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Untargeted metabolomic profiling through liquid chromatography-mass spectrometry (LC-MS) measures a vast array of metabolites within biospecimens, advancing drug development, disease diagnosis, and risk prediction. However, the low throughput of LC-MS poses a major challenge for biomarker discovery, annotation, and experimental comparison, necessitating the merging of multiple datasets. Current data pooling methods encounter practical limitations due to their vulnerability to data variations and hyperparameter dependence. Here we introduce GromovMatcher, a flexible and user-friendly algorithm that automatically combines LC-MS datasets using optimal transport. By capitalizing on feature intensity correlation structures, GromovMatcher delivers superior alignment accuracy and robustness compared to existing approaches. This algorithm scales to thousands of features requiring minimal hyperparameter tuning. Manually curated datasets for validating alignment algorithms are limited in the field of untargeted metabolomics, and hence we develop a dataset split procedure to generate pairs of validation datasets to test the alignments produced by GromovMatcher and other methods. Applying our method to experimental patient studies of liver and pancreatic cancer, we discover shared metabolic features related to patient alcohol intake, demonstrating how GromovMatcher facilitates the search for biomarkers associated with lifestyle risk factors linked to several cancer types.

Learning to Optimize (L2O) stands at the intersection of traditional optimization and machine learning, utilizing the capabilities of machine learning to enhance conventional optimization techniques. As real-world optimization problems frequently share common structures, L2O provides a tool to exploit these structures for better or faster solutions. This tutorial dives deep into L2O techniques, introducing how to accelerate optimization algorithms, promptly estimate the solutions, or even reshape the optimization problem itself, making it more adaptive to real-world applications. By considering the prerequisites for successful applications of L2O and the structure of the optimization problems at hand, this tutorial provides a comprehensive guide for practitioners and researchers alike.

Many flexible families of positive random variables exhibit non-closed forms of the density and distribution functions and this feature is considered unappealing for modelling purposes. However, such families are often characterized by a simple expression of the corresponding Laplace transform. Relying on the Laplace transform, we propose to carry out parameter estimation and goodness-of-fit testing for a general class of non-standard laws. We suggest a novel data-driven inferential technique, providing parameter estimators and goodness-of-fit tests, whose large-sample properties are derived. The implementation of the method is specifically considered for the positive stable and Tweedie distributions. A Monte Carlo study shows good finite-sample performance of the proposed technique for such laws.

We present a scalable machine learning (ML) force-field model for the adiabatic dynamics of cooperative Jahn-Teller (JT) systems. Large scale dynamical simulations of the JT model also shed light on the orbital ordering dynamics in colossal magnetoresistance manganites. The JT effect in these materials describes the distortion of local oxygen octahedra driven by a coupling to the orbital degrees of freedom of $e_g$ electrons. An effective electron-mediated interaction between the local JT modes leads to a structural transition and the emergence of long-range orbital order at low temperatures. Assuming the principle of locality, a deep-learning neural-network model is developed to accurately and efficiently predict the electron-induced forces that drive the dynamical evolution of JT phonons. A group-theoretical method is utilized to develop a descriptor that incorporates the combined orbital and lattice symmetry into the ML model. Large-scale Langevin dynamics simulations, enabled by the ML force-field models, are performed to investigate the coarsening dynamics of the composite JT distortion and orbital order after a thermal quench. The late-stage coarsening of orbital domains exhibits pronounced freezing behaviors which are likely related to the unusual morphology of the domain structures. Our work highlights a promising avenue for multi-scale dynamical modeling of correlated electron systems.

Data assimilation algorithms integrate prior information from numerical model simulations with observed data. Ensemble-based filters, regarded as state-of-the-art, are widely employed for large-scale estimation tasks in disciplines such as geoscience and meteorology. Despite their inability to produce the true posterior distribution for nonlinear systems, their robustness and capacity for state tracking are noteworthy. In contrast, Particle filters yield the correct distribution in the ensemble limit but require substantially larger ensemble sizes than ensemble-based filters to maintain stability in higher-dimensional spaces. It is essential to transcend traditional Gaussian assumptions to achieve realistic quantification of uncertainties. One approach involves the hybridisation of filters, facilitated by tempering, to harness the complementary strengths of different filters. A new adaptive tempering method is proposed to tune the underlying schedule, aiming to systematically surpass the performance previously achieved. Although promising numerical results for certain filter combinations in toy examples exist in the literature, the tuning of hyperparameters presents a considerable challenge. A deeper understanding of these interactions is crucial for practical applications.

This work proposes a novel variational approximation of partial differential equations on moving geometries determined by explicit boundary representations. The benefits of the proposed formulation are the ability to handle large displacements of explicitly represented domain boundaries without generating body-fitted meshes and remeshing techniques. For the space discretization, we use a background mesh and an unfitted method that relies on integration on cut cells only. We perform this intersection by using clipping algorithms. To deal with the mesh movement, we pullback the equations to a reference configuration (the spatial mesh at the initial time slab times the time interval) that is constant in time. This way, the geometrical intersection algorithm is only required in 3D, another key property of the proposed scheme. At the end of the time slab, we compute the deformed mesh, intersect the deformed boundary with the background mesh, and consider an exact transfer operator between meshes to compute jump terms in the time discontinuous Galerkin integration. The transfer is also computed using geometrical intersection algorithms. We demonstrate the applicability of the method to fluid problems around rotating (2D and 3D) geometries described by oriented boundary meshes. We also provide a set of numerical experiments that show the optimal convergence of the method.

This paper addresses the approximation of the mean curvature flow of thin structures for which classical phase field methods are not suitable. By thin structures, we mean surfaces that are not domain boundaries, typically higher codimension objects such as 1D curves in 3D, i.e. filaments, or soap films spanning a boundary curve. To approximate the mean curvature flow of such surfaces, we consider a small thickening and we apply to the thickened set an evolution model that combines the classical Allen-Cahn equation with a penalty term that takes on larger values around the skeleton of the set. The novelty of our approach lies in the definition of this penalty term that guarantees a minimal thickness of the evolving set and prevents it from disappearing unexpectedly. We prove a few theoretical properties of our model, provide examples showing the connection with higher codimension mean curvature flow, and introduce a quasi-static numerical scheme with explicit integration of the penalty term. We illustrate the numerical efficiency of the model with accurate approximations of filament structures evolving by mean curvature flow, and we also illustrate its ability to find complex 3D approximations of solutions to the Steiner problem or the Plateau problem.

Existing approaches for device placement ignore the topological features of computation graphs and rely mostly on heuristic methods for graph partitioning. At the same time, they either follow a grouper-placer or an encoder-placer architecture, which requires understanding the interaction structure between code operations. To bridge the gap between encoder-placer and grouper-placer techniques, we propose a novel framework for the task of device placement, relying on smaller computation graphs extracted from the OpenVINO toolkit using reinforcement learning. The framework consists of five steps, including graph coarsening, node representation learning and policy optimization. It facilitates end-to-end training and takes into consideration the directed and acyclic nature of the computation graphs. We also propose a model variant, inspired by graph parsing networks and complex network analysis, enabling graph representation learning and personalized graph partitioning jointly, using an unspecified number of groups. To train the entire framework, we utilize reinforcement learning techniques by employing the execution time of the suggested device placements to formulate the reward. We demonstrate the flexibility and effectiveness of our approach through multiple experiments with three benchmark models, namely Inception-V3, ResNet, and BERT. The robustness of the proposed framework is also highlighted through an ablation study. The suggested placements improve the inference speed for the benchmark models by up to $58.2\%$ over CPU execution and by up to $60.24\%$ compared to other commonly used baselines.

Mobile devices and the Internet of Things (IoT) devices nowadays generate a large amount of heterogeneous spatial-temporal data. It remains a challenging problem to model the spatial-temporal dynamics under privacy concern. Federated learning (FL) has been proposed as a framework to enable model training across distributed devices without sharing original data which reduce privacy concern. Personalized federated learning (PFL) methods further address data heterogenous problem. However, these methods don't consider natural spatial relations among nodes. For the sake of modeling spatial relations, Graph Neural Netowork (GNN) based FL approach have been proposed. But dynamic spatial-temporal relations among edge nodes are not taken into account. Several approaches model spatial-temporal dynamics in a centralized environment, while less effort has been made under federated setting. To overcome these challeges, we propose a novel Federated Adaptive Spatial-Temporal Attention (FedASTA) framework to model the dynamic spatial-temporal relations. On the client node, FedASTA extracts temporal relations and trend patterns from the decomposed terms of original time series. Then, on the server node, FedASTA utilize trend patterns from clients to construct adaptive temporal-spatial aware graph which captures dynamic correlation between clients. Besides, we design a masked spatial attention module with both static graph and constructed adaptive graph to model spatial dependencies among clients. Extensive experiments on five real-world public traffic flow datasets demonstrate that our method achieves state-of-art performance in federated scenario. In addition, the experiments made in centralized setting show the effectiveness of our novel adaptive graph construction approach compared with other popular dynamic spatial-temporal aware methods.