259 research outputs found
Apparent magnitudes in an inhomogeneous universe: the global viewpoint
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
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?
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
The relation between maximal voluntary force in<i> m. palmaris</i> longus and the temporal and spatial summation of muscle fiber recruitment in human subjects
Stability analysis and quasinormal modes of Reissner Nordstr{\o}m Space-time via Lyapunov exponent
We explicitly derive the proper time principal Lyapunov exponent
() and coordinate time () principal Lyapunov exponent
() 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
for
time-like circular geodesics and for Schwarzschild BH it is
. We
further show that their ratio may vary from
orbit to orbit. For instance, Schwarzschild BH at innermost stable circular
orbit(ISCO), the ratio is
and at marginally
bound circular orbit (MBCO) the ratio is calculated to be
. Similarly, for extremal RN
BH the ratio at ISCO is
.
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
Quasilinear hyperbolic Fuchsian systems and AVTD behavior in T2-symmetric vacuum spacetimes
We set up the singular initial value problem for quasilinear hyperbolic
Fuchsian systems of first order and establish an existence and uniqueness
theory for this problem with smooth data and smooth coefficients (and with even
lower regularity). We apply this theory in order to show the existence of
smooth (generally not analytic) T2-symmetric solutions to the vacuum Einstein
equations, which exhibit AVTD (asymptotically velocity term dominated) behavior
in the neighborhood of their singularities and are polarized or half-polarized.Comment: 78 page
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