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Retinal image registration is of utmost importance due to its wide applications in medical practice. In this context, we propose ConKeD, a novel deep learning approach to learn descriptors for retinal image registration. In contrast to current registration methods, our approach employs a novel multi-positive multi-negative contrastive learning strategy that enables the utilization of additional information from the available training samples. This makes it possible to learn high quality descriptors from limited training data. To train and evaluate ConKeD, we combine these descriptors with domain-specific keypoints, particularly blood vessel bifurcations and crossovers, that are detected using a deep neural network. Our experimental results demonstrate the benefits of the novel multi-positive multi-negative strategy, as it outperforms the widely used triplet loss technique (single-positive and single-negative) as well as the single-positive multi-negative alternative. Additionally, the combination of ConKeD with the domain-specific keypoints produces comparable results to the state-of-the-art methods for retinal image registration, while offering important advantages such as avoiding pre-processing, utilizing fewer training samples, and requiring fewer detected keypoints, among others. Therefore, ConKeD shows a promising potential towards facilitating the development and application of deep learning-based methods for retinal image registration.

In this work, we study diversity-aware clustering problems where the data points are associated with multiple attributes resulting in intersecting groups. A clustering solution need to ensure that a minimum number of cluster centers are chosen from each group while simultaneously minimizing the clustering objective, which can be either $k$-median, $k$-means or $k$-supplier. We present parameterized approximation algorithms with approximation ratios $1+ \frac{2}{e}$, $1+\frac{8}{e}$ and $3$ for diversity-aware $k$-median, diversity-aware $k$-means and diversity-aware $k$-supplier, respectively. The approximation ratios are tight assuming Gap-ETH and FPT $\neq$ W[2]. For fair $k$-median and fair $k$-means with disjoint faicility groups, we present parameterized approximation algorithm with approximation ratios $1+\frac{2}{e}$ and $1+\frac{8}{e}$, respectively. For fair $k$-supplier with disjoint facility groups, we present a polynomial-time approximation algorithm with factor $3$, improving the previous best known approximation ratio of factor $5$.

In the conventional change detection (CD) pipeline, two manually registered and labeled remote sensing datasets serve as the input of the model for training and prediction. However, in realistic scenarios, data from different periods or sensors could fail to be aligned as a result of various coordinate systems. Geometric distortion caused by coordinate shifting remains a thorny issue for CD algorithms. In this paper, we propose a reusable self-supervised framework for bitemporal geometric distortion in CD tasks. The whole framework is composed of Pretext Representation Pre-training, Bitemporal Image Alignment, and Down-stream Decoder Fine-Tuning. With only single-stage pre-training, the key components of the framework can be reused for assistance in the bitemporal image alignment, while simultaneously enhancing the performance of the CD decoder. Experimental results in 2 large-scale realistic scenarios demonstrate that our proposed method can alleviate the bitemporal geometric distortion in CD tasks.

The aim of change-point detection is to discover the changes in behavior that lie behind time sequence data. In this article, we study the case where the data comes from an inhomogeneous Poisson process or a marked Poisson process. We present a methodology for detecting multiple offline change-points based on a minimum contrast estimator. In particular, we explain how to handle the continuous nature of the process with the available discrete observations. In addition, we select the appropriate number of regimes via a cross-validation procedure which is really handy here due to the nature of the Poisson process. Through experiments on simulated and real data sets, we demonstrate the interest of the proposed method. The proposed method has been implemented in the R package \texttt{CptPointProcess} R.

In this article, we consider convergence of stochastic gradient descent schemes (SGD), including momentum stochastic gradient descent (MSGD), under weak assumptions on the underlying landscape. More explicitly, we show that on the event that the SGD stays bounded we have convergence of the SGD if there is only a countable number of critical points or if the objective function satisfies Lojasiewicz-inequalities around all critical levels as all analytic functions do. In particular, we show that for neural networks with analytic activation function such as softplus, sigmoid and the hyperbolic tangent, SGD converges on the event of staying bounded, if the random variables modelling the signal and response in the training are compactly supported.

In this paper, we define and study variants of several complexity classes of decision problems that are defined via some criteria on the number of accepting paths of an NPTM. In these variants, we modify the acceptance criteria so that they concern the total number of computation paths instead of the number of accepting ones. This direction reflects the relationship between the counting classes #P and TotP, which are the classes of functions that count the number of accepting paths and the total number of paths of NPTMs, respectively. The former is the well-studied class of counting versions of NP problems introduced by Valiant (1979). The latter contains all self-reducible counting problems in #P whose decision version is in P, among them prominent #P-complete problems such as Non-negative Permanent, #PerfMatch, and #DNF-Sat, thus playing a significant role in the study of approximable counting problems. We show that almost all classes introduced in this work coincide with their `#accepting paths'-definable counterparts, thus providing an alternative model of computation for them. Moreover, for each of these classes, we present a novel family of complete problems, which are defined via TotP-complete problems. This way, we show that all the aforementioned classes have complete problems that are defined via counting problems whose existence version is in P, in contrast to the standard way of obtaining completeness results via counting versions of NP-complete problems. To the best of our knowledge, prior to this work, such results were known only for parity-P and C=P.

In this work we design and analyse a Discrete de Rham (DDR) method for the incompressible Navier-Stokes equations. Our focus is, more specifically, on the SDDR variant, where a reduction in the number of unknowns is obtained using serendipity techniques. The main features of the DDR approach are the support of general meshes and arbitrary approximation orders. The method we develop is based on the curl-curl formulation of the momentum equation and, through compatibility with the Helmholtz-Hodge decomposition, delivers pressure-robust error estimates for the velocity. It also enables non-standard boundary conditions, such as imposing the value of the pressure on the boundary. In-depth numerical validation on a complete panel of tests including general polyhedral meshes is provided. The paper also contains an appendix where bounds on DDR potential reconstructions and differential operators are proved in the more general framework of Polytopal Exterior Calculus.

In this chapter, we propose a non-traditional RCR training in data science that is grounded into a virtue theory framework. First, we delineate the approach in more theoretical detail, by discussing how the goal of RCR training is to foster the cultivation of certain moral abilities. We specify the nature of these abilities: while the ideal is the cultivation of virtues, the limited space allowed by RCR modules can only facilitate the cultivation of superficial abilities or proto-virtues, which help students to familiarize with moral and political issues in the data science environment. Third, we operationalize our approach by stressing that (proto-)virtue acquisition (like skill acquisition) occurs through the technical and social tasks of daily data science activities, where these repetitive tasks provide the opportunities to develop (proto-)virtue capacity and to support the development of ethically robust data systems. Finally, we discuss a concrete example of how this approach has been implemented. In particular, we describe how this method is applied to teach data ethics to students participating in the CODATA-RDA Data Science Summer Schools.

This study introduces a novel methodology for modelling patient emotions from online patient experience narratives. We employed metadata network topic modelling to analyse patient-reported experiences from Care Opinion, revealing key emotional themes linked to patient-caregiver interactions and clinical outcomes. We develop a probabilistic, context-specific emotion recommender system capable of predicting both multilabel emotions and binary sentiments using a naive Bayes classifier using contextually meaningful topics as predictors. The superior performance of our predicted emotions under this model compared to baseline models was assessed using the information retrieval metrics nDCG and Q-measure, and our predicted sentiments achieved an F1 score of 0.921, significantly outperforming standard sentiment lexicons. This method offers a transparent, cost-effective way to understand patient feedback, enhancing traditional collection methods and informing individualised patient care. Our findings are accessible via an R package and interactive dashboard, providing valuable tools for healthcare researchers and practitioners.

Forecasting has always been at the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities. The large number of forecasting applications calls for a diverse set of forecasting methods to tackle real-life challenges. This article provides a non-systematic review of the theory and the practice of forecasting. We provide an overview of a wide range of theoretical, state-of-the-art models, methods, principles, and approaches to prepare, produce, organise, and evaluate forecasts. We then demonstrate how such theoretical concepts are applied in a variety of real-life contexts. We do not claim that this review is an exhaustive list of methods and applications. However, we wish that our encyclopedic presentation will offer a point of reference for the rich work that has been undertaken over the last decades, with some key insights for the future of forecasting theory and practice. Given its encyclopedic nature, the intended mode of reading is non-linear. We offer cross-references to allow the readers to navigate through the various topics. We complement the theoretical concepts and applications covered by large lists of free or open-source software implementations and publicly-available databases.