Optimal Transport Distances to Characterize Electronic Excitations

Understanding the character of electronic excitations is important in computational and reaction mechanistic studies, but their classification from simulations remains an open problem. Distances based on optimal transport have proven very useful in a plethora of classification problems and, therefore, seem a natural tool to try to tackle this challenge. We propose and investigate a new diagnostic Θ based on the Sinkhorn divergence from optimal transport. We evaluate a k-NN classification algorithm on Θ, the popular Λ diagnostic, and their combination, and assess their performance in labeling excitations, finding that (i) the combination only slightly improves the classification, (ii) Rydberg excitations are not separated well in any setting, and (iii) Θ breaks down for charge transfer in small molecules. We then define a length-scale-normalized version of Θ and show that the result correlates closely with Λ for results obtained with Gaussian basis functions. Finally, we discuss the orbital dependence of our approach and explore an orbital-independent version. Using an optimized combination of the optimal transport and overlap diagnostics together with a different metric is in our opinion the most promising for future classification studies

Spin Resolution of the Electron-Gas Correlation Energy: Positive same-spin contribution

The negative correlation energy per particle of a uniform electron gas of density parameter $r_s$ and spin polarization $\zeta$ is well known, but its spin resolution into up-down, up-up, and down-down contributions is not. Widely-used estimates are incorrect, and hamper the development of reliable density functionals and pair distribution functions. For the spin resolution, we present interpolations between high- and low-density limits that agree with available Quantum Monte Carlo data. In the low-density limit for $\zeta = 0$, we find that the same-spin correlation energy is unexpectedly positive, and we explain why. We also estimate the up and down contributions to the kinetic energy of correlation.Comment: new version, to appear in PRB Rapid Communicatio

Optimal transport distances to characterise electronic excitations

Understanding the character of electronic excitations is important in computational and mechanistic studies, but their classification from numerical simulations remains an open problem despite significant progress in density-based and exciton wavefunction-based descriptors. We propose and investigate a new diagnostic based on the Sinkhorn divergence from optimal transport, which is highly sensitive to translations and hence promising for the identification of charge transfer excitations. In spite of this, we show through numerical simulations on a representative set of molecules that the new diagnostic is not able to separate charge transfer from Rydberg excitations in practice, which can be explained by its inability to distinguish between translational and diffusive processes. We trained a $k$-NN classification algorithm on the optimal transport diagonistic, the popular $\Lambda$ diagnostic as well as their combination, and assessed its performance in labelling excitations, finding that (i) The combination improves the classification, (ii) Rydberg excitations are not separated well in any setting, suggesting that key information on the diffusivity of the excited state is missing and (iii) the optimal transport diagnostic breaks down for charge transfer in small molecules.Comment: 6 pages, 4 figure

Evaluation of uncertainties in regional climate change simulations

We have run two regional climate models (RCMs) forced by three sets of initial and boundary conditions to form a 2×3 suite of 10-year climate simulations for the continental United States at approximately 50 km horizontal resolution. The three sets of driving boundary conditions are a reanalysis, an atmosphere-ocean coupled general circulation model (GCM) current climate, and a future scenario of transient climate change. Common precipitation climatology features simulated by both models included realistic orographic precipitation, east-west transcontinental gradients, and reasonable annual cycles over different geographic locations. However, both models missed heavy cool-season precipitation in the lower Mississippi River basin, a seemingly common model defect. Various simulation biases (differences) produced by the RCMs are evaluated based on the 2×3 experiment set in addition to comparisons with the GCM simulation. The RCM performance bias is smallest, whereas the GCM-RCM downscaling bias (difference between GCM and RCM) is largest. The boundary forcing bias (difference between GCM current climate driven run and reanalysis-driven run) and intermodel bias are both largest in summer, possibly due to different subgrid scale processes in individual models. The ratio of climate change to biases, which we use as one measure of confidence in projected climate changes, is substantially larger than 1 in several seasons and regions while the ratios are always less than 1 in summer. The largest ratios among all regions are in California. Spatial correlation coefficients of precipitation were computed between simulation pairs in the 2×3 set. The climate change correlation is highest and the RCM performance correlation is lowest while boundary forcing and intermodel correlations are intermediate. The high spatial correlation for climate change suggests that even though future precipitation is projected to increase, its overall continental-scale spatial pattern is expected to remain relatively constant. The low RCM performance correlation shows a modeling challenge to reproduce observed spatial precipitation patterns

A Spectral Bernstein Theorem

We study the spectrum of the Laplace operator of a complete minimal properly immersed hypersurface $M$ in $\R^{n+1}$. (1) Under a volume growth condition on extrinsic balls and a condition on the unit normal at infinity, we prove that $M$ has only essential spectrum consisting of the half line $[0, +\infty)$. This is the case when $\lim_{\tilde{r}\to +\infty}\tilde{r}\kappa_i=0$, where $\tilde{r}$ is the extrinsic distance to a point of $M$ and $\kappa_i$ are the principal curvatures. (2) If the $\kappa_i$ satisfy the decay conditions $|\kappa_i|\leq 1/\tilde{r}$, and strict inequality is achieved at some point $y\in M$, then there are no eigenvalues. We apply these results to minimal graphic and multigraphic hypersurfaces.Comment: 16 pages. v2. Final version: minor revisions, we add Proposition 3.2. Accepted for publication in the Annali di Matematica Pura ed Applicata, on the 05/03/201

post hoc analysis of the effect of baseline characteristics on treatment duration in patients with metastatic castration resistant prostate cancer mcrpc receiving cabazitaxel in the compassionate use cup expanded access programs eap and capristana registry

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Global regularity of weak solutions to quasilinear elliptic and parabolic equations with controlled growth

We establish global regularity for weak solutions to quasilinear divergence form elliptic and parabolic equations over Lipschitz domains with controlled growth conditions on low order terms. The leading coefficients belong to the class of BMO functions with small mean oscillations with respect to $x$.Comment: 24 pages, to be submitte