Gravitational Entropy in Cosmological Models

We discuss whether an appropriately defined dimensionless scalar function might be an acceptable candidate for the gravitational entropy, by explicitly considering Szekeres and Bianchi type VI _h models that admit an isotropic singularity. We also briefly discuss other possible gravitational entropy functions, including an appropriate measure of the velocity dependent Bel-Robinson tensor. PACS: 04.20.-q 95.30.Sf 98.80.Jk     

Inhomogeneous Cosmologies, the Copernican Principle and the Cosmic Microwave Background: More on the EGS Theorem

We discuss inhomogeneous cosmological models which satisfy the Copernican principle. We construct some inhomogeneous cosmological models starting from the ansatz that the all the observers in the models view an isotropic cosmic microwave background. We discuss multi-fluid models, and illustrate how more general inhomogeneous models may be derived, both in General Relativity and in scalar-tensor theories of gravity. Thus we illustrate that the cosmologicalprinciple, the assumption that the Universe we live in is spatially homogeneous, does not necessarily follow from the Copernican principle and the high isotropy of the cosmic microwave background. We also present some new conformally flat two-fluid solutions of Einstein's field equations.     

Evaluating and clustering retrosynthesis pathways with learned strategy

With recent advances in the computer-aided synthesis planning (CASP) powered by data science and machine learning, modern CASP programs can rapidly identify thousands of potential pathways for a given target molecule. However, the lack of a holistic pathway evaluation mechanism makes it challenging to systematically prioritize strategic pathways except for using some simple heuristics. Herein, we introduce a data-driven approach to evaluate the relative strategic levels of retrosynthesis pathways using a dynamic tree-structured long short-term memory (tree-LSTM) model. We first curated a retrosynthesis pathway database, containing 238k patent-extracted pathways along with ∼55 M artificial pathways generated from an open-source CASP program, ASKCOS. The tree-LSTM model was trained to differentiate patent-extracted and artificial pathways with the same target molecule in order to learn the strategic relationship among single-step reactions within the patent-extracted pathways. The model achieved a top-1 ranking accuracy of 79.1% to recognize patent-extracted pathways. In addition, the trained tree-LSTM model learned to encode pathway-level information into a representative latent vector, which can facilitate clustering similar pathways to help illustrate strategically diverse pathways generated from CASP programs.

Tree-structured long short-term memory neural model learns to understand the retrosynthesis design strategies from patent-extracted retrosynthetic pathway data.     

Fluid spacetimes admitting covariantly constant vectors and tensors

Spacetimes admitting a covariantly constant vector and satisfying the Einstein field equations for a perfect fluid, a viscous heat-conducting fluid, or an anisotropic fluid are studied. It is found that the only possible perfect fluid spacetimes are the Einstein static universe and stiff-matter spacetimes with an isolated spatial co-ordinate, while the possible viscous fluid and anisotropic fluid spacetimes, although more abundant than their perfect fluid counterparts, must satisfy a number of strong restrictions. Examples illustrating most of the various possible situations are given. The paper concludes with a study of covariantly constant second-rank tensors in fluid spacetimes; the only possible solutions that do not also admit a covariantly constant vector are restricted to 2+2 spacetimes.