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International audience; Pyrene fluorescence after a high-energy electronic excitation exhibits a prominent band shoulder not present after excitation at low energies. The standard assignment of this shoulder as a non-Kasha emission from the second-excited state (S2 ) has been recently questioned. To elucidate this issue, we simulated the fluorescence of pyrene using two different theoretical approaches based on the vertical convolution and nonadiabatic dynamics with nuclear ensemble approaches. To conduct the necessary nonadiabatic dynamics simulations with high-lying electronic states and deal with fluorescence timescales of about 100 ns of this large molecule, we developed new computational protocols. The results from both approaches confirm that the band shoulder is, in fact, due to S2 emission. We show that the non-Kasha behavior is a dynamic-equilibrium effect, not caused by a metastable S2 minimum. However, it requires considerable vibrational energy, which can only be achieved in collisionless regimes after transitions into highly excited states. This strict condition explains why the S2 emission was not observed in some experiments.

Nonadiabatic dynamics simulations in the long timescale (much longer than 10 ps) are the next challenge in computational photochemistry. This paper delimits the scope of what we expect from methods to run such simulations: they should work in full nuclear dimensionality, be general enough to tackle any type of molecule, and not require unrealistic computational resources. We examine the main methodological challenges we should venture to advance the field, including the computational costs of the electronic structure calculations, stability of the integration methods, accuracy of the nonadiabatic dynamics algorithms and software optimization. Based on simulations designed to shed light on each of these issues, we show how machine learning may be a crucial element for long time-scale dynamics, either as a surrogate for electronic structure calculations or aiding the parameterization of model Hamiltonians. We show that conventional methods for integrating classical equations should be adequate to extended simulations up to 1 ns and that surface hopping agrees semi-quantitatively with wave packet propagation in the weak-coupling regime. We also describe our optimization of the Newton-X program to reduce computational overheads in data processing and storage.This article is part of the theme issue ���Chemistry without the Born���Oppenheimer approximation���.

Given uniformly homeomorphic metric spaces $X$ and $Y$, it is proved that the hyperspaces $C(X)$ and $C(Y)$ are uniformly homeomorphic, where $C(X)$ denotes the collection of all nonempty closed subsets of $X$, and is endowed with Hausdorff distance. Gerald Beer has proved that the hyperspace $C(X)$ is Atsuji when $X$ is either compact or uniformly discrete. An Atsuji space is a generalization of compact metric spaces as well as of uniformly discrete spaces. In this article, we investigate the space $C(X)$ when $X$ is Atsuji, and a class of Atsuji subspaces of $C(X)$ is obtained. Using the obtained results, some fixed point results for continuous maps on Atsuji spaces are obtained., Comment: 9

Most knowledge graph use cases are data-centric, focusing on representing data entities and their semantic relationships. There are no published success stories to represent large-scale complicated business logic with knowledge graph technologies. In this paper, we will share our innovative and practical approach to representing complicated U.S. and Canadian income tax compliance logic (calculations and rules) via a large-scale knowledge graph. We will cover how the Tax Knowledge Graph is constructed and automated, how it is used to calculate tax refunds, reasoned to find missing info, and navigated to explain the calculated results. The Tax Knowledge Graph has helped transform Intuit's flagship TurboTax product into a smart and personalized experience, accelerating and automating the tax preparation process while instilling confidence for millions of customers., Comment: KDD2020 International Workshop on Knowledge Graph: Mining Knowledge Graph for Deep Insights. See: https://suitclub.ischool.utexas.edu/IWKG_KDD2020/index.html. 6 pages, 9 figures

Shimizu and Takahashi have shown that every decreasing sequence of nonempty, bounded, closed, convex subsets of a complete, uniformly Takahashi convex metric space has nonempty intersection. It is well known that the Menger convexity is a generalization of the Takahashi convexity. In this article, we acquire a nonempty intersection property, in terms of the Hausdorff metric, for Menger convex metric spaces, that also provides a class of reflexive Menger convex spaces. We apply this result to discuss the fixed point results for generalized hybrid mappings defined on Menger convex spaces., Comment: 17 pages

The classical Cantor's intersection theorem states that in a complete metric space $X$, intersection of every decreasing sequence of nonempty closed bounded subsets, with diameter approaches zero, has exactly one point. In this article, we deal with decreasing sequences $\{K_n\}$ of nonempty closed bounded subsets of a metric space $X$, for which the Hausdorff distance $H(K_n, K_{n+1})$ tends to $0$, as well as for which the excess of $K_n$ over $X\setminus K_n$ tends to $0$. We achieve nonempty intersection properties in metric spaces. The obtained results also provide partial generalizations of Cantor's theorem., Comment: 9 pages

K-fusion frames are generalizations of fusion frames in frame theory. This article characterizes various kinds of property of K-fusion frames. Several perturbation results on K-fusion frames are formulated and analyzed., Comment: 11 pages