Limited path percolation in complex networks

We study the stability of network communication after removal of a fraction q=1-p of links under the assumption that communication is effective only if the shortest path between nodes i and j after removal is shorter than al(ij)(a> or =1) where l(ij) is the shortest path before removal. For a large class of networks, we find analytically and numerically a new percolation transition at p(c)=(kappa(0)-1)((1-a)/a), where kappa(0) [triple bond] / and k is the node degree. Above p(c), order N nodes can communicate within the limited path length al(ij), while below p(c), N(delta) (delta<1) nodes can communicate. We expect our results to influence network design, routing algorithms, and immunization strategies, where short paths are most relevant.     

Affine gravity,Palatini formalism and charges

Affine gravity and the Palatini formalism contribute both to produce a simple and unique formula for calculating charges at spatial and null infinity for Lovelock type Lagrangians whose variational derivatives do not depend on second-order derivatives of the field components. The method is based on the covariant generalization due to Julia and Silva of the Regge–Teitelboim procedure that was used to define properly the mass in the classical formulation of Einstein’s theory of gravity. Numerous applications reproduce standard results obtained by other secure but mostly specialized method like in ADM energy for asymptotically flat spacetimes and in Abbot and Deser for asymptotically de Sitter and anti-de Sitter spacetimes, both at spatial infinity. As a novel application we calculate the Bondi energy loss in five dimensional gravity, based on the asymptotic solution given by Tanabe et al. and obtain, as expected, the same result. We also give the for Einstein–Gauss–Bonnet gravity and find the superpotential for Lovelock theories of gravity when the number of dimensions tends to infinity with maximally symmetrical boundaries. The paper is written in standard component formalism.     

NMR studies of structure and reorganization dynamics of an [6Li]-allylic lithium compound complexed to [14N,15N]-N,N,N',N'-tetramethylethylenediamine: inversion and ligand lithium exchange

Proton, 13C, 6Li, and 15N NMR line-shape studies of exo,exo-1-trimethylsilyl-3-(dimethylethylsilyl)allyllithium-6Li complexed to [14N,15N]-N,N,N',N'-tetramethylethylenediamine (TMEDA) 2 as a function of temperature and of added diamine reveal the dynamics of three fast equilibrium reorganization processes. These are (with DeltaH values in kilocalories per mole and DeltaS values in entropic units): mutual exchange of lithium between two 2 molecules (6.3, -21), exchange of TMEDA between its free and complexed states (5.0 and -22), and first-order transfer of complexed ligand between the allyl faces (7.0 and -20). Intermediates that are dimeric in TMEDA are proposed for the first two of these reorganization processes.     

A One‐Pot Organometallic Route from a 4‐Alkenylpyridine to a 4,4‐Spiro‐Linked Ethyl 1,4‐Dihydropyridine‐1‐carboxylate

In a one‐pot process without isolation of intermediates, (but‐3‐en‐1‐yl)pyridine ( 13 ) is treated sequentially with dicyclohexylborane, trimethylaluminium, and ethyl carbonochloridate yielding ethyl 1,4‐dihydro‐4,4‐(tetramethylene)pyridine‐1‐carboxylate (=ethyl 8‐azaspiro[4.5]deca‐6,9‐diene‐8‐carboxylate; 2 ) in 46% yield based on starting alkenylpyridine 13 (Scheme 5).     

Building custom polysaccharides in vitro with an efficient, broad-specificity xyloglucan glycosynthase and a fucosyltransferase

The current drive for applications of biomass-derived compounds, for energy and advanced materials, has led to a resurgence of interest in the manipulation of plant polymers. The xyloglucans, a family of structurally complex plant polysaccharides, have attracted significant interest due to their intrinsic high affinity for cellulose, both in muro and in technical applications. Moreover, current cell wall models are limited by the lack of detailed structure-property relationships of xyloglucans, due to a lack of molecules with well-defined branching patterns. Here, we have developed a new, broad-specificity "xyloglucan glycosynthase", selected from active-site mutants of a bacterial endoxyloglucanase, which catalyzed the synthesis of high molar mass polysaccharides, with complex side-chain structures, from suitable glycosyl fluoride donor substrates. The product range was further extended by combination with an Arabidopsis thaliana α(1→2)-fucosyltransferase to achieve the in vitro synthesis of fucosylated xyloglucans typical of dicot primary cell walls. These enzymes thus comprise a toolkit for the controlled enzymatic synthesis of xyloglucans that are otherwise impossible to obtain from native sources. Moreover, this study demonstrates the validity of a chemo-enzymatic approach to polysaccharide synthesis, in which the simplicity and economy of glycosynthase technology is harnessed together with the exquisite specificity of glycosyltransferases to control molecular complexity.     

Complex protein patterns formation via salt-induced self-assembly and droplet evaporation

Complex and elegant protein patterns in rosette, scallop, Chinese arrow and dendrite shapes at macroscopic length scales were prepared using salt-induced molecular self-assembly and droplet evaporation methods. The direct visual observation method using fluorescence microscopy was adopted to characterize the formation of these protein patterns in situ. Further studies from an optical interferometric profiler have shown that both rosette and scalloped protein patterns are hierarchical structures of concentric rings consisting of many prism-like columnar stacks, with each of the stack having thousands of protein molecules. Systematic experimental studies were performed to investigate the influence of salt concentration, protein concentration and evaporation rate on the morphologies of protein patterns. Upon the analysis of the representative fluorescent microscope images some theoretical explanations, based on Deegan’s theory on the “coffee ring” effect and the dynamic self-assembly mechanism, were proposed to illustrate the dynamics for the formation of different protein patterns. Two different evaporation modes have been found: edge-enhanced evaporation for low salt concentration solutions, i.e., the higher evaporation rate exists at the edge of the droplet; center-enhanced evaporation for high salt concentration solutions, in which faster evaporation occurs at the droplet center consisting of a lot of crystallized salts.     

Synthesis of [ethylene-1-(eta(5)-4,5,6,7-tetrahydro-1-indenyl)-2- (eta(5)-4',5',6',7'-tetrahydro-2'-indenyl)]titanium dichloride, the elusive isomer of the Brintzinger-type ansa-titanocenes

We present a short synthesis of 1-(2-indenyl)-2-(3-indenyl)ethane (5) and a method for its conversion to the ansa-metallocene [ethylene(eta5-inden-1-yl)(eta5-inden-2-yl)]titanium dichloride (13). The synthetic strategy applied to prepare bisindene 5 relies on the efficient alkylation of 2-(phenylsulfonyl)indane followed by HMPA-assisted E1cB-elimination of phenylsulfinate. This tandem sequence circumvents the predisposition of indene to undergo C(1)-alkylation and enables access to C(2)-substituted indenes. The key step in the synthesis of the title ansa-titanocene (4) features a previously unreported equilibration step to generate the bis(indenide anion) of 5. Complexation with TiCl4.(THF)2 followed by hydrogenation of the product metallocene furnishes ansa-titanocene 4.