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This brief paper provides an introduction to non-discrimination law in Europe. It answers the questions: What are the key characteristics of non-discrimination law in Europe, and how do the different statutes relate to one another? Our main target group is computer scientists and users of artificial intelligence (AI) interested in an introduction to non-discrimination law in Europe. Notably, non-discrimination law in Europe differs significantly from non-discrimination law in other countries, such as the US. We aim to describe the law in such a way that non-lawyers and non-European lawyers can easily grasp its contents and challenges. The paper shows that the human right to non-discrimination, to some extent, protects individuals against private actors, such as companies. We introduce the EU-wide non-discrimination rules which are included in a number of EU directives, and also explain the difference between direct and indirect discrimination. Significantly, an organization can be fined for indirect discrimination even if the company, or its AI system, discriminated by accident. The last section broadens the horizon to include bias-relevant law and cases from the GDPR, the EU AI Act, and related statutes. Finally, we give reading tips for those inclined to learn more about non-discrimination law in Europe.

This paper introduces a novel code-to-code search technique that enhances the performance of Large Language Models (LLMs) by including both static and dynamic features as well as utilizing both similar and dissimilar examples during training. We present the first-ever code search method that encodes dynamic runtime information during training without the need to execute either the corpus under search or the search query at inference time and the first code search technique that trains on both positive and negative reference samples. To validate the efficacy of our approach, we perform a set of studies demonstrating the capability of enhanced LLMs to perform cross-language code-to-code search. Our evaluation demonstrates that the effectiveness of our approach is consistent across various model architectures and programming languages. We outperform the state-of-the-art cross-language search tool by up to 44.7\%. Moreover, our ablation studies reveal that even a single positive and negative reference sample in the training process results in substantial performance improvements demonstrating both similar and dissimilar references are important parts of code search. Importantly, we show that enhanced well-crafted, fine-tuned models consistently outperform enhanced larger modern LLMs without fine tuning, even when enhancing the largest available LLMs highlighting the importance for open-sourced models. To ensure the reproducibility and extensibility of our research, we present an open-sourced implementation of our tool and training procedures called REINFOREST.

In this paper we discuss the application of Artificial Intelligence (AI) to the exemplary industrial use case of the two-dimensional commissioning problem in a high-bay storage, which essentially can be phrased as an instance of Traveling Salesperson Problem (TSP). We investigate the mlrose library that provides an TSP optimizer based on various heuristic optimization techniques. Our focus is on two methods, namely Genetic Algorithm (GA) and Hill Climbing (HC), which are provided by mlrose. We present improvements for both methods that yield shorter tour lengths, by moderately exploiting the problem structure of TSP. That is, the proposed improvements have a generic character and are not limited to TSP only.

The method of fundamental solutions (MFS), also known as the method of auxiliary sources (MAS), is a well-known computational method for the solution of boundary-value problems. The final solution ("MAS solution") is obtained once we have found the amplitudes of $N$ auxiliary "MAS sources." Past studies have demonstrated that it is possible for the MAS solution to converge to the true solution even when the $N$ auxiliary sources diverge and oscillate. The present paper extends the past studies by demonstrating this possibility within the context of Laplace's equation with Neumann boundary conditions. One can thus obtain the correct solution from sources that, when $N$ is large, must be considered unphysical. We carefully explain the underlying reasons for the unphysical results, distinguish from other difficulties that might concurrently arise, and point to significant differences with time-dependent problems that were studied in the past.

In this paper, we introduce a novel Convolution-based Probability Gradient (CPG) loss for semantic segmentation. It employs convolution kernels similar to the Sobel operator, capable of computing the gradient of pixel intensity in an image. This enables the computation of gradients for both ground-truth and predicted category-wise probabilities. It enhances network performance by maximizing the similarity between these two probability gradients. Moreover, to specifically enhance accuracy near the object's boundary, we extract the object boundary based on the ground-truth probability gradient and exclusively apply the CPG loss to pixels belonging to boundaries. CPG loss proves to be highly convenient and effective. It establishes pixel relationships through convolution, calculating errors from a distinct dimension compared to pixel-wise loss functions such as cross-entropy loss. We conduct qualitative and quantitative analyses to evaluate the impact of the CPG loss on three well-established networks (DeepLabv3-Resnet50, HRNetV2-OCR, and LRASPP_MobileNet_V3_Large) across three standard segmentation datasets (Cityscapes, COCO-Stuff, ADE20K). Our extensive experimental results consistently and significantly demonstrate that the CPG loss enhances the mean Intersection over Union.

This paper addresses the inverse scattering problem in the domain Omega. The input data, measured outside Omega, involve the waves generated by the interaction of plane waves with various directions and unknown scatterers fully occluded inside Omega. The output of this problem is the spatially dielectric constant of these scatterers. Our approach to solving this problem consists of two primary stages. Initially, we eliminate the unknown dielectric constant from the governing equation, resulting in a system of partial differential equations. Subsequently, we develop the Carleman contraction mapping method to effectively tackle this system. It is noteworthy to highlight this method's robustness. It does not request a precise initial guess of the true solution, and its computational cost is not expensive. Some numerical examples are presented.

This paper investigates heterogeneous-cost task allocation with budget constraints (HCTAB), wherein heterogeneity is manifested through the varying capabilities and costs associated with different agents for task execution. Different from the centralized optimization-based method, the HCTAB problem is solved using a fully distributed framework, and a coalition formation game is introduced to provide a theoretical guarantee for this distributed framework. To solve the coalition formation game, a convergence-guaranteed log-linear learning algorithm based on heterogeneous cost is proposed. This algorithm incorporates two improvement strategies, namely, a cooperative exchange strategy and a heterogeneous-cost log-linear learning strategy. These strategies are specifically designed to be compatible with the heterogeneous cost and budget constraints characteristic of the HCTAB problem. Through ablation experiments, we demonstrate the effectiveness of these two improvements. Finally, numerical results show that the proposed algorithm outperforms existing task allocation algorithms and learning algorithms in terms of solving the HCTAB problem.

Early identification of Mild Cognitive Impairment (MCI) subjects who will eventually progress to Alzheimer Disease (AD) is challenging. Existing deep learning models are mostly single-modality single-task models predicting risk of disease progression at a fixed timepoint. We proposed a multimodal hierarchical multi-task learning approach which can monitor the risk of disease progression at each timepoint of the visit trajectory. Longitudinal visit data from multiple modalities (MRI, cognition, and clinical data) were collected from MCI individuals of the Alzheimer Disease Neuroimaging Initiative (ADNI) dataset. Our hierarchical model predicted at every timepoint a set of neuropsychological composite cognitive function scores as auxiliary tasks and used the forecasted scores at every timepoint to predict the future risk of disease. Relevance weights for each composite function provided explanations about potential factors for disease progression. Our proposed model performed better than state-of-the-art baselines in predicting AD progression risk and the composite scores. Ablation study on the number of modalities demonstrated that imaging and cognition data contributed most towards the outcome. Model explanations at each timepoint can inform clinicians 6 months in advance the potential cognitive function decline that can lead to progression to AD in future. Our model monitored their risk of AD progression every 6 months throughout the visit trajectory of individuals. The hierarchical learning of auxiliary tasks allowed better optimization and allowed longitudinal explanations for the outcome. Our framework is flexible with the number of input modalities and the selection of auxiliary tasks and hence can be generalized to other clinical problems too.

In this paper, we present refined generalization bounds for the Deep Ritz Method (DRM) and Physics-Informed Neural Networks (PINNs). For the DRM, we focus on two prototype elliptic PDEs: Poisson equation and static Schr\"odinger equation on the $d$-dimensional unit hypercube with the Neumann boundary condition. And sharper generalization bounds are derived based on the localization techniques under the assumptions that the exact solutions of the PDEs lie in the Barron spaces or the general Sobolev spaces. For the PINNs, we investigate the general linear second elliptic PDEs with Dirichlet boundary condition via the local Rademacher complexity in the multi-task learning.

In this paper we study the a posteriori bounds for a conforming piecewise linear finite element approximation of the Signorini problem. We prove new rigorous a posteriori estimates of residual type in $L^{p}$, for $p \in (4,\infty)$ in two spatial dimensions. This new analysis treats the positive and negative parts of the discretisation error separately, requiring a novel sign- and bound-preserving interpolant, which is shown to have optimal approximation properties. The estimates rely on the sharp dual stability results on the problem in $W^{2,(4 - \varepsilon)/3}$ for any $\varepsilon \ll 1$. We summarise extensive numerical experiments aimed at testing the robustness of the estimator to validate the theory.