Symmetric spaces of higher rank do not admit differentiable compactifications

Any nonpositively curved symmetric space admits a topological compactification, namely the Hadamard compactification. For rank one spaces, this topological compactification can be endowed with a differentiable structure such that the action of the isometry group is differentiable. Moreover, the restriction of the action on the boundary leads to a flat model for some geometry (conformal, CR or quaternionic CR depending of the space). One can ask whether such a differentiable compactification exists for higher rank spaces, hopefully leading to some knew geometry to explore. In this paper we answer negatively.Comment: 13 pages, to appear in Mathematische Annale

The interface between the stellar wind and interstellar medium around R Cassiopeiae revealed by far-infrared imaging

The circumstellar dust shells of intermediate initial-mass (about 1 to 8 solar masses) evolved stars are generated by copious mass loss during the asymptotic giant branch phase. The density structure of their circumstellar shell is the direct evidence of mass loss processes, from which we can investigate the nature of mass loss. We used the AKARI Infrared Astronomy Satellite and the Spitzer Space Telescope to obtain the surface brightness maps of an evolved star R Cas at far-infrared wavelengths, since the temperature of dust decreases as the distance from the star increases and one needs to probe dust at lower temperatures, i.e., at longer wavelengths. The observed shell structure and the star's known proper motion suggest that the structure represents the interface regions between the dusty wind and the interstellar medium. The deconvolved structures are fitted with the analytic bow shock structure to determine the inclination angle of the bow shock cone. Our data show that (1) the bow shock cone of 1 - 5 x 10^-5 solar masses (dust mass) is inclined at 68 degrees with respect to the plane of the sky, and (2) the dust temperature in the bow shock cone is raised to more than 20 K by collisional shock interaction in addition to the ambient interstellar radiation field. By comparison between the apex vector of the bow shock and space motion vector of the star we infer that there is a flow of interstellar medium local to R Cas whose flow velocity is at least 55.6 km/s, consistent with an environment conducive to dust heating by shock interactions.Comment: 7 pages, 2 figures, accepted for publication in Astronomy and Astrophysic

A General Framework for Recursive Decompositions of Unitary Quantum Evolutions

Decompositions of the unitary group U(n) are useful tools in quantum information theory as they allow one to decompose unitary evolutions into local evolutions and evolutions causing entanglement. Several recursive decompositions have been proposed in the literature to express unitary operators as products of simple operators with properties relevant in entanglement dynamics. In this paper, using the concept of grading of a Lie algebra, we cast these decompositions in a unifying scheme and show how new recursive decompositions can be obtained. In particular, we propose a new recursive decomposition of the unitary operator on $N$ qubits, and we give a numerical example.Comment: 17 pages. To appear in J. Phys. A: Math. Theor. This article replaces our earlier preprint "A Recursive Decomposition of Unitary Operators on N Qubits." The current version provides a general method to generate recursive decompositions of unitary evolutions. Several decompositions obtained before are shown to be as a special case of this general procedur

Generalized conductance sum rule in atomic break junctions

When an atomic-size break junction is mechanically stretched, the total conductance of the contact remains approximately constant over a wide range of elongations, although at the same time the transmissions of the individual channels (valence orbitals of the junction atom) undergo strong variations. We propose a microscopic explanation of this phenomenon, based on Coulomb correlation effects between electrons in valence orbitals of the junction atom. The resulting approximate conductance quantization is closely related to the Friedel sum rule.Comment: 4 pages, 1 figure, appears in Proceedings of the NATO Advanced Research Workshop ``Size dependent magnetic scattering'', Pecs, Hungary, May 28 - June 1, 200

Cavitation inception of a van der Waals fluid at a sack-wall obstacle

Cavitation in a liquid moving past a constraint is numerically investigated by means of a free-energy lattice Boltzmann simulation based on the van der Waals equation of state. The fluid is streamed past an obstacle and, depending on the pressure drop between inlet and outlet, vapor formation underneath the corner of the sack-wall is observed. The circumstances of cavitation formation are investigated and it is found that the local bulk pressure and mean stress are insufficient to explain the phenomenon. Results obtained in this study strongly suggest that the viscous stress, interfacial contributions to the local pressure, and the Laplace pressure are relevant to the opening of a vapor cavity. This can be described by a generalization of Joseph's criterion that includes these contributions. A macroscopic investigation measuring mass flow rate behavior and discharge coefficient was also performed. As theoretically predicted, mass flow rate increases linearly with the square root of the pressure drop. However, when cavitation occurs, the mass flow growth rate is reduced and eventually it collapses into a choked flow state. In the cavitating regime, as theoretically predicted and experimentally verified, the discharge coefficient grows with the Nurick cavitation number

Testing Radiatively-Inefficient Accretion Flow Theory: an XMM-Newton Observation of NGC 3998

We present the results of a 10 ks XMM-Newton observation of NGC 3998, a ``type-I'' LINER galaxy. Our goal is to test the extent to which radiatively-inefficient accretion flow (RIAF) models and/or scaled-down AGN models are consistent with the observed properties of NGC 3998. The upper-limit for narrow Fe-K emission derived from a combined fit of the XMM-Newton and BeppoSAX spectra is 25 eV, which is one of the strictest limits to date for any AGN. This significantly rules out Fe-K emission as is expected to be observed in typical Seyfert 1 galaxies. The lack of any reflection features suggests that any optically-thick, geometrically-thin accretion disk must be truncated, probably at a radius of order 100-300 R_s. RIAF models fit the UV to X-ray spectral energy distribution of NGC 3998 reasonably well. In these models the mid-IR flux also constrains the emission from any outer thin disk component that might be present. The UV to X-ray SED is also consistent with a Comptonized thin disk with a very low accretion rate, in which case the lack of Fe-K emission may be due to an ionized accretion disk. Accretion models in general do not account for the observed radio flux of NGC 3998, and the radio flux may be due to a jet. Recent jet models may also be consistent with the nuclear fluxes of NGC 3998 in general, including the X-ray, optical/UV and mid-IR bands. We also derive nuclear fluxes using archival HST WFPC2 data to constrain the SED of NGC 3998. We discuss a possible OM U band and USNO-B detection of the NGC 3998 ULX.Comment: Accepted for publication in ApJ. 13 pages and 5 figures formatted with emulateapj. Version with black-and-white only plots available at http://www.pha.jhu.edu/~ptak/paper

Transfer of K-types on local theta lifts of characters and unitary lowest weight modules

In this paper we study representations of the indefinite orthogonal group O(n,m) which are local theta lifts of one dimensional characters or unitary lowest weight modules of the double covers of the symplectic groups. We apply the transfer of K-types on these representations of O(n,m), and we study their effects on the dual pair correspondences. These results provide examples that the theta lifting is compatible with the transfer of K-types. Finally we will use these results to study subquotients of some cohomologically induced modules

Time-optimal synthesis of unitary transformations in coupled fast and slow qubit system

In this paper, we study time-optimal control problems related to system of two coupled qubits where the time scales involved in performing unitary transformations on each qubit are significantly different. In particular, we address the case where unitary transformations produced by evolutions of the coupling take much longer time as compared to the time required to produce unitary transformations on the first qubit but much shorter time as compared to the time to produce unitary transformations on the second qubit. We present a canonical decomposition of SU(4) in terms of the subgroup SU(2)xSU(2)xU(1), which is natural in understanding the time-optimal control problem of such a coupled qubit system with significantly different time scales. A typical setting involves dynamics of a coupled electron-nuclear spin system in pulsed electron paramagnetic resonance experiments at high fields. Using the proposed canonical decomposition, we give time-optimal control algorithms to synthesize various unitary transformations of interest in coherent spectroscopy and quantum information processing.Comment: 8 pages, 3 figure

Benchmarking airborne laser scanning tree segmentation algorithms in broadleaf forests shows high accuracy only for canopy trees

Individual tree segmentation from airborne laser scanning data is a longstanding and important challenge in forest remote sensing. Tree segmentation algorithms are widely available, but robust intercomparison studies are rare due to the difficulty of obtaining reliable reference data. Here we provide a benchmark data set for temperate and tropical broadleaf forests generated from labelled terrestrial laser scanning data. We compared the performance of four widely used tree segmentation algorithms against this benchmark data set. All algorithms performed reasonably well on the canopy trees. The point cloud-based algorithm AMS3D (Adaptive Mean Shift 3D) had the highest overall accuracy, closely followed by the 2D raster based region growing algorithm Dalponte2016 +. However, all algorithms failed to accurately segment the understory trees. This result was consistent across both forest types. This study emphasises the need to assess tree segmentation algorithms directly using benchmark data, rather than comparing with forest indices such as biomass or the number and size distribution of trees. We provide the first openly available benchmark data set for tropical forests and we hope future studies will extend this work to other regions

Long-term retrospective assessment of a transmission hotspot for human alveolar echinococcosis in mid-west China

Background Human alveolar echinococcosis caused by infection with Echinococcus multilocularis is one of the most potentially pathogenic helminthic zoonoses. Transmission occurs involving wildlife cycles typically between fox and small mammal intermediate hosts. In the late 1980s/early 1990s a large focus of human AE was identified in poor upland agricultural communities in south Gansu Province, China. More detailed investigations in 1994–97 expanded community screening and identified key risk factors of dog ownership and landscape type around villages that could support susceptible rodent populations. A crash of the dog population (susceptible domestic definitive host) in the early 1990s appeared to stop transmission. Methodology/Findings We subsequently undertook follow-up eco-epidemiological studies based on human population screening and dog survey, in 2005/6 and in 2014/15. Our observations show a decrease in human AE prevalence, especially marked in the 11–30 year old age category. In 2015, although the dog population had recovered and in addition, forest protection and the reforestation of some areas may have favoured red fox (wild definitive host) population growth, there was no evidence of infection in owned dogs. Conclusions/Significance Those observations suggest that over decades socio-ecological changes resulted in a cascade of factors that exacerbated and then interrupted parasite emergence, with probable elimination of peri-domestic transmission of E. multilocularis in this area, despite the relative proximity of large active transmission foci on the eastern Tibetan Plateau. This study case exemplifies how anthropogenic land use and behavioural changes can modify emergence events and the transmission of endemic zoonotic parasite infections, and subsequently the importance of considering processes over the long-term in a systems approach in order to understand pathogen and disease distribution