A conjugate-gradient-type rational Krylov subspace method for ill-posed problems

Conjugated gradients on the normal equation (CGNE) is a popular method to regularise linear inverse problems. The idea of the method can be summarized as minimising the residuum over a suitable Krylov subspace. It is shown that using the same idea for the shift-and-invert rational Krylov subspace yields an order-optimal regularisation scheme

New Global F-theory GUTs with U(1) symmetries

We construct global F-theory GUTs with SU(5) x U(1) gauge group defined by specifying a fully resolved Calabi-Yau fourfold and consistent four-form G-flux. Its specific U(1) charged matter spectrum allows the desired Yukawa couplings, but forbids dangerous proton decay operators. The model we find: (1) does not follow from an underlying higgsed E8 gauge group (2) leaves the class of theories that can be analyzed with current split-spectral cover techniques. This avoids recently proposed no-go theorems for models with hypercharge flux, as required to break the GUT group. The appearance of additional fields is related geometrically to considering a more general class of sections and 4-1 splits. We show explicitly that the four-dimensional chiral matter index can still be computed using three-dimensional one-loop Chern-Simons terms.Comment: 24 pages, 2 figure

Complete Intersection Fibers in F-Theory

Global F-theory compactifications whose fibers are realized as complete intersections form a richer set of models than just hypersurfaces. The detailed study of the physics associated with such geometries depends crucially on being able to put the elliptic fiber into Weierstrass form. While such a transformation is always guaranteed to exist, its explicit form is only known in a few special cases. We present a general algorithm for computing the Weierstrass form of elliptic curves defined as complete intersections of different codimensions and use it to solve all cases of complete intersections of two equations in an ambient toric variety. Using this result, we determine the toric Mordell-Weil groups of all 3134 nef partitions obtained from the 4319 three-dimensional reflexive polytopes and find new groups that do not exist for toric hypersurfaces. As an application, we construct several models that cannot be realized as toric hypersurfaces, such as the first toric SU(5) GUT model in the literature with distinctly charged 10 representations and an F-theory model with discrete gauge group Z_4 whose dual fiber has a Mordell-Weil group with Z_4 torsion.Comment: 41 pages, 4 figures and 18 tables; added references in v

Stochasticity & Predictability in Terrestrial Planet Formation

Terrestrial planets are thought to be the result of a vast number of gravitational interactions and collisions between smaller bodies. We use numerical simulations to show that practically identical initial conditions result in a wide array of final planetary configurations. This is a result of the chaotic evolution of trajectories which are highly sensitive to minuscule displacements. We determine that differences between systems evolved from virtually identical initial conditions can be larger than the differences between systems evolved from very different initial conditions. This implies that individual simulations lack predictive power. For example, there is not a reproducible mapping between the initial and final surface density profiles. However, some key global properties can still be extracted if the statistical spread across many simulations is considered. Based on these spreads, we explore the collisional growth and orbital properties of terrestrial planets which assemble from different initial conditions (we vary the initial planetesimal distribution, planetesimal masses, and giant planet orbits). Confirming past work, we find that the resulting planetary systems are sculpted by sweeping secular resonances. Configurations with giant planets on eccentric orbits produce fewer and more massive terrestrial planets on tighter orbits than those with giants on circular orbits. This is further enhanced if the initial mass distribution is biased to the inner regions. In all cases, the outer edge of the system is set by the final location of the $\nu_6$ resonance and we find that the mass distribution peaks at the $\nu_5$ resonance. Using existing observations, we find that extrasolar systems follow similar trends. Although differences between our numerical modelling and exoplanetary systems remain, we suggest that CoRoT-7, HD 20003, and HD 20781 may host undetected giant planets.Comment: replaced to match published version, 20 pages, 11 figures, published in MNRAS, simulation outputs available at https://cheleb.net/astro/sp15

Slow Excitation Trapping in Quantum Transport with Long-Range Interactions

Long-range interactions slow down the excitation trapping in quantum transport processes on a one-dimensional chain with traps at both ends. This is counter intuitive and in contrast to the corresponding classical processes with long-range interactions, which lead to faster excitation trapping. We give a pertubation theoretical explanation of this effect.Comment: 4 pages, 3 figure

High-throughput isolation of ultra-pure plasmid DNA by a robotic system

BACKGROUND: With the availability of complete genomes, a systematic inventory of cellular processes becomes achievable. This requires assessing the function of all individual genes. Transfection of plasmid DNA into cell culture cells is an essential technique for this aim as it allows functional overexpression or downregulation of genes. While many robotic systems isolate plasmids for sequencing purposes, for more demanding applications such as transfections there is a shortage of robots for the high-throughput isolation of plasmid DNA. RESULTS: Here we describe a custom-made, automated device, which uses a special protocol to isolate plasmid DNAs with a purity sufficient for efficient transfections into mammalian cells. Approximately 1,600 ultra pure plasmids can be isolated in a 96-well plate format within 12 hours. As a unique feature the robot comprises the integration of a centrifuge instead of expensive columns, the use of a custom-made pipetting head with a movable gripper, especially designed shaking platforms and an acetone wash facility. CONCLUSION: Using this robot we demonstrate how centrifugation steps with multiple precipitations, most notably through a precipitation step of SDS in isopropanol, lead to high purity plasmid DNA and make possible high-throughput transfections into mammalian cells for functional gene annotations