week practicum. The Redirect Behavior Model (RBM) is a proactive communication model that provides scripted guidelines for teachers to follow while they redirect inappropriate student behavior. The pre-service teachers were given extensive training on the RBM and were able to implement the model during an extensive field placement. Participants were 31 undergraduate pre-service teacher candidates, majoring in secondary education and enrolled in a junior-level classroom management course. The participants were trained in all three phases of the Redirect Behavior Model (RBM) prior to engaging in an extensive field practicum. Participants responded to an informal survey to explore students’ self-efficacy about their knowledge and ability to manage student behavior. Paired samples t tests were used to evaluate possible differences between pre- and posttests for the two sets of items (knowledge and self-efficacy). The purpose of this study was to examine the impact of training in the RBM on pre-service teachers’ self-efficacy in classroom management