Objective

The study aimed to develop an efficient method for computing the running of the coupling in non-Abelian gauge theories in dimensions greater than one, with a focus on improving computational performance.

Method

The researchers employed a dual formulation of the Hamiltonian using periodic lattices and loop variables, applying Gauss law to establish a local variational basis for loops. This approach was tested on small toroidal configurations of \(SU(2)\) Yang-Mills theory to minimize truncation errors.

Results

The proposed method enabled computations at arbitrary values of the bare coupling and lattice spacing, achieving percent-level precision for ground state energy and plaquette expectation values. This was accomplished significantly faster than traditional methods.

Significance

The findings present a new resource-efficient framework for the analytical and computational treatment of non-Abelian gauge theories, which is crucial for advancing research in quantum computing and for simulating relevant gauge theories in particle physics and condensed matter.

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Objective

The study aims to introduce and analyze mobility-based compartmental models in epidemiology, addressing the limitations of classical models that assume a homogeneous population, which can lead to inaccurate predictions regarding disease spread and final pandemic size.

Method

A mobility-based SIRS (Susceptible-Infected-Recovered) model is proposed, incorporating individual mobility as a variable affecting disease transmission. The model describes disease dynamics through density functions associated with the three compartments (S, I, R) based on an individual's mobility. Mobility distributions are inferred from real-time data of the infected population using a machine-learning approach.

Results

The proposed mobility-based model predicts a smaller final pandemic size than classical models with the same basic reproduction number, effectively countering the common overestimation seen in standard epidemiological models. Sufficient conditions for uniquely identifying the mobility distribution using the time series of the infected population are established. Predicted mobility distributions reflect real-world data trends, indicating the impact of individual mobility on disease spread.

Significance

The findings indicate the importance of incorporating individual-level mobility in compartmental models for more accurate epidemiological predictions. The study contributes to the methodological framework for identifying mobility patterns from epidemiological data, enhancing public health planning.

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Objective

The study aims to introduce the syntheseus framework to address systematic shortcomings in the evaluation of retrosynthesis algorithms, which have been affected by inconsistent benchmarks.

Method

The authors developed a benchmarking library that enforces best practices for evaluating both single-step and multi-step retrosynthesis algorithms. This library facilitates a consistent and comparative analysis of existing models.

Results

Re-evaluations of existing algorithms revealed significant changes in their rankings, suggesting that previous evaluations may have inaccurately represented the performance of certain methods.

Significance

The findings highlight the necessity for a standardized evaluation approach in automated synthesis planning, which is crucial for advancing methods that ensure synthesizability in molecular discovery workflows. The syntheseus framework provides a structured solution to promote accurate assessments in future evaluations.

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Objective

The study aims to explore the role and impact of edge features in graph-based models, focusing on how these features enhance the understanding of interactions and relationships between nodes.

Method

The study employs a comprehensive analysis of various types of edge features, including topological, geometric, and temporal characteristics. It utilizes graph theory principles and machine learning techniques to evaluate the predictive accuracy of models that incorporate these edge features.

Results

The analysis reveals that models incorporating diverse edge features exhibit significantly improved predictive accuracy. A clear correlation is established between the richness of edge features and the effectiveness of the models evaluated.

Significance

The findings underscore the importance of edge features in enhancing model performance in graph-based analyses. This research opens avenues for future investigations into novel edge features and their applications across multiple domains, potentially leading to improved methodologies for analyzing complex graph data.

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