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Dr Xiang Xiang Wang (Michigan State University)5/21/26, 11:00 AMNew Advancements in Tensor Decomposition and ComputationMinisymposium Talk
Single-cell data are typically represented in Euclidean space, which limits the ability to capture intrinsic correlations and multiscale geometric structure. We propose a multiscale framework based on Grassmann manifolds that represents single-cell RNA-seq data through subspace geometry across multiple scales.
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Mr Augustine (Runshi) Tang (University of Wisconsin-Madison)5/21/26, 11:25 AMNew Advancements in Tensor Decomposition and ComputationMinisymposium Talk
Canonical Polyadic (CP) tensor decomposition is a fundamental technique for analyzing high-dimensional tensor data. While the Alternating Least Squares (ALS) algorithm is widely used for computing CP decomposition due to its simplicity and empirical success, its theoretical foundation, particularly regarding statistical optimality and convergence behavior, remain underdeveloped, especially...
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Dr Andrew McCormack (University of Alberta)5/21/26, 11:50 AMNew Advancements in Tensor Decomposition and ComputationMinisymposium Talk
Matrix or tensor data often has structured rows, columns, or more generally modes. In particular, a mode may have a natural ordering that can be leveraged to obtain parsimonious representations of the data. To this end, the concept of the nondecreasing (ND) rank is introduced in this talk. A tensor has an ND rank of r if it can be represented as a sum of r outer products of vectors, with each...
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Ms Yidan Mei (Yale University)5/21/26, 2:00 PMNew Advancements in Tensor Decomposition and ComputationMinisymposium Talk
Transform-based tensor products, including the T-product and its more general form, namely the higher-order tensor-tensor product, have been widely used in image processing, signal reconstruction, and robotics. While invertible transforms enable tensor computations to be carried out via matrix operations in the transform domain, the resulting storage and computational costs remain prohibitive...
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Dr Neriman Tokcan (University of Massachusetts Boston)5/21/26, 2:50 PMNew Advancements in Tensor Decomposition and ComputationMinisymposium Talk
High-throughput genomics and omics technologies generate data with intrinsic multi-way structure arising from multiple samples, molecular features, experimental conditions, and biological contexts. Standard matrix-based methods often obscure this structure through flattening or aggregation. Tensor-based representations provide a natural mathematical framework for preserving and exploiting the...
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Dr Carmeliza Navasca (University of Alabama at Birmingham)5/22/26, 8:45 AMNew Advancements in Tensor Decomposition and ComputationMinisymposium Talk
We study optimal control problems arising from partial differential equations. More specifically, we look at the optimal control of Allen-Cahn Equation (ACE) with a source term. ACE is well known for modeling phase transitions and thus, has many applications, apart from physics (semiconductors), in biological systems, material science and image processing. ACE models cellular membranes which...
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Jeff Borggaard (Virginia Tech)5/22/26, 9:10 AMNew Advancements in Tensor Decomposition and ComputationMinisymposium Talk
Multivariate polynomial approximations to Hamilton-Jacobi-Bellman equations can be expressed using Kronecker products leading to very large, but structured, linear systems. Their structure appears as n-way generalizations of Lyapunov or generalized Lyapunov equations. For monomial terms of degree d, their dimension scales as the number of state dimensions n raised to the d. For...
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Anna Konstorum5/22/26, 9:35 AMNew Advancements in Tensor Decomposition and ComputationMinisymposium Talk
Symmetric tensor diagonalization has applications in statistics and signal processing. Unlike for real symmetric matrices, there is no guarantee that a real-valued symmetric tensor is diagonalizable. Therefore, one generally approaches the problem as an approximate tensor diagonalization (ATD) problem. In this talk, we show that Jacobi-type methods for ATD that naturally extend the Jacobi...
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