相关论文: A canonical transformation theory from extended no…
Based on a recent paper by Rothe and Sch\"afer on compact binary systems, explicit expressions for canonical center and relative coordinates in terms of standard canonical coordinates are derived for spinless objects up to second…
It is a long-standing challenge to accurately and efficiently compute thermodynamic quantities of many-body systems at thermal equilibrium. The conventional methods, e.g., Markov chain Monte Carlo, require many steps to equilibrate. The…
Lithium is a typical quantum solid, characterized by cubic structures at ambient pressure. As the pressure increases, it forms more complex structures and undergoes a metal-to-semiconductor transformation, complicating theoretical and…
The process industry's high expectations for Digital Twins require modeling approaches that can generalize across tasks and diverse domains with potentially different data dimensions and distributional shifts i.e., Foundational Models.…
Over recent years, a lot of progress has been achieved in understanding of the relationship between localization and transport of energy in essentially nonlinear oscillatory systems. In this paper we are going to demonstrate that the…
For multiple multivariate data sets, we derive conditions under which Generalized Canonical Correlation Analysis (GCCA) improves classification performance of the projected datasets, compared to standard Canonical Correlation Analysis (CCA)…
As pointed out by Linus Pauling in his classic work on the relationship between crystal packing and ionic radius ratio, a difference in atomic size can be accommodated more readily by an ordered structure than by a disordered one. Because…
This paper revisits the well-studied fixed point problem from a unified viewpoint of mathematical modeling and canonical duality theory, i.e. the original problem is first reformulated as a nonconvex optimization problem, its well-posedness…
Canonical correlation analysis (CCA) is a technique for measuring the association between two multivariate data matrices. A regularized modification of canonical correlation analysis (RCCA) which imposes an $\ell_2$ penalty on the CCA…
The behavior of polyatomic molecules around their equilibrium positions can be regarded as quantum coupled anharmonic oscillators. Solving the corresponding Schr\"odinger equations can interpret or predict experimental spectra of molecules.…
We initiate a holographic study of coupling-dependent heavy ion collisions by analysing for the first time the effects of leading-order, inverse coupling constant corrections. In the dual description, this amounts to colliding gravitational…
We present Deep Generalized Canonical Correlation Analysis (DGCCA) -- a method for learning nonlinear transformations of arbitrarily many views of data, such that the resulting transformations are maximally informative of each other. While…
The chemical ordering transition in a binary alloy is examined using classical density functional theory for a binary mixture. The ordered lattice is assumed to be obtained from the disordered lattice by a volume change only, as in L1_2…
Concurrent multiscale methods play an important role in modeling and simulating materials with defects, aiming to achieve the balance between accuracy and efficiency. Atomistic-to-continuum (a/c) coupling methods, a typical class of…
We extend the notion of canonical ordering (initially developed for planar triangulations and 3-connected planar maps) to cylindric (essentially simple) triangulations and more generally to cylindric (essentially internally) $3$-connected…
The past years have seen the success of a novel multiscale energetic formalism in a variety of ocean and engineering fluid applications. In a self-contained way, this study introduces it to the atmospheric dynamical diagnostics, with…
Continuous normalizing flows are known to be highly expressive and flexible, which allows for easier incorporation of large symmetries and makes them a powerful computational tool for lattice field theories. Building on previous work, we…
The technological performances of metallic compounds are largely influenced by atomic ordering. Although there is a general consensus that successful theories of metallic systems should account for the quantum nature of the electronic glue,…
The offset linear canonical transform encompassing the numerous integral transforms, is a promising tool for analyzing non-stationary signals with more degrees of freedom. In this paper, we generalize the windowed offset linear canonical…
Canonical transformations are ubiquitous in Hamiltonian mechanics, since they not only describe the fundamental invariance of the theory under phase-space reparameterisations, but also generate the dynamics of the system. In the first part…