The lower tail: Poisson approximation revisited

The well‐known “Janson's inequality” gives Poisson‐like upper bounds for the lower tail probability when X is the sum of dependent indicator random variables of a special form. We show that, for large deviations, this inequality is optimal whenever X is approximately Poisson, i.e., when the dependencies are weak. We also present correlation‐based approaches that, in certain symmetric applications, yield related conclusions when X is no longer close to Poisson. As an illustration we, e.g., consider subgraph counts in random graphs, and obtain new lower tail estimates, extending earlier work (for the special case ) of Janson, ?uczak and Ruciński. © 2015 Wiley Periodicals, Inc. Random Struct. Alg., 48, 219–246, 2016     

Late-stage C−H Functionalization of Tryptophan-Containing Peptides with Thianthrenium Salts: Conjugation and Ligation

Bioorthogonal late-stage diversification of structurally complex peptides bears enormous potential for drug discovery and molecular imaging, among other applications. Herein, we report on a palladium-catalyzed C−H arylation of tryptophan-containing peptides with readily accessible and modular arylthianthrenium salts. Under exceedingly mild reaction conditions, the late-stage diversification of structurally complex peptides was accomplished. The tunability and ease of preparation of arylthianthrenium salts allowed the expedient stitching of tryptophan-containing peptides with drug, natural product, and peptidic scaffolds by forging sterically congested biaryl linkages. The robustness of the palladium catalysis regime was reflected by the full tolerance of a plethora of sensitive and coordinating functional groups. Hence, our manifold enabled efficient access to highly decorated, labelled, conjugated, and ligated linear and cyclic peptides.     

A chiral stannate as an "ansa" pi-arene ligand in rhodium chemistry

Reaction of the triamido stannate MeSi[SiMe(2)N[(R)-CHMePh]](3)SnLi (1) with 0.5 molar equivalent of [RhCl(olefin)(2)](2) (olefin = COE, C(2)H(4)) or [RhCl(P(i)Pr(3))(2)](2) yielded the Rh-Sn complexes [MeSi[SiMe(2)N[(R)-CHMePh]](2)[SiMe(2)N[(R)-CHMe(eta(6)-C(6)H(5))]SnRh(L)] (L = COE: 2a, C(2)H(4): 2b, P(i)Pr(3) 3); their intramolecular eta(6)-coordination, along with the tin-rhodium bond, represents the first "ansa" pi-arene/stannate system.     

Strong subtournaments containing a given vertex in regular multipartite tournaments

If x is a vertex of a digraph D, then we denote by d⁺(x) and d⁻(x) the outdegree and the indegree of x, respectively. The global irregularity of a digraph D is defined by

     

Synthesis of novel structurally simplified estrogen analogues

A library of 17 novel estrogen analogues 3 and 4 containing different substituents at rings A and D (steroid nomenclature) was prepared in a five- to seven-step synthesis. The key transformation is a Sonogashira-coupling of cyclic vinyl iodides of type 7 or 8 with phenylacetylenes of type 9. Reduction of the keto function in 3 led to the estradiol analogue 5.     

Enantioselective total synthesis of the oral contraceptive desogestrel by a double Heck reaction

A novel enantioselective total synthesis of the oral contraceptive desogestrel (2) is described, in which the tetracyclic steroid core is formed by a sequence of two consecutive Heck reactions. Conversion of the known enantiopure diketone 7 led to the chiral bicycle 6 which was used for a diastereoselective intermolecular Heck reaction with vinyliodide 5 to give 15. In the following intramolecular Heck reaction, the tetracyclic ring system was formed to give 4, from which the synthesis of desogestrel (2) was furnished.