Evolutionary snowdrift game incorporating costly punishment in structured populations

The role of punishment and the effects of a structured population in promoting cooperation are important issues. Within a recent model of snowdrift game (SG) incorporating a costly punishing strategy (P), we study the effects of a population connected through a square lattice. The punishers, who carry basically a cooperative (C) character, are willing to pay a cost α$\alpha$ so as to punish a non-cooperative (D) opponent by β$\beta$. Depending on α$\alpha$, β$\beta$, the cost-to-benefit ratio r$r$ in SG, and the initial conditions, the system evolves into different phases that could be homogeneous or inhomogeneous. The spatial structure imposes geometrical constraint on how one agent is affected by neighboring agents. Results of extensive numerical simulations, both for the steady state and the dynamics, are presented. Possible phases are identified and discussed, and isolated phases in the r–β$r\text{–}\beta$ space are identified as special local structures of strategies that are stable due to the lattice structure. In contrast to a well-mixed population where punishers are suppressed due to the cost of punishment, the altruistic punishing strategy can flourish and prevail for appropriate values of the parameters, implying an enhancement in cooperation by imposing punishments in a structured population. The system could evolve to a phase corresponding to the coexistence of C, D, and P strategies at some particular payoff parameters, and such a phase is absent in a well-mixed population. The pair approximation, a commonly used analytic approach, is extended from a two-strategy system to a three-strategy system. We show that the pair approximation can, at best, capture the numerical results only qualitatively. Due to the improper way of including spatial correlation imposed by the lattice structure, the approximation does not give the frequencies of C, D, and P accurately and fails to give the homogeneous AllD and AllP phases.     

Synthesis and structure of two tetranuclear osmium carbonyl isotopomers: a crystallographic isotope effect

A synthetic route to [Os4(mu-H)(mu-OH)(mu-CO)(CO)12] ( 1) has been devised through the activation of [Os4(CO)14] with Me3NO. The pyrolysis and photolysis of the reactant in the presence of a trace amount of water produces 1 in low yield. The solid-state structure of [Os4(mu-H)(mu-OH)(mu-CO)(CO)12 x H2O] (1 x H2O) reveals a butterfly Os4 skeleton with bridging H, OH and CO ligands as well as hydrogen-bonded molecules of water in the crystal lattice. A low-temperature 13C{1H} NMR spectroscopic study revealed a merry-go-round exchange of CO ligands around the Os3 plane containing the asymmetric bridging CO. The exposure of 1 x H2O to D2O yielded [Os4(mu-H)(mu-OD)(mu-CO)(CO)12]2. Although the solid-state, intramolecular structure of 2 closely matched that of 1 x H2O, the intermolecular structure did not: its crystal lattice contained no water of crystallization, a previously unreported crystallographic isotope effect.     

Synthesis and thermal chemistry of copper (I) guanidinates

Copper (I) guanidinate dimers were generated by a salt metathesis route and structurally characterized. The guanidinates differed from the known amidinate dimers because of a large torsion of the dimer ring. This had a direct effect on their thermal chemistry. The thermal reactivity was investigated by several methods, including a novel temperature-resolved, gas-phase method that was monitored by mass spectrometry. The copper guanidinates underwent carbodiimide deinsertion to produce copper metal at temperatures between 225 -and 250 degrees C in the gas phase and at 125 degrees C in solution. The amidinate investigated also showed copper deposition at 190 degrees C in the gas phase, and 135 degrees C in solution, but without carbodiimide deinsertion. The guanidinate compounds deposited crystalline copper at 225 degrees C in a simple chemical vapor deposition experiment.     

New synthetic routes to a disulfidodinickel(II) complex: characterization and reactivity of a Ni2(mu-eta2:eta2-S2) core

Activation of elemental sulfur by the monovalent nickel complex [PhTt (tBu)]Ni(CO) [PhTt(tBu)=phenyl{tris[(tert-butylmethyl)thio]methyl}borate] generates the disulfidodinickel(II) complex 2. This species is alternatively accessible via thermal decomposition of [PhTt (tBu)]Ni(SCPh3). Spectroscopic, magnetic, and X-ray diffraction studies establish that 2 contains a mu-eta(2):eta(2)-S2 ligand that fosters antiferromagnetic exchange coupling between the Ni (II) ions. This observation is in contrast to the lighter congener, oxygen, which strongly favors the bis(mu-oxo)dinickel(III) structure. 2 oxidizes PPh 3 to SPPh3 and reacts with O2, generating several products, one of which has been identified as [(PhTt (tBu))Ni]2(mu-S) (3).     

Ultra-performance liquid chromatography/time-of-flight mass spectrometry based metabolomics of raw and steamed Panax notoginseng

At present, metabolite profiling is of growing importance in herbal medicine fields such as breeding, formulation, quality control and clinical trials. This preliminary study indicated that ultra-performance liquid chromatography/time-of-flight mass spectrometry (UPLC/TOFMS)-based metabolomics allows direct detection of down-stream derivatives of metabolites, arising from the herbal formulation process. This analytical approach allows the discrimination and tentative authentication of unique biomarkers related to different herbal extracts using unsupervised multivariate principal component analysis (PCA). The tentative identification of biomarkers is complemented significantly by the accurate mass measurement of TOFMS and the high resolution and high retention time reproducibility rendered by UPLC. The application of this approach in herbal extract discrimination and ginsenoside biomarker discovery of raw and steamed Panax notoginseng (Burk.) F.H. Chen is demonstrated and discussed.     

Sterically bulky tris(triazolyl)borate ligands as water-soluble analogues of tris(pyrazolyl)borate

The recently synthesized 3-tert-butyl-5-methyl-1,2,4-triazole reacted with KBH4 to give the new potassium tris(3-tert-butyl-5-methyl-1,2,4-triazolyl)borate K(Ttz(tBu,Me)) ligand. Ttz(tBu,Me) formed a four-coordinate (Ttz(tBu,Me))CoCl complex and five-coordinate (Ttz(tBu,Me))CoNO3 and (Ttz(tBu,Me))ZnOAc complexes. When these complexes were compared to their Tp(tBu,Me) analogues, it was found that Ttz(tBu,Me) resulted in negligible steric differences. K(Ttz(tBu,Me)) is more water-soluble than K(Tp(tBu,Me)), so bulky tris(triazolyl)borate ligands should lead to functional models for enzyme active sites in an aqueous environment and the creation of water-soluble analogues of Tp catalysts.     

Edge Colouring of K2n with Spanning Star-Forests Receiving Distinct Colours

 Let S _ni be a star of size n _i and let S=S _n1∪…∪S _nk≠S _2n−3∪S ₁ or S ₂∪S ₂ be a spanning star-forest of the complete graph K _2n. We prove that K _2n has a proper (2n−1)-edge-colouring such that all the edges of S receive distinct colours. This result is very useful in the study of total-colourings of graphs. Received: March 8, 1995 / Revised: May 16, 1997     

Pyrrole Denitrogenation and Fragmentation of Tetramethylethylenediamine Promoted by a NbII Cluster

A nitrogen center was abstracted from a pyrrolyl ring to form the dinuclear nitrido- and dienyl-bridged complex 1 during the reaction of [{(tmeda)Nb^IICl}₂(μ-Cl)₃Li(tmeda)] with the lithium salt of 2,5-dimethylpyrrole (tmeda=N,N,N′,N′-tetramethylethylenediamine). A second product from this reaction is the amido-carbene-hydride niobium complex 2 , which likewise forms under C−N bond cleavage.     

Synthesis and Structure of a Chromium(III) Complex Supported by a β-diketiminate and an Enediolate Ligand

Abstract  

The complex (bis(2,6-diisopropylphenyl)pentane-2,4-ketiminato)(9,10-dihydro-9,10-(ethenediolato)anthracene)(tetrahydrofuran)chromium(III) (1) has been synthesized and structurally characterized. Complex 1 crystallizes in the spacegroup Cc with the crystal cell parameters a = 22.285 (3) ?, b = 9.3317 (13) ?, c = 40.782 (6) ?, β = 99.338 (3)°, V = 8369 (2) ?³, and Z = 8. Two symmetry unique complex molecules were located in the asymmetric unit making Z′ = 2. The chromium atoms display square pyramidal coordination with THF located in the axial position. The previously neutral α-diketone moiety has been reduced by two electrons to an enediolate group with a corresponding increase of oxidation state of the chromium center.