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11:00am to 12:00pm - 340P - Machine Learning Baolin Wu - (Department of Epidemiology and Biostatistics, UCI) Leverage large-scale genetic data for efficient and improved estimation of genetic ancestry Genetic admixture estimation has been widely studied and proven very useful in ancestry inference and genome-wide association studies. Existing methods and tools, such as ADMIXTUER and OpenADMIXTURE, often encountered identifiability issues and convergence problems due to the model complexity and ultrahigh dimensionality of the parameter space. In this talk, we provide some analytical insights to characterize the convergence of admixture models and present an innovative and scalable statistical modeling framework to further improve the accuracy of genetic ancestry estimation. Specifically, we will discuss (1) a novel transfer learning approach that can leverage outside biobank summary data just using allele frequency; and (2) a novel LASSO penalized clustering model that can seamlessly rank/select important ancestry informative markers. These newly proposed approaches were applied to public GWAS data to demonstrate their competitive performance. |
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2:00pm - RH 340P - Logic Set Theory Nicolas Cuervo Ovalle - (Universidad de los Andes (visiting UCI)) Schröder-Bernstein property for metric structures-III (Randomizations) We say that a complete theory T has the Schröder-Bernstein property, or simply, the SB-property, if for any two models M and N of T that are elementary bi-embeddable then they are isomorphic. The purpose of this talk is to study the SB-property in the continuous context for Randomizations. Informally, a randomization of a first order (discrete) model, M, is a two sorted metric structure which consist of a sort of events and a sort of functions with values on the model, usually understood as random variables. More generally, given a complete first order theory T, there is a complete continuous theory known as randomized theory, T^R, which is the common theory of all randomizations of models of T. Randomizations were introduced first by Keisler in [5] and then axiomatized in the continuous setting by Ben Yaacov and Keisler in [4]. Since randomizations where introduced, many authors focused on examining which model theoretic properties of T are preserved on T^R, for example, in [4] and [3] it was shown that properties like ω-categoricity, stability and dependence are preserved. Similarly in [1] it is proved that the existence of prime models is preserved by randomization but notions like minimal models are not preserved. Following these ideas, we will prove that a first order theory T with ≤ ω countable models has the SB-property for countable models if and only if T^R has the SB-property for separable randomizations. This is a joint work with Alexander Berenstein, presented in [2].
References: [1] U. Andrews and H. J. Keisler. Separable models of randomizations. The Journal of Symbolic Logic, pages 1149–1181, 2015. [2] Argoty, C., Berenstein, A. & Cuervo Ovalle, N. The SB-property on metric structures. Archive for Mathematical Logic (2025). https://doi.org/10.1007/s00153-024-00949-y [3] I. Ben Yaacov. Continuous and random vapnik-chervonenkis classes. Israel Journal of Mathematics, 1(173):309–333, 2009. [4] I. Ben Yaacov and H. Jerome Keisler. Randomizations of models as metric structures. Confluentes Mathematici, 1(02):197–223, 2009. [5] H. J. Keisler. Randomizing a model. Advances in Mathematics, 143(1):124–158, 1999 |
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4:00pm to 5:00pm - RH 306 - Applied and Computational Mathematics James Lambers - (University of Southern Mississippi) Scalable time-stepping for nonlinear PDEs based on Krylov subspace spectral methods Krylov subspace spectral (KSS) methods are high-order accurate, explicit time-stepping methods for partial differential equations (PDEs) with stability characteristic of implicit methods. KSS methods compute each Fourier coefficient of the solution from an individualized approximation of the solution operator of the PDE. As a result, KSS methods scale more effectively to higher spatial resolution than other time-stepping approaches. Unfortunately, they are limited to linear PDEs. This talk will present two avenues for broadening their applicability. Exponential Rosenbrock methods are designed for stiff problems such as systems of ODEs that arise from spatial discretization of PDEs; however, these methods rely on computing matrix function-vector products with algorithms that do not scale well. KSS methods’ frequency-dependent approach, designed to circumvent stiffness in linear problems, computes these products with greater scalability. We demonstrate that combining these two classes of methods produces superior scalability for the solution of nonlinear problems. The talk will conclude with a presentation of explicit and implicit multistep formulations of KSS methods to provide a ``best-of-both-worlds’’ situation that combines the efficiency of multistep methods with the stability and scalability of KSS methods. The effectiveness of these ``spectral multistep methods’’ will be demonstrated through numerical experiments. It will also be shown that the region of absolute stability exhibits striking behavior that helps explain the scalability of these methods. Joint work with Chelsea Drum and Bailey Rester. |
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1:00pm to 2:00pm - RH 440R - Dynamical Systems Angxiu Ni - (UC Irvine) On the triad program for sampling parameter-derivatives of of chaos Computing the linear response, or the derivative of long-time-averaged observables with respect to system parameters, is a central problem for many applications. Conventionally, there are three linear response formulas: the path-perturbation formula (including the backpropagation method in machine learning), the divergence formula, and the probability-kernel-differentiation formula. But none works for the general case, which is chaotic, high-dimensional, and small-noise. Then we present our fast response formula for hyperbolic systems, expressed by a pointwisely defined function; some of our ideas are from the classic proof of the hyperbolic linear responses. Hence, people can compute the linear response by sampling, that is, compute the average of some function over an orbit. The fast response formula overcomes all three difficulties under hyperbolicity assumptions. Then we discuss how to further incorporate kernel-differentiation to overcome non-hyperbolicity. |
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2:00pm to 2:50pm - RH 340N - Analysis Xin Dong - (University of Connecticut) Local Rigidity of the Bergman Metric and of the Kähler Carathéodory Metric This talk is based on the joint work with Ruoyi Wang and Bun Wong at UC Riverside. We prove that if the Carathéodory metric on a strictly pseudoconvex domain with a smooth boundary is locally Kähler near the boundary, then the domain is biholomorphic to a ball. We also establish a local rigidity theorem for domains with Bergman metrics of constant holomorphic sectional curvature, and highlight this relationship with the Lu constant. |
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3:00pm to 4:00pm - RH 306 - Differential Geometry Hosea Wondo - (Cornell University) Chern-Ricci Flow on Complex Minimal Surfaces The Chern-Ricci flow is one of several proposed generalisations of the Kahler-Ricci flow in the Hermitian setting. The aim of this talk is twofold. We first outline the behaviour of the Chern-Ricci flow on complex minimal surfaces. Then, motivated by several results on minimal surfaces, we show that the curvature type is independent of the starting metric in its 'class' for long-time solutions. This demonstrates a curvature type independence result that holds for the Kahler case. |
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4:00pm to 5:00pm - RH306 - Differential Geometry Kai Xu - (Duke University) Drawstrings and the geometry of scalar curvature We will discuss a new collapsing phenomenon called drawstrings and its role in several stability problems for scalar curvature. This talk is based on recent joint works with Demetre Kazaras. |
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3:00pm to 4:00pm - 510R Rowland Hall - Combinatorics and Probability Tom Hutchcroft - (Caltech) A new approach to critical phenomena in long-range models Many statistical mechanics models on the lattice (including percolation, self-avoiding walk, the Ising model and so on) have natural "long-range" versions in which vertices interact not only with their neighbours, but with all other vertices in a way that decays with the distance. When this decay is described by a power-law, it can lead to new kinds of critical phenomena that are not present in the short-range models. In this talk I will describe a new approach to the study of these models, leading to some striking new results with surprisingly easy proofs |
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9:00am to 9:50am - Zoom - Inverse Problems Jan Bohr - (University of Bonn) Scattering relations and biholomorphisms |