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We consider Maxwell eigenvalue problems on uncertain shapes with perfectly conducting TESLA cavities being the driving example. Due to the shape uncertainty, the resulting eigenvalues and eigenmodes are also uncertain and it is well known that the eigenvalues may exhibit crossings or bifurcations under perturbation. We discuss how the shape uncertainties can be modelled using the domain mapping approach and how the deformation mapping can be expressed as coefficients in Maxwell's equations. Using derivatives of these coefficients and derivatives of the eigenpairs, we follow a perturbation approach to compute approximations of mean and covariance of the eigenpairs. For small perturbations, these approximations are faster and more accurate than Monte Carlo or similar sampling-based strategies. Numerical experiments for a three-dimensional 9-cell TESLA cavity are presented.

The need to Fourier transform data sets with irregular sampling is shared by various domains of science. This is the case for example in astronomy or sismology. Iterative methods have been developed that allow to reach approximate solutions. Here an exact solution to the problem for band-limited periodic signals is presented. The exact spectrum can be deduced from the spectrum of the non-equispaced data through the inversion of a Toeplitz matrix. The result applies to data of any dimension. This method also provides an excellent approximation for non-periodic band-limit signals. The method allows to reach very high dynamic ranges ($10^{13}$ with double-float precision) which depend on the regularity of the samples.

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.

Image coding for machines (ICM) aims at reducing the bitrate required to represent an image while minimizing the drop in machine vision analysis accuracy. In many use cases, such as surveillance, it is also important that the visual quality is not drastically deteriorated by the compression process. Recent works on using neural network (NN) based ICM codecs have shown significant coding gains against traditional methods; however, the decompressed images, especially at low bitrates, often contain checkerboard artifacts. We propose an effective decoder finetuning scheme based on adversarial training to significantly enhance the visual quality of ICM codecs, while preserving the machine analysis accuracy, without adding extra bitcost or parameters at the inference phase. The results show complete removal of the checkerboard artifacts at the negligible cost of -1.6% relative change in task performance score. In the cases where some amount of artifacts is tolerable, such as when machine consumption is the primary target, this technique can enhance both pixel-fidelity and feature-fidelity scores without losing task performance.

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.

Due to the subjective nature of image quality assessment (IQA), assessing which image has better quality among a sequence of images is more reliable than assigning an absolute mean opinion score for an image. Thus, IQA models are evaluated by global correlation consistency (GCC) metrics like PLCC and SROCC, rather than mean opinion consistency (MOC) metrics like MAE and MSE. However, most existing methods adopt MOC metrics to define their loss functions, due to the infeasible computation of GCC metrics during training. In this work, we construct a novel loss function and network to exploit Global-correlation and Mean-opinion Consistency, forming a GMC-IQA framework. Specifically, we propose a novel GCC loss by defining a pairwise preference-based rank estimation to solve the non-differentiable problem of SROCC and introducing a queue mechanism to reserve previous data to approximate the global results of the whole data. Moreover, we propose a mean-opinion network, which integrates diverse opinion features to alleviate the randomness of weight learning and enhance the model robustness. Experiments indicate that our method outperforms SOTA methods on multiple authentic datasets with higher accuracy and generalization. We also adapt the proposed loss to various networks, which brings better performance and more stable training.

Optical coherence tomography (OCT) suffers from speckle noise, causing the deterioration of image quality, especially in high-resolution modalities like visible light OCT (vis-OCT). The potential of conventional supervised deep learning denoising methods is limited by the difficulty of obtaining clean data. Here, we proposed an innovative self-supervised strategy called Sub2Full (S2F) for OCT despeckling without clean data. This approach works by acquiring two repeated B-scans, splitting the spectrum of the first repeat as a low-resolution input, and utilizing the full spectrum of the second repeat as the high-resolution target. The proposed method was validated on vis-OCT retinal images visualizing sublaminar structures in outer retina and demonstrated superior performance over conventional Noise2Noise and Noise2Void schemes. The code is available at //github.com/PittOCT/Sub2Full-OCT-Denoising.

While deep neural networks have achieved remarkable performance, data augmentation has emerged as a crucial strategy to mitigate overfitting and enhance network performance. These techniques hold particular significance in industrial manufacturing contexts. Recently, image mixing-based methods have been introduced, exhibiting improved performance on public benchmark datasets. However, their application to industrial tasks remains challenging. The manufacturing environment generates massive amounts of unlabeled data on a daily basis, with only a few instances of abnormal data occurrences. This leads to severe data imbalance. Thus, creating well-balanced datasets is not straightforward due to the high costs associated with labeling. Nonetheless, this is a crucial step for enhancing productivity. For this reason, we introduce ContextMix, a method tailored for industrial applications and benchmark datasets. ContextMix generates novel data by resizing entire images and integrating them into other images within the batch. This approach enables our method to learn discriminative features based on varying sizes from resized images and train informative secondary features for object recognition using occluded images. With the minimal additional computation cost of image resizing, ContextMix enhances performance compared to existing augmentation techniques. We evaluate its effectiveness across classification, detection, and segmentation tasks using various network architectures on public benchmark datasets. Our proposed method demonstrates improved results across a range of robustness tasks. Its efficacy in real industrial environments is particularly noteworthy, as demonstrated using the passive component dataset.

In this paper we develop a linear expectile hidden Markov model for the analysis of cryptocurrency time series in a risk management framework. The methodology proposed allows to focus on extreme returns and describe their temporal evolution by introducing in the model time-dependent coefficients evolving according to a latent discrete homogeneous Markov chain. As it is often used in the expectile literature, estimation of the model parameters is based on the asymmetric normal distribution. Maximum likelihood estimates are obtained via an Expectation-Maximization algorithm using efficient M-step update formulas for all parameters. We evaluate the introduced method with both artificial data under several experimental settings and real data investigating the relationship between daily Bitcoin returns and major world market indices.

Although measuring held-out accuracy has been the primary approach to evaluate generalization, it often overestimates the performance of NLP models, while alternative approaches for evaluating models either focus on individual tasks or on specific behaviors. Inspired by principles of behavioral testing in software engineering, we introduce CheckList, a task-agnostic methodology for testing NLP models. CheckList includes a matrix of general linguistic capabilities and test types that facilitate comprehensive test ideation, as well as a software tool to generate a large and diverse number of test cases quickly. We illustrate the utility of CheckList with tests for three tasks, identifying critical failures in both commercial and state-of-art models. In a user study, a team responsible for a commercial sentiment analysis model found new and actionable bugs in an extensively tested model. In another user study, NLP practitioners with CheckList created twice as many tests, and found almost three times as many bugs as users without it.