Addition reactions of ethoxycarbonylnitrene and ethoxycarbonylnitrenium ion to allylic ethers

Ethoxycarbonylnitrene (EtOCON) generated by α-elimination adds cleanly to allylic ethers giving substituted aziridines. Similar addition via nitrenium ion (EtOCONH⁺) gives derivatives of β-amino alcohols.     

Synthesis of β,β-branched β-amino ester derivatives through spiroaziridination of (α-trimethylsilanylmethyl)cyclohexylidene esters

The reaction of (α-trimethylsilanylmethyl)cyclohexylidene esters with NsONHCO₂Et and CaO produces the N-(ethoxycarbonyl)spiroaziridines which, after ring-opening, gives the corresponding β,β-disubstituted β-amino ester derivatives. The stereochemical outcome of the reaction is influenced by substituents on the cyclohexyl group.     

Unexpected and expeditious entry into trifluoromethyl aziridines from substituted beta-dicarbonyl compounds

[Reaction: see text]. One-pot aziridinations were obtained starting from substituted 2,2,2-trifluoroethyl beta-dicarbonyl compounds with nosyloxycarbamates in the presence of an excess of CaO as base. The unexpected ring closure reaction takes place at room temperature, leading to the N-protected alpha-trifluoromethyl aziridines with good yields. The reaction pathway seems to be influenced by the choice of the base.     

Functionalised enones as starting materials for the construction of aziridine scaffolds

alpha-Substituted beta-keto esters have been transformed by means of a straightforward procedure into aziridine-1,2-dicarboxylates, which have been efficiently converted into alkenyl aziridine-1,2-dicarboxylates through Wittig olefination reaction. The possibility of aziridine ring elaborations and the presence of an olefin function make these new molecules suitable scaffolds for further derivatisation into potential bioactive targets.     

O-Arylsulfonyl hydroxylamines via a decarboxylative rearrangement

(E)-O-Arylsulfonyl-N-(2-nitroalk-2-enyl)hydroxylamines were easily obtained in good yields starting from (E)-nitro allylic alcohols, the crucial step being an inorganic base-catalyzed decarboxylative rearrangement of proposed labile unsaturated carbamates. A possible mechanism for the outcome of the reaction, characterized by the unusual retention of the sulfonyloxy group, is proposed.     

Exact and heuristic approaches for the index tracking problem with UCITS constraints

Index tracking aims at determining an optimal portfolio that replicates the performance of an index or benchmark by investing in a smaller number of constituents or assets. The tracking portfolio should be cheap to maintain and update, i.e., invest in a smaller number of constituents than the index, have low turnover and low transaction costs, and should avoid large positions in few assets, as required by the European Union Directive UCITS (Undertaking for Collective Investments in Transferable Securities) rules. The UCITS rules make the problem hard to be satisfactorily modeled and solved to optimality: no exact methods but only heuristics have been proposed so far. The aim of this paper is twofold. First, we present the first Mixed Integer Quadratic Programming (MIQP) formulation for the constrained index tracking problem with the UCITS rules compliance. This allows us to obtain exact solutions for small- and medium-size problems based on real-world datasets. Second, we compare these solutions with the ones provided by the state-of-art heuristic Differential Evolution and Combinatorial Search for Index Tracking (DECS-IT), obtaining information about the heuristic performance and its reliability for the solution of large-size problems that cannot be solved with the exact approach. Empirical results show that DECS-IT is indeed appropriate to tackle the index tracking problem in such cases. Furthermore, we propose a method that combines the good characteristics of the exact and of the heuristic approaches.     

On the complexity of some subgraph problems

We study the complexity of the problem of deciding the existence of a spanning subgraph of a given graph, and of that of finding a maximum (weight) such subgraph. We establish some general relations between these problems, and we use these relations to obtain new NP-completeness results for maximum (weight) spanning subgraph problems from analogous results for existence problems and from results in extremal graph theory. On the positive side, we provide a decomposition method for the maximum (weight) spanning chordal subgraph problem that can be used, e.g., to obtain a linear (or O(nlogn)) time algorithm for such problems in graphs with vertex degree bounded by 3.     

Alpha-methylene-beta-amino ketone derivatives from beta-ketoallylsilanes

Beta-Ketoallylsilanes are synthesized by the Horner-Emmons reaction starting from novel silylated ketophosphonates and various aldehydes. The reactions of beta-ketoallylsilanes with NsONHCO2Et and CaO produce alpha-methylene-N-(ethoxycarbonyl)-beta-amino ketones through the ring opening of the intermediate aziridine, which is favored by the presence of the trimethylsilyl group. With chiral beta-ketoallylsilanes we obtained a stereoselective amination reaction with a 90% diastereomeric excess. alpha-Methylene-N-(ethoxycarbonyl)-beta-amino ketones are isolated in 39-60% yields and characterized.     

Structural and algorithmic properties for parametric minimum cuts

We consider the minimum s, t-cut problem in a network with parametrized arc capacities. Following the seminal work of Gallo et?al. (SIAM J. Comput. 18(1):30–55, 1989), classes of this parametric problem have been shown to enjoy the nice Structural Property that minimum cuts are nested, and the nice Algorithmic Property that all minimum cuts can be computed in the same asymptotic time as a single minimum cut by using a clever Flow Update step to move from one value of the parameter to the next. We present a general framework for parametric minimum cuts that extends and unifies such results. We define two conditions on parametrized arc capacities that are necessary and sufficient for (strictly) decreasing differences of the parametric cut function. Known results in parametric submodular optimization then imply the Structural Property. We show how to construct appropriate Flow Updates in linear time under the above conditions, implying that the Algorithmic Property also holds under these conditions. We then consider other classes of parametric minimum cut problems, without decreasing differences, for which we establish the Structural and/or the Algorithmic Property, as well as other cases where nested minimum cuts arise.