Severe intensity inhomogeneity (InH) and complex real-world textures cause great difficulties and become two important issues in image segmentation and object extraction applications. Plenty of methods are proposed to...
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The deep linear network (DLN) is a model for implicit regularization in gradient based optimization of overparametrized learning architectures. Training the DLN corresponds to a Riemannian gradient flow, where the Rie...
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Fractional and tempered fractional partial differential equations (PDEs) are effective models of long-range interactions, anomalous diffusion, and non-local effects. Traditional numerical methods for these problems ar...
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We introduce an innovative approach for solving high-dimensional Fokker-Planck-Lévy (FPL) equations in modeling non-Brownian processes across disciplines such as physics, finance, and ecology. We utilize a fracti...
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Multiobjective simulation optimization (MOSO) problems are optimization problems with multiple conflicting objectives, where evaluation of at least one of the objectives depends on a black-box numerical code or real-w...
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We consider the problem of Bayesian inference for bi-variate data observed in time but with observation times which occur non-synchronously. In particular, this occurs in a wide variety of applications in finance, suc...
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When implementing Markov Chain Monte Carlo (MCMC) algorithms, perturbation caused by numerical errors is sometimes inevitable. This paper studies how perturbation of MCMC affects the convergence speed and Monte Carlo ...
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We consider the long time behavior of Wong-Zakai approximations of stochastic differential equations. These piecewise smooth diffusion approximations are of great importance in many areas, such as those with ordinary ...
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Instrumental variables (IV) are a commonly used tool to estimate causal effects from nonrandomized data. An archetype of an IV is a randomized trial with non-compliance where the randomized treatment assignment serves...
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This paper presents theoretical and experimental studies on the superconductivity of Pb0.64Bi0.36 alloy, which is a prototype of strongly coupled superconductors and exhibits one of the strongest coupling under ambien...
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This paper presents theoretical and experimental studies on the superconductivity of Pb0.64Bi0.36 alloy, which is a prototype of strongly coupled superconductors and exhibits one of the strongest coupling under ambient pressure among the materials studied so far. The critical temperature, the specific heat in the superconducting state, and the magnetic critical fields are experimentally determined. Deviations from the single-gap s-wave BCS-like behavior are observed. The electronic structure, phonons, and electron-phonon interactions are analyzed in relation to the metallic Pb, explaining why the Pb-Bi alloy exhibits such a large value of the electron-phonon coupling parameter λ≃2. Superconductivity is studied using the isotropic Eliashberg formalism as well as the anisotropic density functional theory for superconductors. We find that while Pb is a two-gap superconductor with well-defined separate superconducting gaps, in the Pb-Bi alloy an overlapped three-gap-like structure is formed with a strong anisotropy. Furthermore, the chemical disorder, inherent to this alloy, leads to strong electron scattering, which is found to reduce the critical temperature.
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