Search

Asymmetric 3D structures are observed in the outflows of evolved low- and intermediate-mass stars, and are believed to be shaped through the interaction of companions that are hidden within the dense wind. We investigate how triple systems can shape the outflow of AGB stars. We focus on coplanar systems in a hierarchical, stable orbit, consisting of an AGB star with one relatively close companion, and one at large orbital separation. We model a grid of hierarchical triple systems including a wind-launching AGB star, with the smoothed-particle-hydrodynamic Phantom code. We vary the outer companion mass, the AGB wind velocity and the orbital eccentricities to study the impact of these parameters on the wind morphology. Further, we investigate if the outflow of the AGB star R Aql could be shaped by a triple system, by post-processing one of our triple models with a radiative transfer routine, and comparing this to data of the ALMA ATOMIUM programme. The characteristic wind structures resulting from a hierarchical triple system are the following. A large two-edged spiral wake results behind the outer companion star. This structure lies on top of the spiral structure formed by the close binary, which is affected by the orbital motion around the system centre-of-mass. This dense inner spiral pattern interacts with, and strongly impacts, the spiral wake of the outer companion, resulting in a waved-pattern on the outer edge of this spiral wake. From the comparison of our models to the observations of R Aql, we conclude that this circumstellar environment might be shaped by a similar system as the ones modelled in this work, but an elaborate study of the observational data is needed to determine better the orbital parameters and characteristics of the central system., Comment: 20 pages, 19 figures

Binary interactions have been proposed to explain a variety of circumstellar structures seen around evolved stars, including asymptotic giant branch (AGB) stars and planetary nebulae. Studies resolving the circumstellar envelopes of AGB stars have revealed spirals, discs and bipolar outflows, with shaping attributed to interactions with a companion. For the first time, we have used a combined chemical and dynamical analysis to reveal a highly eccentric and long-period orbit for W Aquilae, a binary system containing an AGB star and a main sequence companion. Our results are based on anisotropic SiN emission, the first detections of NS and SiC towards an S-type star, and density structures observed in the CO emission. These features are all interpreted as having formed during periastron interactions. Our astrochemistry-based method can yield stringent constraints on the orbital parameters of long-period binaries containing AGB stars, and will be applicable to other systems., Comment: This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature's AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1038/s41550-023-02154-y

We first show a simple but striking result in bilevel optimization: unconstrained $C^\infty$ smooth bilevel programming is as hard as general extended-real-valued lower semicontinuous minimization. We then proceed to a worst-case analysis of box-constrained bilevel polynomial optimization. We show in particular that any extended-real-valued semi-algebraic function, possibly non-continuous, can be expressed as the value function of a polynomial bilevel program. Secondly, from a computational complexity perspective, the decision version of polynomial bilevel programming is one level above NP in the polynomial hierarchy ($\Sigma^p_2$-hard). Both types of difficulties are uncommon in non-linear programs for which objective functions are typically continuous and belong to the class NP. These results highlight the irremediable hardness attached to general bilevel optimization and the necessity of imposing some form of regularity on the lower level.

Motivated by the widespread use of approximate derivatives in machine learning and optimization, we study inexact subgradient methods with non-vanishing additive errors and step sizes. In the nonconvex semialgebraic setting, under boundedness assumptions, we prove that the method provides points that eventually fluctuate close to the critical set at a distance proportional to $\epsilon^\rho$ where $\epsilon$ is the error in subgradient evaluation and $\rho$ relates to the geometry of the problem. In the convex setting, we provide complexity results for the averaged values. We also obtain byproducts of independent interest, such as descent-like lemmas for nonsmooth nonconvex problems and some results on the limit of affine interpolants of differential inclusions.

The dusty winds of cool evolved stars are a major contributor of the newly synthesised material enriching the Galaxy and future generations of stars. However, the details of the physics and chemistry behind dust formation and wind launching have yet to be pinpointed. Recent spatially resolved observations show the importance of gaining a more comprehensive view of the circumstellar chemistry, but a comparative study of the intricate interplay between chemistry and physics is still difficult because observational details such as frequencies and angular resolutions are rarely comparable. Aiming to overcome these deficiencies, ATOMIUM is an ALMA Large Programme to study the physics and chemistry of the circumstellar envelopes of a diverse set of oxygen-rich evolved stars under homogeneous observing conditions at three angular resolutions between ~0.02"-1.4". Here we summarize the molecular inventory of these sources, and the correlations between stellar parameters and molecular content. Seventeen oxygen-rich or S-type asymptotic giant branch (AGB) and red supergiant (RSG) stars have been observed in several tunings with ALMA Band 6, targeting a range of molecules to probe the circumstellar envelope and especially the chemistry of dust formation close to the star. We systematically assigned the molecular carriers of the spectral lines and measured their spectroscopic parameters and the angular extent of the emission of each line from integrated intensity maps. Across the ATOMIUM sample, we detect 291 transitions of 24 different molecules and their isotopologues. This includes several first detections in oxygen-rich AGB/RSG stars: PO v=1, SO2 v1=1 and v2=2, and several high energy H2O transitions. We also find several first detections in S-type AGB stars: vibrationally excited HCN v2=2,3 and SiS v=4,5,6, as well as first detections of the molecules SiC, AlCl, and AlF in W Aql..., Comment: 19 pages plus appendices, forthcoming publication in Astronomy & Astrophysics

In appropriate frameworks, automatic differentiation is transparent to the user at the cost of being a significant computational burden when the number of operations is large. For iterative algorithms, implicit differentiation alleviates this issue but requires custom implementation of Jacobian evaluation. In this paper, we study one-step differentiation, also known as Jacobian-free backpropagation, a method as easy as automatic differentiation and as performant as implicit differentiation for fast algorithms (e.g., superlinear optimization methods). We provide a complete theoretical approximation analysis with specific examples (Newton's method, gradient descent) along with its consequences in bilevel optimization. Several numerical examples illustrate the well-foundness of the one-step estimator.

In order for robots to follow open-ended instructions like "go open the brown cabinet over the sink", they require an understanding of both the scene geometry and the semantics of their environment. Robotic systems often handle these through separate pipelines, sometimes using very different representation spaces, which can be suboptimal when the two objectives conflict. In this work, we present USA-Net, a simple method for constructing a world representation that encodes both the semantics and spatial affordances of a scene in a differentiable map. This allows us to build a gradient-based planner which can navigate to locations in the scene specified using open-ended vocabulary. We use this planner to consistently generate trajectories which are both shorter 5-10% shorter and 10-30% closer to our goal query in CLIP embedding space than paths from comparable grid-based planners which don't leverage gradient information. To our knowledge, this is the first end-to-end differentiable planner optimizes for both semantics and affordance in a single implicit map. Code and visuals are available at our website: https://usa.bolte.cc/

The Prechtl General Movements Assessment (GMA) has become a clinician and researcher tool-box for evaluating neurodevelopment in early infancy. Given it involves observation of infant movements from video recordings, utilising smartphone applications to obtain these recordings seems like the natural progression for the field. In this review, we look back on the development of apps for acquiring general movement videos, describe the application and research studies of available apps, and discuss future directions of mobile solutions and their usability in research and clinical practice. We emphasise the importance of understanding the background that has led to these developments while introducing new technologies, including the barriers and facilitators along the pathway. The GMApp and Baby Moves App were the first ones developed to increase accessibility of the GMA, with two further apps, NeuroMotion and InMotion, designed since. The Baby Moves app has been applied most frequently. For the mobile future of GMA, we advocate collaboration to boost the field's progression and to reduce research waste. We propose future collaborative solutions including standardisation of cross-sites data collection, adaption to local context and privacy laws, employment of user feedback, and sustainable IT structures enabling continuous software updating., Comment: 19 pages, 3 Figures, 2 Tables

Aims. Through the ATOMIUM project, based on an ALMA large program, we aim to present a consistent view of a sample of 17 nearby cool evolved stars (Aymptotic Giant Branch and red supergiant stars). Methods. Here we present VLT/SPHERE-ZIMPOL polarimetric maps obtained in the visible of 14 out of the 17 ATOMIUM sources. They were obtained contemporaneously with the ALMA high spatial resolution data. To help interpret the polarized signal, we produced synthetic maps of light scattering by dust, through 3D radiative transfer simulations with the RADMC3D code. Results. The degree of linear polarization (DoLP) observed by ZIMPOL spreads across several optical filters. We infer that it primarily probes dust located just outside of the point spread function, and in or near the plane of the sky, with a total optical depth close to unity in the line of sight, representing only a fraction of the total circumstellar dust. The maximum DoLP ranges from 0.03-0.38 depending on the source, fractions that can be reproduced by our 3D pilot models for grains composed of common dust species. The spatial structure of the DoLP shows a diverse set of shapes. Only for three sources do we note a correlation between the ALMA CO and SiO lines, which trace the gas density, and the DoLP, which traces the dust. Conclusion. The clumpiness of the DoLP and the lack of a consistent correlation between the gas and the dust location show that, in the inner circumstellar environment (CSE), dust formation occurs at very specific sites. This has potential consequences for the derived mass-loss rates and dust-to-gas ratio in the inner region of the CSE. Except for $\pi^1$~Gru and perhaps GY Aql, we do not detect interactions between the circumstellar wind and the hypothesized companions that shape the wind at larger scales. This suggests that the orbits of any other companions are tilted out of the plane of the sky., Comment: Accepted for publication in Astronomy & Astrophysics. 22 pages, 15 figures, 5 tables

We leverage path differentiability and a recent result on nonsmooth implicit differentiation calculus to give sufficient conditions ensuring that the solution to a monotone inclusion problem will be path differentiable, with formulas for computing its generalized gradient. A direct consequence of our result is that these solutions happen to be differentiable almost everywhere. Our approach is fully compatible with automatic differentiation and comes with assumptions which are easy to check, roughly speaking: semialgebraicity and strong monotonicity. We illustrate the scope of our results by considering three fundamental composite problem settings: strongly convex problems, dual solutions to convex minimization problems and primal-dual solutions to min-max problems.

Striatal cholinergic interneurons (CINs) use acetylcholine (ACh) and glutamate (Glut) to regulate the striatal network since they express vesicular transporters for ACh (VAChT) and Glut (VGLUT3). However, whether ACh and Glut are released simultaneously and/or independently from cholinergic varicosities is an open question. The answer to that question requires the multichannel detection of vesicular transporters at the level of single synaptic vesicle (SV). Here, we used super-resolution STimulated Emission Depletion microscopy (STED) to characterize and quantify the distribution of VAChT and VGLUT3 in CINs SVs. Nearest-neighbor distances analysis between VAChT and VGLUT3-immunofluorescent spots revealed that 34% of CINs SVs contain both VAChT and VGLUT3. In addition, 40% of SVs expressed only VAChT while 26% of SVs contain only VGLUT3. These results suggest that SVs from CINs have the potential to store simultaneously or independently ACh and/or Glut. Overall, these morphological findings support the notion that CINs varicosities can signal with either ACh or Glut or both with an unexpected level of complexity.

With the use of high-resolution ALMA observations, complex structures that resemble those observed in post-AGB stars and planetary nebulae are detected in the circumstellar envelopes of low-mass evolved stars. These deviations from spherical symmetry are believed to be caused primarily by the interaction with a companion star or planet. With the use of three-dimensional hydrodynamic simulations, we study the impact of a binary companion on the wind morphology and dynamics of an AGB outflow. We classifiy the wind structures and morphology that form in these simulations with the use of a classification parameter, constructed with characteristic parameters of the binary configuration. Finally we conclude that the companion alters the wind expansion velocity through the slingshot mechanism, if it is massive enough., Comment: Proceedings IAU Symposium No. 366, 2021, The origin of outflows in evolved stars

Using the notion of conservative gradient, we provide a simple model to estimate the computational costs of the backward and forward modes of algorithmic differentiation for a wide class of nonsmooth programs. The overhead complexity of the backward mode turns out to be independent of the dimension when using programs with locally Lipschitz semi-algebraic or definable elementary functions. This considerably extends Baur-Strassen's smooth cheap gradient principle. We illustrate our results by establishing fast backpropagation results of conservative gradients through feedforward neural networks with standard activation and loss functions. Nonsmooth backpropagation's cheapness contrasts with concurrent forward approaches, which have, to this day, dimensional-dependent worst-case overhead estimates. We provide further results suggesting the superiority of backward propagation of conservative gradients. Indeed, we relate the complexity of computing a large number of directional derivatives to that of matrix multiplication, and we show that finding two subgradients in the Clarke subdifferential of a function is an NP-hard problem.

Differentiation along algorithms, i.e., piggyback propagation of derivatives, is now routinely used to differentiate iterative solvers in differentiable programming. Asymptotics is well understood for many smooth problems but the nondifferentiable case is hardly considered. Is there a limiting object for nonsmooth piggyback automatic differentiation (AD)? Does it have any variational meaning and can it be used effectively in machine learning? Is there a connection with classical derivative? All these questions are addressed under appropriate nonexpansivity conditions in the framework of conservative derivatives which has proved useful in understanding nonsmooth AD. For nonsmooth piggyback iterations, we characterize the attractor set of nonsmooth piggyback iterations as a set-valued fixed point which remains in the conservative framework. This has various consequences and in particular almost everywhere convergence of classical derivatives. Our results are illustrated on parametric convex optimization problems with forward-backward, Douglas-Rachford and Alternating Direction of Multiplier algorithms as well as the Heavy-Ball method.

Using jointly geometric and stochastic reformulations of nonconvex problems and exploiting a Monge-Kantorovich gradient system formulation with vanishing forces, we formally extend the simulated annealing method to a wide class of global optimization methods. Due to an inbuilt combination of a gradient-like strategy and particles interactions, we call them swarm gradient dynamics. As in the original paper of Holley-Kusuoka-Stroock, the key to the existence of a schedule ensuring convergence to a global minimizer is a functional inequality. One of our central theoretical contributions is the proof of such an inequality for one-dimensional compact manifolds. We conjecture the inequality to be true in a much wider setting. We also describe a general method allowing for global optimization and evidencing the crucial role of functional inequalities {\`a} la {\L}ojasiewicz.

Many tetragonal compounds LnIr$_2$Si$_2$ (Ln = lanthanoid) occur in two polymorphous phases and are therefore well suited to study the relationship between crystal structure and magnetic properties. We have grown GdIr$_2$Si$_2$ single crystals of both polymorphs from a high-temperature indium flux and investigated their anisotropic magnetic properties. The higher symmetric form with the ThCr$_2$Si$_2$ structure (space group $I4/mmm$) orders antiferromagnetically at $T_{\rm N}=87\,\rm K$ while for the lower symmetric compound in the CaBe$_2$Ge$_2$ structure (space group $P4/nmm$) we determined a much lower \neel temperature $T_{\rm N}=12\,\rm K$. Our magnetic characterization of the single crystals reveals that for both compounds the magnetic moments are aligned in the $a-a$ plane of the tetragonal lattice, but that the change of the symmetry strongly effects the inplane alignment of the moment orientation. For Ln$=$Er and Ho, we confirmed the existence of LnIr$_2$Si$_2$ in the space group $P4/nmm$. The magnetic properties of these lower symmetric compounds are in remarkable difference to their related compounds in the space group $I4/mmm$.

Risk minimization for nonsmooth nonconvex problems naturally leads to first-order sampling or, by an abuse of terminology, to stochastic subgradient descent. We establish the convergence of this method in the path-differentiable case and describe more precise results under additional geometric assumptions. We recover and improve results from Ermoliev and Norkin [Cybern. Syst. Anal., 34 (1998), pp. 196--215] by using a different approach: conservative calculus and the ODE method. In the definable case, we show that first-order subgradient sampling avoids artificial critical points with probability one and applies moreover to a large range of risk minimization problems in deep learning, based on the backpropagation oracle. As byproducts of our approach, we obtain several results on integration of independent interest, such as an interchange result for conservative derivatives and integrals or the definability of set-valued parameterized integrals.

The Frank-Wolfe algorithm is a popular method for minimizing a smooth convex function $f$ over a compact convex set $\mathcal{C}$. While many convergence results have been derived in terms of function values, hardly nothing is known about the convergence behavior of the sequence of iterates $(x_t)_{t\in\mathbb{N}}$. Under the usual assumptions, we design several counterexamples to the convergence of $(x_t)_{t\in\mathbb{N}}$, where $f$ is $d$-time continuously differentiable, $d\geq2$, and $f(x_t)\to\min_\mathcal{C}f$. Our counterexamples cover the cases of open-loop, closed-loop, and line-search step-size strategies. We do not assume \emph{misspecification} of the linear minimization oracle and our results thus hold regardless of the points it returns, demonstrating the fundamental pathologies in the convergence behavior of $(x_t)_{t\in\mathbb{N}}$., Comment: 15 pages, 7 figures