Equivalence of switching linear systems by bisimulation

A general notion of hybrid bisimulation is proposed for the class of switching linear systems. Connections between the notions of bisimulation-based equivalence, state-space equivalence, algebraic and input–output equivalence are investigated. An algebraic characterization of hybrid bisimulation and an algorithmic procedure converging in a finite number of steps to the maximal hybrid bisimulation are derived. Hybrid state space reduction is performed by hybrid bisimulation between the hybrid system and itself. By specializing the results obtained on bisimulation, also characterizations of simulation and abstraction are derived. Connections between observability, bisimulation-based reduction and simulation-based abstraction are studied.\ud \u

Invariant higher-order variational problems II

Motivated by applications in computational anatomy, we consider a second-order problem in the calculus of variations on object manifolds that are acted upon by Lie groups of smooth invertible transformations. This problem leads to solution curves known as Riemannian cubics on object manifolds that are endowed with normal metrics. The prime examples of such object manifolds are the symmetric spaces. We characterize the class of cubics on object manifolds that can be lifted horizontally to cubics on the group of transformations. Conversely, we show that certain types of non-horizontal geodesics on the group of transformations project to cubics. Finally, we apply second-order Lagrange--Poincar\'e reduction to the problem of Riemannian cubics on the group of transformations. This leads to a reduced form of the equations that reveals the obstruction for the projection of a cubic on a transformation group to again be a cubic on its object manifold.Comment: 40 pages, 1 figure. First version -- comments welcome

Velocity-space sensitivity of the time-of-flight neutron spectrometer at JET

The velocity-space sensitivities of fast-ion diagnostics are often described by so-called weight functions. Recently, we formulated weight functions showing the velocity-space sensitivity of the often dominant beam-target part of neutron energy spectra. These weight functions for neutron emission spectrometry (NES) are independent of the particular NES diagnostic. Here we apply these NES weight functions to the time-of-flight spectrometer TOFOR at JET. By taking the instrumental response function of TOFOR into account, we calculate time-of-flight NES weight functions that enable us to directly determine the velocity-space sensitivity of a given part of a measured time-of-flight spectrum from TOFOR

Exponential Barycenters of the Canonical Cartan Connection and Invariant Means on Lie Groups

International audienceWhen performing statistics on elements of sets that possess a particular geometric structure, it is desirable to respect this structure. For instance in a Lie group, it would be judicious to have a notion of a mean which is stable by the group operations (composition and inversion). Such a property is ensured for Riemannian center of mass in Lie groups endowed with a bi-invariant Riemannian metric, like compact Lie groups (e.g. rotations). However, bi-invariant Riemannian metrics do not exist for most non compact and non-commutative Lie groups. This is the case in particular for rigid-body transformations in any dimension greater than one, which form the most simple Lie group involved in biomedical image registration. In this paper, we propose to replace the Riemannian metric by an affine connection structure on the group. We show that the canonical Cartan connections of a connected Lie group provides group geodesics which are completely consistent with the composition and inversion. With such a non-metric structure, the mean cannot be defined by minimizing the variance as in Riemannian Manifolds. However, the characterization of the mean as an exponential barycenter gives us an implicit definition of the mean using a general barycentric equation. Thanks to the properties of the canonical Cartan connection, this mean is naturally bi-invariant. We show the local existence and uniqueness of the invariant mean when the dispersion of the data is small enough. We also propose an iterative fixed point algorithm and demonstrate that the convergence to the invariant mean is at least linear. In the case of rigid-body transformations, we give a simple criterion for the global existence and uniqueness of the bi-invariant mean, which happens to be the same as for rotations. We also give closed forms for the bi-invariant mean in a number of simple but instructive cases, including 2D rigid transformations. For general linear transformations, we show that the bi-invariant mean is a generalization of the (scalar) geometric mean, since the determinant of the bi-invariant mean is the geometric mean of the determinants of the data. Finally, we extend the theory to higher order moments, in particular with the covariance which can be used to define a local bi-invariant Mahalanobis distance

Relationship of edge localized mode burst times with divertor flux loop signal phase in JET

A phase relationship is identified between sequential edge localized modes (ELMs) occurrence times in a set of H-mode tokamak plasmas to the voltage measured in full flux azimuthal loops in the divertor region. We focus on plasmas in the Joint European Torus where a steady H-mode is sustained over several seconds, during which ELMs are observed in the Be II emission at the divertor. The ELMs analysed arise from intrinsic ELMing, in that there is no deliberate intent to control the ELMing process by external means. We use ELM timings derived from the Be II signal to perform direct time domain analysis of the full flux loop VLD2 and VLD3 signals, which provide a high cadence global measurement proportional to the voltage induced by changes in poloidal magnetic flux. Specifically, we examine how the time interval between pairs of successive ELMs is linked to the time-evolving phase of the full flux loop signals. Each ELM produces a clear early pulse in the full flux loop signals, whose peak time is used to condition our analysis. The arrival time of the following ELM, relative to this pulse, is found to fall into one of two categories: (i) prompt ELMs, which are directly paced by the initial response seen in the flux loop signals; and (ii) all other ELMs, which occur after the initial response of the full flux loop signals has decayed in amplitude. The times at which ELMs in category (ii) occur, relative to the first ELM of the pair, are clustered at times when the instantaneous phase of the full flux loop signal is close to its value at the time of the first ELM

Inclusive and differential cross-section measurements of t\bartZ production in pp collisions at √s=13 TeV with the ATLAS detector, including EFT and spin-correlation interpretations

Measurements of both the inclusive and differential production cross sections of a top-quark-top-antiquark pair in association with a Z boson (tt¯Z) are presented. Final states with two, three or four isolated leptons (electrons or muons) are targeted. The measurements use the data recorded by the ATLAS detector in pp collisions at s√=13 TeV at the Large Hadron Collider during the years 2015-2018, corresponding to an integrated luminosity of 140 fb−1. The inclusive cross section is measured to be σtt¯Z=0.86±0.04 (stat.)±0.04 (syst.) pb and found to be in agreement with the most advanced Standard Model predictions. The differential measurements are presented as a function of a number of observables that probe the kinematics of the tt¯Z system. Both the absolute and normalised differential cross-section measurements are performed at particle level and parton level for specific fiducial volumes, and are compared with NLO+NNLL theoretical predictions. The results are interpreted in the framework of Standard Model effective field theory and used to set limits on a large number of dimension-6 operators involving the top quark. The first measurement of spin correlations in tt¯Z events is presented: the results are in agreement with the Standard Model expectations, and the null hypothesis of no spin correlations is disfavoured with a significance of 1.8 standard deviations

Observation of quantum entanglement in top-quark pairs using the ATLAS detector

We report the highest-energy observation of entanglement, in top−antitop quark events produced at the Large Hadron Collider, using a proton−proton collision data set with a center-of-mass energy of s√=13 TeV and an integrated luminosity of 140 fb−1 recorded with the ATLAS experiment. Spin entanglement is detected from the measurement of a single observable D, inferred from the angle between the charged leptons in their parent top- and antitop-quark rest frames. The observable is measured in a narrow interval around the top−antitop quark production threshold, where the entanglement detection is expected to be significant. It is reported in a fiducial phase space defined with stable particles to minimize the uncertainties that stem from limitations of the Monte Carlo event generators and the parton shower model in modelling top-quark pair production. The entanglement marker is measured to be D=−0.547±0.002 (stat.)±0.021 (syst.) for 340<mtt¯<380 GeV. The observed result is more than five standard deviations from a scenario without entanglement and hence constitutes both the first observation of entanglement in a pair of quarks and the highest-energy observation of entanglement to date

Haptic Playback: Modeling, Controller Design, and Stability Analysis

With new surgical tools and techniques being continuously introduced, efficient teaching of sensorimotor skills has become an important issue in surgical training. Sensorimotor skills are traditionally taught by a trainer who physically interacts with the trainee. This method is expensive and time consuming. Haptic playback represents an efficient solution to this problem allowing to simultaneously display position and force information to users. The traditional framework used in haptics does not well adapt to this task. This paper proposes a new framework that allows to formally address the issues deriving from simultaneously displaying force and position. This is achieved with the introduction of an information channel and the modeling of the operator as a MISO system. An intuitive and simple model for the user is proposed and validated through experiments with human subjects. The model is then used to design a control strategy, the crossed controller, that exploits both the haptic channel and the information one. The stability of the controlled system can be studied with formal methods. The performance of the crossed controller is finally tested against a more traditional controller through experiments with human subjects