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The attention towards food products characteristics, such as nutritional properties and traceability, has risen substantially in the recent years. Consequently, we are witnessing an increased demand for the development of modern tools to monitor, analyse and assess food quality and authenticity. Within this framework, an essential set of data collection techniques is provided by vibrational spectroscopy. In fact, methods such as Fourier near infrared and mid infrared spectroscopy have been often exploited to analyze different foodstuffs. Nonetheless, existing statistical methods often struggle to deal with the challenges presented by spectral data, such as their high dimensionality, paired with strong relationships among the wavelengths. Therefore, the definition of proper statistical procedures accounting for the peculiarities of spectroscopy data is paramount. In this work, motivated by two dairy science applications, we propose an adaptive functional regression framework for spectroscopy data. The method stems from the trend filtering literature, allowing the definition of a highly flexible and adaptive estimator able to handle different degrees of smoothness. We provide a fast optimization procedure that is suitable for both Gaussian and non Gaussian scalar responses, and allows for the inclusion of scalar covariates. Moreover, we develop inferential procedures for both the functional and the scalar component thus enhancing not only the interpretability of the results, but also their usability in real world scenarios. The method is applied to two sets of MIR spectroscopy data, providing excellent results when predicting milk chemical composition and cows' dietary treatments. Moreover, the developed inferential routine provides relevant insights, potentially paving the way for a richer interpretation and a better understanding of the impact of specific wavelengths on milk features.

We are interested in numerical algorithms for computing the electrical field generated by a charge distribution localized on scale $l$ in an infinite heterogeneous correlated random medium, in a situation where the medium is only known in a box of diameter $L\gg l$ around the support of the charge. We show that the algorithm of Lu, Otto and Wang, suggesting optimal Dirichlet boundary conditions motivated by the multipole expansion of Bella, Giunti and Otto, still performs well in correlated media. With overwhelming probability, we obtain a convergence rate in terms of $l$, $L$ and the size of the correlations for which optimality is supported with numerical simulations. These estimates are provided for ensembles which satisfy a multi-scale logarithmic Sobolev inequality, where our main tool is an extension of the semi-group estimates established by the first author. As part of our strategy, we construct sub-linear second-order correctors in this correlated setting which is of independent interest.

The spectral clustering algorithm is often used as a binary clustering method for unclassified data by applying the principal component analysis. To study theoretical properties of the algorithm, the assumption of homoscedasticity is often supposed in existing studies. However, this assumption is restrictive and often unrealistic in practice. Therefore, in this paper, we consider the allometric extension model, that is, the directions of the first eigenvectors of two covariance matrices and the direction of the difference of two mean vectors coincide, and we provide a non-asymptotic bound of the error probability of the spectral clustering algorithm for the allometric extension model. As a byproduct of the result, we obtain the consistency of the clustering method in high-dimensional settings.

Science mapping is an important tool to gain insight into scientific fields, to identify emerging research trends, and to support science policy. Understanding the different ways in which different science mapping approaches capture the structure of scientific fields is critical. This paper presents a comparative analysis of two commonly used approaches, topic modeling (TM) and citation-based clustering (CC), to assess their respective strengths, weaknesses, and the characteristics of their results. We compare the two approaches using cluster-to-topic and topic-to-cluster mappings based on science maps of cardiovascular research (CVR) generated by TM and CC. Our findings reveal that relations between topics and clusters are generally weak, with limited overlap between topics and clusters. Only in a few exceptional cases do more than one-third of the documents in a topic belong to the same cluster, or vice versa. CC excels at identifying diseases and generating specialized clusters in Clinical Treatment & Surgical Procedures, while TM focuses on sub-techniques within diagnostic techniques, provides a general perspective on Clinical Treatment & Surgical Procedures, and identifies distinct topics related to practical guidelines. Our work enhances the understanding of science mapping approaches based on TM and CC and delivers practical guidance for scientometricians on how to apply these approaches effectively.

We analyse a numerical scheme for a system arising from a novel description of the standard elastic--perfectly plastic response. The elastic--perfectly plastic response is described via rate-type equations that do not make use of the standard elastic-plastic decomposition, and the model does not require the use of variational inequalities. Furthermore, the model naturally includes the evolution equation for temperature. We present a low order discretisation based on the finite element method. Under certain restrictions on the mesh we subsequently prove the existence of discrete solutions, and we discuss the stability properties of the numerical scheme. The analysis is supplemented with computational examples.

We consider a one-dimensional nonlocal hyperbolic model introduced to describe the formation and movement of self-organizing collectives of animals in homogeneous 1D environments. Previous research has shown that this model exhibits a large number of complex spatial and spatiotemporal aggregation patterns, as evidenced by numerical simulations and weakly nonlinear analysis. In this study, we focus on a particular type of localised patterns with odd/even/no symmetries (which are usually part of snaking solution branches with different symmetries that form complex bifurcation structures called snake-and-ladder bifurcations). To numerically investigate the bifurcating solution branches (to eventually construct the full bifurcating structures), we first need to understand the numerical issues that could appear when using different numerical schemes. To this end, in this study, we consider ten different numerical schemes (the upwind scheme, the MacCormack scheme, the Fractional-Step method, and the Quasi-Steady Wave-Propagation algorithm, combining them with high-resolution methods), while paying attention to the preservation of the solution symmetries with all these schemes. We show several numerical issues: first, we observe the presence of two distinct types of numerical solutions (with different symmetries) that exhibit very small errors; second, in some cases, none of the investigated numerical schemes converge, posing a challenge for the development of numerical continuation algorithms for nonlocal hyperbolic systems; lastly, the choice of the numerical schemes, as well as their corresponding parameters such as time-space steps, exert a significant influence on the type and symmetry of bifurcating solutions.

The modeling and simulation of high-dimensional multiscale systems is a critical challenge across all areas of science and engineering. It is broadly believed that even with today's computer advances resolving all spatiotemporal scales described by the governing equations remains a remote target. This realization has prompted intense efforts to develop model order reduction techniques. In recent years, techniques based on deep recurrent neural networks have produced promising results for the modeling and simulation of complex spatiotemporal systems and offer large flexibility in model development as they can incorporate experimental and computational data. However, neural networks lack interpretability, which limits their utility and generalizability across complex systems. Here we propose a novel framework of Interpretable Learning Effective Dynamics (iLED) that offers comparable accuracy to state-of-the-art recurrent neural network-based approaches while providing the added benefit of interpretability. The iLED framework is motivated by Mori-Zwanzig and Koopman operator theory, which justifies the choice of the specific architecture. We demonstrate the effectiveness of the proposed framework in simulations of three benchmark multiscale systems. Our results show that the iLED framework can generate accurate predictions and obtain interpretable dynamics, making it a promising approach for solving high-dimensional multiscale systems.

Permutation tests are widely recognized as robust alternatives to tests based on the normal theory. Random permutation tests have been frequently employed to assess the significance of variables in linear models. Despite their widespread use, existing random permutation tests lack finite-sample and assumption-free guarantees for controlling type I error in partial correlation tests. To address this standing challenge, we develop a conformal test through permutation-augmented regressions, which we refer to as PALMRT. PALMRT not only achieves power competitive with conventional methods but also provides reliable control of type I errors at no more than $2\alpha$ given any targeted level $\alpha$, for arbitrary fixed-designs and error distributions. We confirmed this through extensive simulations. Compared to the cyclic permutation test (CPT), which also offers theoretical guarantees, PALMRT does not significantly compromise power or set stringent requirements on the sample size, making it suitable for diverse biomedical applications. We further illustrate their differences in a long-Covid study where PALMRT validated key findings previously identified using the t-test, while CPT suffered from a drastic loss of power. We endorse PALMRT as a robust and practical hypothesis test in scientific research for its superior error control, power preservation, and simplicity.

Reinforcement learning of real-world tasks is very data inefficient, and extensive simulation-based modelling has become the dominant approach for training systems. However, in human-robot interaction and many other real-world settings, there is no appropriate one-model-for-all due to differences in individual instances of the system (e.g. different people) or necessary oversimplifications in the simulation models. This requires two approaches: 1. either learning the individual system's dynamics approximately from data which requires data-intensive training or 2. using a complete digital twin of the instances, which may not be realisable in many cases. We introduce two approaches: co-kriging adjustments (CKA) and ridge regression adjustment (RRA) as novel ways to combine the advantages of both approaches. Our adjustment methods are based on an auto-regressive AR1 co-kriging model that we integrate with GP priors. This yield a data- and simulation-efficient way of using simplistic simulation models (e.g., simple two-link model) and rapidly adapting them to individual instances (e.g., biomechanics of individual people). Using CKA and RRA, we obtain more accurate uncertainty quantification of the entire system's dynamics than pure GP-based and AR1 methods. We demonstrate the efficiency of co-kriging adjustment with an interpretable reinforcement learning control example, learning to control a biomechanical human arm using only a two-link arm simulation model (offline part) and CKA derived from a small amount of interaction data (on-the-fly online). Our method unlocks an efficient and uncertainty-aware way to implement reinforcement learning methods in real world complex systems for which only imperfect simulation models exist.

With the increasing availability of large scale datasets, computational power and tools like automatic differentiation and expressive neural network architectures, sequential data are now often treated in a data-driven way, with a dynamical model trained from the observation data. While neural networks are often seen as uninterpretable black-box architectures, they can still benefit from physical priors on the data and from mathematical knowledge. In this paper, we use a neural network architecture which leverages the long-known Koopman operator theory to embed dynamical systems in latent spaces where their dynamics can be described linearly, enabling a number of appealing features. We introduce methods that enable to train such a model for long-term continuous reconstruction, even in difficult contexts where the data comes in irregularly-sampled time series. The potential for self-supervised learning is also demonstrated, as we show the promising use of trained dynamical models as priors for variational data assimilation techniques, with applications to e.g. time series interpolation and forecasting.