Time-series datasets are central in numerous fields of science and engineering, such as biomedicine, Earth observation, and network analysis. Extensive research exists on state-space models (SSMs), which are powerful mathematical tools that allow for probabilistic and interpretable learning on time series. Estimating the model parameters in SSMs is arguably one of the most complicated tasks, and the inclusion of prior knowledge is known to both ease the interpretation but also to complicate the inferential tasks. In this talk, I will introduce a novel joint graphical modeling framework called DGLASSO (Dynamic Graphical Lasso) [1], that bridges the static graphical Lasso model [2] and the causal-based graphical approach for the linear-Gaussian SSM in [3]. I will also present a new inference method within the DGLASSO framework that implements an efficient block alternating majorization-minimization algorithm. The algorithm's convergence is established by departing from modern tools from nonlinear analysis. Experimental validation on synthetic and real weather variability data showcases the effectiveness of the proposed model and inference algorithm.

[1] E. Chouzenoux and V. Elvira. Sparse Graphical Linear Dynamical Systems. Journal of Machine Learning Research, vol. 25, no. 223, pp. 1-53, 2024

[2] J. Friedman, T. Hastie, and R. Tibshirani. Sparse inverse covariance estimation with the graphical LASSO. Biostatistics, vol. 9, no. 3, pp. 432–441, Jul. 2008.

[3] V. Elvira and E. Chouzenoux. Graphical Inference in Linear-Gaussian State-Space Models. IEEE Transactions on Signal Processing, vol. 70, pp. 4757-4771, Sep. 2022.

Over the last decade, adversarial attack algorithms have revealed instabilities in artificial intelligence (AI) tools. These algorithms raise issues regarding safety, reliability and interpretability; especially in high risk settings. Mathematics is at the heart of this landscape, with ideas from  numerical analysis, optimization, and high dimensional stochastic analysis playing key roles. From a practical perspective, there has been a war of escalation between those developing attack and defence strategies. At a more theoretical level, researchers have also studied bigger picture questions concerning the existence and computability of successful attacks. I will present examples of attack algorithms for neural networks in image classification, for transformer models in optical character recognition and for large language models. I will also show how recent generative diffusion models can be used adversarially. From a more theoretical perspective, I will outline recent results on the overarching question of whether, under reasonable assumptions, it is inevitable that AI tools will be vulnerable to attack.

The nematic Helmholtz-Korteweg equation is a fourth-order scalar PDE modelling time-harmonic acoustic waves in nematic Korteweg fluids, such as nematic liquid crystals. Conforming discretizations typically require C1-conforming elements, for example the Argyris element, whose implementation is notoriously challenging - especially in three dimensions - and often demands a high polynomial degree. 
In this talk, we consider an alternative non-conforming C0-hybrid interior penalty method that is both stable and convergent for any polynomial degree greater than two. Classical C0-interior penalty methods employ an H1-conforming subspace and treat the non-conformity with respect to H2 with discontinuous Galerkin techniques. Building on this idea, we use hybridization techniques to improve the computational efficiency of the discretization. We provide a brief overview of the numerical analysis and show numerical examples, demonstrating the method's ability to capture anisotropic propagation of sound in two and three dimensions.