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In this paper, we introduce holiAtlas, a holistic, multimodal and high-resolution human brain atlas. This atlas covers different levels of details of the human brain anatomy, from the organ to the substructure level, using a new dense labelled protocol generated from the fusion of multiple local protocols at different scales. This atlas has been constructed averaging images and segmentations of 75 healthy subjects from the Human Connectome Project database. Specifically, MR images of T1, T2 and WMn (White Matter nulled) contrasts at 0.125 $mm^{3}$ resolution that were nonlinearly registered and averaged using symmetric group-wise normalisation to construct the atlas. At the finest level, the holiAtlas protocol has 350 different labels derived from 10 different delineation protocols. These labels were grouped at different scales to provide a holistic view of the brain at different levels in a coherent and consistent manner. This multiscale and multimodal atlas can be used for the development of new ultra-high resolution segmentation methods that can potentially leverage the early detection of neurological disorders., Comment: 22 pages

In this paper we prove discrete Poincar\'e inequalities that are uniform in the mesh size for the discrete de Rham complex of differential forms developed in [Bonaldi, Di Pietro, Droniou, and Hu, An exterior calculus framework for polytopal methods, J. Eur. Math. Soc., to appear, arXiv preprint 2303.11093]. We unify the underlying ideas behind the Poincar\'e inequalities for all differential operators in the sequence, extending the known inequalities for the gradient, curl, and divergence in three-dimensions to polytopal domains of arbitrary dimension and general topology. A key step in the proof involves deriving specific Poincar\'e inequalities for the cochain complex supported on the polytopal mesh. These inequalities are of independent interest, as they are useful, for instance, in establishing the existence and stability, on domains of generic topology, of solutions of schemes based on Mimetic Finite Differences, Compatible Discrete Operators or Discrete Geometric Approach.

Plug-and-Play methods for image restoration are iterative algorithms that solve a variational problem to restore an image. These algorithms are known to be flexible to changes of degradation and to perform state-of-the-art restoration. Recently, a lot of efforts have been made to explore new algorithms to solve this variational problem based on the Plug-and-Play or REgularization by Denoising (RED) frameworks, such as SNORE that is a converging stochastic gradient descent algorithm. A variant of this algorithm, named SNORE Prox, reaches state-of-the-art performances, especially for inpainting tasks. However, the convergence of SNORE Prox, that can be seen as a stochastic proximal gradient descent, has not been analyzed so far. In this paper, we prove the convergence of SNORE Prox under reasonable non-convex assumptions.

One key ingredient of image restoration is to define a realistic prior on clean images to complete the missing information in the observation. State-of-the-art restoration methods rely on a neural network to encode this prior. Moreover, typical image distributions are invariant to some set of transformations, such as rotations or flips. However, most deep architectures are not designed to represent an invariant image distribution. Recent works have proposed to overcome this difficulty by including equivariance properties within a Plug-and-Play paradigm. In this work, we propose a unified framework named Equivariant Regularization by Denoising (ERED) based on equivariant denoisers and stochastic optimization. We analyze the convergence of this algorithm and discuss its practical benefit.

Empirically, it has been observed that adding momentum to Stochastic Gradient Descent (SGD) accelerates the convergence of the algorithm. However, the literature has been rather pessimistic, even in the case of convex functions, about the possibility of theoretically proving this observation. We investigate the possibility of obtaining accelerated convergence of the Stochastic Nesterov Accelerated Gradient (SNAG), a momentum-based version of SGD, when minimizing a sum of functions in a convex setting. We demonstrate that the average correlation between gradients allows to verify the strong growth condition, which is the key ingredient to obtain acceleration with SNAG. Numerical experiments, both in linear regression and deep neural network optimization, confirm in practice our theoretical results.

The recent rise of deep learning has led to numerous applications, including solving partial differential equations using Physics-Informed Neural Networks. This approach has proven highly effective in several academic cases. However, their lack of physical invariances, coupled with other significant weaknesses, such as an inability to handle complex geometries or their lack of generalization capabilities, make them unable to compete with classical numerical solvers in industrial settings. In this work, a limitation regarding the use of automatic differentiation in the context of physics-informed learning is highlighted. A hybrid approach combining physics-informed graph neural networks with numerical kernels from finite elements is introduced. After studying the theoretical properties of our model, we apply it to complex geometries, in two and three dimensions. Our choices are supported by an ablation study, and we evaluate the generalisation capacity of the proposed approach.

In this work we address the problem of finding serendipity versions of approximate de Rham complexes with enhanced regularity. The starting point is a new abstract construction of general scope which, given three complexes linked by extension and reduction maps, generates a fourth complex with cohomology isomorphic to the former three. This construction is used to devise new serendipity versions of rot-rot and Stokes complexes derived in the Discrete de Rham spirit.

We report on the experimental observation of non-resonant, second-order optical Sum-Frequency Generation (SFG) in five different atomic and molecular gases. The measured signal is attributed to a SFG process by characterizing its intensity scaling and its polarization behavior. We show that the electric quadrupole mechanism cannot explain the observed trends. Our results demonstrate that SFG in the gas phase is about four orders of magnitude stronger than Third Harmonic Generation (THG) and independent from any externally-applied electric fields. These features make this method suitable for gas number density measurements at the picosecond timescale in reactive flows and plasmas.

Plug-and-Play (PnP) algorithms are a class of iterative algorithms that address image inverse problems by combining a physical model and a deep neural network for regularization. Even if they produce impressive image restoration results, these algorithms rely on a non-standard use of a denoiser on images that are less and less noisy along the iterations, which contrasts with recent algorithms based on Diffusion Models (DM), where the denoiser is applied only on re-noised images. We propose a new PnP framework, called Stochastic deNOising REgularization (SNORE), which applies the denoiser only on images with noise of the adequate level. It is based on an explicit stochastic regularization, which leads to a stochastic gradient descent algorithm to solve ill-posed inverse problems. A convergence analysis of this algorithm and its annealing extension is provided. Experimentally, we prove that SNORE is competitive with respect to state-of-the-art methods on deblurring and inpainting tasks, both quantitatively and qualitatively.

We design in this work a discrete de Rham complex on manifolds. This complex, written in the framework of exterior calculus, has the same cohomology as the continuous de Rham complex, is of arbitrary order of accuracy and, in principle, can be designed on meshes made of generic elements (that is, elements whose boundary is the union of an arbitrary number of curved edges/faces). Notions of local (full and trimmed) polynomial spaces are developed, with compatibility requirements between polynomials on mesh entities of various dimensions. We give explicit constructions of such polynomials in 2D, for some meshes made of curved triangles or quadrangles (such meshes are easy to design in many cases, starting from a few charts describing the manifold). The discrete de Rham complex is then used to set up a scheme for the Maxwell equations on a 2D manifold without boundary, and we show that a natural discrete version of the constraint linking the electric field and the electric charge density is satisfied. Numerical examples are provided on the sphere and the torus, based on bespoke analytical solutions and meshes on each of these manifolds.

This paper introduces a novel multimodal and high-resolution human brain cerebellum lobule segmentation method. Unlike current tools that operate at standard resolution ($1 \text{ mm}^{3}$) or using mono-modal data, the proposed method improves cerebellum lobule segmentation through the use of a multimodal and ultra-high resolution ($0.125 \text{ mm}^{3}$) training dataset. To develop the method, first, a database of semi-automatically labelled cerebellum lobules was created to train the proposed method with ultra-high resolution T1 and T2 MR images. Then, an ensemble of deep networks has been designed and developed, allowing the proposed method to excel in the complex cerebellum lobule segmentation task, improving precision while being memory efficient. Notably, our approach deviates from the traditional U-Net model by exploring alternative architectures. We have also integrated deep learning with classical machine learning methods incorporating a priori knowledge from multi-atlas segmentation, which improved precision and robustness. Finally, a new online pipeline, named DeepCERES, has been developed to make available the proposed method to the scientific community requiring as input only a single T1 MR image at standard resolution., Comment: 20 pages

Since the seminal work of [9] and their Physics-Informed neural networks (PINNs), many efforts have been conducted towards solving partial differential equations (PDEs) with Deep Learning models. However, some challenges remain, for instance the extension of such models to complex three-dimensional geometries, and a study on how such approaches could be combined to classical numerical solvers. In this work, we justify the use of graph neural networks for these problems, based on the similarity between these architectures and the meshes used in traditional numerical techniques for solving partial differential equations. After proving an issue with the Physics-Informed framework for complex geometries, during the computation of PDE residuals, an alternative procedure is proposed, by combining classical numerical solvers and the Physics-Informed framework. Finally, we propose an implementation of this approach, that we test on a three-dimensional problem on an irregular geometry.

Posterior sampling has been shown to be a powerful Bayesian approach for solving imaging inverse problems. The recent plug-and-play unadjusted Langevin algorithm (PnP-ULA) has emerged as a promising method for Monte Carlo sampling and minimum mean squared error (MMSE) estimation by combining physical measurement models with deep-learning priors specified using image denoisers. However, the intricate relationship between the sampling distribution of PnP-ULA and the mismatched data-fidelity and denoiser has not been theoretically analyzed. We address this gap by proposing a posterior-L2 pseudometric and using it to quantify an explicit error bound for PnP-ULA under mismatched posterior distribution. We numerically validate our theory on several inverse problems such as sampling from Gaussian mixture models and image deblurring. Our results suggest that the sensitivity of the sampling distribution of PnP-ULA to a mismatch in the measurement model and the denoiser can be precisely characterized.

In this paper we prove Poincar\'e inequalities for the Discrete de Rham (DDR) sequence on a general connected polyhedral domain $\Omega$ of $\mathbb{R}^3$. We unify the ideas behind the inequalities for all three operators in the sequence, deriving new proofs for the Poincar\'e inequalities for the gradient and the divergence, and extending the available Poincar\'e inequality for the curl to domains with arbitrary second Betti numbers. A key preliminary step consists in deriving "mimetic" Poincar\'e inequalities giving the existence and stability of the solutions to topological balance problems useful in general discrete geometric settings. As an example of application, we study the stability of a novel DDR scheme for the magnetostatics problem on domains with general topology., Comment: 24 pages

Next generation EUV sources for photolithography use light produced by laser-produced plasmas (LPP) from ablated tin droplets. A major challenge for extending the lifetime of these devices is mitigating damage caused by deposition of tin debris on the sensitive collection mirror. Especially difficult to stop are high energy (up to 10 keV) highly charged tin ions created in the plasma. Existing solutions include the use of stopping gas, electric fields, and magnetic fields. One common configuration consists of a magnetic field perpendicular to the EUV emission direction, but such a system can result in ion populations that are trapped rather than removed. We investigate a previously unconsidered mitigation geometry consisting of a magnetic null by performing full-orbit integration of the ion trajectories in an EUV system with realistic dimensions, and optimize the coil locations for the null configuration. The magnetic null prevents a fraction of ions from hitting the mirror comparable to that of the perpendicular field, but does not trap any ions due to the chaotic nature of ion trajectories that pass close to the null. This technology can potentially improve LPP-based EUV photolithography system efficiency and lifetime, and may allow for a different, more efficient formulation of buffer gas.

Let $G$ be a graph of even order, and consider $K_G$ as the complete graph on the same vertex set as $G$. A perfect matching of $K_G$ is called a pairing of $G$. If for every pairing $M$ of $G$ it is possible to find a perfect matching $N$ of $G$ such that $M \cup N$ is a Hamiltonian cycle of $K_G$, then $G$ is said to have the Pairing-Hamiltonian property, or PH-property, for short. In 2007, Fink [J. Combin. Theory Ser. B, 97] proved that for every $d\geq 2$, the $d$-dimensional hypercube $\mathcal{Q}_d$ has the PH-property, thus proving a conjecture posed by Kreweras in 1996. In this paper we extend Fink's result by proving that given a graph $G$ having the PH-property, the prism graph $\mathcal{P}(G)$ of $G$ has the PH-property as well. Moreover, if $G$ is a connected graph, we show that there exists a positive integer $k_0$ such that the $k^{\textrm{th}}$-prism of a graph $\mathcal{P}^k(G)$ has the PH-property for all $k \ge k_0$., Comment: 7 pages, 2 figures

In this paper, we present MasakhaPOS, the largest part-of-speech (POS) dataset for 20 typologically diverse African languages. We discuss the challenges in annotating POS for these languages using the UD (universal dependencies) guidelines. We conducted extensive POS baseline experiments using conditional random field and several multilingual pre-trained language models. We applied various cross-lingual transfer models trained with data available in UD. Evaluating on the MasakhaPOS dataset, we show that choosing the best transfer language(s) in both single-source and multi-source setups greatly improves the POS tagging performance of the target languages, in particular when combined with cross-lingual parameter-efficient fine-tuning methods. Crucially, transferring knowledge from a language that matches the language family and morphosyntactic properties seems more effective for POS tagging in unseen languages., Comment: Accepted to ACL 2023 (Main conference)

In this work, following the Discrete de Rham (DDR) paradigm, we develop an arbitrary-order discrete divdiv complex on general polyhedral meshes. The construction rests 1) on discrete spaces that are spanned by vectors of polynomials whose components are attached to mesh entities and 2) on discrete operators obtained mimicking integration by parts formulas. We provide an in-depth study of the algebraic properties of the local complex, showing that it is exact on mesh elements with trivial topology. The new DDR complex is used to design a numerical scheme for the approximation of biharmonic problems, for which we provide detailed stability and convergence analyses.

Through digital imaging, microscopy has evolved from primarily being a means for visual observation of life at the micro- and nano-scale, to a quantitative tool with ever-increasing resolution and throughput. Artificial intelligence, deep neural networks, and machine learning are all niche terms describing computational methods that have gained a pivotal role in microscopy-based research over the past decade. This Roadmap is written collectively by prominent researchers and encompasses selected aspects of how machine learning is applied to microscopy image data, with the aim of gaining scientific knowledge by improved image quality, automated detection, segmentation, classification and tracking of objects, and efficient merging of information from multiple imaging modalities. We aim to give the reader an overview of the key developments and an understanding of possibilities and limitations of machine learning for microscopy. It will be of interest to a wide cross-disciplinary audience in the physical sciences and life sciences.

Over 60,000 songs are released on Spotify every day, and the competition for the listener's attention is immense. In that regard, the importance of captivating and inviting cover art cannot be underestimated, because it is deeply entangled with a song's character and the artist's identity, and remains one of the most important gateways to lead people to discover music. However, designing cover art is a highly creative, lengthy and sometimes expensive process that can be daunting, especially for non-professional artists. For this reason, we propose a novel deep-learning framework to generate cover art guided by audio features. Inspired by VQGAN-CLIP, our approach is highly flexible because individual components can easily be replaced without the need for any retraining. This paper outlines the architectural details of our models and discusses the optimization challenges that emerge from them. More specifically, we will exploit genetic algorithms to overcome bad local minima and adversarial examples. We find that our framework can generate suitable cover art for most genres, and that the visual features adapt themselves to audio feature changes. Given these results, we believe that our framework paves the road for extensions and more advanced applications in audio-guided visual generation tasks., Comment: 8 pages, 6 figures, 4 tables

We are interested in the numerical reconstruction of a vector field with prescribed divergence and curl in a general domain of R 3 or R 2 , not necessarily contractible. To this aim, we introduce some basic concepts of finite element exterieur calculus and rely heavily on recent results of P. Leopardi and A. Stern. The goal of the paper is to take advantage of the links between usual vector calculus and exterior calculus and show the interest of the exterior calculus framework, without too much prior knowledge of the subject. We start by describing the method used for contractible domains and its implementation using the FEniCS library (see fenicsproject.org). We then address the problems encountered with non contractible domains and general boundary conditions and explain how to adapt the method to handle these cases. Finally we give some numerical results obtained with this method, in dimension 2 and 3., Comment: 18 pages, 4 figures

In this paper we present an arbitrary-order fully discrete Stokes complex on general polyhedral meshes. We enriche the fully discrete de Rham complex with the addition of a full gradient operator defined on vector fields and fitting into the complex. We show a complete set of results on the novelties of this complex: exactness properties, uniform Poincar\'e inequalities and primal and adjoint consistency. The Stokes complex is especially well suited for problem involving Jacobian, divergence and curl, like the Stokes problem or magnetohydrodynamic systems. The framework developed here eases the design and analysis of scheme for such problems. Schemes built that way are nonconforming and benefit from the exactness of the complex. We illustrate with the design and study of a scheme to solve the Stokes equations and validate the convergence rates with various numerical tests., Comment: 45 pages, 7 figures. Major modifications done for use in 3 dimensions. See the second version for an analysis focused on the 2-dimensional case