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...     

Enhanced alternating energy minimization methods for stochastic galerkin matrix equations

BIT Numerical Mathematics - In uncertainty quantification, it is commonly required to solve a forward model consisting of a partial differential equation (PDE) with a spatially varying uncertain...     

Integrative Chemical Biology Approaches for Identification and Characterization of “Erasers” for Fatty‐Acid‐Acylated Lysine Residues within Proteins

Acylation of proteins with fatty acids is important for the regulation of membrane association, trafficking, subcellular localization, and activity of many cellular proteins. While significant progress has been made in our understanding of the two major forms of protein acylation with fatty acids, N‐myristoylation and S‐palmitoylation, studies of the acylation of lysine residues, within proteins, with fatty acids have lagged behind. Demonstrated here is the use of integrative chemical biology approaches to examine human sirtuins as de‐fatty‐acid acylases in vitro and in cells. Photo‐crosslinking chemistry is used to investigate enzymes which recognize fatty‐acid acylated lysine. Human Sirt2 was identified as a robust lysine de‐fatty‐acid acylase in vitro. The results also show that Sirt2 can regulate the acylation of lysine residues, of proteins, with fatty acids within cells.     

Redox‐Neutral α‐Allylation of Amines by Combining Palladium Catalysis and Visible‐Light Photoredox Catalysis

An unprecedented α‐allylation of amines was achieved by combining palladium catalysis and visible‐light photoredox catalysis. In this dual catalysis process, the catalytic generation of allyl radical from the corresponding π‐allylpalladium intermediate was achieved without additional metal reducing reagents (redox‐neutral). Various allylation products of amines were obtained in high yields through radical cross‐coupling under mild reaction conditions. Moreover, the transformation was applied to the formal synthesis of 8‐oxoprotoberberine derivatives which show potential anticancer properties.     

Nannocystin A: an Elongation Factor 1 Inhibitor from Myxobacteria with Differential Anti‐Cancer Properties

Cultivation of myxobacteria of the Nannocystis genus led to the isolation and structure elucidation of a class of novel cyclic lactone inhibitors of elongation factor 1. Whole genome sequence analysis and annotation enabled identification of the putative biosynthetic cluster and synthesis process. In biological assays the compounds displayed anti‐fungal and cytotoxic activity. Combined genetic and proteomic approaches identified the eukaryotic translation elongation factor 1α (EF‐1α) as the primary target for this compound class. Nannocystin A ( 1 ) displayed differential activity across various cancer cell lines and EEF1A1 expression levels appear to be the main differentiating factor. Biochemical and genetic evidence support an overlapping binding site of 1 with the anti‐cancer compound didemnin B on EF‐1α. This myxobacterial chemotype thus offers an interesting starting point for further investigations of the potential of therapeutics targeting elongation factor 1.     

Prediction of cathodic E1/21 and E1/22 values for viologen-containing conjugated unimers and dimers from calculated pKb values of the aromatic substituents

A library of 18 conjugated, rod-like compounds with either one or two viologen residues were synthesized and characterized electrochemically. Containing up to 8 aromatic/heterocyclic rings in conjugation, the members of the library differ in the substitution pattern of electron-withdrawing or -donating groups on the aromatic substituents of the viologen units. The first and second half-wave potentials of each member were found to be linearly correlated with the calculated pK_b values of the aromatic end-groups. This relationship will enable the half-wave potentials of related, novel, substituted viologen species to be predicted using a simple, empirical formula.     

Gravitational Field Equations on Fefferman Space–Times

The total space \({\mathfrak M} \approx {\mathbb H}_1 \times S^1\) of the canonical circle bundle over the 3-dimensional Heisenberg group \({\mathbb H}_1\) is a space–time with the Lorentzian metric \(F_{\theta _0}\) (Fefferman’s metric) associated to the canonical Tanaka–Webster flat contact form \(\theta _0\) on \({\mathbb H}_1\). The matter and energy content of \(\mathfrak M\) is described by the energy-momentum tensor \({T}_{\mu \nu }\) (the trace-less Ricci tensor of \(F_{\theta _0}\)) as an effect of the non flat nature of Feferman’s metric \(F_{\theta _0}\). We study the gravitational field equations \(R_{\mu \nu } - (1/2) \, R \, g_{\mu \nu } = {T}_{\mu \nu }\) on \({\mathfrak M}\). We consider the first order perturbation \(g = F_{\theta _0} + \epsilon \, h\), \(\epsilon<< 1\), and linearize the field equations about \(F_{\theta _0}\). We determine a Lorentzian metric g on \({\mathfrak M}\) which solves the linearized field equations corresponding to a diagonal perturbation h.     

Rheology of a dilute suspension of axisymmetric Brownian particles

Explicit results are presented for the complete rheological properties of dilute suspensions of rigid, axisymmetric Brownian particles possessing fore-aft symmetry, when suspended in a Newtonian liquid subjected to a general three-dimensional shearing flow, either steady or unsteady. It is demonstrated that these rheological properties can be expressed in terms of five fundamental material constants (exclusive of the solvent viscosity), which depend only upon the sizes and shapes of the suspended particles. Expressions are presented for these scalar constants for a number of solids of revolution, including spheroids, dumbbells of arbitrary aspect ratio and long slender bodies. These are employed to calculate rheological properties for a variety of different shear flows, including uniaxial and biaxial extensional flows, simple shear flows, and general two-dimensional shear flows. It is demonstrated that the rheological properties appropriate to a general two-dimensional shear flow can be deduced immediately from those for a simple shear flow. This observation greatly extends the utility of much of the prior Couette flow literature, especially the extensive numerical calculations of Scheraga et al. (1951, 1955).The commonality of many disparate results dispersed and diffused in earlier publications is emphasized, and presented from a unified hydrodynamic viewpoint.