On Context Semantics and Interaction Nets

International audienceContext semantics is a tool inspired by Girard' s geometry of interaction. It has had many applications from study of optimal reduction to proofs of complexity bounds. Yet, context semantics have been defined only on $\lambda$-calculus and linear logic. In order to study other languages, in particular languages with more primitives (built-in arithmetic, pattern matching,...) we define a context semantics for a broader framework: interaction nets. These are a well-behaved class of graph rewriting systems. Here, two applications are explored. First, we define a notion of weight, based on context semantics paths, which bounds the length of reduction of nets. Then, we define a denotational semantics for a large class of interaction net systems

A search for passive protoplanetary disks in the Taurus-Auriga star-forming region

We conducted a 12-month monitoring campaign of 33 T Tauri stars (TTS) in Taurus. Our goal was to monitor objects that possess a disk but have a weak Halpha line, a common accretion tracer for young stars, to determine whether they host a passive circumstellar disk. We used medium-resolution optical spectroscopy to assess the objects' accretion status and to measure the Halpha line. We found no convincing example of passive disks; only transition disk and debris disk systems in our sample are non-accreting. Among accretors, we find no example of flickering accretion, leading to an upper limit of 2.2% on the duty cycle of accretion gaps assuming that all accreting TTS experience such events. Combining literature results with our observations, we find that the reliability of traditional Halpha-based criteria to test for accretion is high but imperfect, particularly for low-mass TTS. We find a significant correlation between stellar mass and the full width at 10 per cent of the peak (W10%) of the Halpha line that does not seem to be related to variations in free-fall velocity. Finally, our data reveal a positive correlation between the Halpha equivalent width and its W10%, indicative of a systematic modulation in the line profile whereby the high-velocity wings of the line are proportionally more enhanced than its core when the line luminosity increases. We argue that this supports the hypothesis that the mass accretion rate on the central star is correlated with the Halpha W10% through a common physical mechanism.Comment: accepted for publication in MNRAS; 26 pages, 9 figures, 3 table

Equine meniscal degeneration is associated with medial femorotibial osteoarthritis

Background: There is limited information available concerning normal equine meniscal morphology, its degeneration and role in osteoarthritis (OA). Objectives: To characterise normal equine meniscal morphology and lesions and to explore the relationship between equine meniscal degeneration and femorotibial OA. Study design: Ex vivo cadaveric study. Methods: Menisci were harvested from 7 normal joints (n = 14 menisci) and 15 joints with OA (n = 30 menisci). A macroscopic femorotibial OA score (cartilage degeneration and osteophytosis) was employed to measure disease severity in each compartment. The femoral and tibial meniscal surfaces were scored for macroscopic fibrillation and tears (1–4). Histological sections (regions: cranial and caudal horn; body) were also scored for microscopic fibrillation and tears (0–3) and inner border degeneration (0–3). Results: Partial meniscal tears were present on both femoral and tibial surfaces in all 3 regions and most frequently identified on the femoral surface of the cranial horn of the medial meniscus and body of the lateral meniscus. There was a significantly positive correlation between the global medial meniscal macroscopic scores and osteophyte (r = 0.7, P = 0.002) or cartilage degeneration (r = 0.5, P = 0.03) scores within the medial femorotibial joint. The global medial meniscal macroscopic score was greater (P = 0.004) in the advanced OA joints compared with control joints. Main limitations: The menisci were principally from abattoir specimens without a known clinical history because of the challenge in obtaining a large number of specimens with a clinical diagnosis of femorotibial OA. Conclusions: This study is the first to describe normal equine meniscal morphology and lesions. Meniscal lesions were identified in all segments and on both articular surfaces. Meniscal degeneration significantly correlated with OA severity in the equine medial femorotibial joint. The relationship between OA and meniscal pathology remains to be elucidated

The inner environment of Z~CMa: High-Contrast Imaging Polarimetry with NaCo

Context. Z\,CMa is a binary composed of an embedded Herbig Be and an FU Ori class star separated by $\sim100$ au. Observational evidence indicate a complex environment in which each star has a circumstellar disk and drives a jet, and the whole system is embedded in a large dusty envelope. Aims. We aim to probe the circumbinary environment of Z\,CMa in the inner 400 au in scattered light. Methods. We use high contrast imaging polarimetry with VLT/NaCo at $H$ and $K_s$ bands. Results. The central binary is resolved in both bands. The polarized images show three bright and complex structures: a common dust envelope, a sharp extended feature previously reported in direct light, and an intriguing bright clump located 0\farcs3 south of the binary, which appears spatially connected to the sharp extended feature. Conclusions.We detect orbital motion when compared to previous observations, and report a new outburst driven by the Herbig star. Our observations reveal the complex inner environment of Z\,CMa with unprecedented detail and contrast.Comment: Accepted for publication in A&A Letter

Are planetary nebulae derived from multiple evolutionary scenarios?

Our understanding of planetary nebulae has been significantly enhanced as a result of several recent large surveys (Parker et al., these proceedings). These new discoveries suggest that the `PN phenomenon' is in fact more heterogeneous than previously envisaged. Even after the careful elimination of mimics from Galactic PN catalogues, there remains a surprising diversity in the population of PNe and especially their central stars. Indeed, several evolutionary scenarios are implicated in the formation of objects presently catalogued as PNe. We provide a summary of these evolutionary pathways and give examples of each. Eventually, a full census of local PNe can be used to confront both stellar evolution theory and population synthesis models.Comment: 4 pages, 1 figure. To be published in Planetary Nebulae: an Eye to the Future, Proceedings of IAU Symposium 283, held in Puerto de la Cruz, Tenerife, Spain, July 25-29 201

Discrepancies in Determinations of the Ginzburg-Landau Parameter

Long-standing discrepancies within determinations of the Ginzburg-Landau parameter $\kappa$ from supercritical field measurements on superconducting microspheres are reexamined. The discrepancy in tin is shown to result from differing methods of analyses, whereas the discrepancy in indium is a consequence of significantly differing experimental results. The reanalyses however confirms the lower $\kappa$ determinations to within experimental uncertainties.Comment: submitted to Phys. Rev.

Dialectica Categories for the Lambek Calculus

We revisit the old work of de Paiva on the models of the Lambek Calculus in dialectica models making sure that the syntactic details that were sketchy on the first version got completed and verified. We extend the Lambek Calculus with a \kappa modality, inspired by Yetter's work, which makes the calculus commutative. Then we add the of-course modality !, as Girard did, to re-introduce weakening and contraction for all formulas and get back the full power of intuitionistic and classical logic. We also present the categorical semantics, proved sound and complete. Finally we show the traditional properties of type systems, like subject reduction, the Church-Rosser theorem and normalization for the calculi of extended modalities, which we did not have before

Primary beam effects of radio astronomy antennas -- II. Modelling the MeerKAT L-band beam

After a decade of design and construction, South Africa's SKA-MID precursor MeerKAT has begun its science operations. To make full use of the widefield capability of the array, it is imperative that we have an accurate model of the primary beam of its antennas. We have taken available L-band full-polarization 'astro-holographic' observations of three antennas and a generic electromagnetic simulation and created sparse representations of the beams using principal components and Zernike polynomials. The spectral behaviour of the spatial coefficients has been modelled using discrete cosine transform. We have provided the Zernike-based model over a diameter of 10 deg averaged over the beams of three antennas in an associated software tool (EIDOS) that can be useful in direction-dependent calibration and imaging. The model is more accurate for the diagonal elements of the beam Jones matrix and at lower frequencies. As we get more accurate beam measurements and simulations in the future, especially for the cross-polarization patterns, our pipeline can be used to create more accurate sparse representations of MeerKAT beams.Comment: 16 pages, 18 figures. This is a pre-copyedited, author-produced PDF of an article accepted for publication in MNRAS following peer review. The version of record [K. M. B. Asad et al., 2021] is available online at: https://doi.org/10.1093/mnras/stab10