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With the advent of GRAVITY+, the upgrade to the beam combiner GRAVITY at the Very Large Telescope Interferometer (VLTI), fainter and higher redshift active galactic nuclei (AGNs) are becoming observable, opening an unprecedented opportunity to further our understanding of the cosmic coevolution of supermassive black holes and their host galaxies. To identify an initial sample of high-redshift type 1 AGNs that can be observed with GRAVITY+, we have obtained spectroscopic data with NTT/SOFI of the most promising candidates. Our goal is to measure their broad line region (BLR) fluxes and assess their physical geometries by analysing the spectral profiles of their Balmer lines. We present 29z∼ 2 targets with strong Hαemission in theKband. Their line profiles are strongly non-Gaussian, with a narrow core and broad wings. This can be explained as a combination of rotation and turbulence contributing to the total profile or two physically distinct inner and outer regions. We found small Hαvirial factors, which we attributed to the low full-width-half-maximum (FWHM)/σratios of their non-Gaussian profiles, noting that this can lead to discrepancies in black hole masses derived from scaling relations. We also find two targets that show tentative evidence of BLRs dominated by radial motions. Lastly, we estimated the expected differential phase signals that will be seen with GRAVITY+, which will provide guidance for the observing strategy that will be adopted. 

Abstract Adding synthetic nucleotides to DNA increases the linear information density of DNA molecules. Here we report that it also can increase the diversity of their three-dimensional folds. Specifically, an additional nucleotide (dZ, with a 5-nitro-6-aminopyridone nucleobase), placed at twelve sites in a 23-nucleotides-long DNA strand, creates a fairly stable unimolecular structure (that is, the folded Z-motif, or fZ-motif) that melts at 66.5 °C at pH 8.5. Spectroscopic, gel and two-dimensional NMR analyses show that the folded Z-motif is held together by six reverse skinny dZ⁻:dZ base pairs, analogous to the crystal structure of the free heterocycle. Fluorescence tagging shows that the dZ⁻:dZ pairs join parallel strands in a four-stranded compact down–up–down–up fold. These have two possible structures: one with intercalated dZ⁻:dZ base pairs, the second without intercalation. The intercalated structure would resemble the i-motif formed by dC:dC⁺-reversed pairing at pH ≤ 6.5. This fZ-motif may therefore help DNA form compact structures needed for binding and catalysis. 

Language models are increasingly being deployed for general problem solving across a wide range of tasks, but are still confined to token-level, left-to-right decision-making processes during inference. This means they can fall short in tasks that require exploration, strategic lookahead, or where initial decisions play a pivotal role. To surmount these challenges, we introduce a new framework for language model inference, “Tree of Thoughts” (ToT), which generalizes over the popular “Chain of Thought” approach to prompting language models, and enables exploration over coherent units of text (“thoughts”) that serve as intermediate steps toward problem solving. ToT allows LMs to perform deliberate decision making by considering multiple different reasoning paths and self-evaluating choices to decide the next course of action, as well as looking ahead or backtracking when necessary to make global choices. Our experiments show that ToT significantly enhances language models’ problem-solving abilities on three novel tasks requiring non-trivial planning or search: Game of 24, Creative Writing, and Mini Crosswords. For instance, in Game of 24, while GPT-4 with chain-of-thought prompting only solved 4% of tasks, our method achieved a success rate of 74%. Code repo with all prompts: https://github.com/princeton-nlp/tree-of-thought-llm. 

It is very important to perform magnetostatic analysis accurately and efficiently when it comes to multi-objective optimization of designs of electromagnetic devices, particularly for inductors, transformers, and electric motors. A kernel free boundary integral method (KFBIM) was studied for analyzing 2D magnetostatics problems. Although KFBIM is accurate and computationally efficient, sharp corners can be a major problem for KFBIM. In this paper, an inverse discrete Fourier transform (DFT) based geometry reconstruction is explored to overcome this challenge for smoothening sharp corners. A toroidal inductor core with an air gap (C-core) is used to show the effectiveness of the proposed approach addressing the sharp corner problem. A numerical example demonstrates that the method works for the variable coefficient PDE. In addition, magnetostatic analysis for homogeneous and nonhomogeneous material is presented for the reconstructed geometry, and results carried out from KFBIM are compared with the results of FEM analysis for the original geometry to show the differences and the potential of the proposed method. 

The broad-line region (BLR) of active galactic nuclei (AGNs) traces gas close to the central supermassive black hole (BH). Recent reverberation mapping (RM) and interferometric spectro-astrometry data have enabled detailed investigations of the BLR structure and dynamics as well as estimates of the BH mass. These exciting developments have motivated comparative investigations of BLR structures using different broad emission lines. In this work, we have developed a method to simultaneously model multiple broad lines of the BLR from a single-epoch spectrum. We applied this method to the five strongest broad emission lines (Hα, Hβ, Hγ, Paβ, and He Iλ5876) in the UV-to-near-IR spectrum of NGC 3783, a nearby Type I AGN that has been well studied by RM and interferometric observations. Fixing the BH mass to the published value, we fit these line profiles simultaneously to constrain the BLR structure. We find that the differences between line profiles can be explained almost entirely as being due to different radial distributions of the line emission. We find that using multiple lines in this way also enables one to measure some important physical parameters, such as the inclination angle and virial factor of the BLR. The ratios of the derived BLR time lags are consistent with the expectation of theoretical model calculations and RM measurements. 

We present new Very Large Telescope Interferometer (VLTI)/GRAVITY near-infrared interferometric measurements of the angular size of the innermost hot dust continuum for 14 type 1 active galactic nuclei (AGNs). The angular sizes are resolved on scales of ∼0.7 mas and the inferred ring radii range from 0.028 to 1.33 pc, comparable to those reported previously and a factor of 10−20 smaller than the mid-infrared sizes in the literature. Combining our new data with previously published values, we compiled a sample of 25 AGNs with bolometric luminosity ranging from 10⁴²to 10⁴⁷erg s⁻¹, with which we studied the radius-luminosity (R − L) relation for the hot dust structure. Our interferometric measurements of radius are offset by a factor of 2 from the equivalent relation derived through reverberation mapping. Using a simple model to explore the dust structure’s geometry, we conclude that this offset can be explained if the 2 μm emitting surface has a concave shape. Our data show that the slope of the relation is in line with the canonicalR ∝ L^0.5when using an appropriately non-linear correction for bolometric luminosity. In contrast, using optical luminosity or applying a constant bolometric correction to it results in a significant deviation in the slope, suggesting a potential luminosity dependence on the spectral energy distribution. Over four orders of magnitude in luminosity, the intrinsic scatter around theR − Lrelation is 0.2 dex, suggesting a tight correlation between the innermost hot dust structure size and the AGN luminosity. 

Interparticle sintering can stabilize high-pressure phases of cadmium selenide and cadmium sulfide nanocrystal networks at ambient conditions.