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We derive bounds on the moduli of the eigenvalues of special type of rational matrices using the following techniques/methods: (1) the Bauer-Fike theorem on an associated block matrix of the given rational matrix, (2) by associating a real rational function, along with Rouch$\text{\'e}$ theorem for the rational matrix and (3) by a numerical radius inequality for a block matrix for the rational matrix. These bounds are compared when the coefficients are unitary matrices. Numerical examples are given to illustrate the results obtained.

One persistent obstacle in industrial quality inspection is the detection of anomalies. In real-world use cases, two problems must be addressed: anomalous data is sparse and the same types of anomalies need to be detected on previously unseen objects. Current anomaly detection approaches can be trained with sparse nominal data, whereas domain generalization approaches enable detecting objects in previously unseen domains. Utilizing those two observations, we introduce the hybrid task of domain generalization on sparse classes. To introduce an accompanying dataset for this task, we present a modification of the well-established MVTec AD dataset by generating three new datasets. In addition to applying existing methods for benchmark, we design two embedding-based approaches, Spatial Embedding MLP (SEMLP) and Labeled PatchCore. Overall, SEMLP achieves the best performance with an average image-level AUROC of 87.2 % vs. 80.4 % by MIRO. The new and openly available datasets allow for further research to improve industrial anomaly detection.

There is an ongoing need for scalable tools to aid researchers in both retrospective and prospective standardization of discrete entity types -- such as disease names, cell types or chemicals -- that are used in metadata associated with biomedical data. When metadata are not well-structured or precise, the associated data are harder to find and are often burdensome to reuse, analyze or integrate with other datasets due to the upfront curation effort required to make the data usable -- typically through retrospective standardization and cleaning of the (meta)data. With the goal of facilitating the task of standardizing metadata -- either in bulk or in a one-by-one fashion; for example, to support auto-completion of biomedical entities in forms -- we have developed an open-source tool called text2term that maps free-text descriptions of biomedical entities to controlled terms in ontologies. The tool is highly configurable and can be used in multiple ways that cater to different users and expertise levels -- it is available on PyPI and can be used programmatically as any Python package; it can also be used via a command-line interface; or via our hosted, graphical user interface-based Web application (//text2term.hms.harvard.edu); or by deploying a local instance of our interactive application using Docker.

Researchers would often like to leverage data from a collection of sources (e.g., primary studies in a meta-analysis) to estimate causal effects in a target population of interest. However, traditional meta-analytic methods do not produce causally interpretable estimates for a well-defined target population. In this paper, we present the CausalMetaR R package, which implements efficient and robust methods to estimate causal effects in a given internal or external target population using multi-source data. The package includes estimators of average and subgroup treatment effects for the entire target population. To produce efficient and robust estimates of causal effects, the package implements doubly robust and non-parametric efficient estimators and supports using flexible data-adaptive (e.g., machine learning techniques) methods and cross-fitting techniques to estimate the nuisance models (e.g., the treatment model, the outcome model). We describe the key features of the package and demonstrate how to use the package through an example.

The prediction of protein 3D structure from amino acid sequence is a computational grand challenge in biophysics, and plays a key role in robust protein structure prediction algorithms, from drug discovery to genome interpretation. The advent of AI models, such as AlphaFold, is revolutionizing applications that depend on robust protein structure prediction algorithms. To maximize the impact, and ease the usability, of these novel AI tools we introduce APACE, AlphaFold2 and advanced computing as a service, a novel computational framework that effectively handles this AI model and its TB-size database to conduct accelerated protein structure prediction analyses in modern supercomputing environments. We deployed APACE in the Delta and Polaris supercomputers, and quantified its performance for accurate protein structure predictions using four exemplar proteins: 6AWO, 6OAN, 7MEZ, and 6D6U. Using up to 300 ensembles, distributed across 200 NVIDIA A100 GPUs, we found that APACE is up to two orders of magnitude faster than off-the-self AlphaFold2 implementations, reducing time-to-solution from weeks to minutes. This computational approach may be readily linked with robotics laboratories to automate and accelerate scientific discovery.

While undulatory swimming of elongate limbless robots has been extensively studied in open hydrodynamic environments, less research has been focused on limbless locomotion in complex, cluttered aquatic environments. Motivated by the concept of mechanical intelligence, where controls for obstacle navigation can be offloaded to passive body mechanics in terrestrial limbless locomotion, we hypothesize that principles of mechanical intelligence can be extended to cluttered hydrodynamic regimes. To test this, we developed an untethered limbless robot capable of undulatory swimming on water surfaces, utilizing a bilateral cable-driven mechanism inspired by organismal muscle actuation morphology to achieve programmable anisotropic body compliance. We demonstrated through robophysical experiments that, similar to terrestrial locomotion, an appropriate level of body compliance can facilitate emergent swim through complex hydrodynamic environments under pure open-loop control. Moreover, we found that swimming performance depends on undulation frequency, with effective locomotion achieved only within a specific frequency range. This contrasts with highly damped terrestrial regimes, where inertial effects can often be neglected. Further, to enhance performance and address the challenges posed by nondeterministic obstacle distributions, we incorporated computational intelligence by developing a real-time body compliance tuning controller based on cable tension feedback. This controller improves the robot's robustness and overall speed in heterogeneous hydrodynamic environments.

Most scientific machine learning (SciML) applications of neural networks involve hundreds to thousands of parameters, and hence, uncertainty quantification for such models is plagued by the curse of dimensionality. Using physical applications, we show that $L_0$ sparsification prior to Stein variational gradient descent ($L_0$+SVGD) is a more robust and efficient means of uncertainty quantification, in terms of computational cost and performance than the direct application of SGVD or projected SGVD methods. Specifically, $L_0$+SVGD demonstrates superior resilience to noise, the ability to perform well in extrapolated regions, and a faster convergence rate to an optimal solution.

Evidence to guide healthcare decisions is often limited by a lack of relevant and trustworthy literature as well as difficulty in contextualizing existing research for a specific patient. Large language models (LLMs) could potentially address both challenges by either summarizing published literature or generating new studies based on real-world data (RWD). We evaluated the ability of five LLM-based systems in answering 50 clinical questions and had nine independent physicians review the responses for relevance, reliability, and actionability. As it stands, general-purpose LLMs (ChatGPT-4, Claude 3 Opus, Gemini Pro 1.5) rarely produced answers that were deemed relevant and evidence-based (2% - 10%). In contrast, retrieval augmented generation (RAG)-based and agentic LLM systems produced relevant and evidence-based answers for 24% (OpenEvidence) to 58% (ChatRWD) of questions. Only the agentic ChatRWD was able to answer novel questions compared to other LLMs (65% vs. 0-9%). These results suggest that while general-purpose LLMs should not be used as-is, a purpose-built system for evidence summarization based on RAG and one for generating novel evidence working synergistically would improve availability of pertinent evidence for patient care.

With wide application of Artificial Intelligence (AI), it has become particularly important to make decisions of AI systems explainable and transparent. In this paper, we proposed a new Explainable Artificial Intelligence (XAI) method called ShapG (Explanations based on Shapley value for Graphs) for measuring feature importance. ShapG is a model-agnostic global explanation method. At the first stage, it defines an undirected graph based on the dataset, where nodes represent features and edges are added based on calculation of correlation coefficients between features. At the second stage, it calculates an approximated Shapley value by sampling the data taking into account this graph structure. The sampling approach of ShapG allows to calculate the importance of features efficiently, i.e. to reduce computational complexity. Comparison of ShapG with other existing XAI methods shows that it provides more accurate explanations for two examined datasets. We also compared other XAI methods developed based on cooperative game theory with ShapG in running time, and the results show that ShapG exhibits obvious advantages in its running time, which further proves efficiency of ShapG. In addition, extensive experiments demonstrate a wide range of applicability of the ShapG method for explaining complex models. We find ShapG an important tool in improving explainability and transparency of AI systems and believe it can be widely used in various fields.

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.