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We propose a new family ${\sf Y}_{k,\ell,x,y,[z,w]}$ of modules over the enlarged periodic Temperley--Lieb algebra ${\sf{\cal E}PTL}_N(\beta)$. These modules are built from link states with two marked points, similarly to the modules ${\sf X}_{k,\ell,x,y,z}$ that we constructed in a previous paper. They however differ in the way that defects connect pairwise. We analyse the decomposition of ${\sf Y}_{k,\ell,x,y,[z,w]}$ over the irreducible standard modules ${\sf W}_{k,x}$ for generic values of the parameters $z$ and $w$, and use it to deduce the fusion rules for the fusion $\sf W \times W$ of standard modules. These turn out to be more symmetric than those obtained previously using the modules ${\sf X}_{k,\ell,x,y,z}$. From the work of Graham and Lehrer, it is known that, for $\beta=-q-q^{-1}$ where $q$ is not a root of unity, there exists a set of non-generic values of the twist $y$ for which the standard module ${\sf W}_{\ell,y}$ is indecomposable yet reducible with two composition factors: a radical submodule ${\sf R}_{\ell,y}$ and a quotient module ${\sf Q}_{\ell,y}$. Here, we construct the fusion products $\sf W\times R$, $\sf W\times Q$ and $\sf Q\times Q$, and analyse their decomposition over indecomposable modules. For the fusions involving the quotient modules ${\sf Q}$, we find very simple results reminiscent of $\mathfrak{sl}(2)$ fusion rules. This construction with modules ${\sf Y}_{k,\ell,x,y,[z,w]}$ is a good lattice regularization of the operator product expansion in the underlying logarithmic bulk conformal field theory. Indeed, it fits with the correspondence between standard modules and connectivity operators, and is useful for the calculation of their correlation functions. Remarkably, we show that the fusion rules $\sf W\times Q$ and $\sf Q\times Q$ are consistent with the known fusion rules of degenerate primary fields., Comment: 72 pages

We present a detailed long-term study of the single M6 III giant RZ~Ari to obtain direct and simultaneous measurements of the magnetic field, activity indicators, and radial velocity in order to infer the origin of its activity. We study its magnetic activity in the context of stellar evolution, and for this purpose, we also refined its evolutionary status and Li abundance. In general, for the M giants, little is known about the properties of the magnetic activity and its causes. RZ~Ari posses the strongest surface magnetic field of the known Zeeman-detected M giants and is bright enough to allow a deep study of its surface magnetic structure. The results are expected to shed light on the activity mechanism in these stars.

This work is part of the BinaMIcS project, the aim of which is to understand the interaction between binarity and magnetism in close binary systems. All the studied spectroscopic binaries targeted by the BinaMIcS project encompass hot massive and intermediate-mass stars on the main sequence, as well as cool stars over a wide range of evolutionary stages. The present paper focuses on the binary system FK Aqr, which is composed of two early M dwarfs. Both stars are already known to be magnetically active based on their light curves and detected flare activity. In addition, the two components have large convective envelopes with masses just above the fully convective limit, making the system an ideal target for studying effect of binarity on stellar dynamos. We use spectropolarimetric observations obtained with ESPaDOnS at CFHT in September 2014. Mean Stokes I and V line profiles are extracted using the least-squares deconvolution (LSD) method. The radial velocities of the two components are measured from the LSD Stokes I profiles and are combined with interferometric measurements in order to constrain the orbital parameters of the system. The longitudinal magnetic fields Bl and chromospheric activity indicators are measured from the LSD mean line profiles. The rotational modulation of the Stokes V profiles is used to reconstruct the surface magnetic field structures of both stars via the Zeeman Doppler imaging (ZDI) inversion technique. Maps of the surface magnetic field structures of both components of FK Aqr are presented for the first time. Our study shows that both components host similar large-scale magnetic fields of moderate intensity (Bmean ~ 0.25 kG); both are predominantly poloidal and feature a strong axisymmetric dipolar component. (abridged), Comment: 19 pages, 6 figures, 6 tables + appendices, accepted for publication in A&A, in press

We show that every $n$-vertex triangulation has a connected dominating set of size at most $10n/21$. Equivalently, every $n$ vertex triangulation has a spanning tree with at least $11n/21$ leaves. Prior to the current work, the best known bounds were $n/2$, which follows from work of Albertson, Berman, Hutchinson, and Thomassen (J. Graph Theory \textbf{14}(2):247--258). One immediate consequence of this result is an improved bound for the SEFENOMAP graph drawing problem of Angelini, Evans, Frati, and Gudmundsson (J. Graph Theory \textbf{82}(1):45--64). As a second application, we show that for every set $P$ of $\lceil 11n/21\rceil$ points in $\R^2$ every $n$-vertex planar graph has a one-bend non-crossing drawing in which some set of $11n/21$ vertices is drawn on the points of $P$. The main result extends to $n$-vertex triangulations of genus-$g$ surfaces, and implies that these have connected dominating sets of size at most $10n/21+O(\sqrt{gn})$., Comment: Linear-time algorithm; extension to genus-o(n) surfaces; corrections to proof of Lemma 9

Learning useful data representations without requiring labels is a cornerstone of modern deep learning. Self-supervised learning methods, particularly contrastive learning (CL), have proven successful by leveraging data augmentations to define positive pairs. This success has prompted a number of theoretical studies to better understand CL and investigate theoretical bounds for downstream linear probing tasks. This work is concerned with the temporal contrastive learning (TCL) setting where the sequential structure of the data is used instead to define positive pairs, which is more commonly used in RL and robotics contexts. In this paper, we adapt recent work on Spectral CL to formulate Spectral Temporal Contrastive Learning (STCL). We discuss a population loss based on a state graph derived from a time-homogeneous reversible Markov chain with uniform stationary distribution. The STCL loss enables to connect the linear probing performance to the spectral properties of the graph, and can be estimated by considering previously observed data sequences as an ensemble of MCMC chains., Comment: Accepted to Self-Supervised Learning - Theory and Practice, NeurIPS Workshop, 2023

We present Deep Search DocQA. This application enables information extraction from documents via a question-answering conversational assistant. The system integrates several technologies from different AI disciplines consisting of document conversion to machine-readable format (via computer vision), finding relevant data (via natural language processing), and formulating an eloquent response (via large language models). Users can explore over 10,000 Environmental, Social, and Governance (ESG) disclosure reports from over 2000 corporations. The Deep Search platform can be accessed at: https://ds4sd.github.io., Comment: Accepted at the Demonstration Track of the 38th Annual AAAI Conference on Artificial Intelligence (AAAI 24)

The goal of local certification is to locally convince the vertices of a graph $G$ that $G$ satisfies a given property. A prover assigns short certificates to the vertices of the graph, then the vertices are allowed to check their certificates and the certificates of their neighbors, and based only on this local view, they must decide whether $G$ satisfies the given property. If the graph indeed satisfies the property, all vertices must accept the instance, and otherwise at least one vertex must reject the instance (for any possible assignment of certificates). The goal is to minimize the size of the certificates. In this paper we study the local certification of geometric and topological graph classes. While it is known that in $n$-vertex graphs, planarity can be certified locally with certificates of size $O(\log n)$, we show that several closely related graph classes require certificates of size $\Omega(n)$. This includes penny graphs, unit-distance graphs, (induced) subgraphs of the square grid, 1-planar graphs, and unit-square graphs. These bounds are tight up to a constant factor and give the first known examples of hereditary (and even monotone) graph classes for which the certificates must have linear size. For unit-disk graphs we obtain a lower bound of $\Omega(n^{1-\delta})$ for any $\delta>0$ on the size of the certificates, and an upper bound of $O(n \log n)$. The lower bounds are obtained by proving rigidity properties of the considered graphs, which might be of independent interest., Comment: 36 pages, 16 figures; v4: version revised according to the reviewers comments

Two-dimensional transition metal dichalcogenides (TMDs) for advanced logic transistor technologies are deposited by various modifications of the chemical vapor deposition (CVD) method using a wide variety of precursors. Being a major electrical performance limiter, the TMD crystal grain size strongly differs between the various CVD precursor chemistries from nano- to millimeter-sized crystals. However, it remains unclear how the CVD precursor chemistry affects the nucleation density and resulting TMD crystal grain size. This work postulates guiding principles to design a CVD process for highly crystalline TMD deposition using a quantitative analytical model benchmarked against literature. The TMD nucleation density reduces favorably under low supersaturation conditions, where the metal precursor sorption on the starting surface is reversible and the corresponding metal precursor desorption rate exceeds the overall deposition rate. Such reversible precursor adsorption guarantees efficient long-range gas-phase lateral diffusion of precursor species in addition to short-range surface diffusion, which vitally increases crystal grain size. As such, the proposed model explains the large spread in experimentally observed TMD nucleation densities and crystal grain sizes for state-of-the-art CVD chemistries. Ultimately, it empowers the reader to interpret and modulate precursor adsorption and diffusion reactions through designing CVD precursor chemistries compatible with temperature sensitive application schemes.

Young solar-type stars frequently produce superflares, serving as a unique window into the young Sun-Earth environments. Large solar flares are closely linked to coronal mass ejections (CMEs) associated with filament/prominence eruptions, but its observational evidence for stellar superflares remains scarce. Here, we present a 12-day multi-wavelength campaign observation of young solar-type star EK Draconis (G1.5V, 50-120 Myr age) utilizing TESS, NICER, and Seimei telescope. The star has previously exhibited blueshifted H$\alpha$ absorptions as evidence for a filament eruption associated with a superflare. Our simultaneous optical and X-ray observations identified three superflares of $1.5\times10^{33}$ -- $1.2\times10^{34}$ erg. We report the first discovery of two prominence eruptions on a solar-type star, observed as blueshifted H$\alpha$ emissions at speed of 690 and 430 km s$^{-1}$ and masses of $1.1\times10^{19}$ and $3.2\times10^{17}$ g, respectively. The faster, massive event shows a candidate of post-flare X-ray dimming with the amplitude of up to $\sim$10 \%. Several observational aspects consistently point to the occurrence of a fast CME associated with this event. The comparative analysis of the estimated length scales of flare loops, prominences, possible dimming region, and starspots provides the overall picture of the eruptive phenomena. Furthermore, the energy partition of the observed superflares in the optical and X-ray bands is consistent with flares from the Sun, M-dwarfs, and close binaries, yielding the unified empirical relations. These discoveries provide profound implications of impact of these eruptive events on the early Venus, Earth and Mars and young exoplanets., Comment: 48 pages, 29 figures, 11 tables. Accepted for publication in The Astrophysical Journal

In this paper, we study six slowly rotating mid-to-late M~dwarfs (rotation period $P_{\mathrm{rot}} \approx 40-190\,\mathrm{dy}$) by analysing spectropolarimetric data collected with SPIRou at the Canada-France-Hawaii Telescope as part of the SPIRou Legacy Survey from 2019 to 2022. From $\approx$100--200 Least-Squares-Deconvolved (LSD) profiles of circularly polarised spectra of each star, we confirm the stellar rotation periods of the six M~dwarfs and explore their large-scale magnetic field topology and its evolution with time using both the method based on Principal Component Analysis (PCA) proposed recently and Zeeman-Doppler Imaging. All M~dwarfs show large-scale field variations on the time-scale of their rotation periods, directly seen from the circularly polarised LSD profiles using the PCA method. We detect a magnetic polarity reversal for the fully-convective M~dwarf GJ~1151, and a possible inversion in progress for Gl~905. The four fully-convective M~dwarfs of our small sample (Gl~905, GJ~1289, GJ~1151, GJ~1286) show a larger amount of temporal variations (mainly in field strength and axisymmetry) than the two partly-convective ones (Gl~617B, Gl~408). Surprisingly, the six M~dwarfs show large-scale field strengths in the range between 20 to 200\,G similar to those of M~dwarfs rotating significantly faster. Our findings imply that the large-scale fields of very slowly rotating M~dwarfs are likely generated through dynamo processes operating in a different regime than those of the faster rotators that have been magnetically characterized so far., Comment: 16 pages, 35 figures, accepted for publication in MNRAS

Mapping forest resources and carbon is important for improving forest management and meeting the objectives of storing carbon and preserving the environment. Spaceborne remote sensing approaches have considerable potential to support forest height monitoring by providing repeated observations at high spatial resolution over large areas. This study uses a machine learning approach that was previously developed to produce local maps of forest parameters (basal area, height, diameter, etc.). The aim of this paper is to present the extension of the approach to much larger scales such as the French national coverage. We used the GEDI Lidar mission as reference height data, and the satellite images from Sentinel-1, Sentinel-2 and ALOS-2 PALSA-2 to estimate forest height and produce a map of France for the year 2020. The height map is then derived into volume and aboveground biomass (AGB) using allometric equations. The validation of the height map with local maps from ALS data shows an accuracy close to the state of the art, with a mean absolute error (MAE) of 4.3 m. Validation on inventory plots representative of French forests shows an MAE of 3.7 m for the height. Estimates are slightly better for coniferous than for broadleaved forests. Volume and AGB maps derived from height shows MAEs of 75 tons/ha and 93 m${}^3$/ha respectively. The results aggregated by sylvo-ecoregion and forest types (owner and species) are further improved, with MAEs of 23 tons/ha and 30 m${}^3$/ha. The precision of these maps allows to monitor forests locally, as well as helping to analyze forest resources and carbon on a territorial scale or on specific types of forests by combining the maps with geolocated information (administrative area, species, type of owner, protected areas, environmental conditions, etc.). Height, volume and AGB maps produced in this study are made freely available.

HTTP adaptive streaming (HAS) has emerged as a widely adopted approach for over-the-top (OTT) video streaming services, due to its ability to deliver a seamless streaming experience. A key component of HAS is the bitrate ladder, which provides the encoding parameters (e.g., bitrate-resolution pairs) to encode the source video. The representations in the bitrate ladder allow the client's player to dynamically adjust the quality of the video stream based on network conditions by selecting the most appropriate representation from the bitrate ladder. The most straightforward and lowest complexity approach involves using a fixed bitrate ladder for all videos, consisting of pre-determined bitrate-resolution pairs known as one-size-fits-all. Conversely, the most reliable technique relies on intensively encoding all resolutions over a wide range of bitrates to build the convex hull, thereby optimizing the bitrate ladder for each specific video. Several techniques have been proposed to predict content-based ladders without performing a costly exhaustive search encoding. This paper provides a comprehensive review of various methods, including both conventional and learning-based approaches. Furthermore, we conduct a benchmark study focusing exclusively on various learning-based approaches for predicting content-optimized bitrate ladders across multiple codec settings. The considered methods are evaluated on our proposed large-scale dataset, which includes 300 UHD video shots encoded with software and hardware encoders using three state-of-the-art encoders, including AVC/H.264, HEVC/H.265, and VVC/H.266, at various bitrate points. Our analysis provides baseline methods and insights, which will be valuable for future research in the field of bitrate ladder prediction. The source code of the proposed benchmark and the dataset will be made publicly available upon acceptance of the paper.

Molecular bands of metal oxides and hydrides dominate the optical and near-infrared spectra of M dwarfs. High-resolution spectra of these bands have immense potential for determining many properties of these stars, such as effective temperature, surface gravity, elemental abundances, radial velocity, or surface magnetic fields. Techniques are being developed to do this but remain limited by the current availability and accuracy of molecular data and spectral line lists. This paper reports metal monohydride line lists selected from near-infrared and visible laboratory data to show that specific bands in several electronic transitions can be used to identify CrH, NiH, and FeH in M stars and to determine radial velocities from Doppler shifts. The possibility of measuring magnetic fields is also investigated for FeH and CrH. We used systematic cross-correlation analysis between unpolarised spectra from a selection of M stars and state-specific laboratory line lists. These lists were generated from a combination of existing data and new laboratory laser-excitation spectra recorded at Doppler-limited resolution, in zero-field conditions or in magnetic fields up to 0.6 tesla. Results. We show that transitions at visible wavelengths in FeH and NiH, usually neglected in the analysis of the spectra of M-type stars, do in fact contribute to the spectra, and we demonstrate the influence of magnetic sensitivity on selected transitions in CrH and FeH. Although the new line lists focus on transitions recorded at temperatures significantly lower than those of stellar objects, they remain pertinent because they cover some band-head regions of high spectral density. FeH bands can provide a useful supplement to atomic lines for the analysis of high-resolution optical and near-infrared spectra of M dwarfs. We demonstrate the influence of a magnetic field on CrH signatures around 862 nm., Comment: Accepted for publication in A&A, 10 pages, 12 figures, 2 tables, additional material will be made available at CDS/Vizier