Stability conditions in families

Publications mathématiques de l'IHÉS - We develop a theory of Bridgeland stability conditions and moduli spaces of semistable objects for a family of varieties. Our approach is based...     

Copper-catalyzed functionalization of enynes

The copper-catalyzed functionalization of enyne derivatives has recently emerged as a powerful approach in contemporary synthesis. Enynes are versatile and readily accessible substrates that can undergo a variety of reactions to yield densely functionalized, enantioenriched products. In this perspective, we review copper-catalyzed transformations of enynes, such as boro- and hydrofunctionalizations, copper-mediated radical difunctionalizations, and cyclizations. Particular attention is given to the regiodivergent functionalization of 1,3-enynes, and the current mechanistic understanding of such processes.

The copper-catalyzed functionalization of enynes is a powerful approach to yield densely functionalized products. This review covers various transformations, such as boro- and hydrofunctionalizations, copper-mediated radical difunctionalizations, and cyclizations.     

Crossover mitigation strategies for redox-flow batteries

Redox-flow batteries can, in principle, use a wide range of active materials. However, a number of simultaneous requirements must be met to make a chemistry attractive. One of the most challenging requirements is minimizing transport of active species through the membrane separating the positive and negative electrodes, and the ensuing inefficiency and capacity loss. Developing technologies to mitigate crossover, and strategies for recovering from its consequences, will enable development of successful systems with new active materials. The rate and impact of crossover depend on the nature of the active materials and their fate after they transport across the separator. Accordingly, electrolyte solutions can be classified by what happens to the active species at the opposing electrolyte. This behavior also dictates what recovery strategies may be employed, and at what frequency. This review describes desirable attributes for active materials and separators that help diminish crossover, and strategies that can be used to recover from its effects for each of the different classes of electrolytes.     

A Dual Threat: Redox-Activity and Electronic Structures of Well-Defined Donor–Acceptor Fulleretic Covalent-Organic Materials

The effect of donor (D)–acceptor (A) alignment on the materials electronic structure was probed for the first time using novel purely organic porous crystalline materials with covalently bound two- and three-dimensional acceptors. The first studies towards estimation of charge transfer rates as a function of acceptor stacking are in line with the experimentally observed drastic, eight-fold conductivity enhancement. The first evaluation of redox behavior of buckyball- or tetracyanoquinodimethane-integrated crystalline was conducted. In parallel with tailoring the D-A alignment responsible for “static” changes in materials properties, an external stimulus was applied for “dynamic” control of the electronic profiles. Overall, the presented D–A strategic design, with stimuli-controlled electronic behavior, redox activity, and modularity could be used as a blueprint for the development of electroactive and conductive multidimensional and multifunctional crystalline porous materials.     

Octaboraneyl Complexes of Nickel: Monomers for Redox-Active Coordination Polymers

Herein, we establish the preparation, characterization, and reactivity of a new diphosphine ligand, 1,2-bis(di(3-dicyclohexylboraneyl)propylphosphino)ethane (P₂B^Cy₄), a scaffold that contains four pendant boranes. An entryway into the coordination chemistry of P₂B^Cy₄ is established by using nickel, providing the octaboraneyl complex [Ni(P₂B^Cy₄)₂]—this species contains a boron-rich secondary coordination sphere that reacts readily with Lewis bases. In the case of 4,4′-bipyridine, an air-sensitive coordination polymer is obtained. Characterization of this material by solid-state NMR and EPR spectroscopy reveals the presence of a charge-transfer polymer, which forms as a function of intramolecular Ni→4,4′-bpy electron transfer (ET), providing an array of oxidized nickel sites and reduced 4,4′-bpy radical anion sites. Notably, the related intermolecular reaction between the model fragments [Ni(dnppe)₂] (dnppe=1,2-bis(di-n-propylphosphino)ethane) and a bis(boraneyl)-protected 4,4′-bpy, provides no ET. Overall, the P₂B^Cy₄ fragment provides a unique opportunity for Lewis base activation, in one case allowing for the facile construction of monomers for incorporation into redox-active macromolecules.     

Chiral pool based synthesis of pyrrolidinium ionic liquids

Chiral ionic liquids show promising applications in various different fields. A series of pyrrolidinium-based chiral ionic liquids bearing a chiral cation, a chiral anion or both was prepared in good yields using an efficient, economic and simple pathway. The chirality was introduced using (l)-lactate and (l)-menthol derivatives. The resultant chiral compounds were characterized by both spectroscopy and polarimetry. We envision that these new chiral compounds can serve as effective reaction media and chiral catalysts for asymmetric reactions, which are presently being investigated in our lab.     

Programming With Models: Writing Statistical Algorithms for General Model Structures With NIMBLE

We describe NIMBLE, a system for programming statistical algorithms for general model structures within R. NIMBLE is designed to meet three challenges: flexible model specification, a language for programming algorithms that can use different models, and a balance between high-level programmability and execution efficiency. For model specification, NIMBLE extends the BUGS language and creates model objects, which can manipulate variables, calculate log probability values, generate simulations, and query the relationships among variables. For algorithm programming, NIMBLE provides functions that operate with model objects using two stages of evaluation. The first stage allows specialization of a function to a particular model and/or nodes, such as creating a Metropolis-Hastings sampler for a particular block of nodes. The second stage allows repeated execution of computations using the results of the first stage. To achieve efficient second-stage computation, NIMBLE compiles models and functions via C++, using the Eigen library for linear algebra, and provides the user with an interface to compiled objects. The NIMBLE language represents a compilable domain-specific language (DSL) embedded within R. This article provides an overview of the design and rationale for NIMBLE along with illustrative examples including importance sampling, Markov chain Monte Carlo (MCMC) and Monte Carlo expectation maximization (MCEM). Supplementary materials for this article are available online.     

Stereoselective Remote Functionalization via Palladium-Catalyzed Redox-Relay Heck Methodologies

Exploration of novel, three-dimensional chemical space is of growing interest in the drug discovery community and with this comes the challenge for synthetic chemists to devise new stereoselective methods to introduce chirality in a rapid and efficient manner. This Minireview provides a timely summary of the development of palladium-catalyzed asymmetric redox-relay Heck-type processes. These reactions represent an important class of transformation for the selective introduction of remote stereocenters, and have risen to prominence over the past decade. Within this Minireview, the vast scope of these transformations will be showcased, alongside applications to pharmaceutically relevant chiral building blocks and drug substances. To complement this overview, a mechanistic summary and discussion of the current limitations of the transformation are presented, followed by an outlook on future areas of investigation.     

On the stiffness of materials containing a disordered array of microscopic holes or hard inclusions

We study the macroscopic mechanical behavior of materials with microscopic holes or hard inclusions. Specifically, we deal with the effective elastic moduli of composites whose microgeometry consists of either soft or hard isolated inclusions surrounded by an elastic matrix. We approach this problem by taking the stiffness of the inclusion phase to be a complex variable, which we eventually evaluate at the soft or hard limits. Our main result states that there is a certain class of non-physical, negative-definite values of the elastic moduli of the inclusion phase for which the effective tensor does not have infinities or become otherwise singular.We present applications of this result to the estimation of effective moduli and to homogenization theorems. The first application involves using complexanalytic methods to obtain rigorous and accurate bounds on the effective moduli of the high-contrast composites under consideration. We also discuss the variational estimates of Rubenfeld & Keller, which yield a complementary set of bounds on these moduli. The best bounds are given by a combination of the analytical and variational results. As a second application, we show that certain known theorems of homogenization for materials with holes are simple consequences of our main result, and in this connection we establish corresponding new theorems for materials with hard inclusions. While our rederivation of the homogenization theorems for materials with holes can be closely related to other known constructions, it appears that certain elements provided by our main result are essential in the proof of homogenization for the hard-inclusion case.     

The (S−1,S) inventory model and its counterparts in queueing theory

We explore the relationship between the ($S?1,S$) inventory model and three well-known queueing models: the Erlang loss system, the machine-repair model and a two-node Jackson network. Exploiting this relationship allows us to obtain key performance measures of the ($S?1,S$) model, like the so-called virtual outdating time, the number of items on the shelf in steady state, the long-run rate of unsatisfied demands and the distribution of the empty shelf period.