More on trees and Cohen reals

In this paper we analyse some questions concerning trees on κ, both for the countable and the uncountable case, and the connections with Cohen reals. In particular, we provide a proof for one of the implications left open in [6, Question 5.2] about the diagram for regularity properties.     

DIY XES—development of an inexpensive,versatile, and easy to fabricate XES analyzer and sample delivery system

The application of X-ray emission spectroscopy (XES) has grown substantially with the development of X-ray free-electron lasers, third and fourth generation synchrotron sources, and high-power benchtop sources. By providing the high X-ray flux required for XES, these sources broaden the availability and application of this method of probing electronic structure. As the number of sources increase, so does the demand for X-ray emission detection and sample delivery systems that are cost effective and customizable. Here, we present a detailed fabrication protocol for von Hamos X-ray optics and give details for a 3D-printed spectrometer design. Additionally, we outline an automated, externally triggered liquid sample delivery system that can be used to repeatedly deliver nanoliter droplets onto a plastic substrate for measurement. These systems are both low cost, efficient, and easy to recreate or modify depending on the application. A low cost multiple X-ray analyzer system enables measurement of dilute samples, whereas the sample delivery limits sample loss and reproducibly replaces spent sample with fresh sample in the same position. While both systems can be used in a wide range of applications, the design addresses several challenges associated specifically with time-resolved XES (TRXES). As an example application, we show results from TRXES measurements of photosystem II, a dilute, photoactive protein.     

Selective,C-3 Friedel-Crafts acylation to generate functionally diverse,acetylated Imidazo[1,2-a]pyridine derivatives

Carbon-carbon bonds are integral for pharmaceutical discovery and development. Frequently, CC bond reactions utilize expensive catalyst/ligand combinations and/or are low yielding, which can increase time and expenditures in pharmaceutical development. To enhance CC bond formation protocols, we developed a highly efficient, selective, and combinatorially applicable Friedel-Crafts acylation to acetylate the C-3 position of imidazo[1,2-a]pyridines. The reaction, catalyzed by aluminum chloride, is both cost effective and more combinatorial friendly compared to acetylation reactions requiring multiple, stoichiometric equivalents of AlCl₃. The protocol has broad application in the construction of acetylated imidazo[1,2-a]pyridines with an extensive substrate scope. All starting materials are common and the reaction requires inexpensive, conventional heating methods for adaptation in any laboratory. Further, the synthesized compounds are predicted to possess GABA activity through a validated, GABA binding model. The developed method serves as a superior route to generate C-3 acetylated imidazo[1,2-a]pyridine building-blocks for combinatorial synthetic efforts.     

A convergent approach to batzelladine alkaloids. Total syntheses of (+)-batzelladine E, (−)-dehydrobatzelladine C,and (+)-batzelladine K

We recently reported a convergent strategy to access the polycyclic guanidinium alkaloid (+)-batzelladine B via an aldol addition–retro-aldol–aza-Michael addition cascade. Here we describe the application of this approach toward the total syntheses of (+)-batzelladine E, (?)-dehydrobatzelladine C, and (+)-batzelladine K. The identification of suitable methods to functionalize a common tropane core by electrophilic alkynylation and nucleophilic 1,2-addition were essential to generalizing this approach. We provide evidence for the intermediacy of an acylallene species in the cascade reaction.     

Asymptotic enumeration of dense 0-1 matrices with specified line sums

Let s=(s₁,s₂,…,sm) and t=(t₁,t₂,…,tn) be vectors of non-negative integers with . Let B(s,t) be the number of m×n matrices over {0,1} with jth row sum equal to sj for 1?j?m and kth column sum equal to tk for 1?k?n. Equivalently, B(s,t) is the number of bipartite graphs with m vertices in one part with degrees given by s, and n vertices in the other part with degrees given by t. Most research on the asymptotics of B(s,t) has focused on the sparse case, where the best result is that of Greenhill, McKay and Wang (2006). In the case of dense matrices, the only precise result is for the case of equal row sums and equal column sums (Canfield and McKay, 2005). This paper extends the analytic methods used by the latter paper to the case where the row and column sums can vary within certain limits. Interestingly, the result can be expressed by the same formula which holds in the sparse case.     

Preparation and crystal structures of two 3‐anthracenyl isoxazolyl sulfonamides

Lateral metalation and oxidation of 3‐(9′‐anthryl)‐isoxazoles ( 1 ), using Davis' oxaziridine ( 6 ), produced the desired hydroxylation ( 2 ), along with sulfonamide adduct ( 3 ), and in the case of the use of butyl lithium as base, butyl addition products ( 4 ) and ( 5 ). Structures of isoxazole sulfonamides ( 3a ) and ( 5a ), were obtained as the SR/RS‐diastereomer, however, studies indicate that this is a consequence of the crystallization process. Metalation studies with isoxazole ( 8 ) demonstrate that hydroxylation ( 9 ), can be carried out cleanly, minimizing formation of ( 10 ), using camphorsulfonyloxaziridine ( 7 ) as an electrophile.     

A mixed-valence, hexadecamolybdenum cluster with an MoVI cubane "jewel" in a "setting" of five molybdateVI-linked dinuclear MoV nits

The hexadecanuclear, mixed-valence cluster [Mo(16)O(42)(OH)(2)(3-iPrC(3)H(3)N(2))(12)].H(2)O (1), has been synthesized and characterized by X-ray crystallography, IR spectroscopy and mass spectrometry. The C(2)-symmetric complex consists of a cubane Mo(VI) (4)O(4) "jewel" held in a 10-point "setting" comprised of five dinuclear Mo(V) units tethered together by two tetrahedral Mo(VI) centers. The dinuclear units are ligated by twelve 3-isopropylpyrazole units that interact with the Mo--O framework through a network of hydrogen bonds. Structural parameters, charge requirements, and bond valence sum analyses support the assignment of +5 and +6 oxidation states to the dinuclear and cubane/tetrahedral Mo centers, respectively. Space filling models reveal that the pyrazole groups coat much of the surface of the molecule, apart from a number of oxo-rich seams that trace a chiral pattern across the surface. Complex 1 exhibits a unique structure that combines moieties generally atypical of polyoxometalates, viz., a Mo cubane containing only two terminal oxo ligands, and three distinct Mo(V) (2) units (including a 5-coordinate Mo center) tethered into a 10-point "setting" by tetrahedral Mo(VI) centers.     

Metal-assisted in situ formation of a tridentate acetylacetone ligand for complexation of fac-Re(CO)3+ for radiopharmaceutical applications

Reaction of [NEt4]2[ReBr3(CO)3] with 2,4-pentanedione (acac) yields a complex of the type fac-Re(acac)(OH2)(CO)3 (1) under aqueous conditions. 1 was further reacted with a monodentate ligand (pyridine) to yield a fac-Re(acac)(pyridine)(CO)3 complex (2). Complex 1 was found to react with primary amines to generate a Schiff base (imine) in aqueous solutions. When a mixed-nitrogen donor bidentate ligand, 2-(2-aminoethyl)pyridine, that has different coordination affinities for fac-Re(acac)(OH2)(CO)3 was utilized, a unique tridentate ligand was formed in situ utilizing a metal-assisted Schiff base formation to yield a complex fac-Re(CO)3(3[(2-phenylethyl)imino]-2-pentanone) (3). Tridentate ligand formation was found to occur only with the Re-coordinated acac ligand. Reactions of acac with fac-Re(CO)3Br(2-(2-aminoethyl)pyridine) (4) or a mixture of [NEt4]2[ReBr3(CO)3], acac, and 2-(2-aminoethyl)pyridine did not yield the formation of complex 3 in water.     

Exponential family mixed membership models for soft clustering of multivariate data

For several years, model-based clustering methods have successfully tackled many of the challenges presented by data-analysts. However, as the scope of data analysis has evolved, some problems may be beyond the standard mixture model framework. One such problem is when observations in a dataset come from overlapping clusters, whereby different clusters will possess similar parameters for multiple variables. In this setting, mixed membership models, a soft clustering approach whereby observations are not restricted to single cluster membership, have proved to be an effective tool. In this paper, a method for fitting mixed membership models to data generated by a member of an exponential family is outlined. The method is applied to count data obtained from an ultra running competition, and compared with a standard mixture model approach.     

Iridium(III) Complexes Bearing Pyrene‐Functionalized 1,10‐Phenanthroline Ligands as Highly Efficient Sensitizers for Triplet–Triplet Annihilation Upconversion

“Chemistry‐on‐the‐complex” synthetic methods have allowed the selective addition of 1‐ethynylpyrene appendages to the 3‐, 5‐, 3,8‐ and 5,6‐positions of Ir^III‐coordinated 1,10‐phenanthroline via Sonogashira cross‐coupling. The resulting suite of complexes has given rise to the first rationalization of their absorption and emission properties as a function of the number and position of the pyrene moieties. Strong absorption in the visible region (e.g. 3,8‐substituted Ir‐3 : λ_abs=481 nm, ?=52 400 m ^?1 cm^?1) and long‐lived triplet excited states (e.g. 5‐substituted Ir‐2 : τ_T=367.7 μs) were observed for the complexes in deaerated CH₂Cl₂. On testing the series as triplet sensitizers for triplet–triplet annihilation upconversion, those Ir^III complexes bearing pyrenyl appendages at the 3‐ and 3,8‐positions ( Ir‐1 , Ir‐3 ) were found to give optimal upconversion quantum yields (30.2 % and 31.6 % respectively).