17,330 research outputs found

    Proper Classroom Management is Essential for an Effective Elementary School Classroom

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    I am an elementary education major and have a deep love for seeing children make connections, and learn about not only academics but moral values and life lessons. As much as I have learned in different classes over the past four years of my education, I have learned the most during my Practicum and Student Teaching experience as I really have gotten to run my own classroom. I believe that classroom management is the most important tool of strong learning. It provides the atmosphere students need to learn to their best ability. My thesis paper discusses why classroom management is essential to any effective classroom at an elementary school level. I will implement theories of some well-noted authors in the education field, along with sharing my personal experiences in my Practicum and Student Teaching journey. Explored are the reasons behind why a classroom should be managed well, safety issues, relationships, teacher reflection, and more

    Constrained Approximation of Effective Generators for Multiscale Stochastic Reaction Networks and Application to Conditioned Path Sampling

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    Efficient analysis and simulation of multiscale stochastic systems of chemical kinetics is an ongoing area for research, and is the source of many theoretical and computational challenges. In this paper, we present a significant improvement to the constrained approach, which is a method for computing effective dynamics of slowly changing quantities in these systems, but which does not rely on the quasi-steady-state assumption (QSSA). The QSSA can cause errors in the estimation of effective dynamics for systems where the difference in timescales between the "fast" and "slow" variables is not so pronounced. This new application of the constrained approach allows us to compute the effective generator of the slow variables, without the need for expensive stochastic simulations. This is achieved by finding the null space of the generator of the constrained system. For complex systems where this is not possible, or where the constrained subsystem is itself multiscale, the constrained approach can then be applied iteratively. This results in breaking the problem down into finding the solutions to many small eigenvalue problems, which can be efficiently solved using standard methods. Since this methodology does not rely on the quasi steady-state assumption, the effective dynamics that are approximated are highly accurate, and in the case of systems with only monomolecular reactions, are exact. We will demonstrate this with some numerics, and also use the effective generators to sample paths of the slow variables which are conditioned on their endpoints, a task which would be computationally intractable for the generator of the full system.Comment: 31 pages, 7 figure

    Bayesian data assimilation in shape registration

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    In this paper we apply a Bayesian framework to the problem of geodesic curve matching. Given a template curve, the geodesic equations provide a mapping from initial conditions\ud for the conjugate momentum onto topologically equivalent shapes. Here, we aim to recover the well defined posterior distribution on the initial momentum which gives rise to observed points on the target curve; this is achieved by explicitly including a reparameterisation in the formulation. Appropriate priors are chosen for the functions which together determine this field and the positions of the observation points, the initial momentum p0 and the reparameterisation vector field v, informed by regularity results about the forward model. Having done this, we illustrate how Maximum Likelihood Estimators (MLEs) can be used to find regions of high posterior density, but also how we can apply recently developed MCMC methods on function spaces to characterise the whole of the posterior density. These illustrative examples also include scenarios where the posterior distribution is multimodal and irregular, leading us to the conclusion that knowledge of a state of global maximal posterior density does not always give us the whole picture, and full posterior sampling can give better quantification of likely states and the overall uncertainty inherent in the problem
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