Quasidiagonal representations of nilpotent groups

We show that every unitary representation of a discrete solvable virtually nilpotent group G is quasidiagonal. Roughly speaking, this says that every unitary representation of G   approximately decomposes as a direct sum of finite dimensional approximate representations. In operator algebraic terms we show that C^?(G)$C^{?}(G)$ is strongly quasidiagonal.     

Chem1D: a software package for electronic structure calculations on one-dimensional systems

We present a preliminary version of a software package, Chem1D, that performs molecular orbital calculations on one-dimensional atoms and molecules using the unadorned Coulomb operator 1/|x₁ ? x₂|. We describe methods for computing the necessary one- and two-electron integrals and outline the overall structure of the package. We use Chem1D to perform calculations on a set of small molecules and show that one-dimensional chemistry differs in a number of interesting ways from three-dimensional chemistry.     

Supramolecular Design of Unsymmetric Reverse Bolaamphiphiles for Cell‐Sensitive Hydrogel Degradation and Drug Release

Self‐assembly of peptide‐based building units into supramolecular nanostructures creates an important class of biomaterials with robust mechanical properties and improved resistance to premature degradation. Yet, upon aggregation, substrate–enzyme interactions are often compromised because of the limited access of macromolecular proteins to the peptide substrate, leading to either a reduction or loss of responsiveness to biomolecular cues. Reported here is the supramolecular design of unsymmetric reverse bolaamphiphiles (RBA) capable of exposing a matrix metalloproteinase (MMP) substrate on the surface of their filamentous assemblies. Upon addition of MMP‐2, these filaments rapidly break into fragments prior to reassembling into spherical micelles. Using 3D cell culture, it is shown that drug release is commensurate with cell density, revealing more effective cell killing when more cancer cells are present. This design platform could serve as a cell‐responsive therapeutic depot for local chemotherapy.     

Feasibility of ultrasound phase contrast for heating localization

Ultrasound-based methods for temperature monitoring could greatly assist focused ultrasound visualization and treatment planning based on sound speed-induced change in phase as a function of temperature. A method is presented that uses reflex transmission integration, planar projection, and tomographic reconstruction techniques to visualize phase contrast by measuring the sound field before and after heat deposition. Results from experiments and numerical simulations employing a through-transmission setup are presented to demonstrate feasibility of using phase contrast methods for identifying temperature change. A 1.088-MHz focused transducer was used to interrogate a medium with a phase contrast feature, following measurement of the baseline reference field with a hydrophone. A thermal plume in water and a tissue phantom with multiple water columns was used in separate experiments to produce a phase contrast. The reference and phase contrast field scans were numerically backprojected and the phase difference correctly identified the position and orientation of the features. The peak temperature reconstructed from the phase shift was within 0.2 degrees C of the measured temperature in the plume. Simulated results were in good agreement with experimental results. Finally, employment of reflex transmission imaging techniques for adopting a pulse-echo arrangement was simulated, and its future experimental application is discussed.     

A Bass–Heller–Swan formula for pseudoisotopies

The Bass–Heller–Swan formula is a basic calculational tool in pseudoisotopy K-theory. We describe the Nil-groups and the Bass–Heller–Swan splitting for the group of the pseudoisotopies of a closed manifold. We use the methods of controlled topology used in the Bass–Heller–Swan splitting in K-theory.     

Iridium‐Catalyzed Stereoselective Allylic Alkylation Reactions with Crotyl Chloride

The development of the first enantio‐, diastereo‐, and regioselective iridium‐catalyzed allylic alkylation reaction of prochiral enolates to form an all‐carbon quaternary stereogenic center with an aliphatic‐substituted allylic electrophile is disclosed. The reaction proceeds with good to excellent selectivity with a range of substituted tetralone‐derived nucleophiles furnishing products bearing a newly formed vicinal tertiary and all‐carbon quaternary stereodyad. The utility of this protocol is further demonstrated via a number of synthetically diverse product transformations.     

Preparation of unsymmetrical sulfonylureas from N,N'-sulfuryldiimidazoles

The synthetic methods reported in the literature for the preparation of sulfonylureas tend to be restricted in scope or unsuitable for use in parallel synthesis. We have developed a method for preparing sterically congested sulfonylureas based on N,N'-sulfuryldiimidazole that is both convenient and amenable to parallel synthesis. Sequential activation by way of alkylation of the imidazole group using methyl triflate followed by nucleophilic displacement with a variety of amines and anilines afford the unsymmetrical sulfonylurea. Sulfonylureas prepared from anilines were obtained in high yields using N,N'-sulfuryldiimidazole, while the somewhat more sterically congested analogue, N,N'-sulfurylbis-2-methylimidazole, proved to be superior for alkylamines.     

Multiscale quantum propagation using compact-support wavelets in space and time

Orthogonal compact-support Daubechies wavelets are employed as bases for both space and time variables in the solution of the time-dependent Schrodinger equation. Initial value conditions are enforced using special early-time wavelets analogous to edge wavelets used in boundary-value problems. It is shown that the quantum equations may be solved directly and accurately in the discrete wavelet representation, an important finding for the eventual goal of highly adaptive multiresolution Schrodinger equation solvers. While the temporal part of the basis is not sharp in either time or frequency, the Chebyshev method used for pure time-domain propagations is adapted to use in the mixed domain and is able to take advantage of Hamiltonian matrix sparseness. The orthogonal separation into different time scales is determined theoretically to persist throughout the evolution and is demonstrated numerically in a partially adaptive treatment of scattering from an asymmetric Eckart barrier.     

Determination of lipid content and stability in lipid nanoparticles using ultra high-performance liquid chromatography in combination with a Corona Charged Aerosol Detector

For many years, lipid nanoparticles (LNPs) have been used as delivery vehicles for various payloads (especially various oligonucleotides and mRNA), finding numerous applications in drug and vaccine development. LNP stability and bilayer fluidity are determined by the identities and the amounts of the various lipids employed in the formulation and LNP efficacy is determined in large part by the lipid composition which usually contains a cationic lipid, a PEG-lipid conjugate, cholesterol, and a zwitterionic helper phospholipid. Analytical methods developed for LNP characterization must be able to determine not only the identity and content of each individual lipid component (i.e., the parent lipids), but also the associated impurities and degradants. In this work, we describe an efficient and sensitive reversed-phase chromatographic method with charged aerosol detection (CAD) suitable for this purpose. Sample preparation diluent and mobile phase pH conditions are critical and have been optimized for the lipids of interest. This method was validated for its linearity, accuracy, precision, and specificity for lipid analysis to support process and formulation development for new drugs and vaccines.