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Maximal entropy in the moment body
No full textA moment body is a linear projection of the spectraplex, the convex set of trace-one positive semidefinite matrices. Determining whether a given point lies within a given moment body is a problem with numerous applications in quantum state estimation or polynomial optimization. This moment body membership oracle can be addressed with semidefinite programming, for which several off-the-shelf interior-point solvers are available. In this paper, inspired by techniques from quantum information theory, we argue analytically and geometrically that a much more efficient approach consists of minimizing globally a smooth strictly convex log-partition function, dual to a maximum entropy problem. We analyze the curvature properties of this function and we describe a neat geometric pre-conditioning algorithm. A detailed complexity analysis reveals a cubic dependence on the matrix size, similar to a few eigenstructure computations. Basic numerical experiments illustrate that dense (i.e. non-sparse) projections of size 1000 of a dense semidefinite matrix of size 1000-by-1000 can be routinely handled in a few seconds on a standard laptop, thereby moving the main bottleneck in large-scale semidefinite programming almost entirely to efficient gradient storage and manipulation
On the Inefficiency of Atomic Splittable Routing Games over Parallel Links
No full textInternational audienceAbstract Several recent works on non-atomic routing games suggest that the performance degradation of selfish routing with respect to optimal routing is overall low and far from worst-case scenarios. In this work, we study the performance degradation induced by the lack of coordination in an atomic routing game over parallel links in which there are two types of links. The latency function of "cheap" links is of the form c 1 ϕ ( x ) , whereas the latency function of "expensive" links is of the form c 2 ϕ ( x ) , where c_2>c_1 c 2 > c 1 . We obtain an explicit characterization of the optimal and equilibrium flow configurations, and establish sufficient conditions on the latency function ϕ ( x ) under which the worst traffic conditions occur when all users have the same traffic demand and the total traffic demand is such that "expensive" link are marginally used by selfish routing. We also obtain some partial results on the worst network configuration for the inefficiency of selfish routing. All in all, our results suggest that the worst-case scenario for the inefficiency of selfish routing corresponds to very specific traffic conditions and to highly asymmetric network configurations, and thus that the Price of Anarchy is probably an overly pessimistic performance measure for non-cooperative routing games, as advocated in the above-mentioned works
Descriptor System Modeling for Robustness in Control
No full textInternational audienceThe robust control framework considers systems regulated close to an equilibrium point or a trajectory. Under these assumptions the systems are linear but dependent of many intricate features such as uncertainties, neglected dynamics, time-dependent parameters, isolated non-linearities, time-delays... Robustness is achieved when some performance can be assessed even for the worst configuration of these features. Mathematically, it boils down to proving that some complicated non-linear function of many indeterminates is negative when these indeterminates are constrained in sets that are themselves described by non-linear equations. In this talk we show that for many cases the Descriptor System Modeling that combines Algebraic and Differential Equations is highly useful to simplify (linearize) the problems. Combined to the S-variable approach which cleverly exploits Finsler's lemma, it provides easy to code Semi-Definite Programming relaxations. These numerically tractable relaxations are conservative, yet Descriptor-based liftings of the model allows to build hierarchies of relaxations with decreasing conservatism. In the talk we will give an insight on these theoretical results illustrated on some simple examples
Self‐assembled silicon@silica metasurfaces with high‐quality resonances in the infrared
No full textInternational audience2D assemblies of resonant dielectric particles constitute promising materials for the next generation of photonic devices, thanks to their low optical losses and intense electromagnetic response. However, bottom‐up synthesis methods present many difficulties when targeting metasurface applications, particularly due to the high degree of positional disorder and the size dispersion of the resonant particles. This work presents the fabrication of core–shell silicon@silica particles with multipolar resonances in the visible and near‐infrared. These resonant particles are then assembled at an air–water interface into a semi‐ordered array with islands of crystallinity. The assembly is deposited on quartz and the optical properties are characterized with ellipsometry and optical microscopy. The effective medium of this material appears to display a magnetic resonance with a high‐quality factor at ≈945 nm, as demonstrated by a Lorentzian resonance in the permeability. Thus, this is the first bottom‐up synthesis of silicon particle assemblies known to generate optical magnetism, giving promise for the scalable production of high‐performance metasurfaces, in spite of the imperfections associated with bottom‐up fabrication
Iterative aggregation and disaggregation of commodities for the scheduled service network design problem
No full textInternational audienc
Does Electronic Strong Light-Matter Coupling Affect the Ground-State Energy Landscape? An Experimental Study Using Spin-Crossover Molecules
No full textInternational audienceThe effect of strong light-matter coupling on the electronic ground-state energy landscape of a large ensemble of coupled molecules remains an open question, even at the theoretical level, which still suffers from the lack of experimental studies. In the present work, we have conducted a very careful study of the thermodynamic phase equilibrium between the low-spin (LS) and high-spin (HS) states of a molecular spin-crossover (SCO) thin film, strongly coupled to the vacuum field inside a Fabry–Pérot cavity. While the cavity was tuned to be resonant with the intense charge-transfer bands of the SCO complexes in the LS state, allowing a strong-coupling regime to be achieved with a Rabi splitting of up to 670 meV, molecules in the nonabsorbing HS state remain uncoupled to the cavity. Importantly, no significant change in the spin-transition temperature is observed between the LS and HS states under light-matter coupling within the precision limit (1 °C) of our measurements. The present results demonstrate that, although collective strong coupling to electronic excitations can significantly perturb the excited states of molecules, the effect on the ground-state energy levels remains largely negligible (<0.6 meV)
Robust integrated optical feedback interferometry via variable optical attenuation
No full textInternational audienceRobust operation of optical feedback interferometry-based instruments requires controlling the amount of light that is reflected back into the laser. To this end, here we propose an on-chip optical feedback interferometry system with an integrated variable optical attenuator. We develop what we believe to be a novel analytical model for this system, and using a realistic variable optical attenuator design, we show that it can provide high precision displacement measurements in a wide range of the feedback parameter 2 < C < 100 for target distances up to a few centimeters. This paves the way towards short-distance applications in which reflections change significantly, such as the characterization of micro-electro-mechanical systems
Extended URDF: Accounting for parallel mechanism in robot description
No full textInternational audienceRobotic designs played an important role in recent advances by providing powerful robots with complex mechanics. Many recent systems rely on parallel actuation to provide lighter limbs and allow more complex motion. However, these emerging architectures fall outside the scope of most used description formats, leading to difficulties when designing, storing, and sharing the models of these systems. This paper introduces an extension to the widely used Unified Robot Description Format (URDF) to support closed-loop kinematic structures. Our approach relies on augmenting URDF with minimal additional information to allow more efficient modeling of complex robotic systems while maintaining compatibility with existing design and simulation frameworks. This method sets the basic requirement for a description format to handle parallel mechanisms efficiently. We demonstrate the applicability of our approach by providing an open-source collection of parallel robots, along with tools for generating and parsing this extended description format. The proposed extension simplifies robot modeling, reduces redundancy, and improves usability for advanced robotic applications
A formal implementation of Behavior Trees to act in robotics
No full textInternational audienceBehavior Trees (BT) are becoming quite popular as an Acting component of autonomous robotic systems. We propose to define a formal semantics to BT by translating them to a formal language which enables us to perform verification of programs written with BT, as well as runtime verification while these BT execute. This allows us to formally verify BT correctness without requiring BT programmers to master formal languages and without compromising BT most valuable features: modularity, flexibility and reusability. We present the formal framework we use: Fiacre, its language and the produced TTS model; Tina, its model checking tools and Hippo, its runtime verification engine. We then show how the translation from BT to Fiacre is automatically done, the type of formal LTL and CTL properties we can check offline and how to execute the formal model online in place of a regular BT engine. We illustrate our approach on two robotics applications, and show how BT could benefit of other features available in the Fiacre formal framework (state variables, time, etc)