A primal-dual semidefinite programming algorithm tailored to the variational determination of the two-body density matrix

The quantum many-body problem can be rephrased as a variational determination of the two-body reduced density matrix, subject to a set of N-representability constraints. The mathematical problem has the form of a semidefinite program. We adapt a standard primal-dual interior point algorithm in order to exploit the specific structure of the physical problem. In particular the matrix-vector product can be calculated very efficiently. We have applied the proposed algorithm to a pairing-type Hamiltonian and studied the computational aspects of the method. The standard N-representability conditions perform very well for this problem.Comment: 24 pages, 5 figures, submitted to the Journal of Computational Physic

Variational determination of the second-order density matrix for the isoelectronic series of beryllium, neon and silicon

The isoelectronic series of Be, Ne and Si are investigated using a variational determination of the second-order density matrix. A semidefinite program was developed that exploits all rotational and spin symmetries in the atomic system. We find that the method is capable of describing the strong static electron correlations due to the incipient degeneracy in the hydrogenic spectrum for increasing central charge. Apart from the ground-state energy various other properties are extracted from the variationally determined second-order density matrix. The ionization energy is constructed using the extended Koopmans' theorem. The natural occupations are also studied, as well as the correlated Hartree-Fock-like single particle energies. The exploitation of symmetry allows to study the basis set dependence and results are presented for correlation-consistent polarized valence double, triple and quadruple zeta basis sets.Comment: 19 pages, 7 figures, 3 tables v2: corrected typo in Eq. (52

The relative impact of school‐wide positive behavior support on teachers’ perceptions of student behavior across schools, teachers, and students

School‐wide positive behavior support (SWPBS) is a systemic approach for implementing a proactive schoolwide discipline and for improving students’ academic and behavioral outcomes by targeting the school’s organizational and social culture. With a multilevel approach, the present study evaluates the relative effectiveness of SWPBS on teachers’ perceptions of the student behavior (N = 3,295) across schools, teachers, and children using a multilevel approach. We assessed teacher perception of student problem behavior five times during a 3‐year implementation of SWPBS in 23 Dutch schools. Multilevel analyses not only revealed a small increase in perceived prosocial behavior and a small decrease in problems with peers, but also different effects across children, teachers, and schools. Effects were stronger for girls and for students with higher severity of perceived problems at baseline. At teachers’ level, higher mean baseline severity of perceived problems was associated with the reduced impact of SWPBS on perceived emotional problems and problems with peers. At the school level, effects were stronger for regular schools as compared with special needs schools

Transcriptional Response of Zebrafish Embryos Exposed to Neurotoxic Compounds Reveals a Muscle Activity Dependent hspb11 Expression

Acetylcholinesterase (AChE) inhibitors are widely used as pesticides and drugs. Their primary effect is the overstimulation of cholinergic receptors which results in an improper muscular function. During vertebrate embryonic development nerve activity and intracellular downstream events are critical for the regulation of muscle fiber formation. Whether AChE inhibitors and related neurotoxic compounds also provoke specific changes in gene transcription patterns during vertebrate development that allow them to establish a mechanistic link useful for identification of developmental toxicity pathways has, however, yet not been investigated. Therefore we examined the transcriptomic response of a known AChE inhibitor, the organophosphate azinphos-methyl (APM), in zebrafish embryos and compared the response with two non-AChE inhibiting unspecific control compounds, 1,4-dimethoxybenzene (DMB) and 2,4-dinitrophenol (DNP). A highly specific cluster of APM induced gene transcripts was identified and a subset of strongly regulated genes was analyzed in more detail. The small heat shock protein hspb11 was found to be the most sensitive induced gene in response to AChE inhibitors. Comparison of expression in wildtype, ache and sopfixe mutant embryos revealed that hspb11 expression was dependent on the nicotinic acetylcholine receptor (nAChR) activity. Furthermore, modulators of intracellular calcium levels within the whole embryo led to a transcriptional up-regulation of hspb11 which suggests that elevated intracellular calcium levels may regulate the expression of this gene. During early zebrafish development, hspb11 was specifically expressed in muscle pioneer cells and Hspb11 morpholino-knockdown resulted in effects on slow muscle myosin organization. Our findings imply that a comparative toxicogenomic approach and functional analysis can lead to the identification of molecular mechanisms and specific marker genes for potential neurotoxic compounds

Integrating Omic Technologies into Aquatic Ecological Risk Assessment and Environmental Monitoring: Hurdles, Achievements, and Future Outlook

Background: In this commentary we present the findings from an international consortium on fish toxicogenomics sponsored by the U.K. Natural Environment Research Council (Fish Toxicogenomics—Moving into Regulation and Monitoring, held 21–23 April 2008 at the Pacific Environmental Science Centre, Vancouver, BC, Canada). Objectives: The consortium from government agencies, academia, and industry addressed three topics: progress in ecotoxicogenomics, regulatory perspectives on roadblocks for practical implementation of toxicogenomics into risk assessment, and dealing with variability in data sets. Discussion: Participants noted that examples of successful application of omic technologies have been identified, but critical studies are needed to relate molecular changes to ecological adverse outcome. Participants made recommendations for the management of technical and biological variation. They also stressed the need for enhanced interdisciplinary training and communication as well as considerable investment into the generation and curation of appropriate reference omic data. Conclusions: The participants concluded that, although there are hurdles to pass on the road to regulatory acceptance, omics technologies are already useful for elucidating modes of action of toxicants and can contribute to the risk assessment process as part of a weight-of-evidence approach

Towards a System Level Understanding of Non-Model Organisms Sampled from the Environment: A Network Biology Approach

The acquisition and analysis of datasets including multi-level omics and physiology from non-model species, sampled from field populations, is a formidable challenge, which so far has prevented the application of systems biology approaches. If successful, these could contribute enormously to improving our understanding of how populations of living organisms adapt to environmental stressors relating to, for example, pollution and climate. Here we describe the first application of a network inference approach integrating transcriptional, metabolic and phenotypic information representative of wild populations of the European flounder fish, sampled at seven estuarine locations in northern Europe with different degrees and profiles of chemical contaminants. We identified network modules, whose activity was predictive of environmental exposure and represented a link between molecular and morphometric indices. These sub-networks represented both known and candidate novel adverse outcome pathways representative of several aspects of human liver pathophysiology such as liver hyperplasia, fibrosis, and hepatocellular carcinoma. At the molecular level these pathways were linked to TNF alpha, TGF beta, PDGF, AGT and VEGF signalling. More generally, this pioneering study has important implications as it can be applied to model molecular mechanisms of compensatory adaptation to a wide range of scenarios in wild populations

Single-particle energies and density of states in density functional theory

Time-dependent density functional theory (TD-DFT) is commonly used as the foundation to obtain neutral excited states and transition weights in DFT, but does not allow direct access to density of states and single-particle energies, i.e. ionisation energies and electron affinities. Here we show that by extending TD-DFT to a superfluid formulation, which involves operators that break particle-number symmetry, we can obtain the density of states and single-particle energies from the poles of an appropriate superfluid response function. The standard Kohn– Sham eigenvalues emerge as the adiabatic limit of the superfluid response under the assumption that the exchange– correlation functional has no dependence on the superfluid density. The Kohn– Sham eigenvalues can thus be interpreted as approximations to the ionisation energies and electron affinities. Beyond this approximation, the formalism provides an incentive for creating a new class of density functionals specifically targeted at accurate single-particle eigenvalues and bandgaps

Single-particle energies and density of states in density functional theory

Time-dependent density functional theory (TD-DFT) is commonly used as the foundation to obtain neutral excited states and transition weights in DFT, but does not allow direct access to density of states and single-particle energies, i.e. ionisation energies and electron affinities. Here we show that by extending TD-DFT to a superfluid formulation, which involves operators that break particle-number symmetry, we can obtain the density of states and single-particle energies from the poles of an appropriate superfluid response function. The standard Kohn– Sham eigenvalues emerge as the adiabatic limit of the superfluid response under the assumption that the exchange– correlation functional has no dependence on the superfluid density. The Kohn– Sham eigenvalues can thus be interpreted as approximations to the ionisation energies and electron affinities. Beyond this approximation, the formalism provides an incentive for creating a new class of density functionals specifically targeted at accurate single-particle eigenvalues and bandgaps