Polynomial diffeomorphisms of C^2, IV: The measure of maximal entropy and laminar currents

This paper concerns the dynamics of polynomial automorphisms of ${\bf C}^2$. One can associate to such an automorphism two currents $\mu^\pm$ and the equilibrium measure $\mu=\mu^+\wedge\mu^-$. In this paper we study some geometric and dynamical properties of these objects. First, we characterize $\mu$ as the unique measure of maximal entropy. Then we show that the measure $\mu$ has a local product structure and that the currents $\mu^\pm$ have a laminar structure. This allows us to deduce information about periodic points and heteroclinic intersections. For example, we prove that the support of $\mu$ coincides with the closure of the set of saddle points. The methods used combine the pluripotential theory with the theory of non-uniformly hyperbolic dynamical systems

Adding flavour to twistor strings

Twistor string theory is known to describe a wide variety of field theories at tree-level and has proved extremely useful in making substantial progress in perturbative gauge theory. We explore the twistor dual description of a class of N=2 UV-finite super-Yang-Mills theories with fundamental flavour by adding 'flavour' branes to the topological B-model on super-twistor space and comment on the appearance of these objects. Evidence for the correspondence is provided by matching amplitudes on both sides.Comment: 6 pages; contribution to the proceedings for the European Physical Society conference on High Energy Physics in Manchester, 19-25 July 2007. v3: Typos correcte

Problems and Aspects of Energy-Driven Wavefunction Collapse Models

Four problematic circumstances are considered, involving models which describe dynamical wavefunction collapse toward energy eigenstates, for which it is shown that wavefunction collapse of macroscopic objects does not work properly. In one case, a common particle position measuring situation, the apparatus evolves to a superposition of macroscopically distinguishable states (does not collapse to one of them as it should) because each such particle/apparatus/environment state has precisely the same energy spectrum. Second, assuming an experiment takes place involving collapse to one of two possible outcomes which is permanently recorded, it is shown in general that this can only happen in the unlikely case that the two apparatus states corresponding to the two outcomes have disjoint energy spectra. Next, the progressive narrowing of the energy spectrum due to the collapse mechanism is considered. This has the effect of broadening the time evolution of objects as the universe evolves. Two examples, one involving a precessing spin, the other involving creation of an excited state followed by its decay, are presented in the form of paradoxes. In both examples, the microscopic behavior predicted by standard quantum theory is significantly altered under energy-driven collapse, but this alteration is not observed by an apparatus when it is included in the quantum description. The resolution involves recognition that the statevector describing the apparatus does not collapse, but evolves to a superposition of macroscopically different states.Comment: 17 page

Characterisation of Float Rocks at Ireson Hill, Gale Crater

Float rocks discovered by surface missions on Mars have given unique insights into the sedimentary, diagenetic and igneous processes that have operated throughout the planets history. In addition, Gale sedimentary rocks, both float and in situ, record a combination of source compositions and diagenetic overprints. We examine a group of float rocks that were identified by the Mars Science Laboratory missions Curiosity rover at the Ireson Hill site, circa. sol 1600 using ChemCam LIBS, APXS and images from the MastCam, Mars Hand Lens Imager (MAHLI) and ChemCam Remote Micro-Imager (RMI) cameras. Geochemical data provided by the APXS and ChemCam instruments allow us to compare the compositions of these rocks to known rock types from Gale crater, as well as elsewhere on Mars. Ireson Hill is a 15 m long butte in the Murray formation with a dark cap-ping unit with chemical and stratigraphic consistency with the Stimson formation. A total of 6 float rocks have been studied on the butte

Dust from Mars-Analog Plains (Iceland): Physico-Compositional Properties as a Function of Grain-Size Fraction

Dust is a key component of the geological and climatic systems of Earth and Mars. On Mars, dust is ubiquitous. It coats rocks and soils, and, in the atmosphere, it interacts strongly with solar and thermal radiation. Yet, key questions remain about the genesis and fate of martian dust, as well as its sources, composition, and properties. We collected wind-blown dust from basaltic plains in SW Iceland at Skjaldbreiauhraun that represent a geologic Mars-analog environment. Icelandic dust differs from the typical continental sources (e.g. Sahara, Asia) because of its basaltic volcanogenic origin, which is similar to Mars. Dust collection took place in July of 2019 as a complementary project to the SAND-E: Semi-Autonomous Navigation for Detrital Environments project. Here we report preliminary analyses of this Mars-analog dust material, with the goal of understanding the processes that control the physico-chemical proper-ties of the different grain-size fractions

Quantum Theory and Time Asymmetry

The relation between quantum measurement and thermodynamically irreversible processes is investigated. The reduction of the state vector is fundamentally asymmetric in time and shows an observer-relatedness which may explain the double interpretation of the state vector as a representation of physical states as well as of information about them. The concept of relevance being used in all statistical theories of irreversible thermodynamics is shown to be based on the same observer-relatedness. Quantum theories of irreversible processes implicitly use an objectivized process of state vector reduction. The conditions for the reduction are discussed, and I speculate that the final (subjective) observer system might even be carried by a spacetime point.Comment: Latex version of a paper published in 1979 (with minor revisions), 18 page

Canalization of the evolutionary trajectory of the human influenza virus

Since its emergence in 1968, influenza A (H3N2) has evolved extensively in genotype and antigenic phenotype. Antigenic evolution occurs in the context of a two-dimensional 'antigenic map', while genetic evolution shows a characteristic ladder-like genealogical tree. Here, we use a large-scale individual-based model to show that evolution in a Euclidean antigenic space provides a remarkable correspondence between model behavior and the epidemiological, antigenic, genealogical and geographic patterns observed in influenza virus. We find that evolution away from existing human immunity results in rapid population turnover in the influenza virus and that this population turnover occurs primarily along a single antigenic axis. Thus, selective dynamics induce a canalized evolutionary trajectory, in which the evolutionary fate of the influenza population is surprisingly repeatable and hence, in theory, predictable.Comment: 29 pages, 5 figures, 10 supporting figure

Some Like it Hot: The X-Ray Emission of The Giant Star YY Mensae

(Abridged abstract) We present an analysis of the X-ray emission of the rapidly rotating giant star YY Mensae observed by Chandra HETGS and XMM-Newton. Although no obvious flare was detected, the X-ray luminosity changed by a factor of two between the XMM-Newton and Chandra observations taken 4 months apart. The coronal abundances and the emission measure distribution have been derived from three different methods using optically thin collisional ionization equilibrium models. The abundances show an inverse first ionization potential (FIP) effect. We further find a high N abundance which we interpret as a signature of material processed in the CNO cycle. The corona is dominated by a very high temperature (20-40 MK) plasma, which places YY Men among the magnetically active stars with the hottest coronae. Lower temperature plasma also coexists, albeit with much lower emission measure. Line broadening is reported, which we interpret as Doppler thermal broadening, although rotational broadening due to X-ray emitting material high above the surface could be present as well. We use two different formalisms to discuss the shape of the emission measure distribution. The first one infers the properties of coronal loops, whereas the second formalism uses flares as a statistical ensemble. We find that most of the loops in the corona of YY Men have their maximum temperature equal to or slightly larger than about 30 MK. We also find that small flares could contribute significantly to the coronal heating in YY Men. Although there is no evidence of flare variability in the X-ray light curves, we argue that YY Men's distance and X-ray brightness does not allow us to detect flares with peak luminosities Lx <= 10^{31} erg/s with current detectors.Comment: Accepted paper to appear in Astrophysical Journal, issue Nov 10, 2004 (v615). This a revised version. Small typos are corrected. Figure 7 and its caption and some related text in Sct 7.2 are changed, without incidence for the conclusion

Note on New KLT relations

In this short note, we present two results about KLT relations discussed in recent several papers. Our first result is the re-derivation of Mason-Skinner MHV amplitude by applying the S_{n-3} permutation symmetric KLT relations directly to MHV amplitude. Our second result is the equivalence proof of the newly discovered S_{n-2} permutation symmetric KLT relations and the well-known S_{n-3} permutation symmetric KLT relations. Although both formulas have been shown to be correct by BCFW recursion relations, our result is the first direct check using the regularized definition of the new formula.Comment: 15 Pages; v2: minor correction

Evaluation of elicitation methods to quantify Bayes linear models

The Bayes linear methodology allows decision makers to express their subjective beliefs and adjust these beliefs as observations are made. It is similar in spirit to probabilistic Bayesian approaches, but differs as it uses expectation as its primitive. While substantial work has been carried out in Bayes linear analysis, both in terms of theory development and application, there is little published material on the elicitation of structured expert judgement to quantify models. This paper investigates different methods that could be used by analysts when creating an elicitation process. The theoretical underpinnings of the elicitation methods developed are explored and an evaluation of their use is presented. This work was motivated by, and is a precursor to, an industrial application of Bayes linear modelling of the reliability of defence systems. An illustrative example demonstrates how the methods can be used in practice