Interaction Graphs: Full Linear Logic

Interaction graphs were introduced as a general, uniform, construction of dynamic models of linear logic, encompassing all Geometry of Interaction (GoI) constructions introduced so far. This series of work was inspired from Girard's hyperfinite GoI, and develops a quantitative approach that should be understood as a dynamic version of weighted relational models. Until now, the interaction graphs framework has been shown to deal with exponentials for the constrained system ELL (Elementary Linear Logic) while keeping its quantitative aspect. Adapting older constructions by Girard, one can clearly define "full" exponentials, but at the cost of these quantitative features. We show here that allowing interpretations of proofs to use continuous (yet finite in a measure-theoretic sense) sets of states, as opposed to earlier Interaction Graphs constructions were these sets of states were discrete (and finite), provides a model for full linear logic with second order quantification

Logic Programming and Logarithmic Space

We present an algebraic view on logic programming, related to proof theory and more specifically linear logic and geometry of interaction. Within this construction, a characterization of logspace (deterministic and non-deterministic) computation is given via a synctactic restriction, using an encoding of words that derives from proof theory. We show that the acceptance of a word by an observation (the counterpart of a program in the encoding) can be decided within logarithmic space, by reducing this problem to the acyclicity of a graph. We show moreover that observations are as expressive as two-ways multi-heads finite automata, a kind of pointer machines that is a standard model of logarithmic space computation

A boom‐or‐bust approach — the ‘Glass Cannon’ hypothesis in host microbiomes

In Focus: Dunphy, CM, Vollmer, SV, Gouhier, TC. (2021) Host–microbial systems as glass cannons: Explaining microbiome stability in corals exposed to extrinsic perturbations. Journal of Animal Ecology, 90, 1044–1057. The importance of symbiotic microbial communities for the functioning of animal hosts is now well‐documented; however, the interactions between host microbiomes and stress are less well‐understood. Dunphy et al. used a common garden experiment to show that host–microbiomes vary in their resilience across different coral species. The authors then used mathematical modelling to provide novel evidence that species with microbiomes that are regulated by host processes are robust to perturbation from stressors, but that robustness comes at a higher cost to the host. Conversely, species with microbiomes that are regulated by microbial processes are generally much more resilient and cheaper to support, but when disrupted by external stressors, the communities break down entirely—these latter species are termed ‘glass cannons’. This novel hypothesis has important implications for how host microbiomes function in a rapidly changing world that exposes animal hosts to multiple biotic and abiotic perturbations

4D in situ monitoring of the setting of alpha plaster using synchrotron X-ray tomography with high spatial and temporal resolution

International audienceThis paper is dedicated to the in situ follow up of the setting of an α plaster using synchrotron X-ray tomography, with a high spatial resolution, down to 0.3 µm (0.16 µm voxel size), and a high time resolution with a scan every 30 s. This combination of spatial and time resolution is amongst the best reported in the literature so far and is of particular interest for the study of moderately rapid transformation of the microstructure at a small scale. It enables to characterize both the dissolution of hemihydrate particles and the precipitation of gypsum crystals. A dissolution rate for the hemihydrate particles is determined, in good coherence with previous work on β plaster using lab X-ray tomograph. A thickening of gypsum crystals with hydration time is also noted. A quantitative analysis of hydration is performed through the calculation of a microstructural degree of reaction from the X-ray tomography volumes, after peak deconvolution of the gray value histogram at different hydration times

A probabilistic assessment of the chemical and radiological risks of chronic exposure to uranium in freshwater ecosystems

Uranium (U) presents a unique challenge for ecological risk assessments (ERA) because it induces both chemical and radiological toxicity, and the relative importance of these two toxicities differs among the various U source terms (i.e., natural, enriched, depleted). We present a method for the conversion between chemical concentrations (μg L -1) and radiological dose rates (μGy h -1) for a defined set of reference organisms, and apply this conversion method to previously derived chemical and radiological benchmarks to determine the extent to which these benchmarks ensure radiological and chemical protection, respectively, for U in freshwater ecosystems. Results show that the percentage of species radiologically protected by the chemical benchmark decreases with increasing degrees of U enrichment and with increasing periods of radioactive decay. In contrast, the freshwater ecosystem is almost never chemically protected by the radiological benchmark, regardless of the source term or decay period considered, confirming that the risks to the environment from uranium's chemical toxicity generally outweigh those of its radiological toxicity. These results are relevant to developing water quality criteria that protect freshwater ecosystems from the various risks associated with the nuclear applications of U exploitation, and highlight the need for (1) further research on the speciation, bioavailability, and toxicity of U-series radionuclides under different environmental conditions, and (2) the adoption of both chemical and radiological benchmarks for coherent ERAs to be conducted in U-contaminated freshwater ecosystems. © 2009 American Chemical Society