Higher-Dimensional Algebra III: n-Categories and the Algebra of Opetopes

We give a definition of weak n-categories based on the theory of operads. We work with operads having an arbitrary set S of types, or `S-operads', and given such an operad O, we denote its set of operations by elt(O). Then for any S-operad O there is an elt(O)-operad O+ whose algebras are S-operads over O. Letting I be the initial operad with a one-element set of types, and defining I(0) = I, I(i+1) = I(i)+, we call the operations of I(n-1) the `n-dimensional opetopes'. Opetopes form a category, and presheaves on this category are called `opetopic sets'. A weak n-category is defined as an opetopic set with certain properties, in a manner reminiscent of Street's simplicial approach to weak omega-categories. Similarly, starting from an arbitrary operad O instead of I, we define `n-coherent O-algebras', which are n times categorified analogs of algebras of O. Examples include `monoidal n-categories', `stable n-categories', `virtual n-functors' and `representable n-prestacks'. We also describe how n-coherent O-algebra objects may be defined in any (n+1)-coherent O-algebra.Comment: 59 pages LaTex, uses diagram.sty and auxdefs.sty macros, one encapsulated Postscript figure, also available as a compressed Postscript file at http://math.ucr.edu/home/baez/op.ps.Z or ftp://math.ucr.edu/pub/baez/op.ps.

Introduction to special section: Active Fault-Related Folding: Structural Evolution, Geomorphologic Expression, Paleoseismology, and Seismic Hazards

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Investigation of wrought steel railway car wheels : part I, tests of strength properties of wrought steel car wheels

Cover title.Prepared as part of an investigation conducted by the Engineering Experiment Station, University of Illinois at Urbana-Champaign

Stress concentration at fillets, holes, and keyways as found by the plaster-model method

Bibliography: p. 31-32

Extended leaves of absence for the professional improvement of public-school educators

Thesis (Ed.D.)--Boston University

Distributionally Robust Performance Analysis with Applications to Mine Valuation and Risk

We consider several problems motivated by issues faced in the mining industry. In recent years, it has become clear that mines have substantial tail risk in the form of environmental disasters, and this tail risk is not incorporated into common pricing and risk models. However, data sets of the extremal climate behavior that drive this risk are very small, and generally inadequate for properly estimating the tail behavior. We propose a data-driven methodology that comes up with reasonable worst-case scenarios, given the data size constraints, and we incorporate this into a real options based model for the valuation of mines. We propose several different iterations of the model, to allow the end-user to choose the degree to which they wish to specify the financial consequences of the disaster scenario. Next, in order to perform a risk analysis on a portfolio of mines, we propose a method of estimating the correlation structure of high-dimensional max-stable processes. Using the techniques of (Liu Et al, 2017) to map the relationship between normal correlations and max-stable correlations, we can then use techniques inspired by (Bickel et al, 2008, Liu et al, 2014, Rothman et al, 2009) to estimate the underlying correlation matrix, while preserving a sparse, positive-definite structure. The correlation matrices are then used in the calculation of model-robust risk metrics (VaR, CVAR) using the the Sample-Out-of-Sample methodology (Blanchet and Kang, 2017). We conclude with several new techniques that were developed in the field of robust performance analysis, that while not directly applied to mining, were motivated by our studies into distributionally robust optimization in order to address these problems