An approach to verifying and debugging simulation models governed by ordinary differential equations: Part 2. Residuals analysis and a case study

In Part 1 of this paper a methodology for back-to-back testing of simulation software was described. Residuals with error-dependent geometric properties were generated. A set of potential coding errors was enumerated, along with a corresponding set of feature matrices, which describe the geometric properties imposed on the residuals by each of the errors. In this part of the paper, an algorithm is developed to isolate the coding errors present by analysing the residuals. A set of errors is isolated when the subspace spanned by their combined feature matrices corresponds to that of the residuals. Individual feature matrices are compared to the residuals and classified as 'definite', 'possible' or 'impossible'. The status of 'possible' errors is resolved using a dynamic subset testing algorithm. To demonstrate and validate the testing methodology presented in Part 1 and the isolation algorithm presented in Part 2, a case study is presented using a model for biological wastewater treatment. Both single and simultaneous errors that are deliberately introduced into the simulation code are correctly detected and isolated. Copyright (C) 2003 John Wiley Sons, Ltd.

The preparation of zinc(II) and cadmium(II) complexes of the pentadentate N3S2 ligand formed from 2,6-diacetylpyridine and S-benzyldithiocarbazate (H2SNNNS) and the X-ray crystal structure of the novel dimeric [Zn2(SNNNS)2] complex

The pentadentate chelating agent, 2,6-diacetylpyridinebis(S-benzyldithiocarbazate) (H2SNNNS) reacts with zinc(II) and cadmium(II) ions forming stable complexes of empirical formula, [M(SNNNS)] (M=Zn2+, Cd2+; SNNNS2 =doubly deprotonated anionic form of the Schiff base). These complexes have been characterized by a variety of physico-chemical techniques. IR and H-1 NMR spectral evidence indicate that the Schiff base coordinates to the zinc(II) and cadmium(II) ions via the pyridine nitrogen atoms, the azomethine nitrogen atoms and the mercaptide sulfur atoms. The crystal and molecular structure of the zinc(II) complex has been determined by X-ray diffraction. The complex is a dimer in which the pyridine nitrogen atom,the azomethine nitrogen atom and the thiolate sulfur atom from one ligand coordinate to one of the zinc(II) ions whereas the azomethine and thiolate sulfur atoms from another ligand complete pentacoordination around the zinc(II) ion, the ligands being coordinated in their deprotonated forms. The coordination geometry about each zinc(II) can be considered as intermediate between a square-pyramid and trigonal-bipyramid. The cadmium(II) complex is also assigned with a dimeric structure. (C) 2003 Elsevier Ltd. All rights reserved.

Four cytotoxic N4-substituted thiosemicarbazones derived from 2-hydroxynaphthalene-1-carboxaldehyde

The X-ray crystal structures are reported of four novel and potentially O,N,S-tridentate donor ligands that demonstrate antitumour activity. These ligands are 1-[(4-methylthiosemicarbazono)methyl]-2-naphthol, C13H13N3OS, (III), 1-[(4-ethylthiosemicarbazono)methyl]-2-naphthol, C14H15N3OS, (IV), 1-[(4-phenylthiosemicarbazono)methyl]-2-naphthol, C18H15N3OS, (V), and 1-[(4,4-dimethylthiosemicarbazono)methyl]-2-naphthol dimethyl sulfoxide solvate, C14H15N3OS.C2H6OS, (VI). These chelators are N4-substituted thiosemicarbazones, each based on the same parent aldehyde, namely 2-zhydroxynaphthalene-1-carboxaldehyde isonicotinoylhydrazone. Conformational variations within this series are discussed in relation to the optimum conformation for metal-ion binding.

Sex- and race-related differences in cross-sectional geometry and bone density of the femoral mid-shaft in older adults

Background : Femoral shaft fracture incidence increases in older adults and is associated with low-energy trauma. Apart from bone density, the distribution and size of bone contributes to its strength. Aim : To examine if bone geometry and density of the femoral mid-shaft in older adults differs by sex and race, we studied 197 White women, 225 Black women, 242 White men, and 148 Black men aged 70-79 years participating in the Health, Aging, and Body Composition study; a prospective cohort study in the USA. A secondary purpose of the study was to examine the association of site-specific muscle and fat to bone geometry and density. Subjects and methods : Subjects were community-dwelling and reported no difficulty walking one-quarter of a mile or climbing stairs. Mid-femoral volumetric bone mineral density (vBMD, mg cm -3 ), total area (TA), cortical area (CA), medullary area (MA), cross-sectional moments of inertia (CSMI: I x , I y , J ), and muscle and fat areas (cm 2 ) were determined by computed tomography (CT; GE CT-9800, 10 mm slice thickness). Results : vBMD was greater in men than women with no difference by race ( p < 0.001). Bone areas and area moments of inertia were also greater in men than women ( p < 0.001), with Black women having higher values than White women for TA and CA. Standardizing geometric parameters for body size differences by dividing by powers of femur length did not negate the sex difference for TA and MA. Significant differences ( p < 0.05) among the four groups also remained for I x and J . Mid-thigh muscle area was an independent contributor to TA in all groups (Std beta = 0.181-0.351, p < 0.05) as well as CA in women (Std beta = 0.246-0.254, p < 0.01) and CSMI in White women (Std beta = 0.175-0.185, p < 0.05). Further, muscle area was a significant contributor to vBMD in Black women. Conclusion : These results indicate that bone geometry and density of the femoral diaphysis differs primarily by sex, rather than race, in older well-functioning adults. In addition, site-specific muscle area appears to have a potential contributory role to bone geometry parameters, especially in women.

Water sorption into poly[(2-hydroxyethyl methacrylate)-co-(1-vinyl-2-pyrrolidone]at 310 K

Poly(2-hydroxyethyl methacrylate) and copolymers of 2-hydroxyethyl methacrylate (HEMA) and 1-vinyl-2-pyrrolidone (VP) in the form of cylindrical samples (approximate to8mm x 20mm) have been prepared and the sorption of water into these cylinders has been studied by the mass-uptake methods and by magnetic-resonance imaging. The equilibrium water contents for the cylinders were found to vary systematically with the copolymer composition. Diffusion of water into the cylinders was found to follow Fickian behaviour for cylinders with high HEMA contents, with the diffusion coefficients obtained from mass-uptake studies dependent on the copolymer composition, varying from 1.7 x 10(-11) m(2) s(-1) for poly(HEMA) to 2.0 x 10(-11) m(2) s(-1) for poly(HEMA-co-VP) with a composition of 1:1. However, NMR-imaging studies showed that, while the profiles of the water diffusion fronts for cylinders with high HEMA contents were Fickian, that for the 1:1 copolymer was not and indicated that the mechanism was Case III. The polymers which were rich in VP were characterized by a water-sorption process which follows Case-III behaviour. (C) 2003 Society of Chemical Industry.

Cytotoxic iron chelators: Characterization of the structure, solution chemistry and redox activity of ligands and iron complexes of the di-2-pyridyl ketone isonicotinoyl hydrazone (HPKIH) analogues

Di-2-pyridyl ketone isonicotinoyl hydrazone (HPKIH) and a range of its analogues comprise a series of monobasic acids that are capable of binding iron (Fe) as tridentate (N,N,O) ligands. Recently, we have shown that these chelators are highly cytotoxic, but show selective activity against cancer cells. Particularly interesting was the fact that cytotoxicity of the HPKIH analogues is maintained even after complexation with Fe. To understand the potent anti-tumor activity of these compounds, we have fully characterized their chemical properties. This included examination of the solution chemistry and X-ray crystal structures of both the ligands and Fe complexes from this class and the ability of these complexes to mediate redox reactions. Potentiometric titrations demonstrated that all chelators are present predominantly in their charge-neutral form at physiological pH (7.4), allowing access across biological membranes. Keto-enol tautomerism of the ligands was identified, with the tautomers exhibiting distinctly different protonation constants. Interestingly, the chelators form low-spin (diamagnetic) divalent Fe complexes in solution. The chelators form distorted octahedral complexes with Fe-II, with two tridentate ligands arranged in a meridional fashion. Electrochemistry of the Fe complexes in both aqueous and non-aqueous solutions revealed that the complexes are oxidized to their ferric form at relatively high potentials, but this oxidation is coupled to a rapid reaction with water to form a hydrated (carbinolamine) derivative, leading to irreversible electrochemistry. The Fe complexes of the HPKIH analogues caused marked DNA degradation in the presence of hydrogen peroxide. This observation confirms that Fe complexes from the HPKIH series mediate Fenton chemistry and do not repel DNA. Collectively, studies on the solution chemistry and structure of these HPKIH analogues indicate that they can bind cellular Fe and enhance its redox activity, resulting in oxidative damage to vital biomolecules.

Structural definition of the low-temperature phase transition of tris(ethane-1,2-diamine)zinc(II) dinitrate

The 93 K X-ray crystal structure of tris(ethane-1,2-diamine)zinc(II) dinitrate is reported. As predicted by the spectroscopic studies of other workers, there is a reversible phase transition of the structure at low temperature. We have determined this temperature to be 143 K. The structure at this temperature and below resembles that of the room temperature structure, except the crystallographic D-3 symmetry of the complex cation (296 K) is lowered to C-2 ( below 144 K) by subtle changes in cation-anion hydrogen bonding. No change in the conformation of the cation or its bond lengths and angles was found.

1-Ethynyl-2-isopropoxy-3-methoxybenzene

The crystal structure of the title compound, C12H14O2, has been determined at 150 K. Significant intermolecular non-conventional C-H...O interactions involving the terminal acetylinic H atom are observed, which result in a zigzag hydrogen-bonded chain in the b direction.

Synthesis of novel 2-amino-1,3-thiazole-5-carboxylates utilising ultrasonic and thermally mediated aminolysis

Novel 2-amino-1,3-thiazole-5-carboxylates have been synthesised in high yield by unprecedented ultrasonic and thermally mediated nucleophilic displacement of bromide from ethyl 2-bromo-1,3-thiazole-5-carboxylate by primary, secondary and aryl amines.

The synthesis and X-ray crystal structure of 6-bromo-2,4,4-trimethyl-cyclohex-2-enone

Regiospecific bromination of 2,4,4-trimethyl-cyclohex-2-enone was achieved and the X-ray crystal structure of 6-bromo-2,4,4-trimethyl-cyclohex-2-enone is presented.