Aligning simulation models: A case study and results

This paper develops the concepts and methods of a process we will call “alignment of computational models” or “docking” for short. Alignment is needed to determine whether two models can produce the same results, which in turn is the basis for critical experiments and for tests of whether one model can subsume another. We illustrate our concepts and methods using as a target a model of cultural transmission built by Axelrod. For comparison we use the Sugarscape model developed by Epstein and Axtell. The two models differ in many ways and, to date, have been employed with quite different aims. The Axelrod model has been used principally for intensive experimentation with parameter variation, and includes only one mechanism. In contrast, the Sugarscape model has been used primarily to generate rich “artificial histories”, scenarios that display stylized facts of interest, such as cultural differentiation driven by many different mechansims including resource availability, migration, trade, and combat. The Sugarscape model was modified so as to reproduce the results of the Axelrod cultural model. Among the questions we address are: what does it mean for two models to be equivalent, how can different standards of equivalence be statistically evaluated, and how do subtle differences in model design affect the results? After attaining a “docking” of the two models, the richer set of mechanisms of the Sugarscape model is used to provide two experiments in sensitivity analysis for the cultural rule of Axelrod's model. Our generally positive experience in this enterprise has suggested that it could be beneficial if alignment and equivalence testing were more widely practiced among computational modelers.     

Synthesis of the One-dimensional Compound (Ph4P)[In(P2Se6)] in a Ph4P+-Containing Selenophosphate Flux,and Structure of [In(P2Se6)2]5– – a Discrete Molecular Fragment of the [In(P2Se6)]nn– Chain

The reaction of one equivalent of In with a molten flux of (Ph₄P)₂Se₅ and P₂Se₅ (1 : 2), at 250 °C gave the (Ph₄P)[In(P₂Se₆)] ( I ). Stoichiometric elemental synthesis at 750 °C produced the Cs₅In(P₂Se₆)₂ ( II ). The thin, yellow crystals of ( I ), and the irregular, dark orange crystals of ( II ), appear to be air- and water-stable. Compound ( I ) crystallizes in the monoclinic space group C2/c (no. 15) and at 23 °C: a = 23.127(7) Å, b = 6.564(1) Å, c = 19.083(3) Å, β = 97.42(2)°, V = 2873(1) ų, Z = 4, final R/R_w = 4.4/5.2%. Compound ( II ) crystallizes in the tetragonal space group P4₂/m (no. 84) and at 23 °C: a = b = 13.886(1) Å, c = 7.597(2) Å, V = 1464.9(3) ų, Z = 2, final R/R_w = 3.9/5.1%. Compound ( I ) contains infinite [In(P₂Se₆)]_n^n– with a structure related to that of K₂FeP₂Se₆. Compound ( II ) contains the discrete [In(P₂Se₆)₂]^5– which can be viewed as a fragment of the [In(P₂Se₆)]_n^n– chain.     

Identification of a novel series of alkylitaconic acids in wood cultures of Ceriporiopsis subvermispora by gas chromatography/mass spectrometry.

A novel series of long-chain unsaturated dicarboxylic acids consisting of a long aliphatic chain attached to the C-3 position of itaconic acid has been identified by gas chromatography/mass spectrometry during in vitro decay of eucalypt wood by the white-rot basidiomycete Ceriporiopsis subvermispora. The major compounds were identified as tetradecyl-, 7-hexadecenyl- and hexadecylitaconic acids by their mass fragmentation patterns. Other members of the same compound series, identified as dodecanyl-, tridecanyl-, tetradecenyl-, pentadecanyl-, octadecenyl- and octadecanylitaconic acids, were present in very minor amounts or traces. Whereas hexadecenylitaconic acid has already been reported in cultures of C. subvermispora, to our knowledge this is the first report of the presence of the other alkylitaconic acids in fungal cultures. These new alkylitaconic-type metabolites may constitute a source for peroxidizable lipids involved in lignin degradation during wood decay by C. subvermispora and other white-rot basidiomycetes.     

Syntheses of rac/meso-{PhP(3-t-Bu-C5H3)2}-Zr{RN(CH2)3NR}, structural analyses of rac-{PhP(3-t-Bu-C5H3)2}Zr{RN(CH2)3NR} (where R is SiMe3 or Ph), and meso to rac isomerization

Syntheses of rac/meso-{PhP(3-t-Bu-C₅H₃)₂}Zr{Me₃SiN(CH₂)₃NSiMe₃} (rac-3/meso-3) and rac/meso-{PhP(3-t-Bu-C₅H₃)₂}Zr{PhN(CH₂)₃NPh} (rac-4/meso-4) were achieved by metallation of K₂[PhP(3-t-Bu-C₅H₃)₂] · 1.3 THF (2) with Zr{RN(CH₂)₃NR}Cl₂(THF)₂ (where R = SiMe₃ or Ph, respectively) using ethereal solvent. These isomeric pairs were characterized by ¹H, ¹³C{¹H}, and ³¹P{¹H} NMR spectroscopy; rac-3 and rac-4 were also examined via single crystal X-ray crystallography. The structures of rac-3 and rac-4 are notable in the tendency of the cyclopentadienyl rings towards η³ coordination. While isolated samples of rac-3/meso-3 and rac-4/meso-4 slowly isomerize in tetrahydrofuran-d₈ to equilibrium ratios, the isomerization rate for 3 is more than 15-fold greater than that for 4. In addition, equilibrium ratios are rapidly reached when isolated samples of rac-3/meso-3 and rac-4/meso-4 are exposed to tetrabutylammonium chloride in tetrahydrofuran-d₈ solvent. We propose that a nucleophile (either chloride or the phosphine interannular linker) brings about dissociation of one cyclopentadienyl ring, thus promoting the rac/meso isomerization mechanism.