The Experts below are selected from a list of 866658 Experts worldwide ranked by ideXlab platform
Miguel Sanchez - One of the best experts on this subject based on the ideXlab platform.
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further results on the smoothability of cauchy hypersurfaces and cauchy Time Functions
2006Co-Authors: Antonio N Bernal, Miguel SanchezAbstract:Recently, folk questions on the smoothability of Cauchy hypersurfaces and Time Functions of a globally hyperbolic spaceTime M, have been solved. Here we give further results, applicable to several problems: (1) Any compact spacelike acausal submanifold H with boundary can be extended to a spacelike Cauchy hypersurface S. If H were only achronal, counterexamples to the smooth extension exist, but a continuous extension (in fact, valid for any compact achronal subset K) is still possible. (2) Given any spacelike Cauchy hypersurface S, a Cauchy temporal function \(\mathcal{T}\) (i.e., a smooth function with past-directed Timelike gradient everywhere, and Cauchy hypersurfaces as levels) with \(S= \mathcal{T}^{-1}(0)\) is constructed – thus, the spaceTime splits orthogonally as \(\mathbb{R} \Times S\) in a canonical way. Even more, accurate versions of this last result are obtained if the Cauchy hypersurface S were non-spacelike (including non-smooth, or achronal but non-acausal).
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further results on the smoothability of cauchy hypersurfaces and cauchy Time Functions
2005Co-Authors: Antonio N Bernal, Miguel SanchezAbstract:Recently, folk questions on the smoothability of Cauchy hypersurfaces and Time Functions of a globally hyperbolic spaceTime M, have been solved. Here we give further results, applicable to several problems: (1) Any compact spacelike acausal submanifold H with boundary can be extended to a spacelike Cauchy hypersurface S. If H were only achronal, counterexamples to the smooth extension exist, but a continuous extension (in fact, valid for any compact achronal subset K) is still possible. (2) Given any spacelike Cauchy hypersurface S, a Cauchy temporal function T (i.e., a smooth function with past-directed Timelike gradient everywhere, and Cauchy hypersurfaces as levels) with S equal to one of the levels, is constructed -thus, the spaceTime splits orthogonally as $R \Times S$ in a canonical way. Even more, accurate versions of this result are obtained if the Cauchy hypersurface S were non-spacelike (including non-smooth, or achronal but non-acausal).
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smoothness of Time Functions and the metric splitting of globally hyperbolic spaceTimes
2005Co-Authors: Antonio N Bernal, Miguel SanchezAbstract:The folk questions in Lorentzian Geometry which concerns the smoothness of Time Functions and slicings by Cauchy hypersurfaces, are solved by giving simple proofs of: (a) any globally hyperbolic spaceTime (M, g) admits a smooth Time function Open image in new window whose levels are spacelike Cauchy hyperfurfaces and, thus, also a smooth global splitting Open image in new window if a spaceTime M admits a (continuous) Time function t then it admits a smooth (Time) function Open image in new window with Timelike gradient Open image in new window on all M.
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Smoothness of Time Functions and the metric splitting of globally hyperbolic spaceTimes
2005Co-Authors: Antonio N Bernal, Miguel SanchezAbstract:The folk questions in Lorentzian Geometry, which concerns the smoothness of Time Functions and slicings by Cauchy hypersurfaces, are solved by giving simple proofs of: (a) any globally hyperbolic spaceTime $(M,g)$ admits a smooth Time function $\tau$ whose levels are spacelike Cauchy hyperfurfaces and, thus, also a smooth global splitting $M= \R \Times {\cal S}$, $g= - \beta(\tau,x) d\tau^2 + \bar g_\tau $, (b) if a spaceTime $M$ admits a (continuous) Time function $t$ (i.e., it is stably causal) then it admits a smooth (Time) function $\tau$ with Timelike gradient $\nabla \tau$ on all $M$.
Antonio N Bernal - One of the best experts on this subject based on the ideXlab platform.
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further results on the smoothability of cauchy hypersurfaces and cauchy Time Functions
2006Co-Authors: Antonio N Bernal, Miguel SanchezAbstract:Recently, folk questions on the smoothability of Cauchy hypersurfaces and Time Functions of a globally hyperbolic spaceTime M, have been solved. Here we give further results, applicable to several problems: (1) Any compact spacelike acausal submanifold H with boundary can be extended to a spacelike Cauchy hypersurface S. If H were only achronal, counterexamples to the smooth extension exist, but a continuous extension (in fact, valid for any compact achronal subset K) is still possible. (2) Given any spacelike Cauchy hypersurface S, a Cauchy temporal function \(\mathcal{T}\) (i.e., a smooth function with past-directed Timelike gradient everywhere, and Cauchy hypersurfaces as levels) with \(S= \mathcal{T}^{-1}(0)\) is constructed – thus, the spaceTime splits orthogonally as \(\mathbb{R} \Times S\) in a canonical way. Even more, accurate versions of this last result are obtained if the Cauchy hypersurface S were non-spacelike (including non-smooth, or achronal but non-acausal).
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further results on the smoothability of cauchy hypersurfaces and cauchy Time Functions
2005Co-Authors: Antonio N Bernal, Miguel SanchezAbstract:Recently, folk questions on the smoothability of Cauchy hypersurfaces and Time Functions of a globally hyperbolic spaceTime M, have been solved. Here we give further results, applicable to several problems: (1) Any compact spacelike acausal submanifold H with boundary can be extended to a spacelike Cauchy hypersurface S. If H were only achronal, counterexamples to the smooth extension exist, but a continuous extension (in fact, valid for any compact achronal subset K) is still possible. (2) Given any spacelike Cauchy hypersurface S, a Cauchy temporal function T (i.e., a smooth function with past-directed Timelike gradient everywhere, and Cauchy hypersurfaces as levels) with S equal to one of the levels, is constructed -thus, the spaceTime splits orthogonally as $R \Times S$ in a canonical way. Even more, accurate versions of this result are obtained if the Cauchy hypersurface S were non-spacelike (including non-smooth, or achronal but non-acausal).
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smoothness of Time Functions and the metric splitting of globally hyperbolic spaceTimes
2005Co-Authors: Antonio N Bernal, Miguel SanchezAbstract:The folk questions in Lorentzian Geometry which concerns the smoothness of Time Functions and slicings by Cauchy hypersurfaces, are solved by giving simple proofs of: (a) any globally hyperbolic spaceTime (M, g) admits a smooth Time function Open image in new window whose levels are spacelike Cauchy hyperfurfaces and, thus, also a smooth global splitting Open image in new window if a spaceTime M admits a (continuous) Time function t then it admits a smooth (Time) function Open image in new window with Timelike gradient Open image in new window on all M.
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Smoothness of Time Functions and the metric splitting of globally hyperbolic spaceTimes
2005Co-Authors: Antonio N Bernal, Miguel SanchezAbstract:The folk questions in Lorentzian Geometry, which concerns the smoothness of Time Functions and slicings by Cauchy hypersurfaces, are solved by giving simple proofs of: (a) any globally hyperbolic spaceTime $(M,g)$ admits a smooth Time function $\tau$ whose levels are spacelike Cauchy hyperfurfaces and, thus, also a smooth global splitting $M= \R \Times {\cal S}$, $g= - \beta(\tau,x) d\tau^2 + \bar g_\tau $, (b) if a spaceTime $M$ admits a (continuous) Time function $t$ (i.e., it is stably causal) then it admits a smooth (Time) function $\tau$ with Timelike gradient $\nabla \tau$ on all $M$.
Pushkin Kachroo - One of the best experts on this subject based on the ideXlab platform.
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traffic assignment using a density based travel Time function for intelligent transportation systems
2016Co-Authors: Pushkin Kachroo, Shankar SastryAbstract:This paper presents and shows why density-based travel-Time function is consistent with the fundamental diagram from traffic theory and then reviews the applications of travel Time in intelligent transportation systems. This paper presents a density-based travel-Time function that does not have the ill-posedness that is present in flow-based travel-Time Functions. The classic steady-state traffic assignment is cast using this new travel-Time function, and corresponding mathematical programming formulations are proposed. It is shown that the modified Beckman formulation based on the density-based travel-Time function provides a unique solution for link flows and link densities where the Wardrop condition has nonunique values for arc traffic densities.
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travel Time dynamics for intelligent transportation systems theory and applications
2016Co-Authors: Pushkin Kachroo, Shankar S SastryAbstract:This paper demonstrates the limitation of the flow-based travel Time Functions. This paper presents a density-based travel Time function and further develops a fundamental model of travel Time dynamics that is built from a given fundamental traffic relationship and vehicle characteristics. The travel Time dynamics produce an asymmetric one-sided coupled system of hyperbolic partial differential equations, where the first equation represents the macroscopic traffic dynamics. The existence of the solution for the mathematical model is then presented. The main contribution of this paper is the mathematical development and analysis of the real-Time model of travel Time. Moreover, this paper also shows various intelligent transportation system applications where travel Time is an important factor and where this new model would be extremely useful and important.
Georgios B. Giannakis - One of the best experts on this subject based on the ideXlab platform.
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Kernel-Based Reconstruction of Space-Time Functions on Dynamic Graphs
2017Co-Authors: Daniel Romero, Vassilis N. Ioannidis, Georgios B. GiannakisAbstract:Graph-based methods pervade the inference toolkits of numerous disciplines including sociology, biology, neuroscience, physics, chemistry, and engineering. A challenging problem encountered in this context pertains to determining the attributes of a set of vertices given those of another subset at possibly diffe-rent Time instants. Leveraging spatiotemporal dynamics can drastically reduce the number of observed vertices, and hence the sampling cost. Alleviating the limited flexibility of the existing approaches, the present paper broadens the kernel-based graph function estimation framework to reconstruct Time-evolving Functions over possibly Time-evolving topologies. This approach inherits the versatility and generality of kernel-based methods, for which no knowledge on distributions or second-order statistics is required. Systematic guidelines are provided to construct two families of space-Time kernels with complementary strengths: the first facilitates judicious control of regularization on a space-Time frequency plane, whereas the second accommodates Time-varying topologies. Batch and online estimators are also put forth. The latter comprise a novel kernel Kalman filter, developed to reconstruct space-Time Functions at affordable computational cost. Numerical tests with real datasets corroborate the merits of the proposed methods relative to competing alternatives.
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Kernel-based Reconstruction of Space-Time Functions on Dynamic Graphs
2016Co-Authors: Daniel Romero, Vassilis N. Ioannidis, Georgios B. GiannakisAbstract:Graph-based methods pervade the inference toolkits of numerous disciplines including sociology, biology, neuroscience, physics, chemistry, and engineering. A challenging problem encountered in this context pertains to determining the attributes of a set of vertices given those of another subset at possibly different Time instants. Leveraging spatiotemporal dynamics can drastically reduce the number of observed vertices, and hence the cost of sampling. Alleviating the limited flexibility of existing approaches, the present paper broadens the existing kernel-based graph function reconstruction framework to accommodate Time-evolving Functions over possibly Time-evolving topologies. This approach inherits the versatility and generality of kernel-based methods, for which no knowledge on distributions or second-order statistics is required. Systematic guidelines are provided to construct two families of space-Time kernels with complementary strengths. The first facilitates judicious control of regularization on a space-Time frequency plane, whereas the second can afford Time-varying topologies. Batch and online estimators are also put forth, and a novel kernel Kalman filter is developed to obtain these estimates at affordable computational cost. Numerical tests with real data sets corroborate the merits of the proposed methods relative to competing alternatives.
Françoise Courboulex - One of the best experts on this subject based on the ideXlab platform.
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global catalog of earthquake rupture velocities shows anticorrelation between stress drop and rupture velocity
2017Co-Authors: Agnès Chounet, Martin Vallée, Mathieu Causse, Françoise CourboulexAbstract:Abstract Application of the SCARDEC method provides the apparent source Time Functions together with seismic moment, depth, and focal mechanism, for most of the recent earthquakes with magnitude larger than 5.6–6. Using this large dataset, we have developed a method to systematically invert for the rupture direction and average rupture velocity V r, when unilateral rupture propagation dominates. The approach is applied to all the shallow (z
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stress drop variability of shallow earthquakes extracted from a global database of source Time Functions
2016Co-Authors: Françoise Courboulex, Martin Vallée, Matthieu Causse, Agnès ChounetAbstract:We use the new global database of source Time Functions (STFs) and focal mechanisms proposed by Vallee (2013) using the automatic SCARDEC method (Vallee et al., 2011) to constrain earthquake rupture duration and variability. This database has the advantage of being very consistent since all the events with moment magnitudes Mw>5.8 that have occurred during the last 20 years were reanalyzed with the same method and the same station configuration. We analyze 1754 shallow earthquakes (depth<35 km) and use high‐quality criteria for the STFs, which result in the selection of 660 events. Among these, 313 occurred on the subduction interface (SUB events) and 347 outside (NOT‐SUB events). We obtain that for a given magnitude, STF duration is log normally distributed and that STFs are longer for SUB than NOT‐SUB events. We then estimate the stress drop using a proxy for the rupture process duration obtained from the measurement of the maximum amplitude of the STF. The resulting stress drop is independent of magnitude and is about 2.5 Times smaller for the subduction events compared with the other events. Assuming a constant rupture velocity and source model, the resulting standard deviation of the stress drop is 1.13 for the total dataset (natural log), and about 1 for separate datasets. These values are significantly lower than the ones generally obtained from corner‐frequency analyses with global databases (∼1.5 for Allmann and Shearer, 2009) and are closer to the values inferred from strong‐motion measurements (∼0.5 as reported by Cotton et al., 2013). This indicates that the epistemic variability is reduced by the use of STF properties, which allows us to better approach the natural variability of the source process, related to stress‐drop variability and/or variation in the rupture velocity.
