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Wheeled props in algebra, geometry and quantization [PDF]
, 2010 These are expanded notes of author's talk at the ECM 2008 attempting to give an elementary introduction into the main ideas of the theory of wheeled props for beginners, and also a survey of its most recent major applications (ranging from algebra and ...
Merkulov, S. A.
core +1 more source
Quantum gravity observables: observation, algebras, and mathematical structure*
Journal of Physics A: Mathematical and TheoreticalAbstract The questions of describing observables and observation in quantum gravity appear to be centrally important to its physics. A relational approach holds significant promise, and a classification of different types of relational observables (gravitationally dressed, field relational, and more general) is outlined.
openaire +2 more sources
Local equivalence and refinements of Rasmussen's s‐invariant
Journal of Topology, Volume 19, Issue 1, March 2026.Abstract Inspired by the notions of local equivalence in monopole and Heegaard Floer homology, we introduce a version of local equivalence that combines odd Khovanov homology with equivariant even Khovanov homology into an algebraic package called a local even–odd (LEO) triple.
Nathan M. Dunfield +2 more
wiley +1 more source
Conformal Coordinates for Molecular Geometry: From 3D to 5D
Journal of Computational Chemistry, Volume 47, Issue 4, February 5, 2026.The figure illustrates the conformal representation of ℝ3$$ {\mathbb{R}}^3 $$ in a non‐Euclidean five‐dimensional space ℍ$$ \mathbb{H} $$. Each point x∈ℝ3$$ x\in {\mathbb{R}}^3 $$ is described with two additional vectors, e0$$ {e}_0 $$ and e∞$$ {e}_{\infty } $$, so that Euclidean distances in ℝ3$$ {\mathbb{R}}^3 $$ can be recovered via inner products ...
Jesus Camargo +2 more
wiley +1 more source
Machine Learning Assisted Fluorescent Sensor Array for Sensing Applications
Advanced Sensor Research, Volume 5, Issue 2, February 2026.Chemical analysis is being revolutionized by the combination of the high‐dimensional, multi‐channel signals generated by fluorescent sensor arrays and the powerful data analysis enabled by machine learning. This review covers state‐of‐the‐art studies that use machine learning techniques for the identification and quantification of fluorescent sensor ...
Haobo Guo +2 more
wiley +1 more source
Efficient Dynamics: Reduced‐Order Modeling of the Time‐Dependent Schrödinger Equation
Advanced Physics Research, Volume 5, Issue 2, February 2026.Reduced‐order modeling (ROM) approaches for the time‐dependent Schrödinger equation are investigated, highlighting their ability to simulate quantum dynamics efficiently. Proper Orthogonal Decomposition, Dynamic Mode Decomposition, and Reduced Basis Methods are compared across canonical systems and extended to higher dimensions.
Kolade M. Owolabi
wiley +1 more source
Sharp commutator estimates of all order for Coulomb and Riesz modulated energies
Communications on Pure and Applied Mathematics, Volume 79, Issue 2, Page 207-292, February 2026.Abstract We prove functional inequalities in any dimension controlling the iterated derivatives along a transport of the Coulomb or super‐Coulomb Riesz modulated energy in terms of the modulated energy itself. This modulated energy was introduced by the second author and collaborators in the study of mean‐field limits and statistical mechanics of ...
Matthew Rosenzweig, Sylvia Serfaty
wiley +1 more source
Spectral Parameter Power Series Representation for Regular Solutions of the Radial Dirac System
Mathematical Methods in the Applied Sciences, Volume 49, Issue 3, Page 2098-2113, February 2026.ABSTRACT A spectral parameter power series (SPPS) representation for the regular solution of the radial Dirac system with complex coefficients is obtained, as well as a SPPS representation for the (entire) characteristic function of the corresponding spectral problem on a finite interval. Based on the SPPS representation, a numerical method for solving
Emmanuel Roque, Sergii M. Torba
wiley +1 more source
Definition and Computation of Tensor‐Based Generalized Function Composition
Numerical Linear Algebra with Applications, Volume 33, Issue 1, February 2026.ABSTRACT Functions are fundamental to mathematics as they offer a structured and analytical framework to express relations between variables. While scalar and matrix‐based functions are well‐established, higher‐order tensor‐based functions have not been as extensively explored.
Remy Boyer
wiley +1 more source
Analyzing the Free States of one Quantum Resource Theory as Resource States of Another
Advanced Quantum Technologies, Volume 9, Issue 2, February 2026.The article investigates how free states in one quantum resource theory can become highly resourceful in another. It systematically studies multipartite entanglement, fermionic non‐Gaussianity, imaginarity, realness, spin coherence, Clifford non‐stabilizerness, Sn‐equivariance, and non‐uniform entanglement, combining rigorous analytical tools and ...
Andrew E. Deneris +5 more
wiley +1 more source