The autoconjugacy of a generalized Collatz map

Many of the 2-adic properties of the 3x+1 map generalize to the analogous mx+r map, where m and r are odd integers. We introduce the corresponding autoconjugacy map, prove some simple properties of it and make some further conjectures in the general setting, including weak versions of the periodicity and divergent trajectories conjectures

Performativity and affectivity: Lesson observations in England's Further Education colleges

Teaching and learning observations (TLOs) are used in educational environments worldwide to measure and improve quality and support professional development. TLOs can be positive, for teachers who enjoy opportunities to ‘perform’ their craft and/or engage in professional dialogue. However, if this crucial, collaborative developmental element is missing, a TLO becomes intrinsically evaluative in nature and creates complex emotions – within and beyond the classroom. For some teachers, affective reactions to perceived managerial intrusion into their professional space has a negative impact on them, and in turn, their students’ learning. International research on TLOs has focused on schools or universities. My research centres specifically on England’s Further Education colleges (FE). Through Interpretive Interactionism, I investigate the different expectations, relationships and identities of teachers and (mis)conceptions of ‘authenticity’ in TLOs. Teaching involves our unique (dis)embodied ‘performativity’ (Butler, 2004) or ‘emotional practice’ which is interpreted and judged by others (Denzin, 1989). Using the concept of ‘aesthetic labour’ (Witz, et al., 2003), I argue that rather than promoting positive transformation through reflection, TLOs promote a rejection of emotional ‘genuineness’ that causes anxiety through a fracturing of personal and professional identities. Improving the effectiveness of TLOs should perhaps encompass explicit dialogue about the affectivity involved in the process

Dynamic Motion Modelling for Legged Robots

An accurate motion model is an important component in modern-day robotic systems, but building such a model for a complex system often requires an appreciable amount of manual effort. In this paper we present a motion model representation, the Dynamic Gaussian Mixture Model (DGMM), that alleviates the need to manually design the form of a motion model, and provides a direct means of incorporating auxiliary sensory data into the model. This representation and its accompanying algorithms are validated experimentally using an 8-legged kinematically complex robot, as well as a standard benchmark dataset. The presented method not only learns the robot's motion model, but also improves the model's accuracy by incorporating information about the terrain surrounding the robot

Designing Professional Learning Tasks for Mathematics Learning Trajectories

In this paper, we present an emerging set of learning conjectures and design principles to be used in the development of professional learning tasks that support elementary teachers’ learning of mathematics learning trajectories. We outline our theoretical perspective on teacher knowledge of learning trajectories, review the literature concerning mathematics professional learning tasks, offer a set of initial conjectures about teacher learning of learning trajectories, and articulate a set of principles to guide the design of tasks. We conclude with an example of one learning trajectory professional learning task taken from our current research project

Regolith grain sizes of Saturn's rings inferred from Cassini-CIRS far-infrared spectra

We analyze far-infrared (10-650 cm$^{-1}$) emissivity spectra of Saturn's main rings obtained by the Cassini Composite Infrared Spectrometer (CIRS). In modeling of the spectra, the single scattering albedos of regolith grains are calculated using the Mie theory, diffraction is removed with the delta-Eddington approximation, and the hemispherical emissivities of macroscopic free-floating ring particles are calculated using the Hapke's isotropic scattering model. Only pure crystalline water ice is considered and the size distribution of regolith grains is estimated. We find that good fits are obtained if the size distribution is broad ranging from 1 $\mu$m to 1-10 cm with a power law index of $\sim 3$. This means that the largest regolith grains are comparable to the smallest free-floating particles in size and that the power law indices for both free-floating particles and regolith grains are similar to each other. The apparent relative abundance of small grains increases with decreasing solar phase angle (or increasing mean temperature). This trend is particularly strong for the C ring and is probably caused by eclipse cooling in Saturn's shadow, which relatively suppresses warming up of grains larger than the thermal skin depth ($\sim$ 1 mm) under subsequent solar illumination.Comment: 42pages, 10 figures, accepted for publication in Icaru

CHIP Expansions to Higher-Income Children in Three States: Profiles of Eligibility and Insurance Coverage

Summarizes findings on how changes in eligibility rules for children's public health insurance programs affected 2002-09 coverage rates and the number of uninsured children in Illinois, Pennsylvania, and Washington. Compares results by scope of reform

Destination Station: Bringing The International Space Station to Communities Across the United States

Today, space is no longer just a field of advanced technological development and of scientific research of excellence, but has become an essential asset for everyday life. Space has spurred countless scientific and technological achievements which are commonly used in aeronautics, medicine, material science and production, in information and communications technology. In parallel, more and more services are carried out through the use of space applications, ranging from detection of natural disasters and environmental monitoring to global navigation and telecommunication. Using space missions to build a better understanding of the universe fulfills our centuries-old curiosity and leads humanity into the future, opening up new frontiers of knowledge. The International Astronautical Congresses have always represented an arena in which issues have been discussed with friendship and among experts: scientists, technicians and managers from universities, agencies, research centres and industry. At the same time it introduces students and young professionals to the field

Chances, counterfactuals and similarity

John Hawthorne in a recent paper takes issue with Lewisian accounts of counterfactuals, when relevant laws of nature are chancy. I respond to his arguments on behalf of the Lewisian, and conclude that while some can be rebutted, the case against the original Lewisian account is strong. I develop a neo-Lewisian account of what makes for closeness of worlds. I argue that my revised version avoids Hawthorne’s challenges. I argue that this is closer to the spirit of Lewis’s first (non-chancy) proposal than is Lewis’s own suggested modification