Results 11 to 20 of about 104,383 (159)
Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real-World Data. [PDF]
Adv Intell DiscovThis 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 ...
Ren Y, Wei GW.
europepmc +2 more sources
Common subbundles and intersections of divisors
, 2002 Let V_0 and V_1 be complex vector bundles over a space X. We use the theory of divisors on formal groups to give obstructions in generalised cohomology that vanish when V_0 and V_1 can be embedded in a bundle U in such a way that V_0\cap V_1 has ...
Crabb +6 more
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Singularities and Semistable Degenerations for Symplectic Topology [PDF]
, 2017 We overview our recent work defining and studying normal crossings varieties and subvarieties in symplectic topology. This work answers a question of Gromov on the feasibility of introducing singular (sub)varieties into symplectic topology in the case of
McLean, Mark +2 more
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AI in chemical engineering: From promise to practice
AIChE Journal, EarlyView.Abstract Artificial intelligence (AI) in chemical engineering has moved from promise to practice: physics‐aware (gray‐box) models are gaining traction, reinforcement learning complements model predictive control (MPC), and generative AI powers documentation, digitization, and safety workflows.
Jia Wei Chew +4 more
wiley +1 more source
Global Topological Dirac Synchronization
Journal of Physics: ComplexitySynchronization is a fundamental dynamical state of interacting oscillators, observed, e.g., in natural biological rhythms and in the brain. Global synchronization which occurs when non-linear or chaotic oscillators placed on the nodes of a network ...
Timoteo Carletti +3 more
doaj +1 more source
Embedding, compression and fiberwise homotopy theory
, 2002 Given Poincare spaces M and X, we study the possibility of compressing embeddings of M x I in X x I down to embeddings of M in X. This results in a new approach to embedding in the metastable range both in the smooth and Poincare duality categories ...
Browder +12 more
core +3 more sources
Revealing Protein–Protein Interactions Using a Graph Theory‐Augmented Deep Learning Approach
Advanced Intelligent Discovery, EarlyView.This study presents a fast, cost‐efficient approach for classifying protein–protein interactions by integrating graph‐theory parametrization with deep learning (DL). Multiscale features extracted from graph‐encoded polarized‐light microscopy (PLM) images enable accurate prediction of binding strengths.
Bahar Dadfar +5 more
wiley +1 more source
, 2005 We prove two kinds of fibering theorems for maps X --> P, where X and P are Poincare spaces. The special case of P = S^1 yields a Poincare duality analogue of the fibering theorem of Browder and Levine.Comment: Published by Algebraic and Geometric ...
John R Klein, Klein, Wall
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Invariant Measure and Universality of the 2D Yang–Mills Langevin Dynamic
Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT We prove that the Yang–Mills (YM) measure for the trivial principal bundle over the two‐dimensional torus, with any connected, compact structure group, is invariant for the associated renormalised Langevin dynamic. Our argument relies on a combination of regularity structures, lattice gauge‐fixing and Bourgain's method for invariant measures ...
Ilya Chevyrev, Hao Shen
wiley +1 more source
How (not) to Cage an Electron: The Perfluoro Cage Effect as an Extrinsic Molecular Property
Helvetica Chimica Acta, EarlyView.A rigorous definition within Kohn–Sham density functional theory is presented for the notion of an caged electron inside perfluorinated fullerenes as radical anions. ABSTRACT The notion of a (molecular) electron cage was coined for the unique hosting capacity of perfluorocubane, suggesting the “encapsulation of an electron” within the highly symmetric ...
Andreas Riedmiller +2 more
wiley +1 more source