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Koopmans-compliant (KC) functionals have been shown to provide accurate spectral properties through a generalized condition of piecewise linearity of the total energy as a function of the fractional addition/removal of an electron to/from any orbital. We a ...
Federated learning is a useful framework for centralized learning from distributed data under practical considerations of heterogeneity, asynchrony, and privacy. Federated architectures are frequently deployed in deep learning settings, which generally giv ...
In this note we prove an explicit formula for the lower semicontinuous envelope of some functionals defined on real polyhedral chains. More precisely, denoting by H:R→[0,∞) an even, subadditive, and lower semicontinuous function with H(0)=0, and by ΦH the ...
We present new results concerning the approximation of the total variation, ∫Ω∣∇u∣, of a function u by non-local, non-convex functionals of the form $$ \Lambda_\delta u = \int_{\Omega} \int_{\Omega} \frac{\delta \varphi \big( |u(x) - ...
Small-molecule binding in metal-organic frameworks (MOFs) can be accurately studied both experimentally and computationally, provided the proper tools are employed. Herein, we compare and contrast properties associated with guest binding by means of densit ...
We prove that a general condition introduced by Colombo and Gobbino to study limits of curves of maximal slope allows us to characterize also minimizing movements along a sequence of functionals as curves of maximal slope of a limit functional. ...
In empirical risk optimization, it has been observed that stochastic gradient implementations that rely on random reshuffling of the data achieve better performance than implementations that rely on sampling the data uniformly. Recent works have pursued ju ...
We prove sharp regularity results for a general class of functionals of the type w↦∫F(x,w,Dw)dx,featuring non-standard growth conditions and non-uniform ellipticity properties. The model case is given by the double phase integral w↦∫b(x,w)(|Dw|p+a(x)|Dw|q) ...
We present new results concerning the approximation of the total variation, integral(Omega)vertical bar del u vertical bar, of a function u by non-local, non-convex functionals of the form Lambda delta(u) = integral(Omega)integral(Omega)delta phi(vertical ...
The strong growth condition (SGC) is known to be a sufficient condition for linear convergence of the stochastic gradient method using a constant step-size γ (SGM-CS). In this paper, we provide a necessary condition, for the linear convergence of SGM-CS, t ...
