机器具有准备时间的双目标平行机排序问题

本文讨论机器具有准备时间的双目标平行机排序问题，目标函数为完工时间和最优条件下极小化最大完工时间．通过对SPT排序的性质的分析，给出了最优排序的下界．在此基础上证明了SPT排序的误差界为3／2，并且是紧界．     

Frames with Transitive Structures

A classical result in the theory of uniform spaces is that any topological space with a base of clopen sets admits a uniformity with a transitive base and the uniform topology of such a space has a base of clopen sets. This paper presents a pointfree generalization of this, both to uniform and quasi-uniform frames, together with various properties concerning total boundedness, compactifications and completions.     

Bounds for the Perron root, singularity/nonsingularity conditions, and eigenvalue inclusion sets

Using a unified approach based on the monotonicity property of the Perron root and its circuit extension, a series of exact two-sided bounds for the Perron root of a nonnegative matrix in terms of paths in the associated directed graph is obtained. A method for deriving the so-called mixed upper bounds is suggested. Based on the upper bounds for the Perron root, new diagonal dominance type conditions for matrices are introduced. The singularity/nonsingularity problem for matrices satisfying such conditions is analyzed, and the associated eigenvalue inclusion sets are presented. In particular, a bridge connecting Gerschgorin disks with Brualdi eigenvalue inclusion sets is found. Extensions to matrices partitioned into blocks are proposed.     

Tensor train completion: Local recovery guarantees via Riemannian optimization

In this work, we estimate the number of randomly selected elements of a tensor that with high probability guarantees local convergence of Riemannian gradient descent for tensor train completion. We derive a new bound for the orthogonal projections onto the tangent spaces based on the harmonic mean of the unfoldings' singular values and introduce a notion of core coherence for tensor trains. We also extend the results to tensor train completion with auxiliary subspace information and obtain the corresponding local convergence guarantees.     

Automated solvent system screening for the preparative countercurrent chromatography of pharmaceutical discovery compounds

A fully automated countercurrent chromatography system has been constructed to rapidly screen the commonly used heptane/ethyl acetate/methanol/water solvent system series and translate the results to preparative scale separations. The system utilizes “on‐demand” preparation of the heptane/ethyl acetate/methanol/water solvent system upper and lower phases. Elution‐extrusion countercurrent chromatography was combined with non‐dynamic equilibrium injection reducing the screening time for each heptane/ethyl acetate/methanol/water system to 17 min. The result enabled solvent system development to be reduced to under 2 h. The countercurrent chromatography system was interfaced with a mass spectrometer to allow selective detection of target components in crude medicinal chemistry reaction mixtures. Mass‐directed preparative countercurrent chromatography purification was demonstrated for the first time using a synthetic tetrazole epoxide derived from a routine medicinal chemistry support workflow.     

Directed Self‐Assembly of Diblock Copolymer Thin Films on Prepatterned Metal Nanoarrays

The sequential layer by layer self‐assembly of block copolymer (BCP) nanopatterns is an effective approach to construct 3D nanostructures. Here large‐scale highly ordered metal nano­arrays prepared from solvent annealed thin films of polystyrene‐block‐poly(2‐vinylpyridine) (PS‐b‐P2VP) diblock copolymer are used to direct the assembly of the same BCP. The influence of initial loading concentration of metal precursor, the type of metal nanoparticle (gold, platinum, and silver), and the nanoparticle–substrate interaction on the directed assembly behavior of the upper BCP layer have been focused. It is found that the upper BCP film can be completely directed by the gold nanoarray with P2VP domain exclusively located between two adjacent gold nanowires or nanodots, which behaves the same way as on the platinum nanoarray. While the silver nanoarray can be destroyed during the upper BCP self‐assembly with the silver nanoparticles assembled into the P2VP domain. Based on the discussions of the surface energy of nanoparticles and the interplay between nanoparticle–substrate interaction and nanoparticle–polymer interaction, it is concluded that the effect of immobilization of nanoparticles on the substrate, together with entropy effect to minimize the energetically unfavorable chain stretching contributes to the most effective alignment between each layer.

     

Directed Assembly of Soft Anisotropic Nanoparticles by Colloid Electrospinning

Directed assembly of triblock copolymer worms to produce nanostructured fibers is achieved via colloid electrospinning. These copolymer worms are conveniently prepared by polymerization‐induced self‐assembly in concentrated aqueous dispersion. Addition of a second water‐soluble component, poly(vinyl alcohol), is found to be critical for the production of well‐defined fibers: trial experiments performed using the worms alone produce only spherical microparticles. Transmission electron microscopy studies confirm that the worm morphology survives electrospinning and the worms become orientated parallel to the main axis of the fibers during their generation. The average deviant angle (θ_dev) between the worm orientation and fiber axis decreases from 17° to 9° as the worm/PVA mass ratio increases from 1.15:1 to 5:1, indicating a greater degree of worm alignment within fibers with higher worm contents and smaller fiber diameters. Thus triblock copolymer fibers of ≈300 ± 120 nm diameter can be readily produced that comprise aligned worms on the nanoscale.

     

Low rank matrix recovery from rank one measurements

We study the recovery of Hermitian low rank matrices $X\in {\mathbb{C}}^{n\times n}$ from undersampled measurements via nuclear norm minimization. We consider the particular scenario where the measurements are Frobenius inner products with random rank-one matrices of the form $a_j{a}_j^{?}$ for some measurement vectors $a_1,\dots ,a_m$, i.e., the measurements are given by $b_j=\mathrm{tr}(X{a}_j{a}_j^{?})$. The case where the matrix $X=x{x}^{?}$ to be recovered is of rank one reduces to the problem of phaseless estimation (from measurements $b_j=|〈x,a_j〉{|}^2$) via the PhaseLift approach, which has been introduced recently. We derive bounds for the number m of measurements that guarantee successful uniform recovery of Hermitian rank r matrices, either for the vectors $a_j$, $j=1,\dots ,m$, being chosen independently at random according to a standard Gaussian distribution, or $a_j$ being sampled independently from an (approximate) complex projective t-design with $t=4$. In the Gaussian case, we require $m\ge Crn$ measurements, while in the case of 4-designs we need $m\ge \mathit{Cr}n\log ?(n)$. Our results are uniform in the sense that one random choice of the measurement vectors $a_j$ guarantees recovery of all rank r-matrices simultaneously with high probability. Moreover, we prove robustness of recovery under perturbation of the measurements by noise. The result for approximate 4-designs generalizes and improves a recent bound on phase retrieval due to Gross, Krahmer and Kueng. In addition, it has applications in quantum state tomography. Our proofs employ the so-called bowling scheme which is based on recent ideas by Mendelson and Koltchinskii.