An Explicit Framework for Interaction Nets

Interaction nets are a graphical formalism inspired by Linear Logic proof-nets often used for studying higher order rewriting e.g. \Beta-reduction. Traditional presentations of interaction nets are based on graph theory and rely on elementary properties of graph theory. We give here a more explicit presentation based on notions borrowed from Girard's Geometry of Interaction: interaction nets are presented as partial permutations and a composition of nets, the gluing, is derived from the execution formula. We then define contexts and reduction as the context closure of rules. We prove strong confluence of the reduction within our framework and show how interaction nets can be viewed as the quotient of some generalized proof-nets

Graph Creation, Visualisation and Transformation

We describe a tool to create, edit, visualise and compute with interaction nets - a form of graph rewriting systems. The editor, called GraphPaper, allows users to create and edit graphs and their transformation rules using an intuitive user interface. The editor uses the functionalities of the TULIP system, which gives us access to a wealth of visualisation algorithms. Interaction nets are not only a formalism for the specification of graphs, but also a rewrite-based computation model. We discuss graph rewriting strategies and a language to express them in order to perform strategic interaction net rewriting

Nanoscatterer-assisted fluorescence amplification technique

Weak fluorescence signals, which are important in research and applications, are often masked by the background. Different amplification techniques are actively investigated. Here, a broadband, geometry-independent and flexible feedback scheme based on the random scattering of dielectric nanoparticles allows the amplification of a fluorescence signal by partial trapping of the radiation within the sample volume. Amplification of up to a factor of 40 is experimentally demonstrated in ultrapure water with dispersed TiO2 nanoparticles (30 to 50 nm in diameter) and fluorescein dye at 200 μ mol concentration (pumped with 5 ns long, 3 mJ laser pulses at 490 nm). The measurements show a measurable reduction in linewidth at the emission peak, indicating that feedback-induced stimulated emission contributes to the large gain observed

The Comet Interceptor Mission

Here we describe the novel, multi-point Comet Interceptor mission. It is dedicated to the exploration of a little-processed long-period comet, possibly entering the inner Solar System for the first time, or to encounter an interstellar object originating at another star. The objectives of the mission are to address the following questions: What are the surface composition, shape, morphology, and structure of the target object? What is the composition of the gas and dust in the coma, its connection to the nucleus, and the nature of its interaction with the solar wind? The mission was proposed to the European Space Agency in 2018, and formally adopted by the agency in June 2022, for launch in 2029 together with the Ariel mission. Comet Interceptor will take advantage of the opportunity presented by ESA’s F-Class call for fast, flexible, low-cost missions to which it was proposed. The call required a launch to a halo orbit around the Sun-Earth L2 point. The mission can take advantage of this placement to wait for the discovery of a suitable comet reachable with its minimum ΔV capability of 600 ms−1. Comet Interceptor will be unique in encountering and studying, at a nominal closest approach distance of 1000 km, a comet that represents a near-pristine sample of material from the formation of the Solar System. It will also add a capability that no previous cometary mission has had, which is to deploy two sub-probes – B1, provided by the Japanese space agency, JAXA, and B2 – that will follow different trajectories through the coma. While the main probe passes at a nominal 1000 km distance, probes B1 and B2 will follow different chords through the coma at distances of 850 km and 400 km, respectively. The result will be unique, simultaneous, spatially resolved information of the 3-dimensional properties of the target comet and its interaction with the space environment. We present the mission’s science background leading to these objectives, as well as an overview of the scientific instruments, mission design, and schedule

Encoding Left Reduction in the λ-Calculus with Interaction Nets

This paper presents a simple implementation of the -calculus in the interaction net paradigm. It is based on a two-fold translation. -terms are coded (for duplication) or decoded (for execution) and reduction is achieved by switching between these two states: decoding corresponds to head reduction and encoding to left reductio

Hard combinators

International audienceWe present a simple system of four symbols and seven rules that can be used to translate a subclass of graph relabeling systems called hard interaction nets

Hard combinators

International audienceWe present a simple system of four symbols and seven rules that can be used to translate a subclass of graph relabeling systems called hard interaction nets