On the “log rank”-conjecture in communication complexity

We show the existence of a non-constant gap between the communication complexity of a function and the logarithm of the rank of its input matrix. We consider the following problem: each of two players gets a perfect matching between twon-element sets of vertices. Their goal is to decide whether or not the union of the two matcliings forms a Hamiltonian cycle. We prove:

1. The rank of the input matrix over the reals for this problem is 2 ^O(n) .
2. The non-deterministic communication complexity of the problem is Ω(nloglogn).

Our result also supplies a superpolynomial gap between the chromatic number of a graph and the rank of its adjacency matrix. Another conclusion from the second result is an Ω(nloglogn) lower bound for the graph connectivity problem in the non-deterministic case. We make use of the theory of group representations for the first result. The second result is proved by an information theoretic argument.     

Method for combinatorial screening of moisture vapor transmission rate

A high-throughput method for screening the moisture vapor transmission rate of barrier films was developed. This moisture high-throughput screening (MHTS) technique is based upon a Nafion-crystal violet (CVN) sensor that changes color from yellow to green upon absorption of water. Using an appropriate set of known standards, the slope of absorbance (at 630 nm) as a function of time can be converted into moisture vapor transmission rate (MVTR) values that agree with those obtained using ASTM F1290. High-throughput screening was demonstrated by depositing 20 emulsion-based poly(vinylidene chloride) films, using a 48-well template, of varying thicknesses onto the CVN sensor film and aging at 40 degrees C and 90% relative humidity for 72 h. MVTR values were accurately determined to a level of 0.9 g/m(2).day, at which point side-diffusion of moisture between the barrier and sensor films prevented observation of lower values. Larger sample size and edge-sealing are two proposed methods for improving the sensitivity of MHTS.     

Wannier states of molecular impurity in a liquid rare gas

We have measured the vacuum ultraviolet absorption spectra of CH₃I in solid and in liquid krypton in the spectral region 2000–1450 Å. In both phases we have observed two Wannier series n(²E_{$\text{3}\text{2}$}) and n(²E_{$\text{1}\text{2}$}) up to n = 3. Information has been obtained concerning the features of the conduction band in a liquid rare gas.     

Alpha-N-acetylmannosamine (ManNAc) synthesis via rhodium(II)-catalyzed oxidative cyclization of glucal 3-carbamates

[reaction: see text] Glucal 3-carbamates 1 and 7 underwent oxidative cyclization with iodobenzene diacetate or iodosobenzene in the presence of Rh2(OAc)4, providing mannosamine 2-N,3-O-oxazolidinones. With iodosobenzene, incorporation of 4-penten-1-ol provided a readily separable anomeric mixture of n-pentenyl glycosides, with the anomers exhibiting pronounced differences in reactivity as glycosyl donors. N-acylation of the sugar oxazolidinones led to alpha-selective glycosyl donors for the elaboration of various 2-mannosamine frameworks. Alternatively, the anomeric n-pentenyl glycosides of N-Cbz 2-mannosamine oxazolidinones were converted separately to oxazolidinone-opened derivatives 28alpha and 28beta. These served as stereoconvergent glycosyl donors, and the alpha-linked products were readily advanced to a variety of N-acetylmannosamine (ManNAc) frameworks, using an intramolecular O-->N acetyl transfer as the final step.     

Voltammetric studies on the reduction of polyoxometalate anions in ionic liquids

The electrochemical reduction of tetrabutylammonium salts of isostructural pairs of polyoxometalates [Bu4N]2[M6O19], [Bu4N]4[alpha-SiM12O40], and [Bu4N]4[alpha-S2M18O62] (M = Mo or W) has been investigated at glassy carbon electrodes in dissolved and surface-confined states in ionic liquids and other media. In the ionic liquid 1-n-butyl-3-methylimidazolium hexafluorophosphate [BMIM][PF(6)], between two and six reversible one-electron-transfer processes were detected. Detailed studies on the process [alpha-S2W18O62](4-/5-) in a range of ionic liquids, water, and conventional organic solvents (containing 0.1 M electrolyte) suggest that the polarity of the medium plays a key role in the determination of the reversible potential. Reduction processes involving very highly charged [alpha-S2W18O62](8-/9-/10-) species are strongly influenced by the purity of the medium.     

A Highly Stable,Capacity Dense Carboxylate Viologen Anolyte towards Long-Duration Energy Storage

Aqueous organic redox flow batteries (AORFBs) have received increasing attention as an emergent battery technology for grid-scale renewable energy storage. However, physicochemical properties of redox-active organic electrolytes remain fine refinement to maximize their performance in RFBs. Herein, we report a carboxylate functionalized viologen derivative, N,N′-dibutyrate-4,4′-bipyridinium, (CBu)₂V , as a highly stable, high capacity anolyte material under near pH neutral conditions. (CBu)₂V can achieve solubility of 2.1 M and display a reversible, kinetically fast reduction at −0.43 V vs NHE at pH 9. DFT studies revealed that the high solubility of (CBu)₂V is attributed to its high molecular polarity while its negative reduction potential is benefitted from electron-donating carboxylate groups. A 0.89 V ( CBu)₂V /(NH)₄Fe(CN)₆ AORFB demonstrated exceptional energy storage performance, specifically, 100 % capacity retention with a discharge energy density of 9.5 Wh L⁻¹ for 1000 cycles, power densities of up to 85 mW cm⁻², and an energy efficiency of 70 % at 60 mA cm⁻². (CBu)₂V not only represents the most capacity dense viologen with pendant ionic groups and also exhibits the longest (1200 hours or 50 days) and the most stable flow battery performance to date.     

In Vitro Proof of Concept of a First-Generation Growth-Accommodating Heart Valved Conduit for Pediatric Use

Currently available heart valve prostheses have no growth potential, requiring children with heart valve diseases to endure multiple valve replacement surgeries with compounding risks. This study demonstrates the in vitro proof of concept of a biostable polymeric trileaflet valved conduit designed for surgical implantation and subsequent expansion via transcatheter balloon dilation to accommodate the growth of pediatric patients and delay or avoid repeated open-heart surgeries. The valved conduit is formed via dip molding using a polydimethylsiloxane-based polyurethane, a biocompatible material shown here to be capable of permanent stretching under mechanical loading. The valve leaflets are designed with an increased coaptation area to preserve valve competence at expanded diameters. Four 22 mm diameter valved conduits are tested in vitro for hydrodynamics, balloon dilated to new permanent diameters of 23.26 ± 0.38 mm, and then tested again. Upon further dilation, two valved conduits sustain leaflet tears, while the two surviving devices reach final diameters of 24.38 ± 0.19 mm. After each successful dilation, the valved conduits show increased effective orifice areas and decreased transvalvular pressure differentials while maintaining low regurgitation. These results demonstrate concept feasibility and motivate further development of a polymeric balloon-expandable device to replace valves in children and avoid reoperations.     

Reactivity of electrochemically generated rhenium (II) Tricarbonyl alpha-diimine complexes: a reinvestigation of the oxidation of luminescent Re(CO)3(alpha-Diimine)Cl and related compounds

The oxidative electrochemistry of luminescent rhenium (I) complexes of the type Re(CO) 3(LL)Cl, 1, and Re(CO) 3(LL)Br, 2, where LL is an alpha-diimine, was re-examined in acetonitrile. These compounds undergo metal-based one-electron oxidations, the products of which undergo rapid chemical reaction. Cyclic voltammetry results imply that the electrogenerated rhenium (II) species 1 ( + ) and 2 ( + ) disproportionate, yielding [Re(CO) 3(LL)(CH 3CN)] (+), 7, and additional products. Double potential step chronocoulometry experiments confirm that 1 ( + ) and 2 ( + ) react via second-order processes and, furthermore, indicate that the rate of disproportionation is influenced by the basicity and steric requirements of the alpha-diimine ligands. The simultaneous generation of rhenium (I) and (III) carbonyl products was detected upon the bulk oxidation of 1 using infrared spectroelectrochemistry. The rhenium (III) products are assigned as [Re(CO) 3(LL)Cl 2] (+), 5; an inner-sphere electron-transfer mechanism of the disproportionation is proposed on the basis of the apparent chloride transfer. Chemically irreversible two-electron reduction of 5 yields 1 and Cl (-). No direct spectroscopic evidence was obtained for the generation of rhenium (III) tricarbonyl bromide disproportionation products, [Re(CO) 3(LL)Br 2] (+), 6; this is attributed to their relatively rapid decomposition to 7 and dibromine. In addition, the 17-electron radical cations, 7 ( + ), were successfully characterized using infrared spectroelectrochemistry.