Compositional abstraction and safety synthesis using overlapping symbolic models

In this paper, we develop a compositional approach to abstraction and safety synthesis for a general class of discrete time nonlinear systems. Our approach makes it possible to define a symbolic abstraction by composing a set of symbolic subsystems that are overlapping in the sense that they can share some common state variables. We develop compositional safety synthesis techniques using such overlapping symbolic subsystems. Comparisons, in terms of conservativeness and of computational complexity, between abstractions and controllers obtained from different system decompositions are provided. Numerical experiments show that the proposed approach for symbolic control synthesis enables a significant complexity reduction with respect to the centralized approach, while reducing the conservatism with respect to compositional approaches using non-overlapping subsystems

Reachability Analysis of Neural Networks with Uncertain Parameters

The literature on reachability analysis methods for neural networks currently only focuses on uncertainties on the network's inputs. In this paper, we introduce two new approaches for the reachability analysis of neural networks with additional uncertainties on their internal parameters (weight matrices and bias vectors of each layer), which may open the field of formal methods on neural networks to new topics, such as safe training or network repair. The first and main method that we propose relies on existing reachability analysis approach based on mixed monotonicity (initially introduced for dynamical systems). The second proposed approach extends the ESIP (Error-based Symbolic Interval Propagation) approach which was first implemented in the verification tool Neurify, and first mentioned in the publication of the tool VeriNet. Although the ESIP approach has been shown to often outperform the mixed-monotonicity reachability analysis in the classical case with uncertainties only on the network's inputs, we show in this paper through numerical simulations that the situation is greatly reversed (in terms of precision, computation time, memory usage, and broader applicability) when dealing with uncertainties on the weights and biases

Interval Reachability Analysis using Second-Order Sensitivity

We propose a new approach to compute an interval over-approximation of the finite time reachable set for a large class of nonlinear systems. This approach relies on the notions of sensitivity matrices, which are the partial derivatives representing the variations of the system trajectories in response to variations of the initial states. Using interval arithmetics, we first over-approximate the possible values of the second-order sensitivity at the final time of the reachability problem. Then we exploit these bounds and the evaluation of the first-order sensitivity matrices at a few sampled initial states to obtain an over-approximation of the first-order sensitivity, which is in turn used to over-approximate the reachable set of the initial system. Unlike existing methods relying only on the first-order sensitivity matrix, this new approach provides guaranteed over-approximations of the first-order sensitivity and can also provide such over-approximations with an arbitrary precision by increasing the number of samples

Maximum relative speeds of living organisms: why do bacteria perform as fast as ostriches?

International audienceSelf-locomotion is central to animal behaviour and survival. It is generally analysed by focusing on preferred speeds and gaits under particular biological and physical constraints. In the present paper we focus instead on the maximum speed and we study its order-of-magnitude scaling with body size, from bacteria to the largest terrestrial and aquatic organisms. Using data for about 460 species of various taxonomic groups, we find a maximum relative speed of the order of magnitude of ten body lengths per second over a 10 20-fold mass range of running and swimming animals. This result implies a locomotor time scale of the order of one tenth of second, virtually independent on body size, anatomy and locomotion style, whose ubiquity requires an explanation building on basic properties of motile organisms. From first-principle estimates, we relate this generic time scale to other basic biological properties, using in particular the recent generalisation of the muscle specific tension to molecular motors. Finally, we go a step further by relating this time scale to still more basic quantities, as environmental conditions at Earth in addition to fundamental physical and chemical constants

Force per cross-sectional area from molecules to muscles: a general property of biological motors

International audienceWe propose to formally extend the notion of specific tension, i.e. force per cross-sectional area—classically used for muscles, to quantify forces in molecular motors exerting various biological functions. In doing so, we review and compare the maximum tensions exerted by about 265 biological motors operated by about 150 species of different taxonomic groups. The motors considered range from single molecules and motile appendages of microorganisms to whole muscles of large animals. We show that specific tensions exerted by molecular and non-molecular motors follow similar statistical distributions, with in particular, similar medians and (logarithmic) means. Over the 10 19 mass (M) range of the cell or body from which the motors are extracted, their specific tensions vary as M α with α not significantly different from zero. The typical specific tension found in most motors is about 200 kPa, which generalizes to individual molecular motors and microorganisms a classical property of macroscopic muscles. We propose a basic order-of-magnitude interpretation of this result

A web information system for the management and the dissemination of Cultural Heritage data.

Safeguarding and exploiting Cultural Heritage induce the production of numerous and heterogeneous data. The management of these data is an essential task for the use and the diffusion of the information gathered on the field. Previously, the data handling was a hand-made task done thanks to efficient and experienced methods. Until the growth of computer science, other methods have been carried out for the digital preservation and treatment of Cultural Heritage information. The development of computerized data management systems to store and make use of archaeological datasets is then a significant task nowadays. Especially for sites that have been excavated and worked without computerized means, it is now necessary to put all the data produced onto computer. This allows preservation of the information digitally (in addition with the paper documents) and offers new exploitation possibilities, like the immediate connection of different kinds of data for analyses, or the digital documentation of the site for its improvement. Geographical Information Systems have proved their potentialities in this scope, but they are not always adapted to the management of features at the scale of a particular archaeological site. Therefore this paper aims to present the development of a Virtual Research Environment dedicated to the exploitation of intra-site Cultural Heritage data. The Information System produced is based on open-source software modules dedicated to the Internet, so users can avoid being software driven and can register and consult data from different computers. The system gives the opportunity to do exploratory analyses of the data, especially at spatial and temporal levels. The system is compliant to every kind of Cultural Heritage site and allows management of diverse types of data. Some experimentation has been done on sites managed by the Service of the National Sites and Monuments of Luxembourg