Evolving graphs: dynamical models, inverse problems and propagation

Applications such as neuroscience, telecommunication, online social networking, transport and retail trading give rise to connectivity patterns that change over time. In this work, we address the resulting need for network models and computational algorithms that deal with dynamic links. We introduce a new class of evolving range-dependent random graphs that gives a tractable framework for modelling and simulation. We develop a spectral algorithm for calibrating a set of edge ranges from a sequence of network snapshots and give a proof of principle illustration on some neuroscience data. We also show how the model can be used computationally and analytically to investigate the scenario where an evolutionary process, such as an epidemic, takes place on an evolving network. This allows us to study the cumulative effect of two distinct types of dynamics.

Recent oppositely directed trends in solar climate forcings and the global mean surface air temperature. II. Different reconstructions of the total solar irradiance variation and dependence on response time scale

We have previously placed the solar contribution to recent global warming in context using observations and without recourse to climate models. It was shown that all solar forcings of climate have declined since 1987. The present paper extends that analysis to include the effects of the various time constants with which the Earth’s climate system might react to solar forcing. The solar input waveform over the past 100 years is defined using observed and inferred galactic cosmic ray fluxes, valid for either a direct effect of cosmic rays on climate or an effect via their known correlation with total solar irradiance (TSI), or for a combination of the two. The implications, and the relative merits, of the various TSI composite data series are discussed and independent tests reveal that the PMOD composite used in our previous paper is the most realistic. Use of the ACRIM composite, which shows a rise in TSI over recent decades, is shown to be inconsistent with most published evidence for solar influences on pre-industrial climate. The conclusions of our previous paper, that solar forcing has declined over the past 20 years while surface air temperatures have continued to rise, are shown to apply for the full range of potential time constants for the climate response to the variations in the solar forcings.

Anion-directed synthesis of metal-organic frameworks based on 2-picolinate Cu(II) complexes: a ferromagnetic alternating chain and two unprecedented ferromagnetic fish backbone chains

Three new polynuclear copper(II) complexes of 2-picolinic acid (Hpic), {[Cu-2(pic)(3)(H2O)]ClO4}(n) (1), {[Cu-2(pic)(3)(H2O)]BF4}(n) (2), and [Cu-2(pic)3(H2O)(2)(NO3)](n) (3), have been synthesized by reaction of the "metalloligand" [Cu-(pic)(2)] with the corresponding copper(II) salts. The compounds are characterized by single-crystal X-ray diffraction analyses and variable-temperature magnetic measurements. Compounds 1 and 2 are isomorphous and crystallize in the triclinic system with space group P (1) over bar, while 3 crystallizes in the monoclinic system with space group P2(1)/n. The structural analyses reveal that complexes 1 and 2 are constructed by "fish backbone" chains through syn-anti (equatorial-equatorial) carboxylate bridges, which are linked to one another by syn-anti (equatorial-axial) carboxylate bridges, giving rise to a rectangular grid-like two-dimensional net. Complex 3 is formed by alternating chains of syn-anti carboxylate-bridged copper(II) atoms, which are linked together by strong H bonds involving coordinated nitrate ions and water molecules and uncoordinated oxygen atoms from carboxylate groups. The different coordination ability of the anions along with their involvement in the H-bonding network seems to be responsible for the difference in the final polymeric structures. Variable-temperature (2-300 K) magnetic susceptibility measurement shows the presence of weak ferromagnetic coupling for all three complexes that have been fitted with a fish backbone model developed for 1 and 2 (J = 1.74 and 0.99 cm(-1); J' = 0.19 and 0.25 cm(-1), respectively) and an alternating chain model for 3 (J = 1.19 cm(-1) and J' = 1.19 cm(-1)).

Anion directed templated synthesis of mono- and di-Schiff base complexes of Ni(II)

Two sets of Schiff base ligands, set-1 and set-2 have been prepared by mixing the respective diamine (1,2-propanediamine or 1,3-propanediamine) and carbonyl compounds (2-acetylpyridine or pyridine-2-carboxaldehyde) in 1:1 and 1:2 ratios, respectively and employed for the synthesis of complexes with Ni(II) perchlorate and Ni(II) thiocyanate. Ni(II) perchlorate yields the complexes having general formula [NiL2](ClO4)(2) (L = L-1 [N-1-(1-pyridin-2-yl-ethylidine)-propane-1,3-diamine] for complex 1, L-2 [N-1-pyridine-2-ylmethylene-propane1,3-diamine] for complex 2 or L-3 [N-1-(1-pyridine-2-yl-ethylidine)-propane-1,2-diamine] for complex 3) in which the Schiff bases are mono-condensed terdentate whereas Ni(II) thiocyanate results in the formation of tetradentate Schiff base complexes, [NiL](SCN)(2) (L=L-4 [N,N'-bis-(1-pyridine-2-yl-ethylidine)-propane-1,3-diamine] for complex 4, L-5 [NN'-bis(pyridine-2-ylmethyline)-propane-1, 3-diamine] for complex 5 or L-6 [NN'-bis-(1-pyridine-2-yl-ethylidine)-propane- 1, 2-diamine] for complex 6) irrespective of the sets of ligands used. Formation of the complexes has been explained by anion modulation of cation templating effect. All the complexes have been characterized by elemental analyses, spectral and electrochemical results. Single crystal X-ray diffraction studies confirm the structures of four representative members, 1, 3, 4 and 5; all of them have distorted octahedral geometry around Ni(II). The bis-complexes of terdentate ligands, I and 3 are the mer isomers and the complexes of tetradentate ligands, 4 and 5 possess trans geometry. (c) 2007 Elsevier Ltd. All rights reserved.