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1. Dataset: 800 QM/MM minimum energy pathway conformations for the acylation reactions of Toho-1/ampicillin and Toho-1/cefalexin

   https://doi.org/10.5281/zenodo.6341803  

   Song, Zilin; Tao, Peng (January 2022, Zenodo)

   This dataset consists of 800 coordinate files (in the CHARMM psf/cor format) for the QM/MM minimum energy pathways of the acylation reactions between a Class A beta-lactamases (Toho-1) and two beta-lactam antibiotic molecules (ampicillin and cefalexin).</p> These files are:</p> toho_amp.r1-ae.zip: The R1-AE acylation pathways for Toho-1/Ampicillin (200 pathways);</li>toho_amp.r2-ae.zip: The R2-AE acylation pathways for Toho-1/Ampicillin (200 pathways);</li>toho_cex.r1-ae.zip: The R1-AE acylation pathways for Toho-1/Cefalexin (200 pathways);</li>toho_cex.r2-ae.zip: The R2-AE acylation pathways for Toho-1/Cefalexin (200 pathways);</li>energies.zip: the replica energies at B3LYP-D3/6-31+G**/C36 level;</li>chelpgs.zip: the ChElPG charges of all reactant replicas at B3LYP-D3/6-31+G**/C36 level;</li>farrys.zip: the featurzied NumPy arrays for model training;</li>peephole.zip: an example file for how the optimized MEPs look like; </li>dftb3_benchmark.zip: the reference calculations to justify the use of DFTB3/3OB-F/C36 in MEP optimizations, the reference level of theory is B3LYP-D3/6-31G**/C36. </li></ul> The R1-AE pathways are the acylation uses Glu166 as the general base; the R2-AE pathways uses Lys73 and Glu166 as the concerted base. </p> All QM/MM pathways are optimized at the DFTB3/3OB-f/CHARMM36 level of theory. </p> Z. Song et al Mechanistic Insights into Enzyme Catalysis from Explaining Machine-Learned Quantum Mechanical and Molecular Mechanical Minimum Energy Pathways. ACS Physical Chemistry Au, in press. DOI: 10.1021/acsphyschemau.2c00005</p> 

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2. Averages Along the Primes: Improving and Sparse Bounds

   https://doi.org/10.1515/conop-2020-0003  

   Han, Rui; Krause, Ben; Lacey, Michael T.; Yang, Fan (February 2020, Concrete Operators)

   Abstract Consider averages along the prime integers ℙ given by {\mathcal{A}_N}f(x) = {N^{ - 1}}\sum\limits_{p \in \mathbb{P}:p \le N} {(\log p)f(x - p).} These averages satisfy a uniform scale-free ℓ p -improving estimate. For all 1 < p < 2, there is a constant C p so that for all integer N and functions f supported on [0, N ], there holds {N^{ - 1/p'}}{\left\| {{\mathcal{A}_N}f} \right\|_{\ell p'}} \le {C_p}{N^{ - 1/p}}{\left\| f \right\|_{\ell p}}. The maximal function 𝒜 * f = sup N |𝒜 N f | satisfies ( p , p ) sparse bounds for all 1 < p < 2. The latter are the natural variants of the scale-free bounds. As a corollary, 𝒜 * is bounded on ℓ p ( w ), for all weights w in the Muckenhoupt 𝒜 p class. No prior weighted inequalities for 𝒜 * were known. 

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3. Hyperspectral Reflectance for Measuring Canopy‐Level Nutrients and Photosynthesis in a Salt Marsh

   https://doi.org/10.1029/2022JG007088  

   Vázquez‐Lule, Alma; Seyfferth, Angelia L.; Limmer, Matt A.; Mey, Paul; Guevara, Mario; Vargas, Rodrigo (November 2022, Journal of Geophysical Research: Biogeosciences)

   Abstract Salt marsh ecosystems are underrepresented in process‐based models due to their unique location across the terrestrial–aquatic interface. Particularly, the role of leaf nutrients on canopy photosynthesis (F_A) remains unclear, despite their relevance for regulating vegetation growth. We combined multiyear information of canopy‐level nutrients and eddy covariance measurements with canopy surface hyperspectral remote sensing (CSHRS) to quantify the spatial and temporal variability of F_Ain a temperate salt marsh. We found that F_Ashowed a positive relationship with canopy‐level N at the ecosystem scale and for areas dominated bySpartina cynosuroides, but not for areas dominated by shortS. alterniflora. F_Ashowed a positive relationship with canopy‐level P, K, and Na, but a negative relationship with Fe, for areas associated withS. cynosuroides,S. alterniflora, and at the ecosystem scale. We used partial least squares regression (PLSR) with CSHRS and found statistically significant data–model agreements to predict canopy‐level nutrients and F_A. The red‐edge electromagnetic region and ∼770 nm showed the highest contribution of variance in PLSR models for canopy‐level nutrients and F_A, but we propose that underlying sediment biogeochemistry can complicate interpretation of reflectance measurements. Our findings highlight the relevance of spatial variability in salt marshes vegetation and the promising application of CSHRS for linking information of canopy‐level nutrients with F_A. We call for further development of canopy surface hyperspectral methods and analyses across salt marshes to improve our understanding of how these ecosystems will respond to global environmental change. 

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4. Fractional Quantum Hall Effect with Unconventional Pairing in Monolayer Graphene

   https://doi.org/10.1103/PhysRevLett.130.126201  

   Sharma, Anirban; Pu, Songyang; Balram, Ajit C.; Jain, J. K. (March 2023, Physical Review Letters)

   Motivated by the observation of even denominator fractional quantum Hall effect in the n= 3 Landau level of monolayer graphene [Kim et al., Nat. Phys. 15, 154 (2019)], we consider a Bardeen-Cooper-Schrieffer variational state for composite fermions and find that the composite-fermion Fermi sea in this Landau level is unstable to an f-wave pairing. Analogous calculation suggests the possibility of a p-wave pairing of composite fermions at half filling in the n= 2 graphene Landau level, whereas no pairing instability is found at half filling in the n= 0 and n= 1 graphene Landau levels. The relevance of these results to experiments is discussed. 

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5. Quantum algorithms and approximating polynomials for composed functions with shared inputs

   https://doi.org/10.22331/q-2021-09-16-543  

   Bun, Mark; Kothari, Robin; Thaler, Justin (September 2021, Quantum)

   We give new quantum algorithms for evaluating composed functions whose inputs may be shared between bottom-level gates. Let f be an m -bit Boolean function and consider an n -bit function F obtained by applying f to conjunctions of possibly overlapping subsets of n variables. If f has quantum query complexity Q ( f ) , we give an algorithm for evaluating F using O ~ ( Q ( f ) ⋅ n ) quantum queries. This improves on the bound of O ( Q ( f ) ⋅ n ) that follows by treating each conjunction independently, and our bound is tight for worst-case choices of f . Using completely different techniques, we prove a similar tight composition theorem for the approximate degree of f .By recursively applying our composition theorems, we obtain a nearly optimal O ~ ( n 1 − 2 − d ) upper bound on the quantum query complexity and approximate degree of linear-size depth- d AC 0 circuits. As a consequence, such circuits can be PAC learned in subexponential time, even in the challenging agnostic setting. Prior to our work, a subexponential-time algorithm was not known even for linear-size depth-3 AC 0 circuits.As an additional consequence, we show that AC 0 ∘ ⊕ circuits of depth d + 1 require size Ω ~ ( n 1 / ( 1 − 2 − d ) ) ≥ ω ( n 1 + 2 − d ) to compute the Inner Product function even on average. The previous best size lower bound was Ω ( n 1 + 4 − ( d + 1 ) ) and only held in the worst case (Cheraghchi et al., JCSS 2018). 

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