Second-order Lovelock Gravity from Entanglement in Conformal Field Theories

Holographic entanglement entropy and the first law of thermodynamics are believed to decode the gravity theory in the bulk. In particular, assuming the Ryu-Takayanagi (RT)\cite{ryu-takayanagi} formula holds for ball-shaped regions on the boundary around CFT vacuum states implies\cite{Nonlinear-Faulkner} a bulk gravity theory equivalent to Einstein gravity through second-order perturbations. In this paper, we show that the same assumptions can also give rise to second-order Lovelock gravity. Specifically, we generalize the procedure in \cite{Nonlinear-Faulkner} to show that the arguments there also hold for Lovelock gravity by proving through second-order perturbation theory, the entropy calculated using the Wald formula\cite{Wald_noether} in Lovelock also obeys an area law (at least up to second order). Since the equations for second-order perturbations of Lovelock gravity are different in general from the second-order perturbation of the Einstein-Hilbert action, our work shows that the holographic area law cannot determine a unique bulk theory even for second-order perturbations assuming only RT on ball-shaped regions. It is anticipated that RT on all subregions is expected to encode the full non-linear Einstein equations on asymptotically AdS spacetimes.Comment: extensive revision on second-order calculation, appendix adde

SciCode: A Research Coding Benchmark Curated by Scientists

Since language models (LMs) now outperform average humans on many challenging tasks, it has become increasingly difficult to develop challenging, high-quality, and realistic evaluations. We address this issue by examining LMs\u27 capabilities to generate code for solving real scientific research problems. Incorporating input from scientists and AI researchers in 16 diverse natural science sub-fields, including mathematics, physics, chemistry, biology, and materials science, we created a scientist-curated coding benchmark, SciCode. The problems in SciCode naturally factorize into multiple subproblems, each involving knowledge recall, reasoning, and code synthesis. In total, SciCode contains 338 subproblems decomposed from 80 challenging main problems. It offers optional descriptions specifying useful scientific background information and scientist-annotated gold-standard solutions and test cases for evaluation. Claude3.5-Sonnet, the best-performing model among those tested, can solve only 4.6% of the problems in the most realistic setting. We believe that SciCode demonstrates both contemporary LMs\u27 progress towards becoming helpful scientific assistants and sheds light on the development and evaluation of scientific AI in the future.25 pages, 9 figures, 7 table

Trisguanidinate Lanthanide Complexes: Syntheses, Structures, and Catalytic Activity for Mild Amidation of Aldehydes with Amines

A series of new trisguanidinate lanthanide complexes including the first THF-solvated trisguanidinate lanthanum complexes were synthesized and fully characterized. The complexes were found to be efficient catalysts for amidation of aldehydes with amines under mild conditions with a wide scope of substrates including pyrrolidine, piperidine, and morpholine, and one of the intermediates for this process, lanthanum amido complex {[(iPrN)CNHiPr(NC6H4p-Cl)]2La(NHC6H5)}2·C7H8, was isolated

Trisguanidinate Lanthanide Complexes: Syntheses, Structures, and Catalytic Activity for Mild Amidation of Aldehydes with Amines

A series of new trisguanidinate lanthanide complexes including the first THF-solvated trisguanidinate lanthanum complexes were synthesized and fully characterized. The complexes were found to be efficient catalysts for amidation of aldehydes with amines under mild conditions with a wide scope of substrates including pyrrolidine, piperidine, and morpholine, and one of the intermediates for this process, lanthanum amido complex {[(iPrN)CNHiPr(NC6H4p-Cl)]2La(NHC6H5)}2·C7H8, was isolated

Trisguanidinate Lanthanide Complexes: Syntheses, Structures, and Catalytic Activity for Mild Amidation of Aldehydes with Amines

A series of new trisguanidinate lanthanide complexes including the first THF-solvated trisguanidinate lanthanum complexes were synthesized and fully characterized. The complexes were found to be efficient catalysts for amidation of aldehydes with amines under mild conditions with a wide scope of substrates including pyrrolidine, piperidine, and morpholine, and one of the intermediates for this process, lanthanum amido complex {[(iPrN)CNHiPr(NC6H4p-Cl)]2La(NHC6H5)}2·C7H8, was isolated