A note on Khovanov-Rozansky sl2sl_2-homology and ordinary Khovanov homology

In this note we present an explicit isomorphism between Khovanov-Rozansky $sl_2$-homology and ordinary Khovanov homology. This result was originally stated in Khovanov and Rozansky's paper \cite{KRI}, though the details have yet to appear in the literature. The main missing detail is providing a coherent choice of signs when identifying variables in the $sl_2$-homology. Along with the behavior of the signs and local orientations in the $sl_2$-homology, both theories behave differently when we try to extend their definitions to virtual links, which seemed to suggest that the $sl_2$-homology may instead correspond to a different variant of Khovanov homology. In this paper we describe both theories and prove that they are in fact isomorphic by showing that a coherent choice of signs can be made. In doing so we emphasize the interpretation of the $sl_2$-complex as a cube of resolutions.Comment: 19 pages, 11 figures. Expanded introduction and abstract. Remark added to end of section 4.

Dispositions: Real-Time Active Practice

This longitudinal case study followed new teachers from one small undergraduate pre-service program into the first years of teaching. The researcher’s initial study (Hughes, 2014) examined dispositional awareness and development of participants using personal interview data from program graduates, interview data from program faculty, and archived course artifacts. The current study extends the research and shines a light on dispositional development from pre-service through the fourth year of teaching. Using personal interviews, a focus group meeting, and archived course artifacts, the study affirms the significance of dispositions in pre-service preparation and professional practice. The study validates that participants carry dispositional awareness into the fourth year of teaching and also reveals a variety of strategies that new teachers use to grow dispositions. Of significance is the finding that new teachers require a set of dispositional practices for career longevity. This finding exposes the need for increased professional development opportunities related to dispositions during and beyond the first years of teaching

Mighty Teacher Mentors

Teaching is about cultivating curiosity, fostering a love for course content, and making connections with students. Educators who serve as mentors and pass on their passions for the profession and a love for sharing their craft can thoughtfully encourage prospective teachers into the field. This article captures and links one educator’s journey with the teaching mentors that encouraged a contagious love for teaching and learning in her. The article provides encouragement and practical suggestions for educators that desire to learn from authentic mentors and pay it forward with others in the faith. The article is adapted from a chapel talk given at Westmont College by the author on February 24, 2014

Air bearing Patent

Air bearings for spacecraft gyro

Imprisonment and the Right to Freedom of Movement

Government’s use of imprisonment raises distinctive moral issues. Even if government has broad authority to make and to enforce law, government may not be entitled to use imprisonment as a punishment for all the criminal laws it is entitled to make. Indeed, there may be some serious crimes that it is wrong to punish with imprisonment, even if the conditions of imprisonment are humane and even if no adequate alternative punishments are available

Can Resilience Be Our Teacher Super-power?

Teaching is courageous work. Today\u27s teachers face heavy workloads and growing emotional responsibilities as K-12 students and families face complicated hurdles and issues such as mental health issues, immigration, and natural disasters. This essay names resilience, grit, and perseverance as essential dispositions needed to tackle the daily hurdles and unexpected circumstances found in the classroom and pre-service teacher preparation. The author’s reflections lead to practical recommendations with the intention to nurture and cultivate resilience in teachers and school communities

Space structure vibration modes: How many exist? Which ones are important?

This report attempts to shed some light on the two issues raised in the title, namely, how many vibration modes does a real structure have, and which of these modes are important? The surprise-free answers to these two questions are, respectively, an infinite number and the first several modes. The author argues that the absurd subspace (all but the first billion modes) is not a strength of continuum modeling, but, in fact, a weakness. Partial differential equations are not real structures, only mathematical models. This note also explains (1) that the PDE model and the finite element model are, in fact, the same model, the latter being a numerical method for dealing with the former, (2) that modes may be selected on dynamical grounds other than frequency alone, and (3) that long slender rods are useful as primitive cases but dangerous to extrapolate from