Controlling variability in split–merge systems and its impact on performance

We consider split–merge systems with heterogeneous subtask service times and limited output buffer space in which to hold completed but as yet unmerged subtasks. An important practical problem in such systems is to limit utilisation of the output buffer. This can be achieved by judiciously delaying the processing of subtasks in order to cluster subtask completion times. In this paper we present a methodology to find those deterministic subtask processing delays which minimise any given percentile of the difference in times of appearance of the first and the last subtasks in the output buffer. Technically this is achieved in three main steps: firstly, we define an expression for the distribution of the range of samples drawn from \(n\) independent heterogeneous service time distributions. This is a generalisation of the well-known order statistic result for the distribution of the range of \(n\) samples taken from the same distribution. Secondly, we extend our model to incorporate deterministic delays applied to the processing of subtasks. Finally, we present an optimisation scheme to find that vector of delays which minimises a given percentile of the range of arrival times of subtasks in the output buffer. We show the impact of applying the optimal delays on system stability and task response time. Two case studies illustrate the applicability of our approach.     

Paramagnetic active site models for the molybdenum-copper carbon monoxide dehydrogenase

New paramagnetic, heterobimetallic Mo/Cu complexes featuring the Mo(=O)(mu-S)Cu core of O. carboxidovorans carbon monoxide dehydrogenase have been synthesized and structurally and spectroscopically characterized. The complexes exhibit EPR spectra (left graphic) indicative of extensive electron delocalization across the Mo-S-Cu core, in agreement with computational studies identifying the singly-occupied molecular orbital (right graphic).     

On the electronic origins of structural isomerism in the iron-sulfur cubane, [(C(5)H(5))(4)Fe(4)S(4)](2+)

Density functional theory provides new insights into the structural isomerism observed in the cyclopentadienyl-capped iron-sulfur cluster, [(C(5)H(5))(4)Fe(4)S(4)](2+). Two distinct, closely spaced minima have been located, a triplet with D(2) symmetry and a C(2)-symmetric singlet, both of which correspond closely to the structure of one of the known crystal forms of the cation. Thus, the structural diversity in these species reflects genuine molecular bistability rather than simple solid-state packing effects. In contrast, no stable D(2)(d)()-symmetric minimum has been located, suggesting that the reported D(2)(d)() symmetry of the cation in [(C(5)H(5))(4)Fe(4)S(4)][PF(6)](2) may be a crystallographic artifact. In the ruthenium analogue, the more diffuse 4d orbitals stabilize the C(2)-symmetric singlet, which is unambiguously the ground state, but the D(2)-symmetric potential energy surface provides a viable low-energy pathway for the dynamic exchange of the Ru-Ru bonds.     

The enthalpy of formation of 2II CH

The standard enthalpy of formation, δ_fH^o, of² II CH has been determined at converged levels of ab initio electronic structure theory, including high order coupled cluster and full configuration interaction benchmarks. The atomic Gaussian basis sets employed include the (aug)-cc-p(C)VXZ family with X = 3, 4, 5 and 6. Extrapolations to the complete one-particle basis set and the full configuration interaction limits, where appropriate, have been performed to reduce remaining computational errors. Additional improvements in the enthalpy of formation of ²II CH were achieved by appending the valence-only treatment with core-valence correlation, relativistic effects including spin-orbit correlation, and the diagonal Born-Oppenheimer correction. The recommended values for δfH^o ₀ and δA_f H _o ²⁹⁸ of ²II CH are 592.48^+0.47 _?0.56 kJ mol_?1 and 595.93 ^+0.47 _?0.56 kJ mol_?1, respectively.     

Understanding the origin of metal-sulfur vibrations in an oxo-molybdenum dithiolene complex: relevance to sulfite oxidase

X-ray crystallography and resonance Raman (rR) spectroscopy have been used to further characterize (Tp*)MoO(qdt) (Tp* is hydrotris(3,5-dimethyl-1-pyrazolyl)borate and qdt is 2,3-quinoxalinedithiolene), which represents an important benchmark oxomolybdenum mono-dithiolene model system relevant to various pyranopterin Mo enzyme active sites, including sulfite oxidase. The compound (Tp*)MoO(qdt) crystallizes in the triclinic space group, P1, where a = 9.8424 (7) A, b = 11.2323 (8) A, c = 11.9408 (8) A, alpha = 92.7560 (10) degrees, beta = 98.9530 (10) degrees, and gamma = 104.1680 (10) degrees. The (Tp*)MoO(qdt) molecule exhibits the distorted six-coordinate geometry characteristic of related oxo-Mo(V) systems possessing a single coordinated dithiolene ligand. The first coordination sphere bond lengths and angles in (Tp*)MoO(qdt) are very similar to the corresponding structural parameters for (Tp*)MoO(bdt) (bdt is 1,2-benzenedithiolene). The relatively small inner-sphere structural variations observed between (Tp*)MoO(qdt) and (Tp*)MoO(bdt) strongly suggest that geometric effects are not a major contributor to the significant electronic structural differences reported for these two oxo-Mo(V) dithiolenes. Therefore, the large differences observed in the reduction potential and first ionization energy between the two molecules appear to derive primarily from differences in the effective nuclear charges of their respective sulfur donors. However, a subtle perturbation to Mo-S bonding is implied by the nonplanarity of the dithiolene chelate ring, which is defined by the fold angle. This angular distortion (theta = 29.5 degrees in (Tp*)MoO(qdt); 21.3 degrees in (Tp*)MoO(bdt)) observed between the MoS2 and S-C=C-S planes may contribute to the electronic structure of these oxo-Mo dithiolene systems by controlling the extent of S p-Mo d orbital overlap. In enzymes, the fold angle may be dynamically modulated by the pyranopterin, thereby functioning as a transducer of vibrational energy associated with protein conformational changes directly to the active site via changes in the fold angle. This process could effectively mediate charge redistribution at the active site during the course of atom- and electron-transfer processes. The rR spectrum shows bands at 348 and 407 cm(-1). From frequency analysis of the normal modes of the model, [(NH3)3MoO(qdt)]1+, using the Gaussian03 suite of programs, these bands are assigned as mixed-mode Mo-S vibrations of the five-membered Mo-ditholene core structure. Raman spectroscopy has also provided additional evidence for an in-plane pseudo-sigma dithiolene S-Mo d(xy) covalent bonding interaction in (Tp*)MoO(qdt) and related oxo-Mo-dithiolenes that has implications for electron-transfer regeneration of the active site in sulfite oxidase involving the pyranopterin dithiolene.     

Investigation of Thermal Degradation of PVC in the Solid State

The thermal degradation of PVC powders and the inhibition of this process by cadmium laurate was investigated by the measurement of discoloration, diffuse reflectance spectra, and the quantity of hydrochloric acid formed. Kinetic analysis of the data obtained by us previously showed that both the data of color measurements and those of diffuse reflectance spectra may be used conveniently for the calculation of the number of double bonds formed during the degradation.     

Revisiting the polyoxometalate-based late-transition-metal-oxo complexes: the "oxo wall" stands

Terminal oxo complexes of the late transition metals Pt, Pd, and Au have been reported by us in Science and Journal of the American Chemical Society. Despite thoroughness in characterizing these complexes (multiple independent structural methods and up to 17 analytical methods in one case), we have continued to study these structures. Initial work on these systems was motivated by structural data from X-ray crystallography and neutron diffraction and (17)O and (31)P NMR signatures which all indicated differences from all previously published compounds. With significant new data, we now revisit these studies. New X-ray crystal structures of previously reported complexes K(14)[P(2)W(19)O(69)(OH(2))] and "K(10)Na(3)[Pd(IV)(O)(OH)WO(OH(2))(PW(9)O(34))(2)]" and a closer examination of these structures are provided. Also presented are the (17)O NMR spectrum of an (17)O-enriched sample of [PW(11)O(39)](7-) and a careful combined (31)P NMR-titration study of the previously reported "K(7)H(2)[Au(O)(OH(2))P(2)W(20)O(70)(OH(2))(2)]." These and considerable other data collectively indicate that previously assigned terminal Pt-oxo and Au-oxo complexes are in fact cocrystals of the all-tungsten structural analogues with noble metal cations, while the Pd-oxo complex is a disordered Pd(II)-substituted polyoxometalate. The neutron diffraction data have been re-analyzed, and new refinements are fully consistent with the all-tungsten formulations of the Pt-oxo and Au-oxo polyoxometalate species.     

Anatomy of relativistic energy corrections in light molecular systems

Relativistic energy corrections which arise from the use of the Dirac-Coulomb Hamiltonian, and the Gaunt and Breit interaction operators, plus Lamb-shift effects have been determined for the global minima of the ground electronic states of C₂H₆, NH₃, H₂O, [H,C,N], HNCO, HCOOH, SiC₂, SiH^? ₃, and H₂S, and for barrier characteristics for these molecular systems (inversion barrier of NH₃ and SiH^? ₃, barrier to linearity of H₂O, H₂S, and HNCO, rotational barrier of C₂H₆, difference between conformations of HCOOH (Z/E) and SiC₂ (linear/T-shaped), and isomerization barrier of HCN/HNC). The relativistic calculations performed at the Hartree-Fock and the highly correlated CCSD(T) levels employed a wide variety of basis sets. Comparison of the perturbational and the four-component fully variational results indicate that the Coulomb-Pauli Hamiltonian and the lowest order Hamiltonian of direct perturbation theory (DPT(2)) are highly successful for treating the relativistic energy effects in light molecular systems both at a single point on the potential energy hypersurface and along the surface. Electron correlation contributions to the relativistic corrections are relatively small for the systems studied, and are comparable with the 2-electron Darwin correction. Corrections beyond the Dirac-Coulomb treatment are usually rather small, but may become important for high accuracy ab initio calculations.