X-ray Crystal Structure of Trans -UO2(N(SiMe3)2)2(THF)2: One in a Series of Uranyl(VI) Complexes Supported by Bis(trimethylsilyl)amido Ligands

Abstract The title compound trans-UO₂(N(SiMe₃)₂)₂(THF)₂ (1) was synthesized and characterized by X-ray crystallography. The complex crystallizes in the monoclinic space group C2/c (#15) with lattice parameters a = 16.0771(5) ?, b = 13.1196(4) ?, c = 16.9391(6) ?, β = 116.853(1)°, V = 3187.61(18) ?³, Z = 4, D _calc = 1.532 g cm^-3. The six-coordinate uranium(VI) center adopts an all-trans octahedral geometry consisting of mutually trans oxo groups, silylamido ligands, and neutral THF donors. Structural comparisons of this uranyl(VI) bis(amido) complex with a related tris(amido) derivative within the series are made based on symmetry, charge, and coordination number. Graphical Abstract The X-ray crystal structure of the title complex is reported, providing comparisons based on symmetry, charge, and coordination number with a related uranyl(VI) amido derivative within this series.      

Intrinsic ergodicity beyond specification: β-shifts, S-gap shifts, and their factors

We give sufficient conditions for a shift space (Σ, σ) to be intrinsically ergodic, along with sufficient conditions for every subshift factor of Σ to be intrinsically ergodic. As an application, we show that every subshift factor of a β-shift is intrinsically ergodic, which answers an open question included in Mike Boyle’s article “Open problems in symbolic dynamics”. We obtain the same result for S-gap shifts, and describe an application of our conditions to more general coded systems. One novelty of our approach is the introduction of a new version of the specification property that is well adapted to the study of symbolic spaces with a non-uniform structure.     

Selective formation of covalent protein heterodimers with an unnatural amino acid

We report a strategy for the generation of heterodimeric protein conjugates using an unnatural amino acid with orthogonal reactivity. This paper addresses the challenges of site-specificity and homogeneity with respect to the synthesis of bivalent proteins and antibody-drug conjugates. There are numerous antibody-drug conjugates in preclinical and clinical development, yet these are based either on nonspecific lysine coupling chemistry or on disulfide modification made difficult by the large number of cysteines in antibodies. Here, we describe a recombinant approach that can be used to rapidly generate a variety of constructs with defined conjugation sites. Moreover, this methodology results in homogeneous antibody conjugates whose biological, physical, and pharmacological properties can be quantitatively assessed and subsequently optimized. As proof of concept, we have generated anti-Her2 Fab-Saporin conjugates that demonstrate excellent potency in vitro.     

Impact of gradient timing error on the tissue sodium concentration bioscale measured using flexible twisted projection imaging

The rapid biexponential transverse relaxation of the sodium MR signal from brain tissue requires efficient k-space sampling for quantitative imaging in a time that is acceptable for human subjects. The flexible twisted projection imaging (flexTPI) sequence has been shown to be suitable for quantitative sodium imaging with an ultra-short echo time to minimize signal loss. The fidelity of the k-space center location is affected by the readout gradient timing errors on the three physical axes, which is known to cause image distortion for projection-based acquisitions. This study investigated the impact of these timing errors on the voxel-wise accuracy of the tissue sodium concentration (TSC) bioscale measured with the flexTPI sequence. Our simulations show greater than 20% spatially varying quantification errors when the gradient timing errors are larger than 10 μs on all three axes. The quantification is more tolerant of gradient timing errors on the Z-axis. An existing method was used to measure the gradient timing errors with <1 μs error. The gradient timing error measurement is shown to be RF coil dependent, and timing error differences of up to ～16 μs have been observed between different RF coils used on the same scanner. The measured timing errors can be corrected prospectively or retrospectively to obtain accurate TSC values.     

Asymptotic freedom constraints on grand unified gauge theories

Constraints on the fermion and Higgs scalar content of grand unified gauge theories, imposed by the requirement of asymptotic freedom for the gauge couplings, are derived for models which have fermion representations with only color singlets and color triplets. The constraintn _f ≦16 on the numbern _f of flavors of color triplet quarks in pure QCD is removed. Definitive limits are placed on the representation content of theories based on the exceptional groups.     

Molecular dynamics simulation of nanoparticle self-assembly at a liquid-liquid interface

We have used molecular dynamics simulations to investigate the in situ self-assembly of modified hydrocarbon nanoparticles (mean diameter of 1.2 nm) at a water-trichloroethylene (TCE) interface. The nanoparticles were first distributed randomly in the water phase. The MD simulation shows the in situ formation of nanoparticle clusters and the migration of both single particles and clusters from the water phase to the trichloroethylene phase, possibly due to the hydrophobic nature of the nanoparticles. Eventually, the single nanoparticles or clusters equilibrate at the water-TCE interface, and the surrounding liquid molecules pack randomly when in contact with the nanoparticle surfaces. In addition, the simulations show that the water-TCE interfacial thickness analyzed from density profiles is influenced by the presence of nanoparticles either near or in contact with the interface but is independent of the number of nanoparticles present. The nanoparticles, water molecules, and TCE molecules all exhibit diffusion anisotropy.     

Variational calculations with unbounded operators

In a constrained variational calculation, the minimum of the expectation value of an operator H, subject to the constraint that the expectation value of an operator A have a definite value, is sought. Fonte and Schiffrer have recently noted that the Lagrange multiplier method of of determining the solution to this problem fails when the operator A is unbounded. We show that in this case, the expectation value of H can be made arbitrarily close to the unconstrained minimum, for any constrained value of 〈A〉. This result casts doubt on the validity of the results of calculations, in which an unbounded operator (such as the quadrupole moment of a nucleus) is constrained, even if these calculations are carried out using a finite-dimensional basis in which the restricted operator is bounded. Various alternatives to these calculations are discussed.     

Tensor methods for the exceptional group E6

We present a tensor formalism to describe irreducible representations of the exceptional group E₆. Irreducible tensors are characterized by covariant and contravariant indices associated with the irreducible representation 27, and a third (orthogonal-type) index associated with the 78; contractions of these indices with a set of invariant tensors are required to vanish for irreducibility. The formalism is applied to the reduction of Kronecker products of E₆ irreducible representations. As a further illustration of the method, we construct explicitly the Higgs potential for scalar fields in the E₆ representations 27, 78, 351, 351′.     

The direct histogram method for quasiclassical collision dynamics: application to collinear atom-diatom scattering

A method is presented for directly propagating ensembles of collision trajectories, such the histogram-type final state distributions are obtained. A substantial savings over standard quasiclassical methods is possible since only a few trajectory ensembles need to be propagated.