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| http://dx.doi.org/10.1073/pnas.31.12.417 | DOI Listing |
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Learning properties of quantum states without the IID assumption.
Nat Commun
November 2024
Inria, ENS Lyon, UCBL, LIP, Lyon, France.
We develop a framework for learning properties of quantum states beyond the assumption of independent and identically distributed (i.i.d.
View Article and Find Full Text PDFBi-Lipschitz embeddings of the space of unordered -tuples with a partial transportation metric.
Math Ann
March 2024
Division of Computing Science and Mathematics, University of Stirling, Stirling, FK9 4LA UK.
Let be non-empty, open and proper. This paper is concerned with , the space of -integrable Borel measures on equipped with the transportation metric introduced by Figalli and Gigli that allows the creation and destruction of mass on . Alternatively, we show that is isometric to a subset of Borel measures with the ordinary Wasserstein distance, on the one point completion of equipped with the shortcut metric In this article we construct bi-Lipschitz embeddings of the set of unordered -tuples in into Hilbert space.
View Article and Find Full Text PDFStructure of Multi-State Correlation in Electronic Systems.
J Chem Theory Comput
October 2024
Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, Shenzhen 518055, China.
Beyond the Hohenberg-Kohn density functional theory for the ground state, it has been established that the Hamiltonian matrix for a finite number () of lowest eigenstates is a matrix density functional. Its fundamental variable─the matrix density ()─can be represented by, or mapped to, a set of auxiliary, multiconfigurational wave functions expressed as a linear combination of no more than determinant configurations. The latter defines a minimal active space (MAS), which naturally leads to the introduction of the correlation matrix functional, responsible for the electronic correlation effects outside the MAS.
View Article and Find Full Text PDFRobust Recovery of Optimally Smoothed Polymer Relaxation Spectrum from Stress Relaxation Test Measurements.
Polymers (Basel)
August 2024
Department of Technology Fundamentals, Faculty of Production Engineering, University of Life Sciences in Lublin, 20-612 Lublin, Poland.
The relaxation spectrum is a fundamental viscoelastic characteristic from which other material functions used to describe the rheological properties of polymers can be determined. The spectrum is recovered from relaxation stress or oscillatory shear data. Since the problem of the relaxation spectrum identification is ill-posed, in the known methods, different mechanisms are built-in to obtain a smooth enough and noise-robust relaxation spectrum model.
View Article and Find Full Text PDFMartingale solutions and asymptotic behaviors for a stochastic cross-diffusion three-species food chain model with prey-taxis.
Chaos
August 2024
School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, People's Republic of China.
The stochastic food chain model is an important model within the field of ecological research. Since existing models are difficult to describe the influence of cross-diffusion and random factors on the evolution of species populations, this work is concerned with a stochastic cross-diffusion three-species food chain model with prey-taxis, in which the direction of predators' movement is opposite to the gradient of prey, i.e.
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