Unification and Logarithmic Space

We present an algebraic characterization of the complexity classes Logspace and NLogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is inspired from proof theory and more specifically linear logic and Geometry of Interaction. We show how unification can be used to build a model of computation by means of specific subalgebras associated to finite permutations groups. We then prove that whether an observation (the algebraic counterpart of a program) accepts a word can be decided within logarithmic space. We also show that the construction can naturally represent pointer machines, an intuitive way of understanding logarithmic space computing

Polarization state of the optical near-field

The polarization state of the optical electromagnetic field lying several nanometers above complex dielectric structures reveals the intricate light-matter interaction that occurs in this near-field zone. This information can only be extracted from an analysis of the polarization state of the detected light in the near-field. These polarization states can be calculated by different numerical methods well-suited to near--field optics. In this paper, we apply two different techniques (Localized Green Function Method and Differential Theory of Gratings) to separate each polarisation component associated with both electric and magnetic optical near-fields produced by nanometer sized objects. The analysis is carried out in two stages: in the first stage, we use a simple dipolar model to achieve insight into the physical origin of the near-field polarization state. In the second stage, we calculate accurate numerical field maps, simulating experimental near-field light detection, to supplement the data produced by analytical models. We conclude this study by demonstrating the role played by the near-field polarization in the formation of the local density of states.Comment: 9 pages, 11 figures, accepted for publication in Phys. Rev.

Damage-cluster distributions and size effect on strength in compressive failure

We investigate compressive failure of heterogeneous materials on the basis of a continuous progressive damage model. The model explicitely accounts for tensile and shear local damage and reproduces the main features of compressive failure of brittle materials like rocks or ice. We show that the size distribution of damage-clusters, as well as the evolution of an order parameter, the size of the largest damage-cluster, argue for a critical interpretation of fracture. The compressive failure strength follows a normal distribution with a very small size effect on the mean strength, in good agreement with experiments

Classical Structures Based on Unitaries

Starting from the observation that distinct notions of copying have arisen in different categorical fields (logic and computation, contrasted with quantum mechanics) this paper addresses the question of when, or whether, they may coincide. Provided all definitions are strict in the categorical sense, we show that this can never be the case. However, allowing for the defining axioms to be taken up to canonical isomorphism, a close connection between the classical structures of categorical quantum mechanics, and the categorical property of self-similarity familiar from logical and computational models becomes apparent. The required canonical isomorphisms are non-trivial, and mix both typed (multi-object) and untyped (single-object) tensors and structural isomorphisms; we give coherence results that justify this approach. We then give a class of examples where distinct self-similar structures at an object determine distinct matrix representations of arrows, in the same way as classical structures determine matrix representations in Hilbert space. We also give analogues of familiar notions from linear algebra in this setting such as changes of basis, and diagonalisation.Comment: 24 pages,7 diagram

Evidence for a circumplanetary disk around protoplanet PDS 70 b

We present the first observational evidence for a circumplanetary disk around the protoplanet PDS~70~b, based on a new spectrum in the $K$ band acquired with VLT/SINFONI. We tested three hypotheses to explain the spectrum: Atmospheric emission from the planet with either (1) a single value of extinction or (2) variable extinction, and (3) a combined atmospheric and circumplanetary disk model. Goodness-of-fit indicators favour the third option, suggesting circumplanetary material contributing excess thermal emission --- most prominent at $\lambda \gtrsim 2.3 \mu$m. Inferred accretion rates ($\sim 10^{-7.8}$--$10^{-7.3} M_J$ yr$^{-1}$) are compatible with observational constraints based on the H$\alpha$ and Br$\gamma$ lines. For the planet, we derive an effective temperature of 1500--1600 K, surface gravity $\log(g)\sim 4.0$, radius $\sim 1.6 R_J$, mass $\sim 10 M_J$, and possible thick clouds. Models with variable extinction lead to slightly worse fits. However, the amplitude ($\Delta A_V \gtrsim 3$mag) and timescale of variation ($\lesssim$~years) required for the extinction would also suggest circumplanetary material.Comment: 8 pages, 2 figures, 1 table. This is a pre-copyedited, author-produced PDF of an article accepted for publication in ApJL on 2019 May 1

Perception and awareness of accents in young children

This study examines children's metaphonological awareness for accent-related information in connected speech. In the first experiment, 5- to 6-year-old French-speaking children were asked to discriminate between Southern and Northern accented French in a sentence categorization task. It was found that these children were not able to reliably distinguish between these native variations of their own language, but were able to distinguish between their own accent and a strong foreign accent in Experiment 2. These findings were also replicated using a speaker discrimination task in Experiment 3, where children were asked to detect pairs of speakers sharing the same accent amongst speaker pairs with different accents. Whilst these experiments have shown that 5- to 6-year-old children do not use non-familiar regional accents as a discriminatory cue, they are able to perceive the differences between accents, as demonstrated in the AX task used in Experiment 4. The factors underlying the relative lack of awareness for a regional accent as opposed to a foreign accent in childhood are discussed, especially regarding the amount of exposure and the learnability of both types of accents

Some Remarks on the Model Theory of Epistemic Plausibility Models

Classical logics of knowledge and belief are usually interpreted on Kripke models, for which a mathematically well-developed model theory is available. However, such models are inadequate to capture dynamic phenomena. Therefore, epistemic plausibility models have been introduced. Because these are much richer structures than Kripke models, they do not straightforwardly inherit the model-theoretical results of modal logic. Therefore, while epistemic plausibility structures are well-suited for modeling purposes, an extensive investigation of their model theory has been lacking so far. The aim of the present paper is to fill exactly this gap, by initiating a systematic exploration of the model theory of epistemic plausibility models. Like in 'ordinary' modal logic, the focus will be on the notion of bisimulation. We define various notions of bisimulations (parametrized by a language L) and show that L-bisimilarity implies L-equivalence. We prove a Hennesy-Milner type result, and also two undefinability results. However, our main point is a negative one, viz. that bisimulations cannot straightforwardly be generalized to epistemic plausibility models if conditional belief is taken into account. We present two ways of coping with this issue: (i) adding a modality to the language, and (ii) putting extra constraints on the models. Finally, we make some remarks about the interaction between bisimulation and dynamic model changes.Comment: 19 pages, 3 figure

A survey of young, nearby, and dusty stars to understand the formation of wide-orbit giant planets

Direct imaging has confirmed the existence of substellar companions on wide orbits. To understand the formation and evolution mechanisms of these companions, the full population properties must be characterized. We aim at detecting giant planet and/or brown dwarf companions around young, nearby, and dusty stars. Our goal is also to provide statistics on the population of giant planets at wide-orbits and discuss planet formation models. We report a deep survey of 59 stars, members of young stellar associations. The observations were conducted with VLT/NaCo at L'-band (3.8 micron). We used angular differential imaging to reach optimal detection performance. A statistical analysis of about 60 % of the young and southern A-F stars closer than 65 pc allows us to derive the fraction of giant planets on wide orbits. We use gravitational instability models and planet population synthesis models following the core-accretion scenario to discuss the occurrence of these companions. We resolve and characterize new visual binaries and do not detect any new substellar companion. The survey's median detection performance reaches contrasts of 10 mag at 0.5as and 11.5 mag at 1as. We find the occurrence of planets to be between 10.8-24.8 % at 68 % confidence level assuming a uniform distribution of planets in the interval 1-13 Mj and 1-1000 AU. Considering the predictions of formation models, we set important constraints on the occurrence of massive planets and brown dwarf companions that would have formed by GI. We show that this mechanism favors the formation of rather massive clump (Mclump > 30 Mj) at wide (a > 40 AU) orbits which might evolve dynamically and/or fragment. For the population of close-in giant planets that would have formed by CA, our survey marginally explore physical separations (<20 AU) and cannot constrain this population