Spectral Metric Spaces on Extensions of C*-Algebras

We construct spectral triples on C*-algebraic extensions of unital C*-algebras by stable ideals satisfying a certain Toeplitz type property using given spectral triples on the quotient and ideal. Our construction behaves well with respect to summability and produces new spectral quantum metric spaces out of given ones. Using our construction we find new spectral triples on the quantum 2- and 3-spheres giving a new perspective on these algebras in noncommutative geometry.Comment: 29 pages, extensively revised, corrected and improved versio

On spectral triples on crossed products arising from equicontinuous actions

The external Kasparov product is used to construct odd and even spectral triples on crossed products of $C^*$-algebras by actions of discrete groups which are equicontinuous in a natural sense. When the group in question is $\Z$ this gives another viewpoint on the spectral triples introduced by Belissard, Marcolli and Reihani. We investigate the properties of this construction and apply it to produce spectral triples on the Bunce-Deddens algebra arising from the odometer action on the Cantor set and some other crossed products of AF-algebras.Comment: 22 pages (v4 corrects a mistake in the discussion of the equicontinuity condition and modifies the terminology used). The paper will appear in Mathematica Scandinavic

The Effects of Task Demands and Interspersal Ratios on Student Accuracy in Mathematics

The primary purpose of this study is to extend research on increasing accuracy on academic assignments through use of the additive interspersal procedure. Additive interspersal is the addition of brief and/or easy problems among longer, more difficult target problems. Research has shown additive interspersal is effective in promoting student choice in regards to engaging in assignments. Only one study has found an increase in student accuracy on interspersed assignments as compared to control assignments when using additive interspersal. The current study attempted to determine if the results of that study are a statistical outlier or whether the uniqueness of that study using assignments requiring different task demands, can increase problem accuracy. Students (N=52) from three fifth-grade classes completed six math assignments incorporating two task demands and three ratios of interspersal. The interspersal ratios applied were no interspersal, on interspersed problem per three target problems, and one interspersal problem per one target problem. Each of these three ratios was used in two task demands. In the written (low-attention) task, students completed problems via paper and pencil. In the oral (high-attention) task, students had to compute mathematics problems in their head. Results showed students performed more accurately on written tasks compared to oral tasks. A target to interspersal problem ratio of 3:1 on oral tasks led to a significant increase in accuracy compared to the no interspersal and 1:1 interspersal conditions. A target problem to interspersed problem ratio of 1:1 on written tasks led to a significant increase in accuracy when compared to the no interspersal condition. The results of this study suggest the interspersal procedure can be used to increase student accuracy in math. However, the most effective ratio of interspersal to target problems is dependent on task demands. Interspersal studies have shown mixed results regarding student accuracy on assignments under the additive interspersal procedure. Currently, there is no understanding of the causal mechanisms to explain why interspersal increases accuracy in some instances but has no effect in other instances. Future theoretical research that explains the causal mechanism(s) of the interspersal procedure may allow us to maximize its impact on performance

A collaborative research inquiry into issues of male choral participation at the middle and high school level

Choral music and public singing was once regarded as an acceptable and popular socio-cultural activity for males. Through centuries of gradual socio-cultural change male choral participation and public singing became marginalized in the United States. During the past century (1914-2014), adolescent female singers have typically outnumbered male singers at the secondary level. The numerical imbalance between adolescent males and females in secondary choral classrooms is a symptom of a more complicated problem that involves a complex web of perceived physiological, psycho-socio, and schooling barriers. If no single perceived barrier accounted for the lack of male choral participation our collaborative group surmised that no one-dimensional approach would likely succeed in increasing male choral participation. Collaborative inquiry provided a more holistic approach to dealing with the lack of male choral singers at the middle and high school levels and answers questions not adequately addressed by other forms of research. The purpose of this collaborative inquiry was to cooperate with five vocal music practitioners, at two different district sites in the Midwest region of the United States. Our collaborative inquiry group set two broad goals for this study: (1) to implement specific action-oriented strategies in our choral classrooms with the intention of encouraging male choral participation at the middle and high school levels; and (2) to learn more about collaborative inquiry as a research approach and adult learning strategy. My collaborators and I realized a very delicate ecosystem is required for adolescent males and females to engage in singing activities at school. The findings of this inquiry suggest that action-oriented strategies (e.g., single-sex choirs, recruitment and retention activities, same-sex peer role modeling and mentoring) can be implemented in the choral classroom to mitigate the perceived physiological, psycho-socio, and schooling barriers and encourage male choral participation at the secondary level. Our inquiry group found that external issues beyond the control of the choral practitioners (e.g., changes in administration, school schedules, class requirements, and elective choices) were difficult to address. While the goal of encouraging male choral participation continues to be an important issue for everyone that was involved in this inquiry, we came to realize the most important outcome was recognizing the power of collaboration

Program Logic Foundations: Putting the Logic Back into Program Logic

Background: Program logic is one of the most used tools by the public policy evaluator. There is, however, little explanation in the evaluation literature about the logical foundations of program logic or discussion of how it may be determined if a program is logical. This paper was born on a long journey that started with program logic and ended with the logic of evaluation. Consistent throughout was the idea that the discipline of program evaluation is a pragmatic one, concerned with applied social science and effective action in complex, adaptive systems. It gradually became the central claim of this paper that evidence-based policy requires sound reasoning more urgently than further development and testing of scientific theory. This was difficult to reconcile with the observation that much evaluation was conducted within a scientific paradigm, concerned with the development and testing of various types of theory. Purpose: This paper demonstrates the benefits of considering the core essence of a program to be a proposition about the value of a course of action. This contrasts with a research-based paradigm in which programs are considered to be a type of theory, and in which experimental and theory-driven evaluations are conducted. Experimental approaches focus on internal validity of knowledge claims about programs and on discovering stable cause and effect relationships—or, colloquially, ‘what works?’. Theory-driven approaches tend to focus on external validity and in the case of the realist approach, the search for transfactual causal mechanisms—extending the ‘what works’ mantra to include ‘for whom and in what circumstances’. On both approaches, evaluation aspires to be a scientific pursuit for obtaining knowledge of general laws of phenomena, or in the case of realists, replicable context-mechanism-outcome configurations. This paper presents and seeks to justify an approach rooted in logic, and that supports anyone to engage in a reasonable and democratic deliberation about the value of a course of action. It is consistent with systems thinking, complexity and the associated limits to certainty for determining the value of a proposed, or actual, course of action in the social world. It suggests that evaluation should learn from the past and have an eye toward the future, but that it would be most beneficial if concerned with evaluating in the present, in addressing the question ‘is this a good idea here and now? Setting: Not applicable. Intervention: Not applicable Research design: Not applicable. Findings: In seeking foundations of program logic, this paper exposes roots that extend far deeper than the post-enlightenment, positivist and post-positivist social science search for stable cause and effect relationships. These roots lie in the 4th century BCE with Aristotle’s ‘enthymeme’. The exploration leads to conclusions about the need for a greater focus on logic and reasoning in the design and evaluation of programs and interventions for the public good. Science and research are shown to play a crucial role in providing reasons or warrants to support a claim about the value of a course of action; however, one subordinate to the alpha-discipline of logical evaluation and decision making that must consider what is feasible given the context, capability and capacity available, not to mention values and ethics. Program Design Logic (PDL) is presented as an accessible and incremental innovation that may be used to determine if a program makes sense ‘on paper’ in the design stage as well as ‘in reality’ during delivery. It is based on a configurationalist theory of causality and the concepts of ‘necessary’ and ‘sufficient’ conditions. It is intended to guide deliberation and decision making across the life cycle of any intervention intended for the public good. Keywords: Program logic; program theory; theory of change; program design logic; logic of evaluation; theory of causality; INUS conditio

Directed evolution of Vibrio fischeri LuxR for improved response to butanoyl-homoserine lactone

LuxR is the 3-oxohexanoyl-homoserine lactone (3OC6HSL) dependent transcriptional activator of the prototypical acyl-homoserine lactone (AHL) quorum sensing system of Vibrio fischeri. Wild-type LuxR exhibits no response to butanoyl-HSL (C4HSL) in quantitative bioassays at concentrations of up to 1 µM; a previously described LuxR variant (LuxR-G2E) exhibits a broadened response to diverse AHLs, including pentanoyl-HSL (C5HSL), but not to C4HSL. Here, two rounds of directed evolution of LuxR-G2E generated variants of LuxR that responded to C4HSL at concentrations as low as 10 nM. One variant, LuxR-G4E, had only one change, I45F, relative to the parent LuxR-G2E, which itself differs from wild-type at three residues. Dissection of the four mutations within LuxR-G4E demonstrated that at least three of these changes were simultaneously required to achieve any measurable C4HSL response. The four changes improved both sensitivity and specificity towards C4HSL relative to any of the other 14 possible combinations of those residues. These data confirm that LuxR is evolutionarily pliable and suggest that LuxR is not intrinsically asymmetric in its response to quorum sensing signals with different acyl-side chain lengths

America’s Most Divided Sport: Polarization and Inequality in Attitudes about Youth Football

Football may be America’s most popular sport, but with growing evidence of the risk of sport-associated concussions, some adults are reconsidering which sports to encourage children to play. Using data from a nationally representative sample of 958 respondents, we examine how political party, belief in patriotic displays in sport, attention to concussion news, social class, and race are associated with support for children playing each of the five major U.S. sports: baseball, basketball, hockey, soccer, and football. Our findings suggest that unlike other sports, attitudes about youth participation in football are divided by views on patriotism in sport, age, race, education, and attention to concussion news. For many Americans, football is connected to participation in a civil religion, which celebrates national pride and respect for the military. We argue that child safety advocates who aim to steer children away from football must grapple with the deeper cultural and identity-based framework associated with the sport

Why the NBA Shut Down First: How Partisan Polarization Informs Sports and Public Health

owners concluded a conference call regarding the Covid-19 pandemic. They believed that Commissioner Adam Silver would soon announce that games would proceed in empty arenas. While European soccer leagues had canceled matches, just the day before the National Collegiate Athletic Association (NCAA) had taken the more tepid step of announcing that the March Madness tournaments would be played without fans in the stands. There were only about a thousand confirmed cases of coronavirus in the United States at that time, and the NBA owners were divided on how to proceed. According to Ramona Shelburne’s (2020) reporting for ESPN, the respective owners of the Golden State Warriors, the Oklahoma City Thunder, and the Houston Rockets argued for a temporary postponement of games. But the majority of owners prevailed in support of the less drastic plan in which the season would continue as scheduled, albeit without the presence of spectators. Meanwhile, in Oklahoma City, Rudy Gobert, star center for the Utah Jazz, was confined to a hotel room, awaiting the results of a Covid-19 test he had taken that morning. As his teammates warmed up on the Thunder’s court and fans took their seats, Gobert received the news that he had tested positive for the contagious and potentially deadly virus. Minutes from the 8:00 PM EST tipoff, as the general managers of the Jazz and Thunder, Oklahoma City public health officials, and Adam Silver scrambled to formulate a new plan, the arena announcer told fans that there would be a thirty-minute delay of game (Shelburne 2020; Cacciola and Deb 2020). The referees directed players to the locker room where they would don protective gear and wait. Shortly thereafter, arena loudspeakers reassured fans that they were safe, but informed them the game was postponed and they were to exit the arena. For Americans at home, the evening of March 11 offered a startling line-up of television, beginning with a halting and hesitant declaration of a national state of emergency from the White House, followed by news of plummeting stock futures and an announcement that beloved Hollywood couple, Tom Hanks and Rita Wilson, had contracted the disease. Finally, viewers watched a surreal scene unfold at Chesapeake Energy Arena in Oklahoma City as the NBA announced that an unnamed player had tested positive for the Covid-19 virus, leading to an immediate suspension of all games. Silver characterized the suspension order as “a split-second decision” (Shelburne 2020). In the twenty-four hours that followed, the National Hockey League (NHL), Major League Baseball (MLB), Major League Soccer (MLS), and the NCAA all followed suit, but by early March, the conditions were such that it seemed pre-ordained that the NBA should be the league to lead the way. In this chapter, we argue that beyond practical considerations, the NBA’s position as the most socially and culturally progressive of the major U.S. sports leagues informed its decision to suspend games, even as both government officials and other sporting entities dithered