341 research outputs found
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
Gravitational lensing in spherically symmetric static spacetimes with centrifugal force reversal
In Schwarzschild spacetime the value of the radius coordinate is
characterized by three different properties: (a) there is a ``light sphere'',
(b) there is ``centrifugal force reversal'', (c) it is the upper limiting
radius for a non-transparent Schwarschild source to act as a gravitational lens
that produces infinitely many images. In this paper we prove a theorem to the
effect that these three properties are intimately related in {\em any}
spherically symmetric static spacetime. We illustrate the general results with
some examples including black-hole spacetimes and Morris-Thorne wormholes.Comment: 18 pages, 3 eps-figure
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
Gravitational lensing in the strong field limit
We provide an analytic method to discriminate among different types of black
holes on the ground of their strong field gravitational lensing properties. We
expand the deflection angle of the photon in the neighbourhood of complete
capture, defining a strong field limit, in opposition to the standard weak
field limit. This expansion is worked out for a completely generic spherically
symmetric spacetime, without any reference to the field equations and just
assuming that the light ray follows the geodesics equation. We prove that the
deflection angle always diverges logarithmically when the minimum impact
parameter is reached. We apply this general formalism to Schwarzschild,
Reissner-Nordstrom and Janis-Newman-Winicour black holes. We then compare the
coefficients characterizing these metrics and find that different collapsed
objects are characterized by different strong field limits. The strong field
limit coefficients are directly connected to the observables, such as the
position and the magnification of the relativistic images. As a concrete
example, we consider the black hole at the centre of our galaxy and estimate
the optical resolution needed to investigate its strong field behaviour through
its relativistic images.Comment: 10 pages, 5 figures, in press on Physical Review
Genome-wide interrogation of hepatic FXR reveals an asymmetric IR-1 motif and synergy with LRH-1
We used mouse hepatic chromatin enriched with an FXR antibody and chromatin immunoprecipitation-sequencing (ChIP-seq) to evaluate FXR binding on a genome-wide scale. This identified 1656 FXR-binding sites and 10% were located within 2 kb of a transcription start site which is much higher than predicted by random occurrence. A motif search uncovered a canonical nuclear receptor IR-1 site, consistent with in vitro DNA-binding studies reported previously. A separate nuclear receptor half-site for monomeric receptors such as LRH-1 was co-enriched and FXR activation of four newly identified promoters was significantly augmented by an LRH-1 expression vector in a co-transfection assay. There were 1038 genes located within 20 kb of a peak and a gene set enrichment analysis showed that genes identified by our ChIP-seq analysis are highly correlated with genes activated by an FXR-VP16 adenovirus in primary mouse hepatocytes providing functional relevance to the genome-wide binding study. Gene Ontology analysis showed FXR-binding sites close to many genes in lipid, fatty acid and steroid metabolism. Other broad gene clusters related to metabolism, transport, signaling and glycolysis were also significantly enriched. Thus, FXR may have a much wider role in cellular metabolism than previously appreciated
On the exact gravitational lens equation in spherically symmetric and static spacetimes
Lensing in a spherically symmetric and static spacetime is considered, based
on the lightlike geodesic equation without approximations. After fixing two
radius values r_O and r_S, lensing for an observation event somewhere at r_O
and static light sources distributed at r_S is coded in a lens equation that is
explicitly given in terms of integrals over the metric coefficients. The lens
equation relates two angle variables and can be easily plotted if the metric
coefficients have been specified; this allows to visualize in a convenient way
all relevant lensing properties, giving image positions, apparent brightnesses,
image distortions, etc. Two examples are treated: Lensing by a
Barriola-Vilenkin monopole and lensing by an Ellis wormhole.Comment: REVTEX, 11 pages, 12 eps-figures, figures partly improved, minor
revision
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