Guest lectures and seminars - Page 5
Note the non-standard start time!
Abstract: We consider mirror pairs of Calabi-Yau hypersurfaces X and X’ in toric varieties associated to dual reflexive polytopes. We will give a proof through tropical geometry that the Hodge numbers of X and X’ are mirror symmetric. The proof goes by considering tropical homology, and works over the ring of integer numbers. In particular, we can use our spectral sequence with Kris Shaw to explore the connections between the topology of the real part of X and cohomological operations on X’.
This is based on joint work with Diego Matessi.
C*-algebra seminar by Sergey Neshveyev.
Structural equation models are simultaneous equation regression models, whose variables are latent, and measured via a confirmatory factor model (that is, with measurement error and repeated measurements). When the functional form of the simultaneous equation system is unknown, it has previously been observed in simulations that factor scores inputted into non-parametric regression methods approximate the true functional form. Factor scores estimate the latent variables (per person), and several types exist. We provide a theoretical (though population-based) analysis of this procedure, and provide assumptions under which it is theoretically justified in using Bartlett factor scores, which are simple linear transformations of the data. In simulations, we compare this suggestion to an already available though understudied non-linear and computationally heavy procedure, and observe that the simple Bartlett approach appears to work better.
The frictional behavior of surfaces is a problem of great scientific and practical significance. Recent progress in molecular scale modeling allows us to determine the coefficient of friction for nanoscale surfaces from first principles using molecular dynamics modeling. However, inverse design, that is, designing surfaces with specific frictional propeties is still a complex and largely unsolved challenge in part due to the enormous space of possible surface configurations. Here, we demonstrate how we can use physical forward modeling to find the frictional properties of a set of surfaces that can serve as a training set to design machine learning models. In this talk, we demonstrate both discriminative and generative models for frictional surface design and analyze what physical principles the machine learning models have learned in this process.
his talk discusses a nonparametric inference framework for occupation time curves derived from wearable device data. Such curves provide the total time a subject maintains activity above a given level as a function of that level. Taking advantage of the monotonicity and smoothness properties of these curves, we develop a likelihood ratio approach to construct confidence bands for mean occupation time curves. An extension to fitting concurrent functional regression models is also developed. Application to wearable device data from an ongoing study of an experimental gene therapy for mitochondrial DNA depletion syndrome will be discussed. Based on joint work with Hsin-Wen Chang (Academia Sinica).