A view of canonical extension

This is a short survey illustrating some of the essential aspects of the theory of canonical extensions. In addition some topological results about canonical extensions of lattices with additional operations in finitely generated varieties are given. In particular, they are doubly algebraic lattices and their interval topologies agree with their double Scott topologies and make them Priestley topological algebras.Comment: 24 pages, 2 figures. Presented at the Eighth International Tbilisi Symposium on Language, Logic and Computation Bakuriani, Georgia, September 21-25 200

The Leadership Pilgrimage: How a Virtual Pilgrimage Transforms Leaders

Leadership is a journey. However, few leaders embark on the type of journey that fosters greatness. That journey is best described as a pilgrimage, a leadership pilgrimage. A pilgrimage is a sacred journey with a purpose, one that requires vision, focus, and perseverance to complete. During the pilgrimage, pilgrims share a common experience: enlightenment through solitude and sacrifice. The Camino de Santiago is such a journey. It is a powerful metaphor for a leadership pilgrimage: a self-reflective journey leading to leadership enlightenment. This paper explores the impact of a virtual pilgrimage on the Way of St James on leaders as they study five parallels between the Way of St. James and corporate leadership development. The Virtual Leadership Pilgrimage was created during the COVID-19 pandemic. At the time of this writing, the first group of participants is enrolling. They will provide feedback regarding how transformative the Virtual Pilgrimage has been to their leadership experience. Our goal is to combine leadership development with the experience of walking the Way of St. James. Participants, like pilgrims, should stretch themselves in both body and spirit as they travel on their road to personal enlightenment. The virtual experience will mimic the pilgrimage experience through course materials, exercises, reflection, and following the Way of St. James virtually. As they do so, participants will experience the type of enlightenment that pilgrims experience on the Way of St. James

Semiclassical quantization of the diamagnetic hydrogen atom with near action-degenerate periodic-orbit bunches

The existence of periodic orbit bunches is proven for the diamagnetic Kepler problem. Members of each bunch are reconnected differently at self-encounters in phase space but have nearly equal classical action and stability parameters. Orbits can be grouped already on the level of the symbolic dynamics by application of appropriate reconnection rules to the symbolic code in the ternary alphabet. The periodic orbit bunches can significantly improve the efficiency of semiclassical quantization methods for classically chaotic systems, which suffer from the exponential proliferation of orbits. For the diamagnetic hydrogen atom the use of one or few representatives of a periodic orbit bunch in Gutzwiller's trace formula allows for the computation of semiclassical spectra with a classical data set reduced by up to a factor of 20.Comment: 10 pages, 9 figure

Establishing literature circles in one middle school teacher\u27s classroom

Literature circles are a popular method of reading instruction in middle school classrooms. Literature circles are when small groups of students choose one book to read and then meet to discuss it. Students are taught how to discuss a book and use response journals. Implementing literature circles into a reading curriculum requires a great deal of planning. A teacher must make decisions about structure, themes, response journals, discussion groups, assessment and final projects. Literature circles are an evolving teaching method and will not always work the same way each time they are used. I found literature circles to be a positive experience but improvements need to be made in the quality of the discussions and in assessment. Students need more structure to help them prepare for discussion and also need to do more self-reflection. Despite setbacks literature circles are a valuable teaching method to use in reading classes

A duality theoretic view on limits of finite structures: Extended version

A systematic theory of structural limits for finite models has been developed by Nešetřil and Ossona de Mendez. It is based on the insight that the collection of finite structures can be embedded, via a map they call the Stone pairing, in a space of measures, where the desired limits can be computed. We show that a closely related but finer grained space of (finitely additive) measures arises—via Stone-Priestley duality and the notion of types from model theory—by enriching the expressive power of first-order logic with certain “probabilistic operators”. We provide a sound and complete calculus for this extended logic and expose the functorial nature of this construction. The consequences are two-fold. On the one hand, we identify the logical gist of the theory of structural limits. On the other hand, our construction shows that the duality theoretic variant of the Stone pairing captures the adding of a layer of quantifiers, thus making a strong link to recent work on semiring quantifiers in logic on words. In the process, we identify the model theoretic notion of types as the unifying concept behind this link. These results contribute to bridging the strands of logic in computer science which focus on semantics and on more algorithmic and complexity related areas, respectively

a technique for spatial resolution improvement in helium beam radiography

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A DUALITY THEORETIC VIEW ON LIMITS OF FINITE STRUCTURES

A systematic theory of structural limits for finite models has been developed by Nešetřil and Ossona de Mendez. It is based on the insight that the collection of finite structures can be embedded, via a map they call the Stone pairing, in a space of measures, where the desired limits can be computed. We show that a closely related but finer grained space of (finitely additive) measures arises—via Stone-Priestley duality and the notion of types from model theory—by enriching the expressive power of first-order logic with certain “probabilistic operators”. We provide a sound and complete calculus for this extended logic and expose the functorial nature of this construction. The consequences are two-fold. On the one hand, we identify the logical gist of the theory of structural limits. On the other hand, our construction shows that the duality theoretic variant of the Stone pairing captures the adding of a layer of quantifiers, thus making a strong link to recent work on semiring quantifiers in logic on words. In the process, we identify the model theoretic notion of types as the unifying concept behind this link. These results contribute to bridging the strands of logic in computer science which focus on semantics and on more algorithmic and complexity related areas, respectively