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We study accelerated Krasnosel'ki\u{\i}-Mann-type methods with preconditioners in both continuous and discrete time. From a continuous time model, we derive a generalized fast Krasnosel'ki\u{\i}-Mann method, providing a new yet simple proof of convergence that allows for unprecedented flexibility in parameter tuning. Our analysis unifies inertial and anchoring acceleration mechanisms and offers a broad range of parameter choices, which prove beneficial in practice. Additionally, we extend our analysis to the case where preconditioners are allowed to be degenerate, unifying the treatment of various splitting methods and establishing the weak convergence of shadow sequences.

In this paper we introduce, in a Hilbert space setting, a second order dynamical system with asymptotically vanishing damping and vanishing Tikhonov regularization that approaches a multiobjective optimization problem with convex and differentiable components of the objective function. Trajectory solutions are shown to exist in finite dimensions. We prove fast convergence of the function values, quantified in terms of a merit function. Based on the regime considered, we establish both weak and, in some cases, strong convergence of trajectory solutions toward a weak Pareto optimal solution. To achieve this, we apply Tikhonov regularization individually to each component of the objective function. This work extends results from single objective convex optimization into the multiobjective setting., Comment: 37 pages, 2 figures

Tree species classification plays an important role in nature conservation, forest inventories, forest management, and the protection of endangered species. Over the past four decades, remote sensing technologies have been extensively utilized for tree species classification, with Synthetic Aperture Radar (SAR) emerging as a key technique. In this study, we employed TomoSense, a 3D tomographic dataset, which utilizes a stack of single-look complex (SLC) images, a byproduct of SAR, captured at different incidence angles to generate a three-dimensional representation of the terrain. Our research focuses on evaluating multiple tabular machine-learning models using the height information derived from the tomographic image intensities to classify eight distinct tree species. The SLC data and tomographic imagery were analyzed across different polarimetric configurations and geosplit configurations. We investigated the impact of these variations on classification accuracy, comparing the performance of various tabular machine-learning models and optimizing them using Bayesian optimization. Additionally, we incorporated a proxy for actual tree height using point cloud data from Light Detection and Ranging (LiDAR) to provide height statistics associated with the model's predictions. This comparison offers insights into the reliability of tomographic data in predicting tree species classification based on height.

By analyzing the spectral energy distributions (SEDs) of resolved stars in nearby galaxies, we can constrain their stellar properties and line-of-sight dust extinction. From the Scylla survey, we obtain ultraviolet to near-infrared photometry from Wide Field Camera 3 onboard the {\it Hubble Space Telescope} for more than 1.5 million stars in the SMC and LMC. We use the Bayesian Extinction and Stellar Tool (BEAST) to analyze the multi-band SEDs of these sources and characterize their initial masses, ages, metallicities, distances, and line-of-sight extinction properties (e.g.~$A_V$, $R_V$). We apply quality cuts and perform validation simulations to construct a catalog of over 550,000 stars with high-reliability SED fits, which we use to analyze the stellar content and extinction properties of the SMC and LMC. We detect stars with masses as low as 0.6 $M_{\odot}$. Observed stellar age distributions show a jump in stars around 6 Gyrs ago, which is in agreement with other star-formation histories. Extinctions ($A_V$) in both galaxies follow a log-normal distribution. We compare $A_V$ with ancillary gas and dust tracers like $HI$, $H_\alpha$, and far infrared (FIR) dust emission and find positive correlations on a field-by-field basis. We convert observed $A_V$ to predicted dust surface densities using the Draine et. al. (2014) model and find $A_V$-based dust surface densities are a factor of $\sim$2.5 lower than observed FIR-based dust surface densities, a correction factor similar to other studies., Comment: Submitted to ApJ, 31 pages

In this paper, we introduce a novel Extra-Gradient method with anchor term governed by general parameters. Our method is derived from an explicit discretization of a Tikhonov-regularized monotone flow in Hilbert space, which provides a theoretical foundation for analyzing its convergence properties. We establish strong convergence to specific points within the solution set, as well as convergence rates expressed in terms of the regularization parameters. Notably, our approach recovers the fast residual decay rate $O(k^{-1})$ for standard parameter choices. Numerical experiments highlight the competitiveness of the method and demonstrate how its flexible design enhances practical performance.

The proximity of the Large and Small Magellanic Clouds (LMC and SMC) provides the opportunity to study the impact of dwarf-dwarf interactions on their mass assembly with a unique level of detail. To this end, we analyze two-filter broadband imaging of 83 Hubble Space Telescope (HST) pointings covering 0.203 deg$^2$ towards the SMC, extending out to $\sim$3.5 kpc in projection from its optical center. Lifetime star formation histories (SFHs) fit to each pointing independently reveal an outside-in age gradient such that fields in the SMC outskirts are older on average. We measure radial gradients of the lookback time to form 90%, 75% and 50% of the cumulative stellar mass for the first time, finding $\delta$($\tau_{90}$, $\tau_{75}$, $\tau_{50}$)/$\delta$R = (0.61$^{+0.08}_{-0.07}$, 0.65$^{+0.09}_{-0.08}$, 0.82$^{+0.12}_{-0.16}$) Gyr/kpc assuming PARSEC evolutionary models and a commonly used elliptical geometry of the SMC, although our results are robust to these assumptions. The wing of the SMC deviates from this trend, forming 25\% of its cumulative mass over the most recent 3 Gyr due to a best-fit star formation rate that remains approximately constant. Our results are consistent with chemodynamical evidence of a tidally stripped SMC component in the foreground, and imply contributions to the observed SFH from multiple previous LMC-SMC interactions. We also compare our SMC SFH with results from a companion study of the LMC, finding that while the two galaxies present different internal, spatially resolved SFH trends, both the LMC and SMC have similar near-constant lifetime SFHs when viewed globally., Comment: ApJ in press. 40 pages, 18 figures, 5 tables including Appendices

Scylla is a deep Hubble Space Telescope survey of the stellar populations, interstellar medium and star formation in the LMC and SMC. As a pure-parallel complement to the Ultraviolet Legacy Library of Young Stars as Essential Standards (ULLYSES) survey, Scylla obtained 342 orbits of ultraviolet (UV) through near-infrared (IR) imaging of the LMC and SMC with Wide Field Camera 3. In this paper, we describe the science objectives, observing strategy, data reduction procedure, and initial results from our photometric analysis of 96 observed fields. Although our observations were constrained by ULYSSES primary exposures, we imaged all fields in at least two filters (F475W and F814W), and 64% of fields in at least three and as many as seven WFC3 filters spanning the UV to IR. Overall, we reach average 50% completeness of $m_{\rm F225W}=26.0$, $m_{\rm F275W}=26.2$, $m_{\rm F336W}=26.9$, $m_{\rm F475W}=27.8$, $m_{\rm F814W}=25.5$, $m_{\rm F110W}=24.7$, and $m_{\rm F160W}=24.0$ Vega magnitudes in our photometric catalogs, which is faintward of the ancient main sequence turnoff in all filters. The primary science goals of Scylla include characterizing the structure and properties of dust in the MCs, as well as their spatially-resolved star formation and chemical enrichment histories. Our images and photometric catalogs, which represent the widest-area coverage of MCs with HST photometry to date, are available as a high-level science product at the Barbara A. Mikulski Archive for Space Telescopes., Comment: 25 pages, 16 figures, 8 tables. Accepted for publication in ApJS

We present resolved $3.6-250~\mu$m dust spectral energy distribution (SED) fitting for $\sim 800$ nearby galaxies. We measure the distribution of radiation field intensities heating the dust, the dust mass surface density ($\Sigma_{\rm d}$), and the fraction of dust in the form of polycyclic aromatic hydrocarbons (PAHs; $q_{\rm PAH}$). We find that the average interstellar radiation field ($\overline{U}$) is correlated both with stellar mass surface density ($\Sigma_{\star}$) and star formation rate surface density ($\Sigma_{\rm SFR}$), while more intense radiation fields are only correlated with $\Sigma_{\rm SFR}$. We show that $q_{\rm PAH}$ is a steeply decreasing function of $\Sigma_{\rm SFR}$, likely reflecting PAH destruction in H II regions. Galaxy integrated $q_{\rm PAH}$ is strongly, negatively correlated with specific star formation rate (sSFR) and offset from the star-forming ``main sequence'' ($\Delta$MS), suggesting that both metallicity and star formation intensity play a role in setting the global $q_{\rm PAH}$. We also find a nearly constant M$_{\rm d}$/M$_\star$ ratio for galaxies on the main sequence, with a lower ratio for more quiescent galaxies, likely due to their lower gas fractions. From these results, we construct prescriptions to estimate the radiation field distribution in both integrated and resolved galaxies. We test these prescriptions by comparing our predicted $\overline{U}$ to results of SED fitting for stacked "main sequence" galaxies at $0

Accurately estimating forest biomass is crucial for global carbon cycle modelling and climate change mitigation. Tree height, a key factor in biomass calculations, can be measured using Synthetic Aperture Radar (SAR) technology. This study applies machine learning to extract forest height data from two SAR products: Single Look Complex (SLC) images and tomographic cubes, in preparation for the ESA Biomass Satellite mission. We use the TomoSense dataset, containing SAR and LiDAR data from Germany's Eifel National Park, to develop and evaluate height estimation models. Our approach includes classical methods, deep learning with a 3D U-Net, and Bayesian-optimized techniques. By testing various SAR frequencies and polarimetries, we establish a baseline for future height and biomass modelling. Best-performing models predict forest height to be within 2.82m mean absolute error for canopies around 30m, advancing our ability to measure global carbon stocks and support climate action.

In this work, we approach the problem of finding the zeros of a continuous and monotone operator through a second-order dynamical system with a damping term of the form $1/t^{r}$, where $r\in [0, 1]$. The system features the time derivative of the operator evaluated along the trajectory, which is a Hessian-driven type damping term when the governing operator comes from a potential. Also entering the system is a time rescaling parameter $\beta(t)$ which satisfies a certain growth condition. We derive $o\left(\frac{1}{t^{2r}\beta(t)}\right)$ convergence rates for the norm of the operator evaluated along the generated trajectories as well as for a gap function which serves as a measure of optimality for the associated variational inequality. The parameter $r$ enters the growth condition for $\beta(t)$: when $r < 1$, the damping $1/t^{r}$ approaches zero at a slower speed than Nesterov's $1/t$ damping; in this case, we are allowed to choose $\beta(t)$ to be an exponential function, thus having linear convergence rates for the involved quantities. We also show weak convergence of the trajectories towards zeros of the governing operator. Through a particular choice for the operator, we establish a connection with the problem of minimizing a smooth and convex function with linear constraints. The convergence rates we derived in the operator case are inherited by the objective function evaluated at the trajectories and for the feasibility gap. We also prove weak convergence of the trajectories towards primal-dual solutions of the problem. A discretization of the dynamical system yields an implicit algorithm that exhibits analogous convergence properties to its continuous counterpart. We complement our theoretical findings with two numerical experiments., Comment: 51 pages

Submillimeter and millimeter wavelengths provide a unique view of the Universe, from the gas and dust that fills and surrounds galaxies to the chromosphere of our own Sun. Current single-dish facilities have presented a tantalising view of the brightest (sub-)mm sources, and interferometers have provided the exquisite resolution necessary to analyse the details in small fields, but there are still many open questions that cannot be answered with current facilities. In this report we summarise the science that is guiding the design of the Atacama Large Aperture Submillimeter Telescope (AtLAST). We demonstrate how tranformational advances in topics including star formation in high redshift galaxies, the diffuse circumgalactic medium, Galactic ecology, cometary compositions and solar flares motivate the need for a 50m, single-dish telescope with a 1-2 degree field of view and a new generation of highly multiplexed continuum and spectral cameras. AtLAST will have the resolution to drastically lower the confusion limit compared to current single-dish facilities, whilst also being able to rapidly map large areas of the sky and detect extended, diffuse structures. Its high sensitivity and large field of view will open up the field of submillimeter transient science by increasing the probability of serendipitous detections. Finally, the science cases listed here motivate the need for a highly flexible operations model capable of short observations of individual targets, large surveys, monitoring programmes, target of opportunity observations and coordinated observations with other observatories. AtLAST aims to be a sustainable, upgradeable, multipurpose facility that will deliver orders of magnitude increases in sensitivity and mapping speeds over current and planned submillimeter observatories., Comment: 47 pages, 12 figures. For further details on AtLAST see https://atlast.uio.no

In this note, we demonstrate that an incorrect statement has been propagated in multiple papers, stemming from the substitution of ``lim'' with ``limsup'' for a sequence in Lemma 1.3 of the paper [J. Schu: Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bull.\ Austral.\ Math.\ Soc.\ 43 (1991), 153--159]. This occurred over a span of more than 20 years, with the earliest paper we identified using this incorrect statement dating back to 2002., Comment: The paper has now 19 pages and contains 211 references. Having in view that Prof. R.I. Bot made some important remarks on the previous version of the paper, I (C. Zalinescu) invited him to become co-author of this work and I am very satisfied that he accepted

In the framework of real Hilbert spaces, we investigate first-order dynamical systems governed by monotone and continuous operators. We demonstrate that when the monotone operator flow is augmented with a Tikhonov regularization term, the resulting trajectory converges strongly to the element of the set of zeros with minimal norm. In addition, rates of convergence in norm for the trajectory's velocity and the operator along the trajectory can be derived in terms of the regularization function. In some particular cases, these rates of convergence can outperform the ones of the coercive operator flows and can be as fast as $O(\frac{1}{t})$ as $t \rightarrow +\infty$. In this way, we emphasize a surprising acceleration feature of the Tikhonov regularization. Additionally, we explore these properties for monotone operator flows that incorporate time rescaling and an anchor point and show that they are closely linked to second-order dynamics with a vanishing damping term. The convergence and convergence rate results we achieve for these systems complement recent findings for the Fast Optimistic Gradient Descent Ascent (OGDA) dynamics. When the monotone operator is defined as the identity minus a nonexpansive operator, the monotone equations transform into a fixed point problem. In such cases, explicitly discretizing the system with Tikhonov regularization, enhanced by an anchor point, leads to the Halpern fixed point iteration. We identify two regimes for the regularization sequence which ensure that the generated sequence of iterates converges strongly to the fixed point nearest to the anchor point. Furthermore, we establish a general theoretical framework that provides convergence rates for the vanishing of the discrete velocity and the fixed point residual. For certain regularization sequences, we derive specific convergence rates that align with those observed in continuous time., Comment: 39 pages. The rates of convergence have been obtained using weaker conditions for the regularizing function

Encryption on the internet with the shift to HTTPS has been an important step to improve the privacy of internet users. However, there is an increasing body of work about extracting information from encrypted internet traffic without having to decrypt it. Such attacks bypass security guarantees assumed to be given by HTTPS and thus need to be understood. Prior works showed that the variable bitrates of video streams are sufficient to identify which video someone is watching. These works generally have to make trade-offs in aspects such as accuracy, scalability, robustness, etc. These trade-offs complicate the practical use of these attacks. To that end, we propose a deep metric learning framework based on the triplet loss method. Through this framework, we achieve robust, generalisable, scalable and transferable encrypted video stream detection. First, the triplet loss is better able to deal with video streams not seen during training. Second, our approach can accurately classify videos not seen during training. Third, we show that our method scales well to a dataset of over 1000 videos. Finally, we show that a model trained on video streams over Chrome can also classify streams over Firefox. Our results suggest that this side-channel attack is more broadly applicable than originally thought. We provide our code alongside a diverse and up-to-date dataset for future research., Comment: Published in the WI-IAT 2023 proceedings

Dimensionality reduction algorithms are often used to visualise high-dimensional data. Previously, studies have used prior information to enhance or suppress expected patterns in projections. In this paper, we adapt such techniques for domain knowledge guided interactive exploration. Inspired by Mapper and STAD, we present three types of lens functions for UMAP, a state-of-the-art dimensionality reduction algorithm. Lens functions enable analysts to adapt projections to their questions, revealing otherwise hidden patterns. They filter the modelled connectivity to explore the interaction between manually selected features and the data's structure, creating configurable perspectives each potentially revealing new insights. The effectiveness of the lens functions is demonstrated in two use cases and their computational cost is analysed in a synthetic benchmark. Our implementation is available in an open-source Python package: https://github.com/vda-lab/lensed_umap., Comment: 11 pages, 5 figures, submitted to IEEE Transactions on Visualization and Computer Graphics

In our pursuit of finding a zero for a monotone and Lipschitz continuous operator $M : \R^n \rightarrow \R^n$ amidst noisy evaluations, we explore an associated differential equation within a stochastic framework, incorporating a correction term. We present a result establishing the existence and uniqueness of solutions for the stochastic differential equations under examination. Additionally, assuming that the diffusion term is square-integrable, we demonstrate the almost sure convergence of the trajectory process $X(t)$ to a zero of $M$ and of $\|M(X(t))\|$ to $0$ as $t \rightarrow +\infty$. Furthermore, we provide ergodic upper bounds and ergodic convergence rates in expectation for $\|M(X(t))\|^2$ and $\langle M(X(t), X(t)-x^*\rangle$, where $x^*$ is an arbitrary zero of the monotone operator. Subsequently, we apply these findings to a minimax problem. Finally, we analyze two temporal discretizations of the continuous-time models, resulting in stochastic variants of the Optimistic Gradient Descent Ascent and Extragradient methods, respectively, and assess their convergence properties.

Understanding the physical processes that regulate star formation and galaxy evolution are major areas of activity in modern astrophysics. Nearby galaxies offer unique opportunities to inspect interstellar medium (ISM), star formation (SF), radiative, dynamic and magnetic physics in great detail from sub-galactic (kpc) scales to sub-cloud (sub-pc) scales, from quiescent galaxies to starbursts, and from field galaxies to overdensities. In this case study, we discuss the major breakthroughs in this area of research that will be enabled by the Atacama Large Aperture Submillimeter Telescope (AtLAST), a proposed 50-m single-dish submillimeter telescope. The new discovery space of AtLAST comes from its exceptional sensitivity, in particular to extended low surface brightness emission, a very large 2 degree field of view, and correspondingly high mapping efficiency. This paper focuses on four themes which will particularly benefit from AtLAST: 1) the LMC and SMC, 2) extragalactic magnetic fields, 3) the physics and chemistry of the interstellar medium, and 4) star formation and galaxy evolution. With ~1000-2000h surveys each, AtLAST could deliver deep dust continuum maps of the entire LMC and SMC fields at parsec-scale resolution, high-resolution maps of the magnetic field structure, gas density, temperature and composition of the dense and diffuse ISM in ~100 nearby galaxies, as well as the first large-scale blind CO survey in the nearby Universe, delivering molecular gas masses for up to 10^6 galaxies (3 orders of magnitude more than current samples). Through such observing campaigns, AtLAST will have a profound impact on our understanding of the baryon cycle and star formation across a wide range of environments., Comment: 29 pages, 11 figues, submitted to Open Research Europe as part of the AtLAST collection: https://open-research-europe.ec.europa.eu/collections/atlast/about

As we learn more about the multi-scale interstellar medium (ISM) of our Galaxy, we develop a greater understanding for the complex relationships between the large-scale diffuse gas and dust in Giant Molecular Clouds (GMCs), how it moves, how it is affected by the nearby massive stars, and which portions of those GMCs eventually collapse into star forming regions. The complex interactions of those gas, dust and stellar populations form what has come to be known as the ecology of our Galaxy. Because we are deeply embedded in the plane of our Galaxy, it takes up a significant fraction of the sky, with complex dust lanes scattered throughout the optically recognisable bands of the Milky Way. These bands become bright at (sub-)millimetre wavelengths, where we can study dust thermal emission and the chemical and kinematic signatures of the gas. To properly study such large-scale environments, requires deep, large area surveys that are not possible with current facilities. Moreover, where stars form, so too do planetary systems, growing from the dust and gas in circumstellar discs, to planets and planetesimal belts. Understanding the evolution of these belts requires deep imaging capable of studying belts around young stellar objects to Kuiper belt analogues around the nearest stars. Here we present a plan for observing the Galactic Plane and circumstellar environments to quantify the physical structure, the magnetic fields, the dynamics, chemistry, star formation, and planetary system evolution of the galaxy in which we live with AtLAST; a concept for a new, 50m single-dish sub-mm telescope with a large field of view which is the only type of facility that will allow us to observe our Galaxy deeply and widely enough to make a leap forward in our understanding of our local ecology., Comment: 27 pages, submitted to Open Research Europe as part of the AtLAST collection: https://open-research-europe.ec.europa.eu/collections/atlast/about

In this paper, we consider a class of nonconvex and nonsmooth fractional programming problems, which involve the sum of a convex, possibly nonsmooth function composed with a linear operator and a differentiable, possibly nonconvex function in the numerator and a convex, possibly nonsmooth function composed with a linear operator in the denominator. These problems have applications in various fields, including CT reconstruction and sparse signal recovery. We propose an adaptive full-splitting proximal subgradient algorithm with an extrapolated step that addresses the challenge of evaluating the composition in the numerator by decoupling the linear operator from the nonsmooth component. We specifically evaluate the nonsmooth function using its proximal operator, while the linear operator is assessed through forward evaluations. Furthermore, the smooth component in the numerator is evaluated through its gradient, the nonsmooth component in the denominator is managed using its subgradient, and the linear operator in the denominator is also assessed through forward evaluations. We demonstrate subsequential convergence toward an approximate lifted stationary point and ensure global convergence under the Kurdyka-\L ojasiewicz property, all achieved {\it without relying on any full-row rank assumptions regarding the linear operators}. We further explain the reasoning behind aiming for an approximate lifted stationary point. This is exemplified by constructing a scenario illustrating that the algorithm could diverge when seeking exact solutions. Lastly, we present a practical iteration of the algorithm incorporating a nonmonotone line search, significantly enhancing its convergence performance. Our theoretical findings are validated through simulations involving limited-angle CT reconstruction and the robust sharp ratio minimization problem., Comment: 27 pages, 4 figures

We address the problem of finding the zeros of the sum of a maximally monotone operator and a cocoercive operator. Our approach introduces a modification to the forward-backward method by integrating an inertial/momentum term alongside a correction term. We demonstrate that the sequence of iterations thus generated converges weakly towards a solution for the monotone inclusion problem. Furthermore, our analysis reveals an outstanding attribute of our algorithm: it displays rates of convergence of the order $o(1/k)$ for the discrete velocity and the tangent residual approaching zero. These rates for tangent residuals can be extended to fixed-point residuals frequently discussed in the existing literature. Specifically, when applied to minimize a nonsmooth convex function subject to linear constraints, our method evolves into a primal-dual full splitting algorithm. Notably, alongside the convergence of iterates, this algorithm possesses a remarkable characteristic of nonergodic/last iterate $o(1/k)$ convergence rates for both the function value and the feasibility measure. Our algorithm showcases the most advanced convergence and convergence rate outcomes among primal-dual full splitting algorithms when minimizing nonsmooth convex functions with linear constraints., Comment: 36 pages, 8 figures

Clustering algorithms are often used to find subpopulations in exploratory data analysis workflows. Not only the clusters themselves, but also their shape can represent meaningful subpopulations. In this paper, we present FLASC, an algorithm that detects branches within clusters to identify such subpopulations. FLASC builds upon HDBSCAN*, a state-of-the-art density-based clustering algorithm, and detects branches in a post-processing step that describes within-cluster connectivity. Two variants of the algorithm are presented, which trade computational cost for noise robustness. We show that both variants scale similarly to HDBSCAN* in terms of computational cost and provide stable outputs using synthetic data sets, resulting in an efficient flare-sensitive clustering algorithm. In addition, we demonstrate the benefit of branch-detection on two real-world data sets., Comment: Previously, 20 pages, 11 figures, submitted to ACM TKDD. Now, 15 pages, 8 figures, submitted to PeerJ Computer Science (simplified method and rewritten for clarity)

We study monotone variational inequalities that can arise as optimality conditions for constrained convex optimisation or convex-concave minimax problems and propose a novel algorithm that uses only one gradient/operator evaluation and one projection onto the constraint set per iteration. The algorithm, which we call fOGDA-VI, achieves a $o \left( \frac{1}{k} \right)$ rate of convergence in terms of the restricted gap function as well as the natural residual for the last iterate. Moreover, we provide a convergence guarantee for the sequence of iterates to a solution of the variational inequality. These are the best theoretical convergence results for numerical methods for (only) monotone variational inequalities reported in the literature. To empirically validate our algorithm we investigate a two-player matrix game with mixed strategies of the two players. Concluding, we show promising results regarding the application of fOGDA-VI to the training of generative adversarial nets., Comment: Accepted at ICML 2023

The phase behavior is investigated for systems composed of a large number of macromolecular components N, with N greater or equal to 2. Liquid-liquid phase separation is modelled using a virial expansion up to the second order of the concentrations of the components. Formal analytical expressions for the spinodal manifolds in N dimensions are derived that simplify their calculation (by transforming the original problem into inequalities that can be evaluated numerically using linear programming techniques). In addition, a new expression is obtained to calculate the critical manifold and the composition of the co-existing phases. The present analytical procedure complements previous attempts to handle spinodal decomposition for many components using a statistical approach based on Random Matrix Theory. The results are relevant for predicting effects of polydispersity on phase behavior in fields like polymer or food science, and to liquid-liquid phase separation in the cytosol of living cells., Comment: 31 pages, 2 tables, 5 figures

The recovery of a signal from the magnitudes of its transformation, like the Fourier transform, is known as the phase retrieval problem and is of big relevance in various fields of engineering and applied physics. In this paper, we present a fast inertial/momentum based algorithm for the phase retrieval problem and we prove a convergence guarantee for the new algorithm and for the Fast Griffin-Lim algorithm, whose convergence remained unproven in the past decade. In the final chapter, we compare the algorithm for the Short Time Fourier transform phase retrieval with the Griffin-Lim algorithm and FGLA and to other iterative algorithms typically used for this type of problem.

Following the survey Well-being in astrophysics that was sent out in March 2021, to establish how astrophysics researchers, primarily in France, experience their career, some of the results were published in Webb et al. (2021). Here we further analyse the data to determine if gender can cause different experiences in astrophysics. We also study the impact on the well-being of temporary staff (primarily PhD students and postdocs), compared to permanent staff. Whilst more temporary staff stated that they felt permanently overwhelmed than permanent staff, the experiences in astrophysics for the different genders were in general very similar, except in one area. More than three times more females than males experienced harassment or discrimination, rising sharply for gender discrimination and sexual harassment, where all of those having experienced sexual harassment and who had provided their gender in the survey, were female. Further, as previously reported (Webb et al. 2021), 20% of the respondents had suffered mental health issues before starting their career in astrophysics. We found that whilst this group was split approximately equally with regards to males and females, the number rose sharply to almost 45% of astronomers experiencing mental health issues since starting in astrophysics. Of this population, there were 50% more females than males. This excess of females was almost entirely made up of the population of women that had been harassed or discriminated against., Comment: 5 pages, 1 figure, published in the SF2A-2022: Proceedings of the Annual meeting of the French Society of Astronomy and Astrophysics. Eds.: J. Richard, A. Siebert, E. Lagadec, N. Lagarde, O. Venot, J. Malzac, J.-B. Marquette, M. N'Diaye, D. Briot, pp.171-175

We explore evolution in the dust-to-gas ratio with density within four well-resolved Local Group galaxies - the LMC, SMC, M31, and M33. We do this using new ${\it Herschel}$ maps, which restore extended emission that was missed by previous ${\it Herschel}$ reductions. This improved data allows us to probe the dust-to-gas ratio across 2.5 orders of magnitude in ISM surface density. We find significant evolution in the dust-to-gas ratio, with dust-to-gas varying with density within each galaxy by up to a factor 22.4. We explore several possible reasons for this, and our favored explanation is dust grain growth in denser regions of ISM. We find that the evolution of the dust-to-gas ratio with ISM surface density is very similar between M31 and M33, despite their large differences in mass, metallicity, and star formation rate; conversely, we find M33 and the LMC to have very different dust-to-gas evolution profiles, despite their close similarity in those properties. Our dust-to-gas ratios address previous disagreement between UV- and FIR-based dust-to-gas estimates for the Magellanic Clouds, removing the disagreement for the LMC, and considerably reducing it for the SMC - with our new dust-to-gas measurements being factors of 2.4 and 2.0 greater than the previous far-infrared estimates, respectively. We also observe that the dust-to-gas ratio appears to fall at the highest densities for the LMC, M31, and M33; this is unlikely to be an actual physical phenomenon, and we posit that it may be due to a combined effect of dark gas, and changing dust mass opacity., Comment: Accepted for publication in the Astrophysical Journal

The Commission Femmes et Astronomie conducted a statistical study that aims at mapping the presence of women in French professional Astronomy today, and set a starting point for studying its evolution with time. For the year 2021, we proceeded with a sub-set of 8 astronomy and astrophysics institutes, hosting a total of 1060 employees, among which PhD students, post-doctoral researchers, and academic, technical, and administrative staff, representing around 25% of the community. We have investigated how the percentage of women vary with career stage, level of responsibility, job security, and level of income. The results of this preliminary study seem to illustrate the leaky pipeline, with one major bottleneck being the access to permanent positions. It appears that the proportion of women steadily decreases with the security of jobs, with the career stage, with the qualification level and with the income level., Comment: 6 pages, 5 figures

In a Hilbert setting, for convex differentiable optimization, we develop a general framework for adaptive accelerated gradient methods. They are based on damped inertial dynamics where the coefficients are designed in a closed-loop way. Specifically, the damping is a feedback control of the velocity, or of the gradient of the objective function. For this, we develop a closed-loop version of the time scaling and averaging technique introduced by the authors. We thus obtain autonomous inertial dynamics which involve vanishing viscous damping and implicit Hessian driven damping. By simply using the convergence rates for the continuous steepest descent and Jensen's inequality, without the need for further Lyapunov analysis, we show that the trajectories have several remarkable properties at once: they ensure fast convergence of values, fast convergence of the gradients towards zero, and they converge to optimal solutions. Our approach leads to parallel algorithmic results, that we study in the case of proximal algorithms. These are among the very first general results of this type obtained using autonomous dynamics.

The accurate characterization of the severity of the wildfire event strongly contributes to the characterization of the fuel conditions in fire-prone areas, and provides valuable information for disaster response. The aim of this study is to develop an autonomous system built on top of high-resolution multispectral satellite imagery, with an advanced deep learning method for detecting burned area change. This work proposes an initial exploration of using an unsupervised model for feature extraction in wildfire scenarios. It is based on the contrastive learning technique SimCLR, which is trained to minimize the cosine distance between augmentations of images. The distance between encoded images can also be used for change detection. We propose changes to this method that allows it to be used for unsupervised burned area detection and following downstream tasks. We show that our proposed method outperforms the tested baseline approaches., Comment: 5 pages (+3 in appendix), 3 figures (+2 in appendix). Artificial Intelligence for Humanitarian Assistance and Disaster Response Workshop (AI+HADR 2022), 36th Conference on Neural Information Processing Systems (NeurIPS 2022)