Stochastic resonance in hybrid scale-free neuronal networks

We study the phenomenon of stochastic resonance in a system of coupled neurons that are globally excited by a weak periodic input signal. We make the realistic assumption that the chemical and electrical synapses interact in the same neuronal network, hence constituting a hybrid network. By considering a hybrid coupling scheme embedded in the scale-free topology, we show that the electrical synapses are more efficient than chemical synapses in promoting the best correlation between the weak input signal and the response of the system. We also demonstrate that the average degree of neurons within the hybrid scale-free network significantly influences the optimal amount of noise for the occurrence of stochastic resonance, indicating that there also exists an optimal topology for the amplification of the response to the weak input signal. Lastly, we verify that the presented results are robust to variations of the system size.     

Centralizers of Involutions in Locally Finite Groups

The present article deals with locally finite groups G having an involution φ such that C _G (φ) is an SF-group. It is shown that G possesses a normal subgroup B which is a central product of finitely many groups isomorphic to PSL(2, K _i ) or SL(2, K _i ) for some infinite locally finite fields K _i of odd characteristic, such that [G, φ]′/B and G/[G, φ] are both SF-groups.     

Global Well-Posedness for the Generalized Large-Scale Semigeostrophic Equations

We prove existence and uniqueness of global classical solutions to the generalized large-scale semigeostrophic equations with periodic boundary conditions. This family of Hamiltonian balance models for rapidly rotating shallow water includes the L ₁ model derived by R. Salmon in 1985 and its 2006 generalization by the second author. The results are, under the physical restriction that the initial potential vorticity is positive, as strong as those available for the Euler equations of ideal fluid flow in two dimensions. Moreover, we identify a special case in which the velocity field is two derivatives smoother in Sobolev space as compared to the general case. Our results are based on careful estimates which show that, although the potential vorticity inversion is nonlinear, bounds on the potential vorticity inversion operator remain linear in derivatives of the potential vorticity. This permits the adaptation of an argument based on elliptic L ^p theory, proposed by Yudovich in 1963 for proving existence and uniqueness of weak solutions for the two-dimensional Euler equations, to our particular nonlinear situation.     

Optical helicity and Hertz vectors

We study the conserved quantity associated with the dual symmetry of the Maxwell equations, called the optical helicity, by means of transverse Hertz vectors. In the presence of charges, its evolution yields the integral of $\mathit{E}?\mathit{B}$ which is the anomaly term for chiral fermions. We also discuss the helicity change in condensed matter systems where topological magnetoelectric effect emerges. An alternative expression of the optical helicity is also found. Lastly, a dual symmetric Hertz Lagrangian is constructed and its conserved charge is derived.     

Effects of the network structure and coupling strength on the noise-induced response delay of a neuronal network

The Hodgkin-Huxley (H-H) neuron model driven by stimuli just above threshold shows a noise-induced response delay with respect to time to the first spike for a certain range of noise strengths, an effect called “noise delayed decay” (NDD). We study the response time of a network of coupled H-H neurons, and investigate how the NDD can be affected by the connection topology of the network and the coupling strength. We show that the NDD effect exists for weak and intermediate coupling strengths, whereas it disappears for strong coupling strength regardless of the connection topology. We also show that although the network structure has very little effect on the NDD for a weak coupling strength, the network structure plays a key role for an intermediate coupling strength by decreasing the NDD effect with the increasing number of random shortcuts, and thus provides an additional operating regime, that is absent in the regular network, in which the neurons may also exploit a spike time code.     

Purple subphthalocyanine-phthalocyanine dyad: Synthesis,photophysicochemical properties and DFT study

A new phthalocyanine-subphthalocyanine heterodyad ( 5 ) was prepared by Pd(0)-catalyzed Sonogashira coupling reaction between an asymmetrical phthalocyanine ( 3 ) bearing monoiodo and multiple triazolide moieties on its backbone and a subphthalocyanine ( 4 ) bearing axially propargyl group. The structure of this heterodyad ( 5 ) was subsequently confirmed by the conventional spectroscopic techniques. The photophysical and photochemical properties including; fluorescence and singlet oxygen generation of ( 5 ) along with its building chromophores ( 3 ) and ( 4 ) were also investigated. Interestingly, a purple colored solution was observed by this novel dyad which was significantly different from those colors (green or blue) obtained by phthalocyanine-subphthalocyanine conjugates. Based on steady state absorption spectroscopic data and transient absorption results, the synthesized dyad 5 was free of aggregation and there is good energy transfer occurs between Pc and subPc moieties. This result was confirmed using density functional theory (DFT) and time-dependent DFT (TDDFT) analyses: B3LYP exchange-correlation functional and the 6–31 + G(d) basis set.     

Comparison of helical twisting powers of novel fluorinated amphiphilic enantiomers with their hydrogenated counterparts

This is the first report on novel amphiphilic enantiomers as esters of alanine and serine with a partially fluorinated octyl chain (L-APFOE and L-SPFOE), which form intrinsic chiral nematic (N*) phases with water only and exhibit very high helical twisting powers (htps) compared to their hydrogenated counterparts, dodecylesters of L-alanine (L-ADDE) and L-serine (l-SDDE). They also exhibit a wider N* range than those known in the literature. Furthermore, the htps of the chiral dopants mandelic acid (MA) and hexahydromandelic acid (HHMA) in the racemic nematic phase of DL-SPFOE and DL-APFOE are remarkably higher than those in the hydrogenated counterparts. The tremendous increase in chirality (htps) of the same single chiral center is a new phenomenon in micellar N* phases and is attributed to a "pivot" effect of the fluoroalkyl chain. As a result, a "skewed micelle" model is proposed to explain why the htp value of L-APFOE is higher than that of L-SPFOE, and accordingly how the intermicellar chirality transfer (chiral induction) may be visualized. The simplicity of these binary mixtures and the enlargement in htp of the single chiral centers visualized as the "skewed micelle" model may provide a basis vital for future computer modeling of chiral lyotropics.     

Hetero‐ and homo‐leptic Ru(II) catalyzed synthesis of cyclic carbonates from CO2; Synthesis,spectroscopic characterization and electrochemical properties

Based on the a ligand BDPPZ [(9a,13a‐dihydro‐4,5,9,14‐tetraaza‐benzo[b]triphenylene‐11‐yl)‐phenyl‐methanone] (1) and its polypyridyl hetero‐ and homoleptic Ru(II) metal complexes, [Ru(bpy)₂L](PF₆)₂ (2), [Ru(phen)₂L](PF₆)₂ (3), [Ru(dafo)₂L](PF₆)₂ (4), [Ru(dcbpy)₂L](PF₆)₂ (5) and [RuL₃](PF₆)₂ (6) (where, L = ligand, bpy = 2,2′‐bipyridine, phen = 1,10‐phenantroline, dafo = 4,5‐diazafluoren‐9‐one and dcbpy = 3,3′‐dicarboxy‐2,2′‐bipyridine), have been synthesized and characterized by elemental analysis, UV–vis, FT‐IR, ¹H and ¹³C‐NMR spectra (for ligand), molar conductivity measurements and X‐ray powder techniques. The electrochemical parameters of the substituted ligand and its polypyridyl hetero‐ and homoleptic Ru(II) metal complexes are reported by cyclic voltammetry. UV–vis spectroscopy is used to compare the differences between the conjugated π systems in this ligand and its Ru(II) metal complexes. The polypyridyl hetero‐ and homoleptic Ru(II) metal complexes also tested as catalysts for the formation of cyclic organic carbonates from carbon dioxide and liquid epoxides which served as both reactant and solvent. The results showed that the [Ru(L)₃](PF₆)₂ (6) complex is more efficient than the other Ru(II) complexes for the formation of cyclic organic carbonates from carbon dioxide. Copyright © 2010 John Wiley & Sons, Ltd.     

Comparative studies of photophysical and photochemical properties of solketal substituted platinum(II) and zinc(II) phthalocyanine sets

A complete set of platinum(II) solketal substituted phthalocyanines has been synthesized and characterized. To evaluate their potential as Type II photosensitizers for photodynamic therapy, comparative studies of their photophysical and photochemical properties with analogous zinc(II) series have been achieved: electronic absorption, fluorescence quantum yields, lifetimes, and fluorescence quenching by benzoquinone, as well as singlet oxygen generation and photodegradation. It appears that platinum(II) phthalocyanines are worth being used as Type II photosensitizers, as they exhibit good singlet oxygen generation and appropriate photodegradation.     

Microwave Assisted Synthesis of Chitosan Nanoparticles

Chitosan nanoparticles (CHN) were prepared based on ionotropic gelation between low moleculer weight chitosan and sodium tripolyphosphate (TPP) under microwave irradiation. Particle size, zeta potential, and FT-IR techniques were used for characterization of CHN. The influence of reaction time on the nanoparticle size distribution was investigated, and the results showed that the microwave irradiation method evidently decreases the reaction times and particle size over the conventional method. It was determined by the results of the zeta potential measurements that synthesized CHN under microwave irradiation clearly exhibits more homogeneous and stable dispersion.