Variability of spatio-temporal patterns in non-homogeneous rings of spiking neurons

We show that a ring of unidirectionally delay-coupled spiking neurons may possess a multitude of stable spiking patterns and provide a constructive algorithm for generating a desired spiking pattern. More specifically, for a given time-periodic pattern, in which each neuron fires once within the pattern period at a predefined time moment, we provide the coupling delays and/or coupling strengths leading to this particular pattern. The considered homogeneous networks demonstrate a great multistability of various travelling time- and space-periodic waves which can propagate either along the direction of coupling or in opposite direction. Such a multistability significantly enhances the variability of possible spatio-temporal patterns and potentially increases the coding capability of oscillatory neuronal loops. We illustrate our results using FitzHugh-Nagumo neurons interacting via excitatory chemical synapses as well as limit-cycle oscillators.     

Approaches to the enantioselective synthesis of ferrugine and its analogues

A four-step synthetic route, to ferrugine (2α-benzoyltropane), its methyl analogue (2-acetyltropane) and their N-benzyl analogues is reported. The reaction sequence uses tropinone or N-benzylnortropinone aldols as key intermediates. Reduction of aldol derived N-tosylhydrazones and oxidation of the side chain hydroxyl group followed by spontaneous diastereomer equilibration provides the final products. Relative configuration of the exo,anti N-methyl and N-benzyl aldols was retained during N-tosylhydrazone formation. The relative stereochemistry of N-tosylhydrazones was assigned by single crystal diffraction. The final products, ferrugine and its methyl analogue, were synthesized in enantiomerically pure form via asymmetric deprotonation of tropinone using chiral lithium amide/lithium chloride aggregate prepared in situ from (S,S)-N,N-bis(1-phenylethyl)amine hydrochloride.     

Greedy Algorithms for Reduced Bases in Banach Spaces

Given a Banach space X and one of its compact sets $\mathcal{F}$ , we consider the problem of finding a good n-dimensional space X _n ?X which can be used to approximate the elements of $\mathcal{F}$ . The best possible error we can achieve for such an approximation is given by the Kolmogorov width $d_{n}(\mathcal{F})_{X}$ . However, finding the space which gives this performance is typically numerically intractable. Recently, a new greedy strategy for obtaining good spaces was given in the context of the reduced basis method for solving a parametric family of PDEs. The performance of this greedy algorithm was initially analyzed in Buffa et al. (Modél. Math. Anal. Numér. 46:595–603, 2012) in the case $X=\mathcal{H}$ is a Hilbert space. The results of Buffa et al. (Modél. Math. Anal. Numér. 46:595–603, 2012) were significantly improved upon in Binev et al. (SIAM J. Math. Anal. 43:1457–1472, 2011). The purpose of the present paper is to give a new analysis of the performance of such greedy algorithms. Our analysis not only gives improved results for the Hilbert space case but can also be applied to the same greedy procedure in general Banach spaces.     

Efficient synthesis of globoside and isogloboside tetrasaccharides by using beta(1-->3) N-acetylgalactosaminyltransferase/UDP-N-acetylglucosamine C4 epimerase fusion protein

The beta(1-->3) N-acetylgalactosaminyltransferase/UDP-N-acetylglucosamine C4 epimerase fusion protein was constructed and used in coupled enzymatic reactions to synthesize a variety of globotetraose and isoglobotetraose derivatives from the corresponding lactoside acceptors.     

Rotationally resolved electronic spectroscopy of a nonlinear carbon chain radical C6H4

Rotationally resolved electronic spectrum of the origin band in the 2A″-X2A″ transition of a nonlinear carbon chain radical C₆H₄⁺ has been recorded in the 604 nm region using cw cavity ring down spectroscopy. The radical was produced by a discharge through an acetylene-helium mixture in a supersonic planar expansion. The rotational structure has been analysed and precisely determined. A band having a-type prolate rotational structure has also been observed near 581 nm. By considering the results of ab initio calculations this band is assigned to a transition involving the excitation of the ν₁₂ fundamental in the upper 2A″ electronic state of the same C₆H₄⁺ isomer.     

Linear and nonlinear optical studies in photonic crystal alloys

We report on linear transmittance and reflectance as well as on third-harmonic generation in photonic crystal alloys formed by various compositions of polystyrene and poly (methyl methacrylate) colloidal spheres of the same size. These photonic crystal alloys are structurally ordered but contain refractive-index disorder and thus provide a random variation of scattering potential. The stopgap shows a monotonic shift in wavelength as a function of composition that can be fitted by assuming an effective dielectric constant for the colloidal spheres. In each alloy a dramatic enhancement of third-harmonic generation is observed, always on the short-wavelength side of the stopgap.     

The surface tension and density of the Cu-Ag-In alloys

The surface tension and the densities of the Cu-Ag-In alloys have been measured by means of the sessile drop method. The density of these alloys depends linearly on temperature in the case of all the investigated compositions. The surface tension shows a linear dependence on temperature except for the lowest temperatures. For most of the alloys, the surface tension at the lowest temperature is lower than that predicted by the straight line. The experimental values of the surface tension of the Cu-Ag-In alloys are compared with those computed from the model, and quite good agreement is observed.     

Characterization of poly(vinyl alcohol) hydrogel for prosthetic intervertebral disc nucleus

In the recent years, development of intervertebral disc prosthesis has been of great concern to the world of medicine and science. Substitution of the spinal disc or its part being displaced or damaged due to trauma or a disease process for the artificial structure well imitating high tensile properties and elasticity of the real disc would highly improve the existing treatment techniques. In this work, the attempt to develop the PVA-based hydrogel material for artificial spinal disc has been made. The polymer was initially processed with the use of formaldehyde solution as a crosslinking agent and sulfuric acid as a catalyst. Then properties of the material have been altered by saturating the already existing PVA hydrogel with a mixture of hydrophilic and hydrophobic monomers (2-hydroxyethyl methacrylate and methyl methacrylate) and a subsequent exposure to ionizing radiation (⁶⁰Co source). In this way, interpenetrating polymer network has been built on the crosslinked PVA scaffold. Resulting structures were tested for their mechanical behavior at different loads. Series of measurements leading to the determination of the physicochemical properties of created gels including crosslink density and swelling abilities were also performed.     

Mesolytic Scission of C-C Bonds as a Probe for Photoinduced Electron Transfer Reactions of Quinones

Photoinduced electron transfer reactions of chlorinated benzoquinones are investigated using bibenzylic donors that undergo rapid fragmentation upon oxidation. The fragmentation rates and the quantum yields are used to probe the dynamics of back-electron transfer (BET) in two types of radical ion pairs. The triplet ion pairs formed by interception of excited state quinones give products with high quantum yields. The singlet ion pairs formed by irradiation of the charge-transfer (CT) complexes between the quinones and the donors undergo reactions with significantly lower efficiency. The advantage of the first method (triplet quenching) over the CT-irradiation depends on the energetics of BET. It is large for reactions with relatively small DeltaG(et) for BET and it decreases for reactions with more negative DeltaG(bet). The indirectly obtained rates of BET are in excellent agreement with literature data for similar, but unreactive systems, and the rates of C-C bond scission in radical cations generated in these systems are consistent with the thermodynamics of these processes.