A Probabilistic Temporal Logic with Frequency Operators and Its Model Checking

Probabilistic Computation Tree Logic (PCTL) and Continuous Stochastic Logic (CSL) are often used to describe specifications of probabilistic properties for discrete time and continuous time, respectively. In PCTL and CSL, the possibility of executions satisfying some temporal properties can be quantitatively represented by the probabilistic extension of the path quantifiers in their basic Computation Tree Logic (CTL), however, path formulae of them are expressed via the same operators in CTL. For this reason, both of them cannot represent formulae with quantitative temporal properties, such as those of the form "some properties hold to more than 80% of time points (in a certain bounded interval) on the path." In this paper, we introduce a new temporal operator which expressed the notion of frequency of events, and define probabilistic frequency temporal logic (PFTL) based on CTL\star. As a result, we can easily represent the temporal properties of behavior in probabilistic systems. However, it is difficult to develop a model checker for the full PFTL, due to rich expressiveness. Accordingly, we develop a model-checking algorithm for the CTL-like fragment of PFTL against finite-state Markov chains, and an approximate model-checking algorithm for the bounded Linear Temporal Logic (LTL) -like fragment of PFTL against countable-state Markov chains.Comment: In Proceedings INFINITY 2011, arXiv:1111.267

Superdeformation in 198^{198}Po

The $^{174}$Yb($^{29}$Si,5n) reaction at 148 MeV with thin targets was used to populate high-angular momentum states in $^{198}$Po. Resulting $\gamma$ rays were observed with Gammasphere. A weakly-populated superdeformed band of 10 $\gamma$-ray transitions was found and has been assigned to $^{198}$Po. This is the first observation of a SD band in the $A \approx 190$ region in a nucleus with $Z > 83$. The ${\cal J}^{(2)}$ of the new band is very similar to those of the yrast SD bands in $^{194}$Hg and $^{196}$Pb. The intensity profile suggests that this band is populated through states close to where the SD band crosses the yrast line and the angular momentum at which the fission process dominates.Comment: 10 pages, revtex, 2 figs. available on request, submitted to Phys. Rev. C. (Rapid Communications

Spectroscopy of 194^{194}Po

Prompt, in-beam $\gamma$ rays following the reaction $^{170}$Yb + 142 MeV $^{28}$Si were measured at the ATLAS facility using 10 Compton-suppressed Ge detectors and the Fragment Mass Analyzer. Transitions in $^{194}$Po were identified and placed using $\gamma$-ray singles and coincidence data gated on the mass of the evaporation residues. A level spectrum up to J$\approx$10$\hbar$ was established. The structure of $^{194}$Po is more collective than that observed in the heavier polonium isotopes and indicates that the structure has started to evolve towards the more collective nature expected for deformed nuclei.Comment: 8 pages, revtex 3.0, 4 figs. available upon reques

Invariant higher-order variational problems II

Motivated by applications in computational anatomy, we consider a second-order problem in the calculus of variations on object manifolds that are acted upon by Lie groups of smooth invertible transformations. This problem leads to solution curves known as Riemannian cubics on object manifolds that are endowed with normal metrics. The prime examples of such object manifolds are the symmetric spaces. We characterize the class of cubics on object manifolds that can be lifted horizontally to cubics on the group of transformations. Conversely, we show that certain types of non-horizontal geodesics on the group of transformations project to cubics. Finally, we apply second-order Lagrange--Poincar\'e reduction to the problem of Riemannian cubics on the group of transformations. This leads to a reduced form of the equations that reveals the obstruction for the projection of a cubic on a transformation group to again be a cubic on its object manifold.Comment: 40 pages, 1 figure. First version -- comments welcome

Distributed Parametric and Statistical Model Checking

Statistical Model Checking (SMC) is a trade-off between testing and formal verification. The core idea of the approach is to conduct some simulations of the system and verify if they satisfy some given property. In this paper we show that SMC is easily parallelizable on a master/slaves architecture by introducing a series of algorithms that scale almost linearly with respect to the number of slave computers. Our approach has been implemented in the UPPAAL SMC toolset and applied on non-trivial case studies.Comment: In Proceedings PDMC 2011, arXiv:1111.006

Approximations of Shape Metrics and Application to Shape Warping and Empirical Shape Statistics

International audienceThis chapter proposes a framework for dealing with two problems related to the analysis of shapes: the definition of the relevant set of shapes and that of defining a metric on it. Following a recent research monograph by Delfour and Zolésio [8], we consider the characteristic functions of the subsets of ℝ2 and their distance functions. The L 2 norm of the difference of characteristic functions and the L∞ and the W 1,2 norms of the difference of distance functions define interesting topologies, in particular that induced by the well-known Hausdorff distance. Because of practical considerations arising from the fact that we deal with image shapes defined on finite grids of pixels, we restrict our attention to subsets of ℝ2 of positive reach in the sense of Federer [12], with smooth boundaries of bounded curvature. For this particular set of shapes we show that the three previous topologies are equivalent. The next problem we consider is that of warping a shape onto another by infinitesimal gradient descent, minimizing the corresponding distance. Because the distance function involves an inf, it is not differentiable with respect to the shape. We propose a family of smooth approximations of the distance function which are continuous with respect to the Hausdorff topology, and hence with respect to the other two topologies. We compute the corresponding Gâteaux derivatives. They define deformation flows that can be used to warp a shape onto another by solving an initial value problem. We show several examples of this warping and prove properties of our approximations that relate to the existence of local minima. We then use this tool to produce computational de.nitions of the empirical mean and covariance of a set of shape examples. They yield an analog of the notion of principal modes of variation. We illustrate them on a variety of examples

Syn‐rift sediment gravity flow deposition on a Late Jurassic fault‐terraced slope, northern North Sea

Structurally controlled bathymetry in rifts has a significant influence on sediment routing pathways and depositional architecture of sediment gravity flow deposits. In contrast to rift segments characterized by crustal-scale half-grabens, the tectono-stratigraphic evolution of deep-water rift domains characterised by distributed faulting on narrow fault terraces has received little attention. We use 3D broadband seismic data, calibrated by boreholes, from the Lomre and Uer terraces in the northern North Sea rift to investigate Late Jurassic syn-rift sediment gravity flow systems on fault-terraced slopes. The sediment gravity flow fairways were sourced from hinterland drainages via basin margin deltaic systems on the Horda Platform to the southeast. The deep-water sedimentary systems evolve from initial, widespread submarine channelized lobe complexes, through submarine channels, to incised submarine canyons. This progressive confinement of the sediment gravity flow system was concomitant with progressive localization of strain onto the main terrace-bounding faults. Although the normal fault network on the terraces has local impact on deep-water sediment transport and the architecture of gravity flow deposits, it is the regional basin margin to rift axis gradient that dominantly controls deep-water sediment routing. Furthermore, the gravity flow deposits on the Lomre and Uer terraces were predominantly sourced by rift margin deltaic systems, not from erosion of local uplifted footwall crests, emphasising the significance of hinterland catchments in the development of volumetrically significant deep-water syn-rift depositional systems

Recovery of the Historical SN1957D in X-rays with Chandra

SN1957D, located in one of the spiral arms of M83, is one of the small number of extragalactic supernovae that has remained detectable at radio and optical wavelengths during the decades after its explosion. Here we report the first detection of SN1957D in X-rays, as part of a 729 ks observation of M83 with \chandra. The X-ray luminosity (0.3 - 8 keV) is 1.7 (+2.4,-0.3) 10**37 ergs/s. The spectrum is hard and highly self-absorbed compared to most sources in M83 and to other young supernova remnants, suggesting that the system is dominated at X-ray wavelengths by an energetic pulsar and its pulsar wind nebula. The high column density may be due to absorption within the SN ejecta. HST WFC3 images resolve the supernova remnant from the surrounding emission and the local star field. Photometry of stars around SN1957D, using WFC3 images, indicates an age of less than 10**7 years and a main sequence turnoff mass more than 17 solar masses. New spectra obtained with Gemini-South show that the optical spectrum continues to be dominated by broad [O III] emission lines, the signature of fast-moving SN ejecta. The width of the broad lines has remained about 2700 km/s (FWHM). The [O III] flux dropped precipitously between 1989 and 1991, but continued monitoring shows the flux has been almost constant since. In contrast, radio observations over the period 1990-2011 show a decline rate inf the flux proportional to t**-4, far steeper than the rate observed earlier, suggesting that the primary shock has overrun the edge of a pre-SN wind.Comment: 28 pages, including 3 tables and 7 figures, accepted for publication in Ap

John Schuster, Descartes-agonistes: Physico-mathematics, method and corpuscular-mechanism, 1618–1633

We report on a 10 ks simultaneous Chandra/HETG-NuSTAR observation of the Bursting Pulsar, GRO J1744-28, during its third detected outburst since discovery and after nearly 18 years of quiescence. The source is detected up to 60 keV with an Eddington persistent flux level. Seven bursts, followed by dips, are seen with Chandra, three of which are also detected with NuSTAR. Timing analysis reveals a slight increase in the persistent emission pulsed fraction with energy (from 10% to 15%) up to 10 keV, above which it remains constant. The 0.5-70 keV spectra of the persistent and dip emission are the same within errors, and well described by a blackbody (BB), a power-law with an exponential rolloff, a 10 keV feature, and a 6.7 keV emission feature, all modified by neutral absorption. Assuming that the BB emission originates in an accretion disc, we estimate its inner (magnetospheric) radius to be about 4x10^7 cm, which translates to a surface dipole field B~9x10^10 G. The Chandra/HETG spectrum resolves the 6.7 keV feature into (quasi-)neutral and highly ionized Fe XXV and Fe XXVI emission lines. XSTAR modeling shows these lines to also emanate from a truncated accretion disk. The burst spectra, with a peak flux more than an order of magnitude higher than Eddington, are well fit with a power-law with an exponential rolloff and a 10~keV feature, with similar fit values compared to the persistent and dip spectra. The burst spectra lack a thermal component and any Fe features. Anisotropic (beamed) burst emission would explain both the lack of the BB and any Fe components.Comment: 15 pages, 11 figures, Accepted in Ap