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We propose a novel algorithm for the support estimation of partially known Gaussian graphical models that incorporates prior information about the underlying graph. In contrast to classical approaches that provide a point estimate based on a maximum likelihood or a maximum a posteriori criterion using (simple) priors on the precision matrix, we consider a prior on the graph and rely on annealed Langevin diffusion to generate samples from the posterior distribution. Since the Langevin sampler requires access to the score function of the underlying graph prior, we use graph neural networks to effectively estimate the score from a graph dataset (either available beforehand or generated from a known distribution). Numerical experiments demonstrate the benefits of our approach.

This paper aims to front with dimensionality reduction in regression setting when the predictors are a mixture of functional variable and high-dimensional vector. A flexible model, combining both sparse linear ideas together with semiparametrics, is proposed. A wide scope of asymptotic results is provided: this covers as well rates of convergence of the estimators as asymptotic behaviour of the variable selection procedure. Practical issues are analysed through finite sample simulated experiments while an application to Tecator's data illustrates the usefulness of our methodology.

In this paper, we introduce a new shape functional defined for toroidal domains that we call harmonic helicity, and study its shape optimization. Given a toroidal domain, we consider its associated harmonic field. The latter is the magnetic field obtained uniquely up to normalization when imposing zero normal trace and zero electrical current inside the domain. We then study the helicity of this field, which is a quantity of interest in magneto-hydrodynamics corresponding to the L2 product of the field with its image by the Biot--Savart operator. To do so, we begin by discussing the appropriate functional framework and an equivalent PDE characterization. We then focus on shape optimization, and we identify the shape gradient of the harmonic helicity. Finally, we study and implement an efficient numerical scheme to compute harmonic helicity and its shape gradient using finite elements exterior calculus.

We present a pipeline for unbiased and robust multimodal registration of neuroimaging modalities with minimal pre-processing. While typical multimodal studies need to use multiple independent processing pipelines, with diverse options and hyperparameters, we propose a single and structured framework to jointly process different image modalities. The use of state-of-the-art learning-based techniques enables fast inferences, which makes the presented method suitable for large-scale and/or multi-cohort datasets with a diverse number of modalities per session. The pipeline currently works with structural MRI, resting state fMRI and amyloid PET images. We show the predictive power of the derived biomarkers using in a case-control study and study the cross-modal relationship between different image modalities. The code can be found in https: //github.com/acasamitjana/JUMP.

In this article, we decrease the degree of the polynomials on the boundary of the weak functions and modify the definition of the weak laplacian which are introduced in \cite{BiharmonicSFWG} to use the SFWG method for the biharmonic equation. Then we propose the relevant numerical format and obtain the optimal order of error estimates in $H^2$ and $L^2$ norms. Finally, we confirm the estimates using numerical experiments.

In this study, we proposed a design methodology for a piezoelectric energy-harvesting device optimized for maximal power generation at a designated frequency using topology optimization. The proposed methodology emphasizes the design of a unimorph-type piezoelectric energy harvester, wherein a piezoelectric film is affixed to a singular side of a silicon cantilever beam. Both the substrate and the piezoelectric film components underwent concurrent optimization. Constraints were imposed to ensure that the resultant design is amenable to microfabrication, with specific emphasis on the etchability of piezoelectric energy harvesters. Several numerical examples were provided to validate the efficacy of the proposed method. The results showed that the proposed method derives both the substrate and piezoelectric designs that maximize the electromechanical coupling coefficient and allows the eigenfrequency of the device and minimum output voltage to be set to the desired values. Furthermore, the proposed method can provide solutions that satisfy the cross-sectional shape, substrate-depend, and minimum output voltage constraints. The solutions obtained by the proposed method are manufacturable in the field of microfabrication.

We propose a two-step Newton's method for refining an approximation of a singular zero whose deflation process terminates after one step, also known as a deflation-one singularity. Given an isolated singular zero of a square analytic system, our algorithm exploits an invertible linear operator obtained by combining the Jacobian and a projection of the Hessian in the direction of the kernel of the Jacobian. We prove the quadratic convergence of the two-step Newton method when it is applied to an approximation of a deflation-one singular zero. Also, the algorithm requires a smaller size of matrices than the existing methods, making it more efficient. We demonstrate examples and experiments to show the efficiency of the method.

In this paper, we propose to consider various models of pattern recognition. At the same time, it is proposed to consider models in the form of two operators: a recognizing operator and a decision rule. Algebraic operations are introduced on recognizing operators, and based on the application of these operators, a family of recognizing algorithms is created. An upper estimate is constructed for the model, which guarantees the completeness of the extension.

Languages have long been described according to their perceived rhythmic attributes. The associated typologies are of interest in psycholinguistics as they partly predict newborns' abilities to discriminate between languages and provide insights into how adult listeners process non-native languages. Despite the relative success of rhythm metrics in supporting the existence of linguistic rhythmic classes, quantitative studies have yet to capture the full complexity of temporal regularities associated with speech rhythm. We argue that deep learning offers a powerful pattern-recognition approach to advance the characterization of the acoustic bases of speech rhythm. To explore this hypothesis, we trained a medium-sized recurrent neural network on a language identification task over a large database of speech recordings in 21 languages. The network had access to the amplitude envelopes and a variable identifying the voiced segments, assuming that this signal would poorly convey phonetic information but preserve prosodic features. The network was able to identify the language of 10-second recordings in 40% of the cases, and the language was in the top-3 guesses in two-thirds of the cases. Visualization methods show that representations built from the network activations are consistent with speech rhythm typologies, although the resulting maps are more complex than two separated clusters between stress and syllable-timed languages. We further analyzed the model by identifying correlations between network activations and known speech rhythm metrics. The findings illustrate the potential of deep learning tools to advance our understanding of speech rhythm through the identification and exploration of linguistically relevant acoustic feature spaces.

This paper does not describe a working system. Instead, it presents a single idea about representation which allows advances made by several different groups to be combined into an imaginary system called GLOM. The advances include transformers, neural fields, contrastive representation learning, distillation and capsules. GLOM answers the question: How can a neural network with a fixed architecture parse an image into a part-whole hierarchy which has a different structure for each image? The idea is simply to use islands of identical vectors to represent the nodes in the parse tree. If GLOM can be made to work, it should significantly improve the interpretability of the representations produced by transformer-like systems when applied to vision or language