On structural decompositions of finite frames

A frame in an n-dimensional Hilbert space H _n is a possibly redundant collection of vectors {f _i } _i∈I that span the space. A tight frame is a generalization of an orthonormal basis. A frame {f _i } _i∈I is said to be scalable if there exist nonnegative scalars {c _i } _i∈I such that {c _i f _i } _i∈I is a tight frame. In this paper we study the combinatorial structure of frames and their decomposition into tight or scalable subsets by using partially-ordered sets (posets). We define the factor poset of a frame {f _i } _i∈I to be a collection of subsets of I ordered by inclusion so that nonempty J?I is in the factor poset iff {f _j } _j∈J is a tight frame for H _n . We study various properties of factor posets and address the inverse factor poset problem, which inquires when there exists a frame whose factor poset is some given poset P. We then turn our attention to scalable frames and present partial results regarding when a frame can be scaled to have a given factor poset; in doing so we present a bridge between erasure resilience (as studied via prime tight frames) and scalability.     

A coin vibrational motor swimming at low Reynolds number

Low-cost coin vibrational motors, used in haptic feedback, exhibit rotational internal motion inside a rigid case. Because the motor case motion exhibits rotational symmetry, when placed into a fluid such as glycerin, the motor does not swim even though its oscillatory motions induce steady streaming in the fluid. However, a piece of rubber foam stuck to the curved case and giving the motor neutral buoyancy also breaks the rotational symmetry allowing it to swim. We measured a 1 cm diameter coin vibrational motor swimming in glycerin at a speed of a body length in 3 seconds or at 3 mm/s. The swim speed puts the vibrational motor in a low Reynolds number regime similar to bacterial motility, but because of the oscillations of the motor it is not analogous to biological organisms. Rather the swimming vibrational motor may inspire small inexpensive robotic swimmers that are robust as they contain no external moving parts. A time dependent Stokes equation planar sheet model suggests that the swim speed depends on a steady streaming velocity V _stream ~ Re _s ^1/2 U ₀ where U ₀ is the velocity of surface oscillations, and streaming Reynolds number Re _s = U ₀ ² /(ων) for motor angular frequency ω and fluid kinematic viscosity ν.     

Simultaneous determination of glutathione and cysteine concentrations and 2H enrichments in microvolumes of neonatal blood using gas chromatography–mass spectrometry

A method is described whereby the concentrations and ²H isotope enrichment of glutathione (GSH) and cysteine can be simultaneously determined in a single gas chromatography–mass spectrometry run following derivatization as their N,S-ethoxycarbonyl methyl esters. Improvements of the derivatization protocol and the use of a short gas chromatography column combined with single-ion monitoring allow for rapid quantification of these parameters with acceptable precision and reproducibility (coefficient of variation less than 5%). The method makes possible their quantitative measurement in very small volumes (50 μL) of human umbilical cord blood, and is thus suitable for determining the cysteine and GSH concentrations and ²H isotope enrichments in blood samples from neonates or in other conditions in which sample size is restricted. It is shown that the fractional synthesis rate of human umbilical erythrocyte lysates in vitro is several-fold greater than that measured in vivo.     

(S,S)‐4′′‐Cyano‐7,7′′‐dimethoxy‐3′,6′‐dioxodispiro[indane‐2,2′‐piperazine‐5′,2′′‐indane]‐4‐carboxamide methanol solvate: interrupting the amide‐to‐amide hydrogen‐bonded tape

The title methanol solvate, C₂₄H₂₂N₄O₅·CH₃OH, forms an extended three‐dimensional hydrogen‐bonded structure, assisted by the presence of several good donor and acceptor sites. It shows none of the crystal packing features typically expected of piperazinediones, such as amide‐to‐amide R₂²(8) hydrogen bonding. In this structure the methanol solvent appears to play only a space‐filling role; it is not involved in any hydrogen bonding and instead is disordered over several sites. This study reports, to the best of our knowledge, the first crystal structure of an indane‐containing piperazinedione compound which exhibits a three‐dimensional hydrogen‐bonded structure formed by classical (N—H...O and N—H...N) hydrogen‐bonding interactions.     

Electrochemical deposition of a copper carboxylate layer on copper as potential corrosion inhibitor

Carboxylic acids and sodium carboxylates are used to protect metals against aqueous and atmospheric corrosion. In this paper, we describe the application of a layer of copper carboxylate on the surface of a copper electrode by means of cyclic voltammetry technique and tests which measure the corresponding resistance to aqueous corrosion. Unlike the soaking process, which also forms a film on the surface, the use of cyclic voltammetry allows one to follow the deposition process of the copper carboxylates onto the electrode. The modified electrodes have been characterised with infrared spectroscopy. In addition, the corrosion resistance of the film has been investigated using polarisation resistance and Tafel plot measurements.     

Studies of inhibitor binding to the [4Fe-4S] cluster of quinolinate synthase

Stop for NadA! A [4Fe-4S] enzyme, NadA, catalyzes the formation of quinolinic acid in de?novo nicotinamide adenine dinucleotide (NAD) biosynthesis. A structural analogue of an intermediate, 4,5-dithiohydroxyphthalic acid (DTHPA), has an in?vivo NAD biosynthesis inhibiting activity in E. coli. The inhibitory effect can be explained by the coordination of DTHPA thiolate groups to a unique Fe site of the NadA [4Fe-4S] cluster.     

Micropatterning topology on soft substrates affects myoblast proliferation and differentiation

Micropatterning techniques and substrate engineering are becoming useful tools to investigate several aspects of cell-cell interaction biology. In this work, we rationally study how different micropatterning geometries can affect myoblast behavior in the early stage of in vitro myogenesis. Soft hydrogels with physiological elastic modulus (E = 15 kPa) were micropatterned in parallel lanes (100, 300, and 500 μm width) resulting in different local and global myoblast densities. Proliferation and differentiation into multinucleated myotubes were evaluated for murine and human myoblasts. Wider lanes showed a decrease in murine myoblast proliferation: (69 ± 8)% in 100 μm wide lanes compared to (39 ± 7)% in 500 μm lanes. Conversely, fusion index increased in wider lanes: from (46 ± 7)% to (66 ± 7)% for murine myoblasts, and from (15 ± 3)% to (36 ± 2)% for human primary myoblasts, using a patterning width of 100 and 500 μm, respectively. These results are consistent with both computational modeling data and conditioned medium experiments, which demonstrated that wider lanes favor the accumulation of endogenous secreted factors. Interestingly, human primary myoblast proliferation is not affected by patterning width, which may be because the high serum content of their culture medium overrides the effect of secreted factors. These data highlight the role of micropatterning in shaping the cellular niche through secreted factor accumulation, and are of paramount importance in rationally understanding myogenesis in vitro for the correct design of in vitro skeletal muscle models.     

Spontaneous grafting of diazonium salts: chemical mechanism on metallic surfaces

The spontaneous reaction of diazonium salts on various substrates has been widely employed since it consists of a simple immersion of the substrate in the diazonium salt solution. As electrochemical processes involving the same diazonium salts, the spontaneous grafting is assumed to give covalently poly(phenylene)-like bonded films. Resistance to solvents and to ultrasonication is commonly accepted as indirect proof of the existence of a covalent bond. However, the most relevant attempts to demonstrate a metal-C interface bond have been obtained by an XPS investigation of spontaneously grafted films on copper. Similarly, our experiments give evidence of such a bond in spontaneously grafted films on nickel substrates in acetonitrile. In the case of gold substrates, the formation of a spontaneous film was unexpected but reported in the literature in parallel to our observations. Even if no interfacial bond was observed, formation of the films was explained by grafting of aryl cations or radicals on the surface arising from dediazoniation, the film growing later by azo coupling, radical addition, or cationic addition on the grafted phenyl layer. Nevertheless, none of these mechanisms fits our experimental results showing the presence of an Au-N bond. In this work, we present a fine spectroscopic analysis of the coatings obtained on gold and nickel substrates that allow us to propose a chemical structure of such films, in particular, their interface with the substrates. After testing the most probable mechanisms, we have concluded in favor of the involvement of two complementary mechanisms which are the direct reaction of diazonium salts with the gold surface that accounts for the observed Au-N interfacial bonds as well as the formation of aryl cations able to graft on the substrate through Au-C linkages.