20 papers · ranked by Valyu relevance
Ren-Cang Li, Li Wang, Mei Yang
This paper is concerned with Partial Tensor Block-Diagonalization of a multiway tensor by orthonormal matrices so that the extracted block-diagonal part optimally represents the tensor. The basic idea is to maximize the block-diagonal part via the tensor's mode-multiplications by orthonormal matrices. For that reason…
Chen, Han, Sitan Chen, Anru R. Zhang
We present the first deterministic, finite-step algorithm for exact tensor ring (TR) decomposition, addressing an open question about the existence of such procedures. Our method leverages blockwise simultaneous diagonalization to recover TR-cores from a limited number of tensor observations, providing both algebraic…
Merris, Matthew D., Andersen, Tim
—In the evolving domains of Machine Learning and Data Analytics, existing dataset characterization methods such as statistical, structural, and model-based analyses often fail to deliver the deep understanding and insights essential for innovation and explainability. This work surveys the current state-of-the-art…
Michał Ł. Mika, René R. Hiemstra, Dominik Schillinger
We propose a matrix-free inexact preconditioning strategy for elliptic partial differential equations discretized by the isogeometric Galerkin method on tensor-product spline spaces. We base our preconditioner on an approximation of the discrete linear operator by a sum of Kronecker product matrices. The action of its…
Cole Brower, Samuel Rodriguez Bernabeu, Jeff Hammond, John Gunnels + 4 more
Network State Methods Adapted for NVIDIA Blackwell Technology via Emulated FP64 Arithmetic Authors: Cole Brower, Samuel Rodriguez Bernabeu, Jeff Hammond, John Gunnels, Sotiris S. Xantheas, Martin Ganahl, Andor Menczer, Örs Legeza We report cutting-edge performance results via mixed-precision spin-adapted ab initio…
Saritha Kodikara, Brendan Lu, Shuhe Wang, Kim-Anh Lê Cao
Multi-omics studies capture comprehensive molecular profiles across biological layers to understand complex biological processes. A central challenge is integrating information across heterogeneous data types to identify coordinated molecular responses, particularly when measurements are collected longitudinally.…
SeungJoo Lee, Yong-Chan Park, U. Kang, George Vousden
How can we accurately decompose a temporal irregular tensor along while incorporating a related knowledge graph tensor in both offline and online streaming settings? PARAFAC2 decomposition is widely applied to the analysis of irregular tensors consisting of matrices with varying row sizes. In both offline and online…
Balázs Erdős, Christos Chatzis, Jonathan Thorsen, Jakob Stokholm + 3 more
Longitudinal microbiome studies provide critical insights into microbial community dynamics and their relation to host health. Tensor decompositions offer a powerful framework for the unsupervised analysis of such data, yielding interpretable low-dimensional temporal patterns. However, existing approaches based on the…
Xiaoge Zhang, Zhengyu Fang, Kaiyu Tang, Huiyuan Chen + 1 more
Targeted drug therapies offer a promising approach for treating complex diseases, with combinational drug therapies often employed to enhance therapeutic efficacy. However, unintended drug-drug interactions may undermine treatment outcomes or cause adverse side effects. In this work, we propose a novel joint learning…
Benjamin Lieser, Georgy Belousov, Johannes Söding
Background Most popular tools for reconstructing phylogenetic trees from multiple sequence alignments use a model of molecular evolution in which a single substitution matrix or a small set of fixed matrices are shared between all columns. Models with column-specific rate matrices can in principle be fit by automatic…
Alberto Maspero, Federico Murgante
We consider the problem of transfer of energy to high frequencies in a quasilinear Schrödinger equation with sublinear dispersion, on the one dimensional torus. We exhibit initial data undergoing finite but arbitrary large Sobolev norm explosion: their initial norm is arbitrary small in Sobolev spaces of high…
Renaud Vilmart
Tensor trains (or Matrix-Product States) are a data structure used in many fields of computer science and physics. They were recently shown to generalise binary decision diagrams when used over the 2-element Galois field, prompting the question of their reducibility in such a context, when the standard approach, over…
Authors not listed
Most advances in electronic spin-dependent non-adiabatic dynamics focus on refining the underlying dynamics methods. In contrast, this work considers an improved description of spin-orbit coupling by explicitly accounting for its relativistic origins. To this end, we extend a standard one-electron triatomic…
Dionysia Kaziki, Andreas K. Engel, Guido Nolte
Cross-bispectral measures provide a rich description of interactions in EEG signals, but their third-order tensor structure poses substantial challenges for interpretation and dimensionality reduction. We introduce a low-rank tensor decomposition framework specifically designed for cross-bispectral EEG data. The model…
Beheshteh T. Rakhshan, Guillaume Rabusseau
High-dimensional data arise naturally in many areas of science and engineering, including machine learning, signal processing, computational physics, and statistics. Such data are often represented as tensors, multi-dimensional generalizations of matrices. While tensors provide a natural representation for multi-modal…
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We present a comprehensive theoretical analysis of quantum subspace diagonalization methods for molecular electronic structure calculations, establishing rigorous complexity bounds and convergence guarantees. Building on recent developments in adaptive quantum algorithms for chemical systems, we formulate a general…
Karan Ahmadzadeh, Robert Zaleśny, Xin Li, Zilvinas Rinkevicius + 2 more
Aggregation on Dynamic Third-Order Nonlinear Optical Responses: Oligo(thiophene-benzothiadiazole) as a Case Study Authors: Karan Ahmadzadeh, Robert Zaleśny, Xin Li, Zilvinas Rinkevicius, Wei Hu, Patrick Norman Nonlinear optical properties of molecular materials are governed by aggregation and cooperative effects in the…
Authors not listed
In this work, we implement a local-pair natural orbital based coupled-cluster method through the full treatment of quadruple excitations (CCSDTQ). The domain-based local pair natural orbital (DLPNO) approach, which has successfully been applied to lower levels of coupled-cluster theory, is utilized in our algorithm…
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This work presents the implementation of the linear response function for 1D periodic systems at coupled cluster with single and double excitations with periodic boundary conditions level (LR-CCSD-PBC) for the calculation of the frequency-dependent electric dipole-electric dipole polarizability tensor…
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Nonadiabatic effects arising from conical intersections between excited states play a crucial role in the optical properties of a wide range of chromophores and have to be accounted for in first-principles modeling of spectral lineshapes. In this work, we investigate the importance of nonadiabatic effects in the…