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In this paper we show that the random degree constrained process (a time-evolving random graph model with degree constraints) has a local weak limit, provided that the underlying host graphs are high degree almost regular. We, moreover, identify the limit object as a multi-type branching process, by combining coupling arguments with the analysis of a certain recursive tree process. Using a spectral characterization, we also give an asymptotic expansion of the critical time when the giant component emerges in the so-called random $d$-process, resolving a problem of Warnke and Wormald for large $d$., Comment: 53 pages, 3 figures

Voice communication between air traffic controllers (ATCos) and pilots is critical for ensuring safe and efficient air traffic control (ATC). This task requires high levels of awareness from ATCos and can be tedious and error-prone. Recent attempts have been made to integrate artificial intelligence (AI) into ATC in order to reduce the workload of ATCos. However, the development of data-driven AI systems for ATC demands large-scale annotated datasets, which are currently lacking in the field. This paper explores the lessons learned from the ATCO2 project, a project that aimed to develop a unique platform to collect and preprocess large amounts of ATC data from airspace in real time. Audio and surveillance data were collected from publicly accessible radio frequency channels with VHF receivers owned by a community of volunteers and later uploaded to Opensky Network servers, which can be considered an "unlimited source" of data. In addition, this paper reviews previous work from ATCO2 partners, including (i) robust automatic speech recognition, (ii) natural language processing, (iii) English language identification of ATC communications, and (iv) the integration of surveillance data such as ADS-B. We believe that the pipeline developed during the ATCO2 project, along with the open-sourcing of its data, will encourage research in the ATC field. A sample of the ATCO2 corpus is available on the following website: https://www.atco2.org/data, while the full corpus can be purchased through ELDA at http://catalog.elra.info/en-us/repository/browse/ELRA-S0484. We demonstrated that ATCO2 is an appropriate dataset to develop ASR engines when little or near to no ATC in-domain data is available. For instance, with the CNN-TDNNf kaldi model, we reached the performance of as low as 17.9% and 24.9% WER on public ATC datasets which is 6.6/7.6% better than "out-of-domain" but supervised CNN-TDNNf model., Comment: Manuscript under review

Dynamic Mode Decomposition (DMD) describes complex dynamic processes through a hierarchy of simpler coherent features. DMD is regularly used to understand the fundamental characteristics of turbulence and is closely related to Koopman operators. However, verifying the decomposition, equivalently the computed spectral features of Koopman operators, remains a major challenge due to the infinite-dimensional nature of Koopman operators. Challenges include spurious (unphysical) modes, and dealing with continuous spectra, both of which occur regularly in turbulent flows. Residual Dynamic Mode Decomposition (ResDMD), introduced by (Colbrook & Townsend 2021), overcomes some of these challenges through the data-driven computation of residuals associated with the full infinite-dimensional Koopman operator. ResDMD computes spectra and pseudospectra of general Koopman operators with error control, and computes smoothed approximations of spectral measures (including continuous spectra) with explicit high-order convergence theorems. ResDMD thus provides robust and verified Koopmanism. We implement ResDMD and demonstrate its application in a variety of fluid dynamic situations, at varying Reynolds numbers, arising from both numerical and experimental data. Examples include: vortex shedding behind a cylinder; hot-wire data acquired in a turbulent boundary layer; particle image velocimetry data focusing on a wall-jet flow; and acoustic pressure signals of laser-induced plasma. We present some advantages of ResDMD, namely, the ability to verifiably resolve non-linear, transient modes, and spectral calculation with reduced broadening effects. We also discuss how a new modal ordering based on residuals enables greater accuracy with a smaller dictionary than the traditional modulus ordering. This paves the way for greater dynamic compression of large datasets without sacrificing accuracy.

Entangled photon pairs are predicted to linearize and increase the efficiency of two-photon absorption, allowing continuous wave laser diodes to drive ultrafast time-resolved spectroscopy and nonlinear processes. Despite a range of theoretical studies and experimental measurements, inconsistencies persist about the value of the entanglement enhanced interaction cross section. A spectrometer is constructed that can temporally and spectrally characterize the entangled photon state before, during, and after any potential two-photon excitation event. For the molecule Rhodamine 6G, which has a virtual state pathway, any entangled two-photon interaction is found to be equal to or lower than classical, single photon scattering events. This result can account for the discrepancies between the wide variety of entangled two-photon absorption cross sections reported from different measurement techniques. The reported instrumentation can unambiguously separate classical and entangled effects and therefore is of importance for the growing field of nonlinear and multiphoton entangled spectroscopy.

Ariel, the Atmospheric Remote-sensing Infrared Exoplanet Large-survey, was adopted as the fourth medium-class mission in ESA's Cosmic Vision programme to be launched in 2029. During its 4-year mission, Ariel will study what exoplanets are made of, how they formed and how they evolve, by surveying a diverse sample of about 1000 extrasolar planets, simultaneously in visible and infrared wavelengths. It is the first mission dedicated to measuring the chemical composition and thermal structures of hundreds of transiting exoplanets, enabling planetary science far beyond the boundaries of the Solar System. The payload consists of an off-axis Cassegrain telescope (primary mirror 1100 mm x 730 mm ellipse) and two separate instruments (FGS and AIRS) covering simultaneously 0.5-7.8 micron spectral range. The satellite is best placed into an L2 orbit to maximise the thermal stability and the field of regard. The payload module is passively cooled via a series of V-Groove radiators; the detectors for the AIRS are the only items that require active cooling via an active Ne JT cooler. The Ariel payload is developed by a consortium of more than 50 institutes from 16 ESA countries, which include the UK, France, Italy, Belgium, Poland, Spain, Austria, Denmark, Ireland, Portugal, Czech Republic, Hungary, the Netherlands, Sweden, Norway, Estonia, and a NASA contribution., Comment: Ariel Definition Study Report, 147 pages. Reviewed by ESA Science Advisory Structure in November 2020. Original document available at: https://www.cosmos.esa.int/documents/1783156/3267291/Ariel_RedBook_Nov2020.pdf/

Entangled photon spectroscopy is a nascent field that has important implications for measurement and imaging across chemical, biology, and materials fields. Entangled photon spectroscopy potentially offers improved spatial and temporal-frequency resolutions, increased cross sections for multiphoton and nonlinear measurements, and new abilities in inducing or measuring quantum correlations. A critical step in enabling entangled photon spectroscopies is the creation of high-flux entangled sources that can use conventional detectors, as well as provide redundancy for the losses in realistic samples. Here, we report a periodically poled, chirped, lithium tantalate platform that generates entangled photon pairs with a $10^{-7}$ efficiency. For a near watt level diode laser, this results in a near $\mu$W-level flux. The single photon per mode limit that is necessary to maintain non-classical photon behavior is still satisfied by distributing this power over up to an octave-spanning bandwidth. The spectral-temporal photon correlations are observed via a Michelson-type interferometer that measures the broadband Hong-Ou-Mandel two-photon interference. A coherence time of 245 fs for a 10 nm bandwidth in the collinear case and a 62 fs for a 125 nm bandwidth in the non-collinear case is measured using a CW pump laser, and, essentially, collecting the full photon cone. We outline in detail the numerical methods used for designing and tailoring the entangled photons source, such as changing center wavelength or bandwidth, with the ultimate aim of increasing the availability of high-flux UV-Vis entangled photon sources in the optical spectroscopy community.

We launched a community platform for collecting the ATC speech world-wide in the ATCO2 project. Filtering out unseen non-English speech is one of the main components in the data processing pipeline. The proposed English Language Detection (ELD) system is based on the embeddings from Bayesian subspace multinomial model. It is trained on the word confusion network from an ASR system. It is robust, easy to train, and light weighted. We achieved 0.0439 equal-error-rate (EER), a 50% relative reduction as compared to the state-of-the-art acoustic ELD system based on x-vectors, in the in-domain scenario. Further, we achieved an EER of 0.1352, a 33% relative reduction as compared to the acoustic ELD, in the unseen language (out-of-domain) condition. We plan to publish the evaluation dataset from the ATCO2 project.

The Marked Binary Branching Tree (MBBT) is the family tree of a rate one binary branching process, on which points have been generated according to a rate one Poisson point process, with i.i.d. uniformly distributed activation times assigned to the points. In frozen percolation on the MBBT, initially, all points are closed, but as time progresses points can become either frozen or open. Points become open at their activation times provided they have not become frozen before. Open points connect the parts of the tree below and above it and one says that a point percolates if the tree above it is infinite. We consider a version of frozen percolation on the MBBT in which at times of the form $\theta^n$, all points that percolate are frozen. The limiting model for $\theta \to 1$, in which points freeze as soon as they percolate, has been studied before by R\'ath, Swart, and Terpai. We extend their results by showing that there exists a $0<\theta^\ast<1$ such that the model is endogenous for $\theta \leq\theta^\ast$ but not for $\theta>\theta^\ast$. This means that for $\theta \leq \theta^\ast$, frozen percolation is a.s. determined by the MBBT but for $\theta>\theta^\ast$ one needs additional randomness to describe it., Comment: 44 pages, 2 figures, addressed comments of referees, to appear in EJP

We study public goods games played on networks with possibly non-reciprocal relationships between players. Examples for this type of interactions include one-sided relationships, mutual but unequal relationships, and parasitism. It is well known that many simple learning processes converge to a Nash equilibrium if interactions are reciprocal, but this is not true in general for directed networks. However, by a simple tool of rescaling the strategy space, we generalize the convergence result for a class of directed networks and show that it is characterized by transitive weight matrices. Additionally, we show convergence in a second class of networks; those rescalable into networks with weak externalities. We characterize the latter class by the spectral properties of the absolute value of the network's weight matrix and show that it includes all directed acyclic networks., Comment: 44 pages

We consider a finitely generated group acting minimally on a compact space by homeomorphsims, and assume that the Schreier graph of at least one orbit is quasi-isometric to a line. We show that the topological full group of such an action is amenable., Comment: 15 pages

The CHaracterising ExOPlanet Satellite (CHEOPS) was selected in 2012, as the first small mission in the ESA Science Programme and successfully launched in December 2019. CHEOPS is a partnership between ESA and Switzerland with important contributions by ten additional ESA Member States. CHEOPS is the first mission dedicated to search for transits of exoplanets using ultrahigh precision photometry on bright stars already known to host planets. As a follow-up mission, CHEOPS is mainly dedicated to improving, whenever possible, existing radii measurements or provide first accurate measurements for a subset of those planets for which the mass has already been estimated from ground-based spectroscopic surveys and to following phase curves. CHEOPS will provide prime targets for future spectroscopic atmospheric characterisation. Requirements on the photometric precision and stability have been derived for stars with magnitudes ranging from 6 to 12 in the V band. In particular, CHEOPS shall be able to detect Earth-size planets transiting G5 dwarf stars in the magnitude range between 6 and 9 by achieving a photometric precision of 20 ppm in 6 hours of integration. For K stars in the magnitude range between 9 and 12, CHEOPS shall be able to detect transiting Neptune-size planets achieving a photometric precision of 85 ppm in 3 hours of integration. This is achieved by using a single, frame-transfer, back-illuminated CCD detector at the focal plane assembly of a 33.5 cm diameter telescope. The 280 kg spacecraft has a pointing accuracy of about 1 arcsec rms and orbits on a sun-synchronous dusk-dawn orbit at 700 km altitude. The nominal mission lifetime is 3.5 years. During this period, 20% of the observing time is available to the community through a yearly call and a discretionary time programme managed by ESA., Comment: Submitted to Experimental Astronomy

A theorem of Wiegerinck says that the Bergman space over any domain in $\mathbb C$ is either trivial or infinite dimensional. We generalize this theorem in the following form. Let E be a hermitian, holomorphic vector bundle over $\mathbb P^1$, the later equipped with a volume form and $D$ an arbitrary domain in $\mathbb P^1$. Then the space of holomorphic L2 sections of $E$ over $D$ is either equal to $H^0(M,E)$ or it has infinite dimension., Comment: financial support acknowledged

Entangled photons exhibit non-classical light-matter interactions that create new opportunities in materials and molecular science. For example, in entangled two-photon absorption, the intensity-dependence scales linearly as if only one photon was present. The entangled two-photon absorption cross section approaches but does not match the one-photon absorption cross section. The entangled two photon cross section also does not follow classical two photon molecular design motifs. Questions such as these seed the rich but nascent field of entangled light-matter interactions. In this perspective, we use the experimental developments in entangled photon spectroscopy to outline the current status of the field. Now that the fundamental tools are outlined, it is time to start the exploration of how materials, molecules, and devices can control or utilize interactions with entangled photons., Comment: 11 pages, 6 figures. Submitted to Journal of Materials Chemistry C; v2 includes a new section on opportunities in materials science

Metal-oxide-semiconductor junctions are central to most electronic and optoelectronic devices. Here, the element-specificity of broadband extreme ultraviolet (XUV) ultrafast pulses is used to measure the charge transport and recombination kinetics in each layer of a Ni-TiO2-Si junction. After photoexcitation of silicon, holes are inferred to transport from Si to Ni ballistically in ~100 fs, resulting in spectral shifts in the Ni M2,3 XUV edge that are characteristic of holes and the absence of holes initially in TiO2. Meanwhile, the electrons are observed to remain on Si. After picoseconds, the transient hole population on Ni is observed to back-diffuse through the TiO2, shifting the Ti spectrum to higher oxidation state, followed by electron-hole recombination at the Si-TiO2 interface and in the Si bulk. Electrical properties, such as the hole diffusion constant in TiO2 and the initial hole mobility in Si, are fit from these transient spectra and match well with values reported previously.