On separating a fixed point from zero by invariants

Assume a fixed point v∈V^G can be separated from zero by a homogeneous invariant f∈𝕜[V]^G of degree p^rd, where p>0 is the characteristic of the ground field 𝕜 and p,d are coprime. We show that then v can also be separated from zero by an invariant of degree p^r, which we obtain explicitly from f. It follows that the minimal degree of a homogeneous invariant separating v from zero is a p-power.     

Rigidity and curvature estimates for graphical self-shrinkers

Self-shrinkers are hypersurfaces that shrink homothetically under mean curvature flow; these solitons model the singularities of the flow. It is presently known that an entire self-shrinking graph must be a hyperplane. In this paper we show that the hyperplane is rigid in an even stronger sense, namely: for \(2\le n \le 6\), any smooth, complete self-shrinker \(\Sigma ^n\subset \mathbf {R}^{n+1}\) that is graphical inside a large, but compact, set must be a hyperplane. In fact, this rigidity holds within a larger class of almost stable self-shrinkers. A key component of this paper is the procurement of linear curvature estimates for almost stable shrinkers, and it is this step that is responsible for the restriction on n. Our methods also yield uniform curvature bounds for translating solitons of the mean curvature flow.     

Efficient Computation of the Joint Sample Frequency Spectra for Multiple Populations

A wide range of studies in population genetics have employed the sample frequency spectrum (SFS), a summary statistic which describes the distribution of mutant alleles at a polymorphic site in a sample of DNA sequences and provides a highly efficient dimensional reduction of large-scale population genomic variation data. Recently, there has been much interest in analyzing the joint SFS data from multiple populations to infer parameters of complex demographic histories, including variable population sizes, population split times, migration rates, admixture proportions, and so on. SFS-based inference methods require accurate computation of the expected SFS under a given demographic model. Although much methodological progress has been made, existing methods suffer from numerical instability and high computational complexity when multiple populations are involved and the sample size is large. In this article, we present new analytic formulas and algorithms that enable accurate, efficient computation of the expected joint SFS for thousands of individuals sampled from hundreds of populations related by a complex demographic model with arbitrary population size histories (including piecewise-exponential growth). Our results are implemented in a new software package called momi (MOran Models for Inference). Through an empirical study, we demonstrate our improvements to numerical stability and computational complexity.     

Efficient Data Augmentation for Fitting Stochastic Epidemic Models to Prevalence Data

Stochastic epidemic models describe the dynamics of an epidemic as a disease spreads through a population. Typically, only a fraction of cases are observed at a set of discrete times. The absence of complete information about the time evolution of an epidemic gives rise to a complicated latent variable problem in which the state space size of the epidemic grows large as the population size increases. This makes analytically integrating over the missing data infeasible for populations of even moderate size. We present a data augmentation Markov chain Monte Carlo (MCMC) framework for Bayesian estimation of stochastic epidemic model parameters, in which measurements are augmented with subject-level disease histories. In our MCMC algorithm, we propose each new subject-level path, conditional on the data, using a time-inhomogenous continuous-time Markov process with rates determined by the infection histories of other individuals. The method is general, and may be applied to a broad class of epidemic models with only minimal modifications to the model dynamics and/or emission distribution. We present our algorithm in the context of multiple stochastic epidemic models in which the data are binomially sampled prevalence counts, and apply our method to data from an outbreak of influenza in a British boarding school. Supplementary material for this article is available online.     

Darobactin B Stabilises a Lateral-Closed Conformation of the BAM Complex in E. coli Cells

The β-barrel assembly machinery (BAM complex) is essential for outer membrane protein (OMP) folding in Gram-negative bacteria, and represents a promising antimicrobial target. Several conformational states of BAM have been reported, but all have been obtained under conditions which lack the unique features and complexity of the outer membrane (OM). Here, we use Pulsed Electron-Electron Double Resonance (PELDOR, or DEER) spectroscopy distance measurements to interrogate the conformational ensemble of the BAM complex in E. coli cells. We show that BAM adopts a broad ensemble of conformations in the OM, while in the presence of the antibiotic darobactin B (DAR-B), BAM′s conformational equilibrium shifts to a restricted ensemble consistent with the lateral closed state. Our in-cell PELDOR findings are supported by new cryoEM structures of BAM in the presence and absence of DAR-B. This work demonstrates the utility of PELDOR to map conformational changes in BAM within its native cellular environment.     

Ruthenium-Catalyzed C−C Coupling of Terminal Alkynes with Primary Alcohols or Aldehydes: α,β-Acetylenic Ketones (Ynones) via Oxidative Alkynylation

The first metal-catalyzed oxidative alkynylations of primary alcohols or aldehydes to form α,β-acetylenic ketones (ynones) are described. Deuterium labelling studies corroborate a novel reaction mechanism in which alkyne hydroruthenation forms a transient vinylruthenium complex that deprotonates the terminal alkyne to form the active alkynylruthenium nucleophile.     

Cover Picture: Supramolecular Self-Assembly as a Tool To Preserve the Electronic Purity of Perylene Diimide Chromophores (Angew. Chem. Int. Ed. 12/2023)

Organic semiconductors are promising for efficient, printable optoelectronics. However, strong excited-state quenching due to uncontrolled aggregation limits their use in devices. We report on the self-assembly of a supramolecular pseudo-cube formed from six perylene diimides (PDIs). The rigid, shape-persistent cage sets the distance and orientation of the PDIs and suppresses intramolecular rotations and vibrations, leading to non-aggregated, monomer-like properties in solution and the solid state, in contrast to the fast fluorescence quenching in the free ligand. The stabilized excited state and electronic purity in the cage enables the observation of delayed fluorescence due to a bright excited multimer, acting as excited-state reservoir in a rare case of benign inter-chromophore interactions in the cage. We show that self-assembly provides a powerful tool for retaining and controlling the electronic properties of chromophores, and to bring molecular electronics devices within reach.     

Materials Space-Tectonics: Atomic-level Compositional and Spatial Control Methodologies for Synthesis of Future Materials

Reactions occurring at surfaces and interfaces necessitate the creation of well-designed surface and interfacial structures. To achieve a combination of bulk material (i.e., framework) and void spaces, a meticulous process of “nano-architecting” of the available space is necessary. Conventional porous materials such as mesoporous silica, zeolites, and metal–organic frameworks lack advanced cooperative functionalities owing to their largely monotonous pore geometries and limited conductivities. To overcome these limitations and develop functional structures with surface-specific functions, the novel materials space-tectonics methodology has been proposed for future materials synthesis. This review summarizes recent examples of materials synthesis based on designing building blocks (i.e., tectons) and their hybridization, along with practical guidelines for implementing materials syntheses and state-of-the-art examples of practical applications. Lastly, the potential integration of materials space-tectonics with emerging technologies, such as materials informatics, is discussed.     

Light-Activated Assembly of DNA Origami into Dissipative Fibrils

Hierarchical DNA nanostructures offer programmable functions at scale, but making these structures dynamic, while keeping individual components intact, is challenging. Here we show that the DNA A-motif—protonated, self-complementary poly(adenine) sequences—can propagate DNA origami into one-dimensional, micron-length fibrils. When coupled to a small molecule pH regulator, visible light can activate the hierarchical assembly of our DNA origami into dissipative fibrils. This system is recyclable and does not require DNA modification. By employing a modular and waste-free strategy to assemble and disassemble hierarchical structures built from DNA origami, we offer a facile and accessible route to developing well-defined, dynamic, and large DNA assemblies with temporal control. As a general tool, we envision that coupling the A-motif to cycles of dissipative protonation will allow the transient construction of diverse DNA nanostructures, finding broad applications in dynamic and non-equilibrium nanotechnology.