Entropy rigidity of Hilbert and Riemannian metrics

In this paper we provide two new characterizations of real hyperbolic $n$-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: E‐learning 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 – namely, traditional learning and e‐learning organizations – provide educational programs. We focus on the impact of public subsidies to e‐learning 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 ‘pro e‐learning’ public policies. Our first results show that public subsidies enable the e‐learning organization to provide quality‐based and pricing strategies that tend to be similar to those of the brick’n mortar organization. Besides, we find that such short‐term 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 short‐term public policies