1,346 research outputs found
Entropy rigidity of Hilbert and Riemannian metrics
In this paper we provide two new characterizations of real hyperbolic
-space using the Poincar\'e exponent of a discrete group and the volume
growth entropy. The first characterization is in the space of Hilbert metrics
and generalizes a result of Crampon. The second is in the space of Riemannian
metrics with Ricci curvature bounded below and generalizes a result of
Ledrappier and Wang.Comment: 14 pages, some revisions following the referees remarks. To be
published in IMR
On Time Synchronization Issues in Time-Sensitive Networks with Regulators and Nonideal Clocks
Flow reshaping is used in time-sensitive networks (as in the context of IEEE
TSN and IETF Detnet) in order to reduce burstiness inside the network and to
support the computation of guaranteed latency bounds. This is performed using
per-flow regulators (such as the Token Bucket Filter) or interleaved regulators
(as with IEEE TSN Asynchronous Traffic Shaping). Both types of regulators are
beneficial as they cancel the increase of burstiness due to multiplexing inside
the network. It was demonstrated, by using network calculus, that they do not
increase the worst-case latency. However, the properties of regulators were
established assuming that time is perfect in all network nodes. In reality,
nodes use local, imperfect clocks. Time-sensitive networks exist in two
flavours: (1) in non-synchronized networks, local clocks run independently at
every node and their deviations are not controlled and (2) in synchronized
networks, the deviations of local clocks are kept within very small bounds
using for example a synchronization protocol (such as PTP) or a satellite based
geo-positioning system (such as GPS). We revisit the properties of regulators
in both cases. In non-synchronized networks, we show that ignoring the timing
inaccuracies can lead to network instability due to unbounded delay in per-flow
or interleaved regulators. We propose and analyze two methods (rate and burst
cascade, and asynchronous dual arrival-curve method) for avoiding this problem.
In synchronized networks, we show that there is no instability with per-flow
regulators but, surprisingly, interleaved regulators can lead to instability.
To establish these results, we develop a new framework that captures industrial
requirements on clocks in both non-synchronized and synchronized networks, and
we develop a toolbox that extends network calculus to account for clock
imperfections.Comment: ACM SIGMETRICS 2020 Boston, Massachusetts, USA June 8-12, 202
On the convexity of injectivity domains on nonfocal manifolds
Given a smooth nonfocal compact Riemannian manifold, we show that the
so-called Ma--Trudinger--Wang condition implies the convexity of injectivity
domains. This improves a previous result by Loeper and Villani
Weaving Rules into [email protected] for Embedded Smart Systems
Smart systems are characterised by their ability to analyse measured data in
live and to react to changes according to expert rules. Therefore, such systems
exploit appropriate data models together with actions, triggered by
domain-related conditions. The challenge at hand is that smart systems usually
need to process thousands of updates to detect which rules need to be
triggered, often even on restricted hardware like a Raspberry Pi. Despite
various approaches have been investigated to efficiently check conditions on
data models, they either assume to fit into main memory or rely on high latency
persistence storage systems that severely damage the reactivity of smart
systems. To tackle this challenge, we propose a novel composition process,
which weaves executable rules into a data model with lazy loading abilities. We
quantitatively show, on a smart building case study, that our approach can
handle, at low latency, big sets of rules on top of large-scale data models on
restricted hardware.Comment: pre-print version, published in the proceedings of MOMO-17 Worksho
Cluster Magnification & the Mass-Richness Relation in CFHTLenS
Gravitational lensing magnification is measured with a significance of 9.7
sigma on a large sample of galaxy clusters in the Canada-France-Hawaii
Telescope Lensing Survey (CFHTLenS). This survey covers ~154 deg^2 and contains
over 18,000 cluster candidates at redshifts 0.2 <= z <= 0.9, detected using the
3D-Matched Filter cluster-finder of Milkeraitis et al. (2010). We fit
composite-NFW models to the ensemble, accounting for cluster miscentering,
source-lens redshift overlap, as well as nearby structure (the 2-halo term),
and recover mass estimates of the cluster dark matter halos in range of ~10^13
M_sun to 2*10^14 M_sun. Cluster richness is measured for the entire sample, and
we bin the clusters according to both richness and redshift. A mass-richness
relation M_200 = M_0 (N_200 / 20)^beta is fit to the measurements. For two
different cluster miscentering models we find consistent results for the
normalization and slope, M_0 = (2.3 +/- 0.2)*10^13 M_sun, beta = 1.4 +/- 0.1
and M_0 = (2.2 +/- 0.2)*10^13 M_sun, beta = 1.5 +/- 0.1. We find that
accounting for the full redshift distribution of lenses and sources is
important, since any overlap can have an impact on mass estimates inferred from
flux magnification.Comment: 11 pages, 8 figures, Accepted to MNRA
Network-Calculus Service Curves of the Interleaved Regulator
The interleaved regulator (implemented by IEEE TSN Asynchronous Traffic
Shaping) is used in time-sensitive networks for reshaping the flows with
per-flow contracts. When applied to an aggregate of flows that come from a FIFO
system, an interleaved regulator that reshapes the flows with their initial
contracts does not increase the worst-case delay of the aggregate. This
shaping-for-free property supports the computation of end-to-end latency bounds
and the validation of the network's timing requirements. A common method to
establish the properties of a network element is to obtain a network-calculus
service-curve model. The existence of such a model for the interleaved
regulator remains an open question. If a service-curve model were found for the
interleaved regulator, then the analysis of this mechanism would no longer be
limited to the situations where the shaping-for-free holds, which would widen
its use in time-sensitive networks. In this paper, we investigate if
network-calculus service curves can capture the behavior of the interleaved
regulator. We find that an interleaved regulator placed outside of the
shaping-for-free requirements (after a non-FIFO system) can yield unbounded
latencies. Consequently, we prove that no network-calculus service curve exists
to explain the interleaved regulator's behavior. It is still possible to find
non-trivial service curves for the interleaved regulator. However, their
long-term rate cannot be large enough to provide any guarantee (specifically,
we prove that for the regulators that process at least four flows with the same
contract, the long-term rate of any service curve is upper bounded by three
times the rate of the per-flow contract).Comment: 17 pages, 13 figures, 4 table
Locating a weak change using diffuse waves (LOCADIFF) : theoretical approach and inversion procedure
We describe a time-resolved monitoring technique for heterogeneous media. Our
approach is based on the spatial variations of the cross-coherence of coda
waveforms acquired at fixed positions but at different dates. To locate and
characterize a weak change that occurred between successive acquisitions, we
use a maximum likelihood approach combined with a diffusive propagation model.
We illustrate this technique, called LOCADIFF, with numerical simulations. In
several illustrative examples, we show that the change can be located with a
precision of a few wavelengths and its effective scattering cross-section can
be retrieved. The precision of the method depending on the number of source
receiver pairs, time window in the coda, and errors in the propagation model is
investigated. Limits of applications of the technique to real-world experiments
are discussed.Comment: 11 pages, 14 figures, 1 tabl
Bridging the Learning Gap in the Marketfor Higher Education: Eâlearning and Public Subsidies
This article aims at analyzing the adoption patterns which apply on the market for higher education when two types of learning organizations â namely, traditional learning and eâlearning organizations â provide educational programs. We focus on the impact of public subsidies to eâlearning providers in order to evaluate the conditions under which the learning gap is bridged. A
welfare analysis is introduced to estimate the relevance of such âpro eâlearningâ public policies. Our first results show that public subsidies enable the eâlearning organization to provide qualityâbased and pricing strategies that tend to be similar to those of the brickân mortar organization. Besides, we find that such shortâterm policies positively impact on the global level of quality which is provided by both providers. Nevertheless, our welfare analysis underlines contrasted results about the relevance of such shortâterm public policies
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