Comparison of max-plus automata and joint spectral radius of tropical matrices

Weighted automata over the max-plus semiring S are closely related to finitely generated semigroups of matrices over S. In this paper, we use results in automata theory to study two quantities associated with sets of matrices: the joint spectral radius and the ultimate rank. We prove that these two quantities are not computable over the tropical semiring, i.e. there is no algorithm that takes as input a finite set of matrices M and provides as output the joint spectral radius (resp. the ultimate rank) of M. On the other hand, we prove that the joint spectral radius is nevertheless approximable and we exhibit restricted cases in which the joint spectral radius and the ultimate rank are computable. To reach this aim, we study the problem of comparing functions computed by weighted automata over the tropical semiring. This problem is known to be undecidable and we prove that it remains undecidable in some specific subclasses of automata

Perturbations of the local gravity field due to mass distribution on precise measuring instruments: a numerical method applied to a cold atom gravimeter

We present a numerical method, based on a FEM simulation, for the determination of the gravitational field generated by massive objects, whatever geometry and space mass density they have. The method was applied for the determination of the self gravity effect of an absolute cold atom gravimeter which aims at a relative uncertainty of 10-9. The deduced bias, calculated with a perturbative treatment, is finally presented. The perturbation reaches (1.3 \pm 0.1) \times 10-9 of the Earth's gravitational field.Comment: 12 pages, 7 figure

Comparison between two mobile absolute gravimeters: optical versus atomic interferometers

We report a comparison between two absolute gravimeters: the LNE-SYRTE cold atoms gravimeter and FG5#220 of Leibniz Universit\"at of Hannover. They rely on different principles of operation: atomic and optical interferometry. Both are movable which enabled them to participated to the last International Comparison of Absolute Gravimeters (ICAG'09) at BIPM. Immediately after, their bilateral comparison took place in the LNE watt balance laboratory and showed an agreement of 4.3 +/- 6.4 {\mu}Gal

The electric double layer has a life of its own

Using molecular dynamics simulations with recently developed importance sampling methods, we show that the differential capacitance of a model ionic liquid based double-layer capacitor exhibits an anomalous dependence on the applied electrical potential. Such behavior is qualitatively incompatible with standard mean-field theories of the electrical double layer, but is consistent with observations made in experiment. The anomalous response results from structural changes induced in the interfacial region of the ionic liquid as it develops a charge density to screen the charge induced on the electrode surface. These structural changes are strongly influenced by the out-of-plane layering of the electrolyte and are multifaceted, including an abrupt local ordering of the ions adsorbed in the plane of the electrode surface, reorientation of molecular ions, and the spontaneous exchange of ions between different layers of the electrolyte close to the electrode surface. The local ordering exhibits signatures of a first-order phase transition, which would indicate a singular charge-density transition in a macroscopic limit

The 3-PPPS parallel robot with U-shape Base, a 6-DOF parallel robot with simple kinematics

International audienceOne of the main problems associated with the use of 6 DOF parallel robots remains the solving of their kinematic models. This is rarely possible to analytically solve their models thereby justifying the application of numerical methods. These methods are difficult to implement in an industrial controller and can cause solution bifurcations close to singularities resulting in following an unplanned trajectory. Recently, a 3-PPPS robot with U-shaped base was introduced where an analytical kinematic model can be derived. Previously, quaternion parameters were used to represent the orientation of the mobile platform. To allow for simpler model handling, this article introduces the use of Euler angles which have a physical meaning for the users. Compact writing of the direct and inverse kinematic model is thus obtained. Using algebraic and cylindrical decomposition for the workspace, this provides a simpler representation of the largest domain without singularity around the " home " configuration

Workspace Analysis of a 4 Cable-Driven Spatial Parallel Robot

International audienceThis paper presents the static equilibrium workspace of an under-constrained cable-driven robot with four cables taking into account the forces and the moments due to the forces acting on the moving platform. The problem is formulated as a non-linear optimization problem with maintaining static equilibrium as the objective function. The simulations are done using MATLAB. The maximum force on the cables and tilting angle of the platform are used to define the feasible static equilibrium workspace and the results obtained are used to finalize the design of the collaborative cable-driven robot to be installed in existing production lines for the agile handling of parts in a manufacturing industry

Performance evaluation of parallel manipulators for milling application

This paper focuses on the performance evaluation of the parallel manipulators for milling of composite materials. For this application the most significant performance measurements, which denote the ability of the manipulator for the machining are defined. In this case, optimal synthesis task is solved as a multicriterion optimization problem with respect to the geometric, kinematic, kinetostatic, elastostostatic, dynamic properties. It is shown that stiffness is an important performance factor. Previous models operate with links approximation and calculate stiffness matrix in the neighborhood of initial point. This is a reason why a new way for stiffness matrix calculation is proposed. This method is illustrated in a concrete industrial problem

Detecting inertial effects with airborne matter-wave interferometry

Inertial sensors relying on atom interferometry offer a breakthrough advance in a variety of applications, such as inertial navigation, gravimetry or ground- and space-based tests of fundamental physics. These instruments require a quiet environment to reach their performance and using them outside the laboratory remains a challenge. Here we report the first operation of an airborne matter-wave accelerometer set up aboard a 0g plane and operating during the standard gravity (1g) and microgravity (0g) phases of the flight. At 1g, the sensor can detect inertial effects more than 300 times weaker than the typical acceleration fluctuations of the aircraft. We describe the improvement of the interferometer sensitivity in 0g, which reaches 2 x 10-4 ms-2 / \surdHz with our current setup. We finally discuss the extension of our method to airborne and spaceborne tests of the Universality of free fall with matter waves.Comment: 7 pages, 6 figures. The final version of this article is available in OPEN access (free) from the editor website at http://www.nature.com/ncomms/journal/v2/n9/full/ncomms1479.htm

Monotherapy with the PCSK9 inhibitor alirocumab versus ezetimibe in patients with hypercholesterolemia:Results of a 24week, double-blind, randomized Phase 3 trial

Background:Efficacy and safety of alirocumab were compared with ezetimibe in hypercholesterolemic patients at moderate cardiovascular risk not receiving statins or other lipid-lowering therapy. Methods In a Phase 3, randomized, double-blind, double-dummy study (NCT01644474), patients (low-density lipoprotein cholesterol [LDL-C] 100–190 mg/dL, 10-year risk of fatal cardiovascular events = 1%–&lt;5% [systemic coronary risk estimation]) were randomized to ezetimibe 10 mg/day (n = 51) or alirocumab 75 mg subcutaneously (via 1­mL autoinjector) every 2 weeks (Q2W) (n = 52), with dose up-titrated to 150 mg Q2W (also 1 mL) at week 12 if week 8 LDL-C was = 70 mg/dL. Primary endpoint was mean LDL-C % change from baseline to 24 weeks, analyzed using all available data (intent-to-treat approach, ITT). Analyses using on-treatment LDL-C values were also conducted.Results: Mean (SD) baseline LDL-C levels were 141.1 (27.1) mg/dL (alirocumab) and138.3 (24.5) mg/dL (ezetimibe). The 24-week treatment period was completed by 85% of alirocumab and 86% of ezetimibe patients. Least squares mean (SE) LDL-C reductions were 47 (3)% with alirocumab versus 16 (3)% with ezetimibe (ITT; p &lt; 0.0001) and 54 (2)% versus 17 (2)% (on-treatment; p &lt; 0.0001).At week 12, before up-titration, alirocumab 75 mg Q2W reduced LDL-C by 53 (2)% (on-treatment). Injection site reactions were infrequent (&lt; 2% and &lt; 4% of alirocumab and ezetimibe patients, respectively). Conclusions: Alirocumab demonstrated significantly greater LDL-C lowering versus ezetimibe after 24 weeks with the lower 75 mg Q2W dose sufficient to provide = 50% LDL-C reduction in the majority of the patients. Adverse events were comparable between groups.</p