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Analytical and Bioanalytical Chemistry -     

Equiangular tight frames with centroidal symmetry

An equiangular tight frame (ETF) is a set of unit vectors whose coherence achieves the Welch bound, and so is as incoherent as possible. Though they arise in many applications, only a few methods for constructing them are known. Motivated by the connection between real ETFs and graph theory, we introduce the notion of ETFs that are symmetric about their centroid. We then discuss how well-known constructions, such as harmonic ETFs and Steiner ETFs, can have centroidal symmetry. Finally, we establish a new equivalence between centroid-symmetric real ETFs and certain types of strongly regular graphs (SRGs). Together, these results give the first proof of the existence of certain SRGs, as well as the disproofs of the existence of others.     

Pumpless dispensing of a droplet by breaking up a liquid bridge formed by electric induction

Dispensing uniform pico‐to‐nanoliter droplets has become one of essential components in various application fields from high‐throughput bio‐analysis to printing. In this study, a new method is suggested and demonstrated for dispensing a droplet on the top plate with an inverted geometry by using electric field. The process of dispensing droplets consists of two stages: (i) formation of liquid bridge by moving up the charged fluid mass using the electrostatic force between the charges on the fluid mass and the induced charges on the substrate and (ii) its break‐up by the motion of the top plate. Different from conventional electrohydrodynamic methods, electric induction enables the droplets to be dispensed on various surfaces including non‐conducting substrate. The use of capillarity with an inverted geometry removes the need of external pumps or elaborates control for constant flow feed. The droplet diameter has been characterized as a function of the nozzle‐to‐plate distance and the plate moving velocity. The robustness of the present method is shown in terms of nozzle length and applied voltage. Finally, its practical applicability is confirmed by rendering a 19 by 24 array of highly uniform droplets with only 1.8% size variation without use of any active feedback control.     

A Quick and Reproducible Silanization Method by Using Plasma Activation for Hydrophobicity-Based Kinesin Single Molecule Fluorescence–Microscopy Assays

Single-molecule assays often require functionalized surfaces. One approach for microtubule assays renders surfaces hydrophobic and uses amphiphilic blocking agents. However, the optimal hydrophobicity is unclear, protocols take long, produce toxic waste, and are susceptible to failure. Our method uses plasma activation with hydrocarbons for hexamethyldisilazane (HMDS) silanization in the gas phase. We measured the surface hydrophobicity, its effect on how well microtubule filaments were bound to the surface, and the number of nonspecific interactions with kinesin motor proteins. Additionally, we tested and discuss the use of different silanes and activation methods. We found that even weakly hydrophobic surfaces were optimal. Our environmentally friendly method significanty reduced the overall preparation effort and resulted in reproducible, high-quality surfaces with low variability. We expect the method to be applicable to a wide range of other single-molecule assays.     

Hiscotropic rearrangements: hybrids of electrocyclic and sigmatropic reactions

An unusual reaction manifold for cyclopropylcarbinyl cations, uncovered using B3LYP and MP2 calculations, is described. This reaction is a hybrid of a [1,2] sigmatropic hydrogen shift and a two-electron electrocyclic ring opening. These two processes occur through a single transition structure (i.e., they are concerted), although they are not synchronous. We call these reactions "hiscotropic" rearrangements. The potential energy surfaces for these reactions are often complicated, in some cases involving flat plateaus and bifurcations. Torquoselectivity occurs in some cases as a result of favorable orbital interactions between the breaking C-C and C-H bonds.     

Continuous-wave solid-state dye laser

We report the first realization of a cw solid-state dye laser. The laser medium consists of a laser dye (Rhodamine 6G) dissolved in a photopolymer. The UV-cured solution is sandwiched between two DVD substrates. The resonator design was derived from a conventional liquid solvent dye laser geometry. The laser radiation can be tuned from 565 to 615 nm by using a birefringent filter. A pump power of 2 W leads to a cw output power of more than 20 mW.     

Discrete Uncertainty Principles and Sparse Signal Processing

We develop new discrete uncertainty principles in terms of numerical sparsity, which is a continuous proxy for the 0-norm. Unlike traditional sparsity, the continuity of numerical sparsity naturally accommodates functions which are nearly sparse. After studying these principles and the functions that achieve exact or near equality in them, we identify certain consequences in a number of sparse signal processing applications.