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Dynamical systems across the sciences, from electrical circuits to ecological networks, undergo qualitative and often catastrophic changes in behavior, called bifurcations, when their underlying parameters cross a threshold. Existing methods predict oncoming catastrophes in individual systems but are primarily time-series-based and struggle both to categorize qualitative dynamical regimes across diverse systems and to generalize to real data. To address this challenge, we propose a data-driven, physically-informed deep-learning framework for classifying dynamical regimes and characterizing bifurcation boundaries based on the extraction of topologically invariant features. We focus on the paradigmatic case of the supercritical Hopf bifurcation, which is used to model periodic dynamics across a wide range of applications. Our convolutional attention method is trained with data augmentations that encourage the learning of topological invariants which can be used to detect bifurcation boundaries in unseen systems and to design models of biological systems like oscillatory gene regulatory networks. We further demonstrate our method's use in analyzing real data by recovering distinct proliferation and differentiation dynamics along pancreatic endocrinogenesis trajectory in gene expression space based on single-cell data. Our method provides valuable insights into the qualitative, long-term behavior of a wide range of dynamical systems, and can detect bifurcations or catastrophic transitions in large-scale physical and biological systems.

Neural network with quadratic decision functions have been introduced as alternatives to standard neural networks with affine linear one. They are advantageous when the objects to be identified are of compact basic geometries like circles, ellipsis etc. In this paper we investigate the use of such ansatz functions for classification. In particular we test and compare the algorithm on the MNIST dataset for classification of handwritten digits and for classification of subspecies. We also show, that the implementation can be based on the neural network structure in the software Tensorflow and Keras, respectively.

This paper is dedicated to the efficient numerical computation of solutions to the 1D stationary Schr\"odinger equation in the highly oscillatory regime. We compute an approximate solution based on the well-known WKB-ansatz, which relies on an asymptotic expansion w.r.t. the small parameter $\varepsilon$. Assuming that the coefficient in the equation is analytic, we derive an explicit error estimate for the truncated WKB series, in terms of $\varepsilon$ and the truncation order $N$. For any fixed $\varepsilon$, this allows to determine the optimal truncation order $N_{opt}$ which turns out to be proportional to $\varepsilon^{-1}$. When chosen this way, the resulting error of the optimally truncated WKB series behaves like $\mathcal{O}(\varepsilon^{-2}\exp(-r/\varepsilon))$, with some parameter $r>0$. The theoretical results established in this paper are confirmed by several numerical examples.

Effective recommendation systems rely on capturing user preferences, often requiring incorporating numerous features such as universally unique identifiers (UUIDs) of entities. However, the exceptionally high cardinality of UUIDs poses a significant challenge in terms of model degradation and increased model size due to sparsity. This paper presents two innovative techniques to address the challenge of high cardinality in recommendation systems. Specifically, we propose a bag-of-words approach, combined with layer sharing, to substantially decrease the model size while improving performance. Our techniques were evaluated through offline and online experiments on Uber use cases, resulting in promising results demonstrating our approach's effectiveness in optimizing recommendation systems and enhancing their overall performance.

Network time series are becoming increasingly relevant in the study of dynamic processes characterised by a known or inferred underlying network structure. Generalised Network Autoregressive (GNAR) models provide a parsimonious framework for exploiting the underlying network, even in the high-dimensional setting. We extend the GNAR framework by introducing the $\textit{community}$-$\alpha$ GNAR model that exploits prior knowledge and/or exogenous variables for identifying and modelling dynamic interactions across communities in the underlying network. We further analyse the dynamics of $\textit{Red, Blue}$ and $\textit{Swing}$ states throughout presidential elections in the USA. Our analysis shows that dynamics differ among the state-wise clusters.

Auditory spatial attention detection (ASAD) aims to decode the attended spatial location with EEG in a multiple-speaker setting. ASAD methods are inspired by the brain lateralization of cortical neural responses during the processing of auditory spatial attention, and show promising performance for the task of auditory attention decoding (AAD) with neural recordings. In the previous ASAD methods, the spatial distribution of EEG electrodes is not fully exploited, which may limit the performance of these methods. In the present work, by transforming the original EEG channels into a two-dimensional (2D) spatial topological map, the EEG data is transformed into a three-dimensional (3D) arrangement containing spatial-temporal information. And then a 3D deep convolutional neural network (DenseNet-3D) is used to extract temporal and spatial features of the neural representation for the attended locations. The results show that the proposed method achieves higher decoding accuracy than the state-of-the-art (SOTA) method (94.3% compared to XANet's 90.6%) with 1-second decision window for the widely used KULeuven (KUL) dataset, and the code to implement our work is available on Github: //github.com/xuxiran/ASAD_DenseNet

We initiate the study of Boolean function analysis on high-dimensional expanders. We give a random-walk based definition of high-dimensional expansion, which coincides with the earlier definition in terms of two-sided link expanders. Using this definition, we describe an analog of the Fourier expansion and the Fourier levels of the Boolean hypercube for simplicial complexes. Our analog is a decomposition into approximate eigenspaces of random walks associated with the simplicial complexes. Our random-walk definition and the decomposition have the additional advantage that they extend to the more general setting of posets, encompassing both high-dimensional expanders and the Grassmann poset, which appears in recent work on the unique games conjecture. We then use this decomposition to extend the Friedgut-Kalai-Naor theorem to high-dimensional expanders. Our results demonstrate that a constant-degree high-dimensional expander can sometimes serve as a sparse model for the Boolean slice or hypercube, and quite possibly additional results from Boolean function analysis can be carried over to this sparse model. Therefore, this model can be viewed as a derandomization of the Boolean slice, containing only $|X(k-1)|=O(n)$ points in contrast to $\binom{n}{k}$ points in the $(k)$-slice (which consists of all $n$-bit strings with exactly $k$ ones).

Reinforcement learning can solve decision-making problems and train an agent to behave in an environment according to a predesigned reward function. However, such an approach becomes very problematic if the reward is too sparse and so the agent does not come across the reward during the environmental exploration. The solution to such a problem may be to equip the agent with an intrinsic motivation that will provide informed exploration during which the agent is likely to also encounter external reward. Novelty detection is one of the promising branches of intrinsic motivation research. We present Self-supervised Network Distillation (SND), a class of intrinsic motivation algorithms based on the distillation error as a novelty indicator, where the predictor model and the target model are both trained. We adapted three existing self-supervised methods for this purpose and experimentally tested them on a set of ten environments that are considered difficult to explore. The results show that our approach achieves faster growth and higher external reward for the same training time compared to the baseline models, which implies improved exploration in a very sparse reward environment. In addition, the analytical methods we applied provide valuable explanatory insights into our proposed models.

We tackle the challenging tasks of monitoring on unstable HPC platforms the performance of CFD applications all along their development. We have designed and implemented a monitoring framework, integrated at the end of a CI-CD pipeline. Measures retrieved during the automatic execution of production simulations are analyzed within a visual analytics interface we developed, providing advanced visualizations and interaction. We have validated this approach by monitoring the CFD code Alya over two years, detecting and resolving issues related to the platform, and highlighting performance improvement.

Continuous queries over data streams may suffer from blocking operations and/or unbound wait, which may delay answers until some relevant input arrives through the data stream. These delays may turn answers, when they arrive, obsolete to users who sometimes have to make decisions with no help whatsoever. Therefore, it can be useful to provide hypothetical answers - "given the current information, it is possible that X will become true at time t" - instead of no information at all. In this paper we present a semantics for queries and corresponding answers that covers such hypothetical answers, together with an online algorithm for updating the set of facts that are consistent with the currently available information.