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1. On the rank of a random binary matrix

   https://doi.org/10.1137/1.9781611975482.58  

   Cooper, Colin; Frieze, Alan; Pegden, Wesley (January 2019, Proceedings of the annual ACM-SIAM Symposium on Discrete Algorithms)

   We study the rank of a random n × m matrix An, m; k with entries from GF(2), and exactly k unit entries in each column, the other entries being zero. The columns are chosen independently and uniformly at random from the set of all (nk) such columns. We obtain an asymptotically correct estimate for the rank as a function of the number of columns m in terms of c, n, k, and where m = cn/k. The matrix An, m; k forms the vertex-edge incidence matrix of a k-uniform random hypergraph H. The rank of An, m; k can be expressed as follows. Let |C2| be the number of vertices of the 2-core of H, and | E (C2)| the number of edges. Let m* be the value of m for which |C2| = |E(C2)|. Then w.h.p. for m < m* the rank of An, m; k is asymptotic to m, and for m ≥ m* the rank is asymptotic to m – |E(C2)| + |C2|. In addition, assign i.i.d. U[0, 1] weights Xi, i ∊ 1, 2, … m to the columns, and define the weight of a set of columns S as X(S) = ∑j∊S Xj. Define a basis as a set of n – 1 (k even) linearly independent columns. We obtain an asymptotically correct estimate for the minimum weight basis. This generalises the well-known result of Frieze [On the value of a random minimum spanning tree problem, Discrete Applied Mathematics, (1985)] that, for k = 2, the expected length of a minimum weight spanning tree tends to ζ(3) ∼ 1.202. 

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2. Quantifying the effects of long-range 13C-13C dipolar coupling on measured relaxation rates in RNA

   https://doi.org/10.1007/s10858-021-00368-8  

   Olenginski, Lukasz T.; Dayie, Theodore K. (April 2021, Journal of Biomolecular NMR)

   Abstract Selective stable isotope labeling has transformed structural and dynamics analysis of RNA by NMR spectroscopy. These methods can remove¹³C-¹³C dipolar couplings that complicate¹³C relaxation analyses. While these phenomena are well documented for sites with adjacent¹³C nuclei (e.g. ribose C1′), less is known about so-called isolated sites (e.g. adenosine C2). To investigate and quantify the effects of long-range (> 2 Å)¹³C-¹³C dipolar interactions on RNA dynamics, we simulated adenosine C2 relaxation rates in uniformly [U-¹³C/¹⁵N]-ATP or selectively [2-¹³C]-ATP labeled RNAs. Our simulations predict non-negligible¹³C-¹³C dipolar contributions from adenosine C4, C5, and C6 to C2 longitudinal (R₁) relaxation rates in [U-¹³C/¹⁵N]-ATP labeled RNAs. Moreover, these contributions increase at higher magnetic fields and molecular weights to introduce discrepancies that exceed 50%. This will become increasingly important at GHz fields. Experimental R₁measurements in the 61 nucleotide human hepatitis B virus encapsidation signal ε RNA labeled with [U-¹³C/¹⁵N]-ATP or [2-¹³C]-ATP corroborate these simulations. Thus, in the absence of selectively labeled samples, long-range¹³C-¹³C dipolar contributions must be explicitly taken into account when interpreting adenosine C2 R₁rates in terms of motional models for large RNAs. 

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3. Two-bond ¹³ C– ¹³ C spin-coupling constants in saccharides: dependencies on exocyclic hydroxyl group conformation

   https://doi.org/10.1039/d1cp03320d  

   Lin, Jieye; Meredith, Reagan J.; Oliver, Allen G.; Carmichael, Ian; Serianni, Anthony S. (October 2021, Physical Chemistry Chemical Physics)

   Seven doubly 13 C-labeled isotopomers of methyl β- d -glucopyranoside, methyl β- d -xylopyranoside, methyl β- d -galactopyranoside, methyl β- d -galactopyranosyl-(1→4)-β- d -glucopyranoside and methyl β- d -galactopyranosyl-(1→4)-β- d -xylopyranoside were prepared, crystallized, and studied by single-crystal X-ray crystallography and solid-state 13 C NMR spectroscopy to determine experimentally the dependence of 2 J C1,C3 values in aldopyranosyl rings on the C1–C2–O2–H torsion angle, θ 2 , involving the C2 carbon of the C1–C2–C3 coupling pathway. Using X-ray crystal structures to determine θ 2 in crystalline samples and by selecting compounds that exhibit a relatively wide range of θ 2 values in the crystalline state, 2 J C1,C3 values measured in crystalline samples were plotted against θ 2 and the resulting plot compared to that obtained from density functional theory (DFT) calculations. For θ 2 values ranging from ∼90° to ∼240°, very good agreement was observed between the experimental and theoretical plots, providing strong validation of DFT-calculated spin-coupling dependencies on exocyclic C–O bond conformation involving the central carbon of geminal C–C–C coupling pathways. These findings provide new experimental evidence supporting the use of 2 J CCC values as non-conventional spin-coupling constraints in MA′AT conformational modeling of saccharides in solution, and the use of NMR spin-couplings not involving coupled hydroxyl hydrogens as indirect probes of C–O bond conformation. Solvomorphism was observed in crystalline βGal-(1→4)-βGlcOCH 3 wherein the previously-reported methanol solvate form was found to spontaneously convert to a monohydrate upon air-drying, leading to small but discernible conformational changes in, and a new crystalline form of, this disaccharide. 

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4. Mechanistic insights of cycling stability of ferrocene catholytes in aqueous redox flow batteries

   https://doi.org/10.1039/D1EE03251H  

   Luo, Jian; Hu, Maowei; Wu, Wenda; Yuan, Bing; Liu, T. Leo (March 2022, Energy & Environmental Science)

   Water soluble ferrocene (Fc) derivatives are promising cathode materials for aqueous organic redox flow batteries (AORFBs) towards scalable energy storage. However, their structure–performance relationship and degradation mechanism in aqueous electrolytes remain unclear. Herein, physicochemical and electrochemical properties, battery performance, and degradation mechanisms of three Fc catholytes, (ferrocenylmethyl)trimethylammonium chloride (C1-FcNCl), (2-ferrocenyl-ethyl)trimethylammonium chloride (C2-FcNCl), and (3-ferrocenyl-propyl)trimethylammonium chloride (C3-FcNCl) in pH neutral aqueous electrolytes were systemically investigated. UV-Vis and gas chromatography (GC) studies confirmed the thermal and photolytic C x -Cp − ligand dissociation decomposition pathways of both discharged and charged states of C1-FcNCl and C2-FcNCl catholytes. In contrast, in the case of the C3-FcNCl catholyte, the electron-donating 3-(trimethylammonium)propyl group strengthens the coordination between the C 3 -Cp − ligand and the Fe 3+ or Fe 2+ center and thus mitigates the ligand-dissociation degradation. Consistently, the Fc electrolytes displayed cycling stability in both half-cell and full-cell flow batteries in the order of C1-FcNCl < C2-FcNCl < C3-FcNCl. 

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5. High Curie temperature ferromagnetic structures of (Sb2Te3)1−x(MnSb2Te4)x with x = 0.7–0.8

   https://doi.org/10.1038/s41598-023-34585-y  

   Levy, Ido; Forrester, Candice; Ding, Xiaxin; Testelin, Christophe; Krusin-Elbaum, Lia; Tamargo, Maria C. (December 2023, Scientific Reports)

   Abstract Magnetic topological materials are promising for realizing novel quantum physical phenomena. Among these, bulk Mn-rich MnSb 2 Te 4 is ferromagnetic due to Mn Sb antisites and has relatively high Curie temperatures (T C ), which is attractive for technological applications. We have previously reported the growth of materials with the formula (Sb 2 Te 3 ) 1−x (MnSb 2 Te 4 ) x , where x varies between 0 and 1. Here we report on their magnetic and transport properties. We show that the samples are divided into three groups based on the value of x (or the percent septuple layers within the crystals) and their corresponding T C values. Samples that contain x < 0.7 or x > 0.9 have a single T C value of 15–20 K and 20–30 K, respectively, while samples with 0.7 < x < 0.8 exhibit two T C values, one (T C1 ) at ~ 25 K and the second (T C2 ) reaching values above 80 K, almost twice as high as any reported value to date for these types of materials. Structural analysis shows that samples with 0.7 < x < 0.8 have large regions of only SLs, while other regions have isolated QLs embedded within the SL lattice. We propose that the SL regions give rise to a T C1 of ~ 20 to 30 K, and regions with isolated QLs are responsible for the higher T C2 values. Our results have important implications for the design of magnetic topological materials having enhanced properties. 

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