LLT polynomials,chromatic quasisymmetric functions and graphs with cycles

We use a Dyck path model for unit-interval graphs to study the chromatic quasisymmetric functions introduced by Shareshian and Wachs, as well as unicellular LLT polynomials, revealing some parallel structure and phenomena regarding their $\mathrm{e}$-positivity.The Dyck path model is also extended to circular arc digraphs to obtain larger families of polynomials, giving a new extension of LLT polynomials. Carrying over a lot of the non-circular combinatorics, we prove several statements regarding the $\mathrm{e}$-coefficients of chromatic quasisymmetric functions and LLT polynomials, including a natural combinatorial interpretation for the $\mathrm{e}$-coefficients for the line graph and the cycle graph for both families. We believe that certain $\mathrm{e}$-positivity conjectures hold in all these families above.Furthermore, beyond the chromatic analogy, we study vertical-strip LLT polynomials, which are modified Hall–Littlewood polynomials.     

Limit on nonlocality in any world in which communication complexity is not trivial

Bell proved that quantum entanglement enables two spacelike separated parties to exhibit classically impossible correlations. Even though these correlations are stronger than anything classically achievable, they cannot be harnessed to make instantaneous (faster than light) communication possible. Yet, Popescu and Rohrlich have shown that even stronger correlations can be defined, under which instantaneous communication remains impossible. This raises the question: Why are the correlations achievable by quantum mechanics not maximal among those that preserve causality? We give a partial answer to this question by showing that slightly stronger correlations would result in a world in which communication complexity becomes trivial.     

Personalized Metabolic Profile by Synergic Use of NMR and HRMS

A new strategy that takes advantage of the synergism between NMR and UHPLC–HRMS yields accurate concentrations of a high number of compounds in biofluids to delineate a personalized metabolic profile (SYNHMET). Metabolite identification and quantification by this method result in a higher accuracy compared to the use of the two techniques separately, even in urine, one of the most challenging biofluids to characterize due to its complexity and variability. We quantified a total of 165 metabolites in the urine of healthy subjects, patients with chronic cystitis, and patients with bladder cancer, with a minimum number of missing values. This result was achieved without the use of analytical standards and calibration curves. A patient’s personalized profile can be mapped out from the final dataset’s concentrations by comparing them with known normal ranges. This detailed picture has potential applications in clinical practice to monitor a patient’s health status and disease progression.     

Application of deuterated THENA for assigning the absolute configuration of chiral secondary alcohols

The structure of a constrained bicyclic chiral derivatizing agent (CDA), 1,2,3,4-tetrahydro-1,4-epoxynaphthalene-1-carboxylic acid, THENA 1, was modified by replacing both exo-methylene protons with deuterium atoms. The modified CDA, THENA-d₂2, could be used to assign the absolute configuration of chiral secondary alcohols with good reliability. Compared with THENA, the multiplicity of the methylene proton signals in the ¹H NMR spectra of THENA-d₂ derivatives is less complicated and the new CDA thus offers simpler NMR spectra for data interpretation.     

The h-SbxWO3+2x Oxygen Excess Antimony Tungsten Bronze

We describe the previously unreported oxygen excess hexagonal antimony tungsten bronze with composition Sb_0.5W₃O₁₀, in the following denoted as h-Sb_xWO_3+2x with x=0.167, to demonstrate its analogy to classical A_xWO₃ tungsten bronzes. This compound forms in a relatively narrow temperature range between 580 °C<T<620 °C. It was obtained as a dark-blue polycrystalline powder, and as thin, needle-shaped, blue single crystals. h-Sb_xWO_3+2x crystallizes in the hexagonal space group P6/mmm with the cell parameters a=7.4369(4) Å and c=3.7800(2) Å. The antimony and excess oxygen occupy the hexagonal channels within the network of corner-sharing WO₆ octahedra. h-Sb_xWO_3+2x has a resistivity of ρ_{300 K}≈1.28 mΩ cm at room temperature, with little if any temperature-dependence on cooling. DFT calculations on a simplified model for this compound find a metallic-like electronic structure with the Fermi level falling within rather flat bands, especially around the Γ point.     

Field Study and Evaluation of KrCl* Far UV-C Device Capability for Inactivation of Phi6 Bacteriophage

“Far UV-C” is an effective disinfection method that can be deployed in occupied areas. Commercially available Krypton Chloride (KrCl*) excimer lamps filtered to emit at 222 nm are effective in disinfecting pathogens and safe for human exposure up to an allowable threshold exposure, which is much longer than for conventional UV lamps emitting at 254 nm. Laboratory and controlled field testing of a filtered KrCl* excimer lamp for disinfection of a virus suspended in a thin film aqueous solution in an occupied office setting was conducted. Complete inactivation of almost 6 log (99.9999%) of Phi6 bacteriophage virus was achieved in ~20 min of exposure time in a field setting, equivalent to a dose of about 10 mJ cm⁻². The Phi6 inactivation rate constant for the field test results were not statistically different from laboratory values (P > 0.05, paired t-test). When positioned at 1 m distance from possible human exposure, this device can be used safely for almost 4.5 h of continuous direct exposure without any acute or long-term adverse health effects. This study illustrates the applicability and deployment of Far UV-C for pathogen reduction and can help in decision making for implementation of Far UV-C for disinfection in human-occupied environments.     

Addition Reactions of Sulfenyl and Sulfinyl Chlorides with 3‐Phenyl‐1‐azabicyclo[1.1.0]butane

The reactions of 3‐phenyl‐1‐azabicyclo[1.1.0]butane with α‐chlorosulfenyl chlorides and sulfinyl chlorides lead to the corresponding sulfenamides and sulfinamides, respectively, which possess an azetidine ring. It is proposed that a two‐step mechanism occurs involving an intermediate carbenium ion, which is formed by the addition of the electrophile at the N‐atom and cleavage of the N(1)? C(3) bond. The structures of 9b and 10b are established by X‐ray crystallography.     

Interaction of mixed-donor macrocycles containing the 1,10-phenanthroline subunit with selected transition and post-transition metal ions: metal ion recognition in competitive liquid-liquid solvent extraction of Cu(II), Zn(II), Pb(II), Cd(II), Ag(I), and Hg(II)

Two new mixed aza-thia crowns 5-aza-2,8-dithia[9]-(2,9)-1,10-phenanthrolinophane (L(4)) and 2,8-diaza-5-thia[9]-(2,9)-1,10-phenanthrolinophane (L(7)) have been synthesized and characterized. The coordination behavior of L(4) and L(7) toward the metal ions Cu(II), Zn(II), Pb(II), Cd(II), Hg(II), and Ag(I) was studied in aqueous solution by potentiometric methods, in CD3CN/D2O 4:1 (v/v) by (1)H NMR titrations and in the solid state. The data obtained were compared with those available for the coordination behavior toward the same metal ions of structurally analogous mixed donor macrocyclic ligands L(1)-L(3), L(5), L(6): all these contain a phenanthroline subunit but have only S/O/N(aromatic) donor groups in the remaining portion of the ring and are, therefore, less water-soluble than L(4) and L(7). The complexes [Cd(NO3)2(L(5))], [Pb(L(7))](ClO4)2 x 1/2MeCN, [Pb(L(4))](ClO4)2 x MeCN, and [Cu(L(7))](ClO4)2 x 3/2MeNO2 were characterized by X-ray crystallography. The efficacy of L(1)-L(7) in competitive liquid-liquid metal ion extraction of Cu(II), Zn(II), Cd(II), Pb(II), Ag(I), and Hg(II) was assessed. In the absence of Hg(II), a clear extraction selectivity for Ag(I) was observed in all systems investigated.     

Use of Lanthanide‐Containing Polyoxometalates to Sensitise the Emission of Fluorescent Labelled Serum Albumin

Monitoring the interaction of biomolecules is important, and the use of energy transfer is a principal technique in elucidating nanoscale interactions. Lanthanide compounds are promising luminescent probes for biological samples as their emission is longer‐lived than any native autofluorescence. Polyoxometalates (POMs) are interesting structural motifs to incorporate lanthanides, offering low toxicity and a size pertinent for biological applications. Here, we employ iso‐structured POMs containing either terbium or europium and assess their interaction with serum albumin by sensitisation of a fluorescent tag on the protein via LRET (luminescence resonance energy transfer) by exciting the lanthanide. Time‐resolved measurements showed energy transfer with an efficiency of over 90 % for the POM–protein systems. The Tb–POM results were relatively straightforward, while those with the iso‐structured Eu–POM were complicated by the effect of protein shielding from the aqueous environment.