Results 31 to 40 of about 690 (213)
Advanced Intelligent Discovery, EarlyView.This article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Yiming Ren, Guo‐Wei Wei
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Weighted Hardy spaces: shift invariant and coinvariant subspaces, linear systems and operator model theory [PDF]
Acta Scientiarum Mathematicarum, 2013 The Sz.-Nagy--Foias model theory for $C_{\cdot 0}$ contraction operators combined with the Beurling-Lax theorem establishes a correspondence between any two of four kinds of objects: shift-invariant subspaces, operator-valued inner functions, conservative discrete-time input/state/output linear systems, and $C_{\cdot 0}$ Hilbert-space contraction ...
Ball, Joseph A., Bolotnikov, Vladimir
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Advanced Intelligent Discovery, EarlyView.This article outlines how artificial intelligence could reshape the design of next‐generation transistors as traditional scaling reaches its limits. It discusses emerging roles of machine learning across materials selection, device modeling, and fabrication processes, and highlights hierarchical reinforcement learning as a promising framework for ...
Shoubhanik Nath +4 more
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Robust Representation Learning for Clean Feature Discovery in Incomplete Multi‐View Clustering
Advanced Intelligent Systems, EarlyView.Robust feature discovery in incomplete multi‐view clustering is achieved by coupling RPCA‐based clean representation recovery with neural‐network‐assisted graph learning. The resulting RIMVC framework constructs cleaner and more discriminative graph‐structured representations from incomplete and noisy multi‐view data, improving clustering robustness ...
Ping Hu +4 more
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A Language‐Guided Multimodal Foundation Model for Zero‐Shot and Multi‐Task Brain Signal Analysis
Advanced Intelligent Systems, EarlyView.METIS aligns brain signals with natural‐language instructions to enable zero‐shot and multi‐task brain signal analysis. Pretrained on over 70 000 h of EEG and iEEG recordings, it generalizes across sleep stage classification, epilepsy detection, and neurological disorder diagnosis, providing a scalable foundation model for clinically meaningful brain ...
Mingzhi Chen +3 more
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On structural controllability in complex networks with periodic switching topologies
Asian Journal of Control, EarlyView.Abstract This paper investigates the structural controllability of complex networks with periodic switching topologies. First, several graph transformations that preserve structural controllability are demonstrated. Based on the n‐walk theory, a criterion is derived that determines structural controllability by analyzing only the joint graph within a ...
Jingrui Hou +3 more
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On linear operators with an invariant subspace of functions
, 2004 6 pages, LaTeX, discussion extended, reference ...
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Finite-dimensional invariant subspaces for measurable semigroups of linear operators
Journal of Mathematical Analysis and Applications, 1987 The authors show that on a measurable semigroup S, if the space of weakly left uniformly measurable functions on S (denoted by WLUM(S)) has a left invariant mean, then S satisfies F(n) for every \(n=1,2,...\), where F(n) is the following property: Let E be a separated locally convex space, let T:S\(\times E\to E\) be a weakly measurable action of S on ...
Lau, Anthony T.M, Wong, James C.S
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Machine Learning Paradigm for Advanced Battery Electrolyte Development
Carbon Energy, EarlyView.Electrolyte materials determine ion transport kinetics within the bulk and interphases, ultimately influencing the performance of battery systems. As data‐driven paradigms increasingly reshape materials discovery, this review provides an application‐oriented exploration of the intersection between machine learning and electrolyte science. By evaluating
Chang Su +4 more
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Stochastic Gradient Descent in High Dimensions for Multi‐Spiked Tensor PCA
Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT We study the high‐dimensional dynamics of online stochastic gradient descent (SGD) for the multi‐spiked tensor model. This multi‐index model arises from the tensor principal component analysis (PCA) problem with multiple spikes, where the goal is to estimate the unknown signal vectors within the N$N$‐dimensional unit sphere through maximum ...
Gérard Ben Arous +2 more
wiley +1 more source