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The Dirac–Frenkel principle for reduced density matrices and the Bogoliubov–de Gennes equations
Get PDFThe derivation of effective evolution equations is central to the study of non-stationary quantum many-body systems, and widely used in contexts such as superconductivity, nuclear physics, Bose–Einstein condensation and quantum chemistry. We reformulate the Dirac–Frenkel approximation principle in terms of reduced density matrices and apply it to fermionic and bosonic many-body systems. We obtain the Bogoliubov–de Gennes and Hartree–Fock–Bogoliubov equations, respectively. While we do not prove quantitative error estimates, our formulation does show that the approximation is optimal within the class of quasifree states. Furthermore, we prove well-posedness of the Bogoliubov–de Gennes equations in energy space and discuss conserved quantities
Spatial gene frequency waves under genotype-dependent dispersal
Get PDFDispersal is a crucial factor in natural evolution, since it determines the habitat experienced by any population and defines the spatial scale of interactions between individuals. There is compelling evidence for systematic differences in dispersal characteristics within the same population, i.e. genotype-dependent dispersal. The consequences of genotype-dependent dispersal on other evolutionary phenomena, however, are poorly understood. In this article we investigate the effect of genotype-dependent dispersal on spatial gene frequency patterns, using a generalization of the classical diffusion model of selection and dispersal. Dispersal is characterized by the variance of dispersal (diffusion coefficient) and the mean displacement (directional advection term). We demonstrate that genotype-dependent dispersal may change the qualitative behaviour of Fisher waves, which change from being “pulled” to being “pushed” wave fronts as the discrepancy in dispersal between genotypes increases. The speed of any wave is partitioned into components due to selection, genotype-dependent variance of dispersal, and genotype-dependent mean displacement. We apply our findings to wave fronts maintained by selection against heterozygotes. Furthermore, we identify a benefit of increased variance of dispersal, quantify its effect on the speed of the wave, and discuss the implications for the evolution of dispersal strategies
Local law for random Gram matrices
Get PDFWe prove a local law in the bulk of the spectrum for random Gram matrices XX∗, a generalization of sample covariance matrices, where X is a large matrix with independent, centered entries with arbitrary variances. The limiting eigenvalue density that generalizes the Marchenko-Pastur law is determined by solving a system of nonlinear equations. Our entrywise and averaged local laws are on the optimal scale with the optimal error bounds. They hold both in the square case (hard edge) and in the properly rectangular case (soft edge). In the latter case we also establish a macroscopic gap away from zero in the spectrum of XX∗
Global dosage compensation is ubiquitous in Lepidoptera, but counteracted by the masculinization of the Z chromosome
Get PDFWhile chromosome-wide dosage compensation of the X chromosome has been found in many species, studies in ZW clades have indicated that compensation of the Z is more localized and/or incomplete. In the ZW Lepidoptera, some species show complete compensation of the Z chromosome, while others lack full equalization, but what drives these inconsistencies is unclear. Here, we compare patterns of male and female gene expression on the Z chromosome of two closely related butterfly species, Papilio xuthus and Papilio machaon, and in multiple tissues of two moths species, Plodia interpunctella and Bombyx mori, which were previously found to differ in the extent to which they equalize Z-linked gene expression between the sexes. We find that, while some species and tissues seem to have incomplete dosage compensation, this is in fact due to the accumulation of male-biased genes and the depletion of female-biased genes on the Z chromosome. Once this is accounted for, the Z chromosome is fully compensated in all four species, through the up-regulation of Z expression in females and in some cases additional down-regulation in males. We further find that both sex-biased genes and Z-linked genes have increased rates of expression divergence in this clade, and that this can lead to fast shifts in patterns of gene expression even between closely related species. Taken together, these results show that the uneven distribution of sex-biased genes on sex chromosomes can confound conclusions about dosage compensation and that Z chromosome-wide dosage compensation is not only possible but ubiquitous among Lepidoptera
Shaping bacterial population behavior through computer interfaced control of individual cells
Get PDFBacteria in groups vary individually, and interact with other bacteria and the environment to produce population-level patterns of gene expression. Investigating such behavior in detail requires measuring and controlling populations at the single-cell level alongside precisely specified interactions and environmental characteristics. Here we present an automated, programmable platform that combines image-based gene expression and growth measurements with on-line optogenetic expression control for hundreds of individual Escherichia coli cells over days, in a dynamically adjustable environment. This integrated platform broadly enables experiments that bridge individual and population behaviors. We demonstrate: (i) population structuring by independent closed-loop control of gene expression in many individual cells, (ii) cell-cell variation control during antibiotic perturbation, (iii) hybrid bio-digital circuits in single cells, and freely specifiable digital communication between individual bacteria. These examples showcase the potential for real-time integration of theoretical models with measurement and control of many individual cells to investigate and engineer microbial population behavior
Ein freies Bibliothekssystem für wissenschaftliche Bibliotheken – Werkstattbericht der IST Austria Library
Get PDFAuf der Suche nach einem Bibliothekssystem entschied sich die Forschungseinrichtung IST Austria im Jahr 2014 für das Open-Source-Produkt Koha. In einem ersten Schritt wurden zunächst Grundfunktionen aktiviert um im Anschluss diverse zusätzliche Tools zum Einsatz zu bringen. Die große Flexibilität des Systems erlaubt maßgeschneiderte Lösungen für unterschiedlichste Institutionen. Trotz Herausforderungen kann die Bibliothek auf eine erfolgreiche Implementierung zurückblicken
Flavonol induced changes in PIN2 polarity and auxin transport in the Arabidopsis thaliana rol1 2 mutant require phosphatase activity
Get PDFThe phytohormone auxin is a major determinant and regulatory component important for plant development. Auxin transport between cells is mediated by a complex system of transporters such as AUX1/LAX, PIN, and ABCB proteins, and their localization and activity is thought to be influenced by phosphatases and kinases. Flavonols have been shown to alter auxin transport activity and changes in flavonol accumulation in the Arabidopsis thaliana rol1-2 mutant cause defects in auxin transport and seedling development. A new mutation in ROOTS CURL IN NPA 1 (RCN1), encoding a regulatory subunit of the phosphatase PP2A, was found to suppress the growth defects of rol1-2 without changing the flavonol content. rol1-2 rcn1-3 double mutants show wild type-like auxin transport activity while levels of free auxin are not affected by rcn1-3. In the rol1-2 mutant, PIN2 shows a flavonol-induced basal-to-apical shift in polar localization which is reversed in the rol1-2 rcn1-3 to basal localization. In vivo analysis of PINOID action, a kinase known to influence PIN protein localization in a PP2A-antagonistic manner, revealed a negative impact of flavonols on PINOID activity. Together, these data suggest that flavonols affect auxin transport by modifying the antagonistic kinase/phosphatase equilibrium
Tubulins and brain development – The origins of functional specification
Get PDFThe development of the vertebrate central nervous system is reliant on a complex cascade of biological processes that include mitotic division, relocation of migrating neurons, and the extension of dendritic and axonal processes. Each of these cellular events requires the diverse functional repertoire of the microtubule cytoskeleton for the generation of forces, assembly of macromolecular complexes and transport of molecules and organelles. The tubulins are a multi-gene family that encode for the constituents of microtubules, and have been implicated in a spectrum of neurological disorders. Evidence is building that different tubulins tune the functional properties of the microtubule cytoskeleton dependent on the cell type, developmental profile and subcellular localisation. Here we review of the origins of the functional specification of the tubulin gene family in the developing brain at a transcriptional, translational, and post-transcriptional level. We remind the reader that tubulins are not just loading controls for your average Western blot
Safety verification of nonlinear hybrid systems based on invariant clusters
Get PDFIn this paper, we propose an approach to automatically compute invariant clusters for nonlinear semialgebraic hybrid systems. An invariant cluster for an ordinary differential equation (ODE) is a multivariate polynomial invariant g(u, x)=0, parametric in u, which can yield an infinite number of concrete invariants by assigning different values to u so that every trajectory of the system can be overapproximated precisely by the intersection of a group of concrete invariants. For semialgebraic systems, which involve ODEs with multivariate polynomial right-hand sides, given a template multivariate polynomial g(u, x), an invariant cluster can be obtained by first computing the remainder of the Lie derivative of g(u,x) divided by g(u, x) and then solving the system of polynomial equations obtained from the coefficients of the remainder. Based on invariant clusters and sum-of-squares (SOS) programming, we present a new method for the safety verification of hybrid systems. Experiments on nonlinear benchmark systems from biology and control theory show that our approach is efficient
An abstraction-refinement methodology for reasoning about network games
Get PDF{\em Network games\/} (NGs) are played on directed graphs and are extensively used in network design and analysis.
Search problems for NGs include finding special strategy profiles such as a Nash equilibrium and a
globally optimal solution.
The networks modeled by NGs may be huge. In formal verification, {\em abstraction\/} has proven to be an extremely effective technique for reasoning about systems with big and even infinite state spaces. We describe an abstraction-refinement methodology for reasoning about NGs. Our methodology is based on an abstraction function that maps the state space of an NG to a much smaller state space.
We search for a global optimum and a Nash equilibrium by reasoning on an under- and an over-approximation defined on top of this smaller state space. When the approximations are too coarse to find such profiles, we {\em refine} the abstraction function. Our experimental results demonstrate the efficiency of the methodology