This paper introduces CompressedMediQ, a novel hybrid quantum-classical machine learning pipeline specifically developed to address the computational challenges associated with high-dimensional multi-class neuroimaging data analysis. Standard neuroimaging datasets, such as 4D MRI data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) and Neuroimaging in Frontotemporal Dementia (NIFD), present significant hurdles due to their vast size and complexity. CompressedMediQ integrates classical high-performance computing (HPC) nodes for advanced MRI pre-processing and Convolutional Neural Network (CNN)-PCA-based feature extraction and reduction, addressing the limited-qubit availability for quantum data encoding in the NISQ (Noisy Intermediate-Scale Quantum) era. This is followed by Quantum Support Vector Machine (QSVM) classification. By utilizing quantum kernel methods, the pipeline optimizes feature mapping and classification, enhancing data separability and outperforming traditional neuroimaging analysis techniques. Experimental results highlight the pipeline's superior accuracy in dementia staging, validating the practical use of quantum machine learning in clinical diagnostics. Despite the limitations of NISQ devices, this proof-of-concept demonstrates the transformative potential of quantum-enhanced learning, paving the way for scalable and precise diagnostic tools in healthcare and signal processing.

The global surge in the cases of gastric cancer has prompted an investigation into the potential of gut microbiota as a predictive marker for the disease. The alterations in gut diversity are suspected to be associated with an elevated risk of gastric cancer. This paper delves into finding the correlation between gut microbiota and gastric cancer, focusing on patients who have undergone total and subtotal gastrectomy. Utilizing data mining and statistical learning methods, an analysis was conducted on 16S-RNA sequenced genes obtained from 96 participants with the aim of identifying specific genera of gut microbiota associated with gastric cancer. The study reveals several prominent bacterial genera that could potentially serve as biomarkers assessing the risk of gastric cancer. These findings offer a pathway for early risk assessment and precautionary measures in the diagnosis of gastric cancer. The intricate mechanisms through which these gut microbiotas influence gastric cancer progression warrant further investigation. This research significantly aims to contribute to the growing understanding of the gut-cancer axis and its implications in disease prediction and prevention.

The problem of identifying to which of a given set of classes objects belong is ubiquitous, occurring in many research domains and application areas, including medical diagnosis, financial decision making, online commerce, and national security. But such assignments are rarely completely perfect, and classification errors occur. This means it is necessary to compare classification methods and algorithms to decide which is ``best'' for any particular problem. However, just as there are many different classification methods, so there are many different ways of measuring their performance. It is thus vital to choose a measure of performance which matches the aims of the research or application. This paper is a contribution to the growing literature on the relative merits of different performance measures. Its particular focus is the critical importance of matching the properties of the measure to the aims for which the classification is being made.

We propose a non-intrusive method to build surrogate models that approximate the solution of parameterized partial differential equations (PDEs), capable of taking into account the dependence of the solution on the shape of the computational domain. Our approach is based on the combination of two neural networks (NNs). The first NN, conditioned on a latent code, provides an implicit representation of geometry variability through signed distance functions. This automated shape encoding technique generates compact, low-dimensional representations of geometries within a latent space, without requiring the explicit construction of an encoder. The second NN reconstructs the output physical fields independently for each spatial point, thus avoiding the computational burden typically associated with high-dimensional discretizations like computational meshes. Furthermore, we show that accuracy in geometrical characterization can be further enhanced by employing Fourier feature mapping as input feature of the NN. The meshless nature of the proposed method, combined with the dimensionality reduction achieved through automatic feature extraction in latent space, makes it highly flexible and computationally efficient. This strategy eliminates the need for manual intervention in extracting geometric parameters, and can even be applied in cases where geometries undergo changes in their topology. Numerical tests in the field of fluid dynamics and solid mechanics demonstrate the effectiveness of the proposed method in accurately predict the solution of PDEs in domains of arbitrary shape. Remarkably, the results show that it achieves accuracy comparable to the best-case scenarios where an explicit parametrization of the computational domain is available.

Denoising, the process of reducing random fluctuations in a signal to emphasize essential patterns, has been a fundamental problem of interest since the dawn of modern scientific inquiry. Recent denoising techniques, particularly in imaging, have achieved remarkable success, nearing theoretical limits by some measures. Yet, despite tens of thousands of research papers, the wide-ranging applications of denoising beyond noise removal have not been fully recognized. This is partly due to the vast and diverse literature, making a clear overview challenging. This paper aims to address this gap. We present a clarifying perspective on denoisers, their structure, and desired properties. We emphasize the increasing importance of denoising and showcase its evolution into an essential building block for complex tasks in imaging, inverse problems, and machine learning. Despite its long history, the community continues to uncover unexpected and groundbreaking uses for denoising, further solidifying its place as a cornerstone of scientific and engineering practice.

For overparameterized optimization tasks, such as the ones found in modern machine learning, global minima are generally not unique. In order to understand generalization in these settings, it is vital to study to which minimum an optimization algorithm converges. The possibility of having minima that are unstable under the dynamics imposed by the optimization algorithm limits the potential minima that the algorithm can find. In this paper, we characterize the global minima that are dynamically stable/unstable for both deterministic and stochastic gradient descent (SGD). In particular, we introduce a characteristic Lyapunov exponent which depends on the local dynamics around a global minimum and rigorously prove that the sign of this Lyapunov exponent determines whether SGD can accumulate at the respective global minimum.

Relational representation learning transforms relational data into continuous and low-dimensional vector representations. However, vector-based representations fall short in capturing crucial properties of relational data that are complex and symbolic. We propose geometric relational embeddings, a paradigm of relational embeddings that respect the underlying symbolic structures. Specifically, this dissertation introduces various geometric relational embedding models capable of capturing: 1) complex structured patterns like hierarchies and cycles in networks and knowledge graphs; 2) logical structures in ontologies and logical constraints applicable for constraining machine learning model outputs; and 3) high-order structures between entities and relations. Our results obtained from benchmark and real-world datasets demonstrate the efficacy of geometric relational embeddings in adeptly capturing these discrete, symbolic, and structured properties inherent in relational data.

Incorporating the Forward Forward algorithm into neural network training represents a transformative shift from traditional methods, introducing a dual forward mechanism that streamlines the learning process by bypassing the complexities of derivative propagation. This method is noted for its simplicity and efficiency and involves executing two forward passes the first with actual data to promote positive reinforcement, and the second with synthetically generated negative data to enable discriminative learning. Our experiments confirm that the Forward Forward algorithm is not merely an experimental novelty but a viable training strategy that competes robustly with conventional multi layer perceptron (MLP) architectures. To overcome the limitations inherent in traditional saliency techniques, which predominantly rely on gradient based methods, we developed a bespoke saliency algorithm specifically tailored for the Forward Forward framework. This innovative algorithm enhances the intuitive understanding of feature importance and network decision-making, providing clear visualizations of the data features most influential in model predictions. By leveraging this specialized saliency method, we gain deeper insights into the internal workings of the model, significantly enhancing our interpretative capabilities beyond those offered by standard approaches. Our evaluations, utilizing the MNIST and Fashion MNIST datasets, demonstrate that our method performs comparably to traditional MLP-based models.

Abstract--Efficient satellite communications play an enormously important role in all of our daily lives. This includes the transmission of data for communication purposes, the operation of IoT applications or the provision of data for ground stations. More and more, AI-based methods are finding their way into these areas. This paper gives an overview of current research in the field of intelligent optimization of satellite communication. For this purpose, a text-mining based literature review was conducted and the identified papers were thematically clustered and analyzed. The identified clusters cover the main topics of routing, resource allocation and, load balancing. Through such a clustering of the literature in overarching topics, a structured analysis of the research papers was enabled, allowing the identification of latest technologies and approaches as well as research needs for intelligent optimization of satellite communication.

The classification of time series is essential for extracting meaningful insights and aiding decision-making in engineering domains. Parametric modeling techniques like NARX are invaluable for comprehending intricate processes, such as environmental time series, owing to their easily interpretable and transparent structures. This article introduces a classification algorithm, Logistic-NARX Multinomial, which merges the NARX methodology with logistic regression. This approach not only produces interpretable models but also effectively tackles challenges associated with multiclass classification. Furthermore, this study introduces an innovative methodology tailored for the railway sector, offering a tool by employing NARX models to interpret the multitude of features derived from onboard sensors. This solution provides profound insights through feature importance analysis, enabling informed decision-making regarding safety and maintenance.