Development of rigorous and efficient integral bounds and strategies for the linear-scaling quantum chemical calculation of large molecules

Es wurden neuartige rigorose Integralschranken hergeleitet, die als "Multipole Based Integral Estimates" (MBIE) bezeichnet werden. Mit diesen lässt sich das 1/R-Abklingverhalten zwischen den Ladungsverteilungen von Zweielektronenintegralen im Rahmen von SCF-Verfahren bzw. das 1/R**4- und stärkere Abklingverhaltem im Rahmen von Elektronenkorrelationsmethoden erstmals rigoros berücksichtigen. Die Schranken sind auf alle quantenchemischen Verfahren anwendbar, die auf Zweielektronenintegrale über lokale Orbitale (natürliche oder lokalisierte) zurückgreifen. Durch die Berücksichtigung des 1/R**n-Verhaltens kann die Anzahl an zu berechnenden numerisch signifikanten Integralen bei vollem Erhalt der numerischen Genauigkeit und Zuverlässigkeit drastisch reduziert werden. Dies wird anhand von Anwendungen auf dem Gebiet der linear-skalierenden SCF-Verfahren, Geometrieoptimierungen, Moleküldynamik-Simulationen, sowie MP2-Rechnungen an isolierten und wechselwirkenden Systemen demonstriert. Insbesondere kann das Skalenverhalten von Korrelationsrechnungen im Rahmen der atomorbitalbasierten Møller-Plesset-Störungstheorie zweiter Ordnung (AO-MP2) durch die Ausnutzung des 1/R**4-Verhaltens erstmals rigoros auf linear reduziert werden. Mit Hilfe der MBIE-Schranken werden damit korrelierte Berechnungen an Systemen mit mehr als 1000 Atomen bzw. 10000 Basisfunktionen ohne Verlust an numerischer Genauigkeit möglich.A new kind of rigorous integral bounds was derived, which are termed "Multipole Based Integral Estimates" (MBIE). With these it is possible to exploit for the first time rigorously the 1/R distance decay between charge distributions in two-electron integrals in the context of SCF methods and the 1/R**4 and stronger decay within electron correlation approaches, respectively. The bounds are applicable to all quantum chemical methodologies that rely on (naturally or imposedly) local orbitals. By taking the 1/R**n decay into account, the number of numerically significant integrals that has to be calculated can be reduced drastically, while numerical accuracy and reliability is fully preserved. This is illustrated for applications to linear-scaling SCF approaches, geometry optimizations, molecular dynamics simulations, as well as MP2 calculations for isolated and interacting systems. In particular, by exploiting the 1/R**4 decay the scaling of correlated calculations in the framework of atomic-orbital based Møller-Plesset perturbation theory to second order (AO-MP2) is reduced for the first time rigorously to linear. In this way, the MBIE bounds enable correlated calculations on systems with more than 1000 atoms or 10000 basis functions, respectively, without loss of numerical accuracy

Different origin of the ferromagnetic order in (Ga,Mn)As and (Ga,Mn)N

The mechanism for the ferromagnetic order of (Ga,Mn)As and (Ga,Mn)N is extensively studied over a vast range of Mn concentrations. We calculate the electronic structures of these materials using density functional theory in both the local spin density approximation and the LDA+U scheme, that we have now implemented in the code SIESTA. For (Ga,Mn)As, the LDA+U approach leads to a hole mediated picture of the ferromagnetism, with an exchange constant $N\beta$ =~ -2.8 eV. This is smaller than that obtained with LSDA, which overestimates the exchange coupling between Mn ions and the As $p$ holes. In contrast, the ferromagnetism in wurtzite (Ga,Mn)N is caused by the double-exchange mechanism, since a hole of strong $d$ character is found at the Fermi level in both the LSDA and the LDA+U approaches. In this case the coupling between the Mn ions decays rapidly with the Mn-Mn separation. This suggests a two phases picture of the ferromagnetic order in (Ga,Mn)N, with a robust ferromagnetic phase at large Mn concentration coexisting with a diluted weak ferromagnetic phase.Comment: 12 pages, 11 figure

Inattentive Consumers in Markets for Services

In an experiment on markets for services, we find that consumers are likely to stick to default tariffs and achieve suboptimal outcomes. We find that inattention to the task of choosing a better tariff is likely to be a substantial problem in addition to any task and tariff complexity effect. The institutional setup on which we primarily model our experiment is the UK electricity and gas markets, and our conclusion is that the new measures by the UK regulator Ofgem to improve consumer outcomes are likely to be of limited impact

Universality of the thermodynamic Casimir effect

Recently a nonuniversal character of the leading spatial behavior of the thermodynamic Casimir force has been reported [X. S. Chen and V. Dohm, Phys. Rev. E {\bf 66}, 016102 (2002)]. We reconsider the arguments leading to this observation and show that there is no such leading nonuniversal term in systems with short-ranged interactions if one treats properly the effects generated by a sharp momentum cutoff in the Fourier transform of the interaction potential. We also conclude that lattice and continuum models then produce results in mutual agreement independent of the cutoff scheme, contrary to the aforementioned report. All results are consistent with the {\em universal} character of the Casimir force in systems with short-ranged interactions. The effects due to dispersion forces are discussed for systems with periodic or realistic boundary conditions. In contrast to systems with short-ranged interactions, for $L/\xi \gg 1$ one observes leading finite-size contributions governed by power laws in $L$ due to the subleading long-ranged character of the interaction, where $L$ is the finite system size and $\xi$ is the correlation length.Comment: 11 pages, revtex, to appear in Phys. Rev. E 68 (2003

Integrative miRNA and Gene Expression Profiling Analysis of Human Quiescent Hepatic Stellate Cells.

Unveiling the regulatory pathways maintaining hepatic stellate cells (HSC) in a quiescent (q) phenotype is essential to develop new therapeutic strategies to treat fibrogenic diseases. To uncover the miRNA-mRNA regulatory interactions in qHSCs, HSCs were FACS-sorted from healthy livers and activated HSCs (aHSCs) were generated in vitro. MiRNA Taqman array analysis showed HSCs expressed a low number of miRNAs (n = 259), from which 47 were down-regulated and 212 up-regulated upon activation. Computational integration of miRNA and gene expression profiles revealed that 66% of qHSC-associated miRNAs correlated with more than 6 altered target mRNAs (17,28 ± 10,7 targets/miRNA) whereas aHSC-associated miRNAs had an average of 1,49 targeted genes. Interestingly, interaction networks generated by miRNA-targeted genes in qHSCs were associated with key HSC activation processes. Next, selected miRNAs were validated in healthy and cirrhotic human livers and miR-192 was chosen for functional analysis. Down-regulation of miR-192 in HSCs was found to be an early event during fibrosis progression in mouse models of liver injury. Moreover, mimic assays for miR-192 in HSCs revealed its role in HSC activation, proliferation and migration. Together, these results uncover the importance of miRNAs in the maintenance of the qHSC phenotype and form the basis for understanding the regulatory networks in HSCs