Graphs Identified by Logics with Counting

We classify graphs and, more generally, finite relational structures that are identified by C2, that is, two-variable first-order logic with counting. Using this classification, we show that it can be decided in almost linear time whether a structure is identified by C2. Our classification implies that for every graph identified by this logic, all vertex-colored versions of it are also identified. A similar statement is true for finite relational structures. We provide constructions that solve the inversion problem for finite structures in linear time. This problem has previously been shown to be polynomial time solvable by Martin Otto. For graphs, we conclude that every C2-equivalence class contains a graph whose orbits are exactly the classes of the C2-partition of its vertex set and which has a single automorphism witnessing this fact. For general k, we show that such statements are not true by providing examples of graphs of size linear in k which are identified by C3 but for which the orbit partition is strictly finer than the Ck-partition. We also provide identified graphs which have vertex-colored versions that are not identified by Ck.Comment: 33 pages, 8 Figure

First Fruits of the Spitzer Space Telescope: Galactic and Solar System Studies

This article provides a brief overview of the Spitzer Space Telescope and discusses its initial scientific results on galactic and solar system science.Comment: Review article to appear in slightly different format in Vol.44 of Annual Reviews of Astronomy and Astrophysics, 200

Towards a large-scale quantum simulator on diamond surface at room temperature

Strongly-correlated quantum many-body systems exhibits a variety of exotic phases with long-range quantum correlations, such as spin liquids and supersolids. Despite the rapid increase in computational power of modern computers, the numerical simulation of these complex systems becomes intractable even for a few dozens of particles. Feynman's idea of quantum simulators offers an innovative way to bypass this computational barrier. However, the proposed realizations of such devices either require very low temperatures (ultracold gases in optical lattices, trapped ions, superconducting devices) and considerable technological effort, or are extremely hard to scale in practice (NMR, linear optics). In this work, we propose a new architecture for a scalable quantum simulator that can operate at room temperature. It consists of strongly-interacting nuclear spins attached to the diamond surface by its direct chemical treatment, or by means of a functionalized graphene sheet. The initialization, control and read-out of this quantum simulator can be accomplished with nitrogen-vacancy centers implanted in diamond. The system can be engineered to simulate a wide variety of interesting strongly-correlated models with long-range dipole-dipole interactions. Due to the superior coherence time of nuclear spins and nitrogen-vacancy centers in diamond, our proposal offers new opportunities towards large-scale quantum simulation at room temperatures

Out-of-equilibrium physics in driven dissipative coupled resonator arrays

Coupled resonator arrays have been shown to exhibit interesting many- body physics including Mott and Fractional Hall states of photons. One of the main differences between these photonic quantum simulators and their cold atoms coun- terparts is in the dissipative nature of their photonic excitations. The natural equi- librium state is where there are no photons left in the cavity. Pumping the system with external drives is therefore necessary to compensate for the losses and realise non-trivial states. The external driving here can easily be tuned to be incoherent, coherent or fully quantum, opening the road for exploration of many body regimes beyond the reach of other approaches. In this chapter, we review some of the physics arising in driven dissipative coupled resonator arrays including photon fermionisa- tion, crystallisation, as well as photonic quantum Hall physics out of equilibrium. We start by briefly describing possible experimental candidates to realise coupled resonator arrays along with the two theoretical models that capture their physics, the Jaynes-Cummings-Hubbard and Bose-Hubbard Hamiltonians. A brief review of the analytical and sophisticated numerical methods required to tackle these systems is included.Comment: Chapter that appeared in "Quantum Simulations with Photons and Polaritons: Merging Quantum Optics with Condensed Matter Physics" edited by D.G.Angelakis, Quantum Science and Technology Series, Springer 201

Branch Mode Selection during Early Lung Development

Many organs of higher organisms, such as the vascular system, lung, kidney, pancreas, liver and glands, are heavily branched structures. The branching process during lung development has been studied in great detail and is remarkably stereotyped. The branched tree is generated by the sequential, non-random use of three geometrically simple modes of branching (domain branching, planar and orthogonal bifurcation). While many regulatory components and local interactions have been defined an integrated understanding of the regulatory network that controls the branching process is lacking. We have developed a deterministic, spatio-temporal differential-equation based model of the core signaling network that governs lung branching morphogenesis. The model focuses on the two key signaling factors that have been identified in experiments, fibroblast growth factor (FGF10) and sonic hedgehog (SHH) as well as the SHH receptor patched (Ptc). We show that the reported biochemical interactions give rise to a Schnakenberg-type Turing patterning mechanisms that allows us to reproduce experimental observations in wildtype and mutant mice. The kinetic parameters as well as the domain shape are based on experimental data where available. The developed model is robust to small absolute and large relative changes in the parameter values. At the same time there is a strong regulatory potential in that the switching between branching modes can be achieved by targeted changes in the parameter values. We note that the sequence of different branching events may also be the result of different growth speeds: fast growth triggers lateral branching while slow growth favours bifurcations in our model. We conclude that the FGF10-SHH-Ptc1 module is sufficient to generate pattern that correspond to the observed branching modesComment: Initially published at PLoS Comput Bio

Quantum dynamics in strong fluctuating fields

A large number of multifaceted quantum transport processes in molecular systems and physical nanosystems can be treated in terms of quantum relaxation processes which couple to one or several fluctuating environments. A thermal equilibrium environment can conveniently be modelled by a thermal bath of harmonic oscillators. An archetype situation provides a two-state dissipative quantum dynamics, commonly known under the label of a spin-boson dynamics. An interesting and nontrivial physical situation emerges, however, when the quantum dynamics evolves far away from thermal equilibrium. This occurs, for example, when a charge transferring medium possesses nonequilibrium degrees of freedom, or when a strong time-dependent control field is applied externally. Accordingly, certain parameters of underlying quantum subsystem acquire stochastic character. Herein, we review the general theoretical framework which is based on the method of projector operators, yielding the quantum master equations for systems that are exposed to strong external fields. This allows one to investigate on a common basis the influence of nonequilibrium fluctuations and periodic electrical fields on quantum transport processes. Most importantly, such strong fluctuating fields induce a whole variety of nonlinear and nonequilibrium phenomena. A characteristic feature of such dynamics is the absence of thermal (quantum) detailed balance.Comment: review article, Advances in Physics (2005), in pres

Atmospheric Evolution

Earth's atmosphere has evolved as volatile species cycle between the atmosphere, ocean, biomass and the solid Earth. The geochemical, biological and astrophysical processes that control atmospheric evolution are reviewed from an "Earth Systems" perspective, with a view not only to understanding the history of Earth, but also to generalizing to other solar system planets and exoplanets.Comment: 34 pages, 3 figures, 2 tables. Accepted as a chapter in "Encyclopaedia of Geochemistry", Editor Bill White, Springer-Nature, 201

Spina bifida-predisposing heterozygous mutations in Planar Cell Polarity genes and Zic2 reduce bone mass in young mice

Fractures are a common comorbidity in children with the neural tube defect (NTD) spina bifida. Mutations in the Wnt/planar cell polarity (PCP) pathway contribute to NTDs in humans and mice, but whether this pathway independently determines bone mass is poorly understood. Here, we first confirmed that core Wnt/PCP components are expressed in osteoblasts and osteoclasts in vitro. In vivo, we performed detailed µCT comparisons of bone structure in tibiae from young male mice heterozygous for NTD-associated mutations versus WT littermates. PCP signalling disruption caused by Vangl2 (Vangl2Lp/+) or Celsr1 (Celsr1Crsh/+) mutations significantly reduced trabecular bone mass and distal tibial cortical thickness. NTD-associated mutations in non-PCP transcription factors were also investigated. Pax3 mutation (Pax3Sp2H/+) had minimal effects on bone mass. Zic2 mutation (Zic2Ku/+) significantly altered the position of the tibia/fibula junction and diminished cortical bone in the proximal tibia. Beyond these genes, we bioinformatically documented the known extent of shared genetic networks between NTDs and bone properties. 46 genes involved in neural tube closure are annotated with bone-related ontologies. These findings document shared genetic networks between spina bifida risk and bone structure, including PCP components and Zic2. Genetic variants which predispose to spina bifida may therefore independently diminish bone mass

Differential cargo mobilisation within Weibel-Palade bodies after transient fusion with the plasma membrane.

Inflammatory chemokines can be selectively released from Weibel-Palade bodies (WPBs) during kiss-and-run exocytosis. Such selectivity may arise from molecular size filtering by the fusion pore, however differential intra-WPB cargo re-mobilisation following fusion-induced structural changes within the WPB may also contribute to this process. To determine whether WPB cargo molecules are differentially re-mobilised, we applied FRAP to residual post-fusion WPB structures formed after transient exocytosis in which some or all of the fluorescent cargo was retained. Transient fusion resulted in WPB collapse from a rod to a spheroid shape accompanied by substantial swelling (>2 times by surface area) and membrane mixing between the WPB and plasma membranes. Post-fusion WPBs supported cumulative WPB exocytosis. To quantify diffusion inside rounded organelles we developed a method of FRAP analysis based on image moments. FRAP analysis showed that von Willebrand factor-EGFP (VWF-EGFP) and the VWF-propolypeptide-EGFP (Pro-EGFP) were immobile in post-fusion WPBs. Because Eotaxin-3-EGFP and ssEGFP (small soluble cargo proteins) were largely depleted from post-fusion WPBs, we studied these molecules in cells preincubated in the weak base NH4Cl which caused WPB alkalinisation and rounding similar to that produced by plasma membrane fusion. In these cells we found a dramatic increase in mobilities of Eotaxin-3-EGFP and ssEGFP that exceeded the resolution of our method (∼ 2.4 µm2/s mean). In contrast, the membrane mobilities of EGFP-CD63 and EGFP-Rab27A in post-fusion WPBs were unchanged, while P-selectin-EGFP acquired mobility. Our data suggest that selective re-mobilisation of chemokines during transient fusion contributes to selective chemokine secretion during transient WPB exocytosis. Selective secretion provides a mechanism to regulate intravascular inflammatory processes with reduced risk of thrombosis

Evidence for an excess of B -> D(*) Tau Nu decays

Based on the full BaBar data sample, we report improved measurements of the ratios R(D(*)) = B(B -> D(*) Tau Nu)/B(B -> D(*) l Nu), where l is either e or mu. These ratios are sensitive to new physics contributions in the form of a charged Higgs boson. We measure R(D) = 0.440 +- 0.058 +- 0.042 and R(D*) = 0.332 +- 0.024 +- 0.018, which exceed the Standard Model expectations by 2.0 sigma and 2.7 sigma, respectively. Taken together, our results disagree with these expectations at the 3.4 sigma level. This excess cannot be explained by a charged Higgs boson in the type II two-Higgs-doublet model. We also report the observation of the decay B -> D Tau Nu, with a significance of 6.8 sigma.Comment: Expanded section on systematics, text corrections, improved the format of Figure 2 and included the effect of the change of the Tau polarization due to the charged Higg