Open, Online, Calculus Help Forums: Learning About and From a Public Conversation

This study is an exploration of participation, community, and mathematical understanding in an open, online, calculus help forum. These forums, populated by members from around the world, are locations where students post queries from their coursework and receive assistance from volunteer tutors. The site under investigation has a spontaneous participation structure, meaning that any forum member can respond to a query and contribute to an ongoing discussion. From earlier work, we know that such forums foster mathematical dialogue, contain exchanges with sophisticated pedagogical moves, and exhibit a strong sense of community. In this study, we delve deeper into the functional aspects of activity (such as student positioning and pedagogical moves), the benefits that accrue from participation in tutoring as a communal activity, and the mathematical understanding that is evident in the way problems on limit and related rates are framed and solutions constructed. Based on an observational methodology, we find that the forum provides tutoring for students and support for tutors that is unique from our expectations of other learning environments, such as one-on-one tutoring and computer-based tutoring systems. Students position themselves with authority in the exchanges by making assertions and proposals of action, questioning or challenging others' proposals, and indicating when resolution has been achieved. Tutors, who generally have more experience and expertise than students, provide mathematical guidance, and, in exemplary exchanges, draw the student into making a mathematical discovery. The dedication of tutors to the forum community was evident in the presence of authentic, honest mathematical practices, in the generous provision of alternative perspectives on problems, and in the sincere correction of errors. Some student participants picked up on these aspects of community and expressed excitement and appreciation for this taste of mathematical discourse. The primary contribution of the tutors was their assistance in supporting students as they constructed productive framings for the exercises, and this was the help that students were most in need of. As a result of eavesdropping on this public conversation, we conclude that the forums are a public conversation that should be listened to by educational researchers, teachers, and designers of tutoring systems

Molecular Dynamics Simulation

Condensed matter systems, ranging from simple fluids and solids to complex multicomponent materials and even biological matter, are governed by well understood laws of physics, within the formal theoretical framework of quantum theory and statistical mechanics. On the relevant scales of length and time, the appropriate ‘first-principles’ description needs only the Schroedinger equation together with Gibbs averaging over the relevant statistical ensemble. However, this program cannot be carried out straightforwardly—dealing with electron correlations is still a challenge for the methods of quantum chemistry. Similarly, standard statistical mechanics makes precise explicit statements only on the properties of systems for which the many-body problem can be effectively reduced to one of independent particles or quasi-particles. [...

Tracking the Temporal-Evolution of Supernova Bubbles in Numerical Simulations

The study of low-dimensional, noisy manifolds embedded in a higher dimensional space has been extremely useful in many applications, from the chemical analysis of multi-phase flows to simulations of galactic mergers. Building a probabilistic model of the manifolds has helped in describing their essential properties and how they vary in space. However, when the manifold is evolving through time, a joint spatio-temporal modelling is needed, in order to fully comprehend its nature. We propose a first-order Markovian process that propagates the spatial probabilistic model of a manifold at fixed time, to its adjacent temporal stages. The proposed methodology is demonstrated using a particle simulation of an interacting dwarf galaxy to describe the evolution of a cavity generated by a Supernov

Multivariate Statistical Machine Learning Methods for Genomic Prediction

This book is open access under a CC BY 4.0 license This open access book brings together the latest genome base prediction models currently being used by statisticians, breeders and data scientists. It provides an accessible way to understand the theory behind each statistical learning tool, the required pre-processing, the basics of model building, how to train statistical learning methods, the basic R scripts needed to implement each statistical learning tool, and the output of each tool. To do so, for each tool the book provides background theory, some elements of the R statistical software for its implementation, the conceptual underpinnings, and at least two illustrative examples with data from real-world genomic selection experiments. Lastly, worked-out examples help readers check their own comprehension. The book will greatly appeal to readers in plant (and animal) breeding, geneticists and statisticians, as it provides in a very accessible way the necessary theory, the appropriate R code, and illustrative examples for a complete understanding of each statistical learning tool. In addition, it weighs the advantages and disadvantages of each tool

Multivariate Statistical Machine Learning Methods for Genomic Prediction

This book is open access under a CC BY 4.0 license This open access book brings together the latest genome base prediction models currently being used by statisticians, breeders and data scientists. It provides an accessible way to understand the theory behind each statistical learning tool, the required pre-processing, the basics of model building, how to train statistical learning methods, the basic R scripts needed to implement each statistical learning tool, and the output of each tool. To do so, for each tool the book provides background theory, some elements of the R statistical software for its implementation, the conceptual underpinnings, and at least two illustrative examples with data from real-world genomic selection experiments. Lastly, worked-out examples help readers check their own comprehension. The book will greatly appeal to readers in plant (and animal) breeding, geneticists and statisticians, as it provides in a very accessible way the necessary theory, the appropriate R code, and illustrative examples for a complete understanding of each statistical learning tool. In addition, it weighs the advantages and disadvantages of each tool