Calixarenes as Polyhapto-aromatic Ligands: Alkali Metal Ions and Sulfonated Calixarenes

Crystal structure determinations for the hexarubidium and octacesium derivatives of calix[6]arene hexasulfonic acid, as well as of a new solvate of the pentasodium derivative of calix[4]arene tetrasulfonic acid, and comparison with structural data from the literature for alkali metal complexes of sulfonated calixarenes, have provided further evidence for the importance of interactions with aromatic ~ -electrons for the heavier alkali metal cations. There is evidence as well that this interaction can be enhanced by extended ionization of the sulfonated calixarene.     

Crystal Structure Investigations of Inclusion Complexes Between β-cyclodextrin and Alkyl(aqua)cobaloximes (Alkyl=Butyl,Hexyl and Cyclohexyl)

The crystal and molecular structures of alkylcobaloxime/ g -cyclodextrin ( g -CD) inclusion complexes: butyl(aqua)cobaloxime/ g -CD ( 1 ). hexyl(aqua)cobaloxime/ g -CD ( 2 ) and cyclohexyl(aqua)cobaloxime/ g -CD ( 3 ) were determined by X-ray diffraction analyses. Crystal data for 1 14H 2 O: P 2 1 2 1 2 1 , a =15.1335(3), b =18.9630(2), c =28.1545(5) Å, Z =4; 2 12H 2 O: P 2 1 2 1 2 1 , a =15.1135(4), b =19.1477(5), c =28.2715(7) Å, Z =4; 3 10H 2 O: P 2 1 2 1 2 1 , a =15.6898(2), b =16.9094(2), c =28.9762(2) Å, Z =4. The structural and conformational comparisons for the three g -CD inclusion complexes with their guest molecules as well as other CD inclusion analogs are discussed.     

Low-Energy Dislocation Structure (LEDS) character of dislocation boundaries aligned with slip planes in rolled aluminium

For the specific slip geometry of two sets of coplanar systems (a total of four systems) in fcc metals, the range of dislocation networks in boundaries aligned with one of the two active slip planes is predicted from the Frank equation for boundaries free of long-range elastic stresses. Detailed comparison with experimental data for eight dislocation boundaries in cold-rolled aluminium grains of the 45° ND rotated Cube orientation is conducted. It is concluded that the boundaries are Low-Energy Dislocation Structures, which are in good agreement with the Frank equation while also lowering the energy by dislocation reactions. Cross slip plays a role in the boundary formation process.     

The $-game

We propose a payoff function extending Minority Games (MG) that captures the competition between agents to make money. In contrast with previous MG, the best strategies are not always targeting the minority but are shifting opportunistically between the minority and the majority. The emergent properties of the price dynamics and of the wealth of agents are strikingly different from those found in MG. As the memory of agents is increased, we find a phase transition between a self-sustained speculative phase in which a “stubborn majority” of agents effectively collaborate to arbitrage a market-maker for their mutual benefit and a phase where the market-maker always arbitrages the agents. A subset of agents exhibit a sustained non-equilibrium risk-return profile. Received 5 June 2002 / Received in final form 21 November 2002 Published online 27 January 2003 RID="a" ID="a"e-mail: sornette@unice.fr RID="b" ID="b"CNRS UMR7536 RID="c" ID="c"CNRS UMR6622     

Inevitable self-similar topology of binary trees and their diverse hierarchical density

Self-similar topology, which can be characterized as power law size distribution, has been found in diverse tree networks ranging from river networks to taxonomic trees. In this study, we find that the statistical self-similar topology is an inevitable consequence of any full binary tree organization. We show this by coding a binary tree as a unique bifurcation string. This coding scheme allows us to investigate trees over the realm from deterministic to entirely random trees. To obtain partial random trees, partial random perturbation is added to the deterministic trees by an operator similar to that used in genetic algorithms. Our analysis shows that the hierarchical density of binary trees is more diverse than has been described in earlier studies. We find that the connectivity structure of river networks is far from strict self-similar trees. On the other hand, organization of some social networks is close to deterministic supercritical trees.     

Characterization of complex networks by higher order neighborhood properties

A concept of higher order neighborhood in complex networks, introduced previously [Phys. Rev. E 73, 046101 (2006)], is systematically explored to investigate larger scale structures in complex networks. The basic idea is to consider each higher order neighborhood as a network in itself, represented by a corresponding adjacency matrix, and to settle a plenty of new parameters in order to obtain a best characterization of the whole network. Usual network indices are then used to evaluate the properties of each neighborhood. The identification of high order neighborhoods is also regarded as intermediary step towards the evaluation of global network properties, like the diameter, average shortest path between node, and network fractal dimension. Results for a large number of typical networks are presented and discussed.     

Open dynamic behaviour of financial markets

Open dynamic behaviour of financial markets with internal interactions between agents and with external “fields” from other systems are investigated using the approach of Grossman and Stiglitz for inefficient markets, and Keynes for interference of the market using physics of finance (referred to hereafter as phynance). The simulation results indicate that the NYSE data analyzed in Plerou, V. et al., Nature 421, 130 (2003) can be fitted by an equation of order parameter Φ and local deviation R of type: -(R+0.03) Φ+ 0.6 Φ³ + 0.02 = 0, which is shown to be in remarkable agreement with Plerou's data.     

Correlations in financial time series: established versus emerging markets

Long-time correlations in both well-developed and emerging market indexes are studied. The Hurst exponent as well as detrended fluctuations analysis (DFA) are used as technical tools. Some features that seem to be specific for developing markets are discovered and briefly discussed. Received 17 October 2000