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We show how quantum-inspired 2d tensor networks can be used to efficiently and accurately simulate the largest quantum processors from IBM, namely Eagle (127 qubits), Osprey (433 qubits) and Condor (1121 qubits). We simulate the dynamics of a complex quantum many-body system -- specifically, the kicked Ising experiment considered recently by IBM in Nature 618, p. 500-505 (2023) -- using graph-based Projected Entangled Pair States (gPEPS), which was proposed by some of us in PRB 99, 195105 (2019). Our results show that simple tensor updates are already sufficient to achieve very large unprecedented accuracy with remarkably low computational resources for this model. Apart from simulating the original experiment for 127 qubits, we also extend our results to 433 and 1121 qubits, thus setting a benchmark for the newest IBM quantum machines. We also report accurate simulations for infinitely-many qubits. Our results show that gPEPS are a natural tool to efficiently simulate quantum computers with an underlying lattice-based qubit connectivity, such as all quantum processors based on superconducting qubits.

Large-scale communication networks, such as the internet, rely on routing packets of data through multiple intermediate nodes to transmit information from a sender to a receiver. In this paper, we develop a model of a quantum communication network that routes information simultaneously along multiple paths passing through intermediate stations. We demonstrate that a quantum routing approach can in principle extend the distance over which information can be transmitted reliably. Surprisingly, the benefit of quantum routing also applies to the transmission of classical information: even if the transmitted data is purely classical, delocalising it on multiple routes can enhance the achievable transmission distance. Our findings highlight the potential of a future quantum internet not only for achieving secure quantum communication and distributed quantum computing but also for extending the range of classical data transmission.

A non-intrusive proper generalized decomposition (PGD) strategy, coupled with an overlapping domain decomposition (DD) method, is proposed to efficiently construct surrogate models of parametric linear elliptic problems. A parametric multi-domain formulation is presented, with local subproblems featuring arbitrary Dirichlet interface conditions represented through the traces of the finite element functions used for spatial discretization at the subdomain level, with no need for additional auxiliary basis functions. The linearity of the operator is exploited to devise low-dimensional problems with only few active boundary parameters. An overlapping Schwarz method is used to glue the local surrogate models, solving a linear system for the nodal values of the parametric solution at the interfaces, without introducing Lagrange multipliers to enforce the continuity in the overlapping region. The proposed DD-PGD methodology relies on a fully algebraic formulation allowing for real-time computation based on the efficient interpolation of the local surrogate models in the parametric space, with no additional problems to be solved during the execution of the Schwarz algorithm. Numerical results for parametric diffusion and convection-diffusion problems are presented to showcase the accuracy of the DD-PGD approach, its robustness in different regimes and its superior performance with respect to standard high-fidelity DD methods.

We consider the problem of estimating the marginal independence structure of a Bayesian network from observational data in the form of an undirected graph called the unconditional dependence graph. We show that unconditional dependence graphs of Bayesian networks correspond to the graphs having equal independence and intersection numbers. Using this observation, a Gr\"obner basis for a toric ideal associated to unconditional dependence graphs of Bayesian networks is given and then extended by additional binomial relations to connect the space of all such graphs. An MCMC method, called GrUES (Gr\"obner-based Unconditional Equivalence Search), is implemented based on the resulting moves and applied to synthetic Gaussian data. GrUES recovers the true marginal independence structure via a penalized maximum likelihood or MAP estimate at a higher rate than simple independence tests while also yielding an estimate of the posterior, for which the $20\%$ HPD credible sets include the true structure at a high rate for data-generating graphs with density at least $0.5$.

The aim of this study was to develop a model to accurately identify corresponding points between organ segmentations of different patients for radiotherapy applications. A model for simultaneous correspondence and interpolation estimation in 3D shapes was trained with head and neck organ segmentations from planning CT scans. We then extended the original model to incorporate imaging information using two approaches: 1) extracting features directly from image patches, and 2) including the mean square error between patches as part of the loss function. The correspondence and interpolation performance were evaluated using the geodesic error, chamfer distance and conformal distortion metrics, as well as distances between anatomical landmarks. Each of the models produced significantly better correspondences than the baseline non-rigid registration approach. The original model performed similarly to the model with direct inclusion of image features. The best performing model configuration incorporated imaging information as part of the loss function which produced more anatomically plausible correspondences. We will use the best performing model to identify corresponding anatomical points on organs to improve spatial normalisation, an important step in outcome modelling, or as an initialisation for anatomically informed registrations. All our code is publicly available at //github.com/rrr-uom-projects/Unsup-RT-Corr-Net

Clustering of publication networks is an efficient way to obtain classifications of large collections of research publications. Such classifications can be used to, e.g., detect research topics, normalize citation relations, or explore the publication output of a unit. Citation networks can be created using a variety of approaches. Best practices to obtain classifications using clustering have been investigated, in particular the performance of different publication-publication relatedness measures. However, evaluation of different approaches to normalization of citation relations have not been explored to the same extent. In this paper, we evaluate five approaches to normalization of direct citation relations with respect to clustering solution quality in four data sets. A sixth approach is evaluated using no normalization. To assess the quality of clustering solutions, we use three measures. (1) We compare the clustering solution to the reference lists of a set of publications using the Adjusted Rand Index. (2) Using the Sihouette width measure, we quantity to which extent the publications have relations to other clusters than the one they have been assigned to. (3) We propose a measure that captures publications that have probably been inaccurately assigned. The results clearly show that normalization is preferred over unnormalized direct citation relations. Furthermore, the results indicate that the fractional normalization approach, which can be considered the standard approach, causes inaccurate assignments. The geometric normalization approach has a similar performance as the fractional approach regarding Adjusted Rand Index and Silhouette width but leads to fewer inaccurate assignments. We therefore believe that the geometric approach may be preferred over the fractional approach.

The increasing capacities of large language models (LLMs) present an unprecedented opportunity to scale up data analytics in the humanities and social sciences, augmenting and automating qualitative analytic tasks previously typically allocated to human labor. This contribution proposes a systematic mixed methods framework to harness qualitative analytic expertise, machine scalability, and rigorous quantification, with attention to transparency and replicability. 16 machine-assisted case studies are showcased as proof of concept. Tasks include linguistic and discourse analysis, lexical semantic change detection, interview analysis, historical event cause inference and text mining, detection of political stance, text and idea reuse, genre composition in literature and film; social network inference, automated lexicography, missing metadata augmentation, and multimodal visual cultural analytics. In contrast to the focus on English in the emerging LLM applicability literature, many examples here deal with scenarios involving smaller languages and historical texts prone to digitization distortions. In all but the most difficult tasks requiring expert knowledge, generative LLMs can demonstrably serve as viable research instruments. LLM (and human) annotations may contain errors and variation, but the agreement rate can and should be accounted for in subsequent statistical modeling; a bootstrapping approach is discussed. The replications among the case studies illustrate how tasks previously requiring potentially months of team effort and complex computational pipelines, can now be accomplished by an LLM-assisted scholar in a fraction of the time. Importantly, this approach is not intended to replace, but to augment researcher knowledge and skills. With these opportunities in sight, qualitative expertise and the ability to pose insightful questions have arguably never been more critical.

We propose an approach to compute inner and outer-approximations of the sets of values satisfying constraints expressed as arbitrarily quantified formulas. Such formulas arise for instance when specifying important problems in control such as robustness, motion planning or controllers comparison. We propose an interval-based method which allows for tractable but tight approximations. We demonstrate its applicability through a series of examples and benchmarks using a prototype implementation.

We hypothesize that due to the greedy nature of learning in multi-modal deep neural networks, these models tend to rely on just one modality while under-fitting the other modalities. Such behavior is counter-intuitive and hurts the models' generalization, as we observe empirically. To estimate the model's dependence on each modality, we compute the gain on the accuracy when the model has access to it in addition to another modality. We refer to this gain as the conditional utilization rate. In the experiments, we consistently observe an imbalance in conditional utilization rates between modalities, across multiple tasks and architectures. Since conditional utilization rate cannot be computed efficiently during training, we introduce a proxy for it based on the pace at which the model learns from each modality, which we refer to as the conditional learning speed. We propose an algorithm to balance the conditional learning speeds between modalities during training and demonstrate that it indeed addresses the issue of greedy learning. The proposed algorithm improves the model's generalization on three datasets: Colored MNIST, Princeton ModelNet40, and NVIDIA Dynamic Hand Gesture.

Graph representation learning for hypergraphs can be used to extract patterns among higher-order interactions that are critically important in many real world problems. Current approaches designed for hypergraphs, however, are unable to handle different types of hypergraphs and are typically not generic for various learning tasks. Indeed, models that can predict variable-sized heterogeneous hyperedges have not been available. Here we develop a new self-attention based graph neural network called Hyper-SAGNN applicable to homogeneous and heterogeneous hypergraphs with variable hyperedge sizes. We perform extensive evaluations on multiple datasets, including four benchmark network datasets and two single-cell Hi-C datasets in genomics. We demonstrate that Hyper-SAGNN significantly outperforms the state-of-the-art methods on traditional tasks while also achieving great performance on a new task called outsider identification. Hyper-SAGNN will be useful for graph representation learning to uncover complex higher-order interactions in different applications.