261 research outputs found

    Apparent magnitudes in an inhomogeneous universe: the global viewpoint

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    Apparent magnitudes are important for high precision cosmology. It is generally accepted that weak gravitational lensing does not affect the relationship between apparent magnitude and redshift. By considering metric perturbations it is shown that objects observed in an inhomogeneous universe have, on average, higher apparent magnitudes than those observed at the same redshift in a homogeneous universe.Comment: 2 pages, Latex, with aastex and emulateapj

    On Differential Privacy and Traffic State Estimation Problem for Connected Vehicles

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    This letter focuses on the problem of traffic state estimation for highway networks with junctions in the form of on- and off-ramps while maintaining differential privacy of traffic data. Two types of sensors are considered, fixed sensors such as inductive loop detectors and connected vehicles which provide traffic density and speed data. The celebrated nonlinear second-order Aw-Rascle- Zhang (ARZ) model is utilized to model the traffic dynamics. The model is formulated as a nonlinear state-space difference equation. Sensitivity relations are derived for the given data which are then used to formulate a differentially private mechanism which adds a Gaussian noise to the data to make it differentially private. A Moving Horizon Estimation (MHE) approach is implemented for traffic state estimation using a linearized ARZ model. MHE is compared with Kalman Filter variants namely Extended Kalman Filter, Ensemble Kalman Filter and Unscented Kalman Filter. Several research and engineering questions are formulated and analysis is performed to find corresponding answers.Comment: TO APPEAR IN THE 61ST IEEE CONFERENCE ON DECISION AND CONTROL (CDC), CANCUN, MEXICO, DECEMBER 2022. arXiv admin note: text overlap with arXiv:2209.0284

    Where Should Traffic Sensors Be Placed on Highways?

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    This paper investigates the practical engineering problem of traffic sensors placement on stretched highways with ramps. Since it is virtually impossible to install bulky traffic sensors on each highway segment, it is crucial to find placements that result in optimized network-wide, traffic observability. Consequently, this results in accurate traffic density estimates on segments where sensors are not installed. The substantial contribution of this paper is the utilization of control-theoretic observability analysis -- jointly with integer programming -- to determine traffic sensor locations based on the nonlinear dynamics and parameters of traffic networks. In particular, the celebrated asymmetric cell transmission model is used to guide the placement strategy jointly with observability analysis of nonlinear dynamic systems through Gramians. Thorough numerical case studies are presented to corroborate the proposed theoretical methods and various computational research questions are posed and addressed. The presented approach can also be extended to other models of traffic dynamics

    Deep sea nature-based solutions to climate change

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    The deep sea (below 200 m depth) is the largest carbon sink on Earth. It hosts abundant biodiversity that underpins the carbon cycle and provides provisioning, supporting, regulating and cultural ecosystem services. There is growing attention to climate-regulating ocean ecosystem services from the scientific, business and political sectors. In this essay we synthesize the unique biophysical, socioeconomic and governance characteristics of the deep sea to critically assess opportunities for deep-sea blue carbon to mitigate climate change. Deep-sea blue carbon consists of carbon fluxes and storage including carbon transferred from the atmosphere by the inorganic and organic carbon pumps to deep water, carbon sequestered in the skeletons and bodies of deep-sea organisms, carbon buried within sediments or captured in carbonate rock. However, mitigating climate change through deep-sea blue carbon enhancement suffers from lack of scientific knowledge and verification, technological limitations, potential environmental impacts, a lack of cooperation and collaboration, and underdeveloped governance. Together, these issues suggest that deep-sea climate change mitigation is limited. Thus, we suggest that a strong focus on blue carbon is too limited a framework for managing the deep sea to contribute to international goals, including the Sustainable Development Goals (SDGs), the Paris Agreement and the post-2020 Biodiversity Goals. Instead, the deep sea can be viewed as a more holistic nature-based solution, including many ecosystem services and biodiversity in addition to climate. Environmental impact assessments (EIAs), area-based management, pollution reduction, moratoria, carbon accounting and fisheries management are tools in international treaties that could help realize benefits from deep-sea, nature-based solutions

    Stability analysis and quasinormal modes of Reissner Nordstr{\o}m Space-time via Lyapunov exponent

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    We explicitly derive the proper time (τ)(\tau) principal Lyapunov exponent (λp\lambda_{p}) and coordinate time (tt) principal Lyapunov exponent (λc\lambda_{c}) for Reissner Nordstr{\o}m (RN) black hole (BH) . We also compute their ratio. For RN space-time, it is shown that the ratio is λpλc=r0r02−3Mr0+2Q2\frac{\lambda_{p}}{\lambda_{c}}=\frac{r_{0}}{\sqrt{r_{0}^2-3Mr_{0}+2Q^2}} for time-like circular geodesics and for Schwarzschild BH it is λpλc=r0r0−3M\frac{\lambda_{p}}{\lambda_{c}}=\frac{\sqrt{r_{0}}}{\sqrt{r_{0}-3M}}. We further show that their ratio λpλc\frac{\lambda_{p}}{\lambda_{c}} may vary from orbit to orbit. For instance, Schwarzschild BH at innermost stable circular orbit(ISCO), the ratio is λpλc∣rISCO=6M=2\frac{\lambda_{p}}{\lambda_{c}}\mid_{r_{ISCO}=6M}=\sqrt{2} and at marginally bound circular orbit (MBCO) the ratio is calculated to be λpλc∣rmb=4M=2\frac{\lambda_{p}}{\lambda_{c}}\mid_{r_{mb}=4M}=2. Similarly, for extremal RN BH the ratio at ISCO is λpλc∣rISCO=4M=223\frac{\lambda_{p}}{\lambda_{c}}\mid_{r_{ISCO}=4M}=\frac{2\sqrt{2}}{\sqrt{3}}. We also further analyse the geodesic stability via this exponent. By evaluating the Lyapunov exponent, it is shown that in the eikonal limit , the real and imaginary parts of the quasi-normal modes of RN BH is given by the frequency and instability time scale of the unstable null circular geodesics.Comment: Accepted in Pramana, 07/09/201
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