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Joshua Pickard

Publications and source records attributed to Joshua Pickard.

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EHR-MPC: Inference-Time Control for Sepsis Treatment with Generative Patient Digital Twins

Sepsis is a leading cause of mortality, yet optimal treatment policies remain contested. Existing reinforcement learning (RL) approaches learn fixed strategies for sepsis treatment, limiting adaptability to changing clinical objectives during inference. We propose EHRMPC, a framework that decouples learning patient dynamics from optimizing treatment by training a patient digital twin in the form of a generative electronic health record (EHR) model. The digital twin predicts clinical trajectories under interventions and enables model predictive control (MPC) to optimize treatments via inference-time planning over simulations. We evaluate EHR-MPC on a multicenter ICU sepsis cohort spanning 8 hospitals in the Mass General Brigham health system using both off-policy importance sampling and on-policy simulation-based evaluation. Relative to RL baselines, EHR-MPC achieves comparable off-policy performance and improved simulation performance. Unlike RL, this work frames sepsis treatment optimization as inference-time control over learned patient dynamics, establishing a general framework for decision making with generative clinical models.

stat.ML

Data-Driven Tensor Decomposition Identification of Homogeneous Polynomial Dynamical Systems

Homogeneous polynomial dynamical systems (HPDSs), which can be equivalently represented by tensors, are essential for modeling higher-order networked systems, including ecological networks, chemical reactions, and multi-agent robotic systems. However, identifying such systems from data is challenging due to the rapid growth in the number of parameters with increasing system dimension and polynomial degree. In this article, we adopt compact and scalable representations of HPDSs leveraging low-rank tensor decompositions, including tensor train, hierarchical Tucker, and canonical polyadic decompositions. These representations exploit the intrinsic multilinear structure of HPDSs and substantially reduce the dimensionality of the parameter space. Rather than identifying the full dynamic tensor, we develop a data-driven framework that directly learns the underlying factor tensors or matrices in the associated decompositions from time-series data. The resulting identification problem is solved using alternating least-squares algorithms tailored to each tensor decomposition, achieving both accuracy and computational efficiency. We further analyze the robustness of the proposed framework in the presence of measurement noise and characterize data informativity. Finally, we demonstrate the effectiveness of our framework with numerical examples.

eess.SY

Structural Controllability of Large-Scale Hypergraphs

Controlling real-world networked systems, including ecological, biomedical, and engineered networks that exhibit higher-order interactions, remains challenging due to inherent nonlinearities and large system scales. Despite extensive studies on graph controllability, the controllability properties of hypergraphs remain largely underdeveloped. Existing results focus primarily on exact controllability, which is often impractical for large-scale hypergraphs. In this article, we develop a structural controllability framework for hypergraphs by modeling hypergraph dynamics as polynomial dynamical systems. In particular, we extend classical notions of accessibility and dilation from linear graph-based systems to polynomial hypergraph dynamics and establish a hypergraph-based criterion under which the topology guarantees satisfaction of classical Lie-algebraic and Kalman-type rank conditions for almost all parameter choices. We further derive a topology-based lower bound on the minimum number of driver nodes required for structural controllability and leverage this bound to design a scalable driver node selection algorithm combining dilation-aware initialization via maximum matching with greedy accessibility expansion. We demonstrate the effectiveness and scalability of the proposed framework through numerical experiments on hypergraphs with tens to thousands of nodes and higher-order interactions.

math.OC

HIF: The hypergraph interchange format for higher-order networks

Many empirical systems contain complex interactions of arbitrary size, representing, for example, chemical reactions, social groups, co-authorship relationships, and ecological dependencies. These interactions are known as higher-order interactions and the collection of these interactions comprise a higher-order network, or hypergraph. Hypergraphs have established themselves as a popular and versatile mathematical representation of such systems and a number of software packages written in various programming languages have been designed to analyze these networks. However, the ecosystem of higher-order network analysis software is fragmented due to specialization of each software's programming interface and compatible data representations. To enable seamless data exchange between higher-order network analysis software packages, we introduce the Hypergraph Interchange Format (HIF), a standardized format for storing higher-order network data. HIF supports multiple types of higher-order networks, including undirected hypergraphs, directed hypergraphs, and abstract simplicial complexes, while actively exploring extensions to represent multiplex hypergraphs, temporal hypergraphs, and ordered hypergraphs. To accommodate the wide variety of metadata used in different contexts, HIF also includes support for attributes associated with nodes, edges, and incidences. This initiative is a collaborative effort involving authors, maintainers, and contributors from prominent hypergraph software packages. This project introduces a JSON schema with corresponding documentation and unit tests, example HIF-compliant datasets, and tutorials demonstrating the use of HIF with several popular higher-order network analysis software packages.

physics.soc-ph

Language Model Powered Digital Biology with BRAD

Recent advancements in Large Language Models (LLMs) are transforming biology, computer science, engineering, and every day life. However, integrating the wide array of computational tools, databases, and scientific literature continues to pose a challenge to biological research. LLMs are well-suited for unstructured integration, efficient information retrieval, and automating standard workflows and actions from these diverse resources. To harness these capabilities in bioinformatics, we present a prototype Bioinformatics Retrieval Augmented Digital assistant (BRAD). BRAD is a chatbot and agentic system that integrates a variety of bioinformatics tools. The Python package implements an AI \texttt{Agent} that is powered by LLMs and connects to a local file system, online databases, and a user's software. The \texttt{Agent} is highly configurable, enabling tasks such as Retrieval-Augmented Generation, searches across bioinformatics databases, and the execution of software pipelines. BRAD's coordinated integration of bioinformatics tools delivers a context-aware and semi-autonomous system that extends beyond the capabilities of conventional LLM-based chatbots. A graphical user interface (GUI) provides an intuitive interface to the system.

cs.AI

Dynamic Sensor Selection for Biomarker Discovery

Advances in methods of biological data collection are driving the rapid growth of comprehensive datasets across clinical and research settings. These datasets provide the opportunity to monitor biological systems in greater depth and at finer time steps than was achievable in the past. Classically, biomarkers are used to represent and track key aspects of a biological system. Biomarkers retain utility even with the availability of large datasets, since monitoring and interpreting changes in a vast number of molecules remains impractical. However, given the large number of molecules in these datasets, a major challenge is identifying the best biomarkers for a particular setting Here, we apply principles of observability theory to establish a general methodology for biomarker selection. We demonstrate that observability measures effectively identify biologically meaningful sensors in a range of time series transcriptomics data. Motivated by the practical considerations of biological systems, we introduce the method of dynamic sensor selection (DSS) to maximize observability over time, thus enabling observability over regimes where system dynamics themselves are subject to change. This observability framework is flexible, capable of modeling gene expression dynamics and using auxiliary data, including chromosome conformation, to select biomarkers. Additionally, we demonstrate the applicability of this approach beyond genomics by evaluating the observability of neural activity These applications demonstrate the utility of observability-guided biomarker selection for across a wide range of biological systems, from agriculture and biomanufacturing to neural applications and beyond.

q-bio.MN

Geometric Aspects of Observability of Hypergraphs

In this paper we consider aspects of geometric observability for hypergraphs, extending our earlier work from the uniform to the nonuniform case. Hypergraphs, a generalization of graphs, allow hyperedges to connect multiple nodes and unambiguously represent multi-way relationships which are ubiquitous in many real-world networks including those that arise in biology. We consider polynomial dynamical systems with linear outputs defined according to hypergraph structure, and we propose methods to evaluate local, weak observability.

math.DS

Structural Controllability of Polysystems via Directed Hypergraph Representation

This document explores structural controllability of polynomial dynamical systems or polysystems. We extend Lin's concept of structural controllability for linear systems, offering hypergraph-theoretic methods to rapidly assess strong controllability. Our main result establishes that a polysytem is structurally controllable when its hypergraph representation contains no hyperedge dilation and no inaccessible vertices. We propose two efficient, scalable algorithms to validate these conditions.

math.OC

Kronecker Product of Tensors and Hypergraphs: Structure and Dynamics

Hypergraphs and tensors extend classic graph and matrix theory to account for multiway relationships, which are ubiquitous in engineering, biological, and social systems. While the Kronecker product is a potent tool for analyzing the coupling of systems in graph or matrix contexts, its effectiveness in capturing multiway interactions remains elusive. In this article, we present a comprehensive exploration of algebraic, structural, and spectral properties of the tensor Kronecker product. We express Tucker and tensor train decompositions and various tensor eigenvalues in terms of the tensor Kronecker product. Additionally, we utilize the tensor Kronecker product to form Kronecker hypergraphs, a tensor-based hypergraph product, and investigate the structure and stability of polynomial dynamics on Kronecker hypergraphs. Finally, we provide numerical examples to demonstrate the utility of the tensor Kronecker product in computing Z-eigenvectors, various tensor decompositions, and determining the stability of polynomial systems.

math.DS

Observability of Hypergraphs

In this paper we develop a framework to study observability for uniform hypergraphs. Hypergraphs, being extensions of graphs, allow edges to connect multiple nodes and unambiguously represent multi-way relationships which are ubiquitous in many real-world networks. We extend the canonical homogeneous polynomial or multilinear dynamical system on uniform hypergraphs to include linear outputs, and we derive a Kalman-rank-like condition for assessing the local weak observability. We propose an exact techniques for determining the local observability criterion, and we propose a greedy heuristic to determine the minimum set of observable nodes. Numerical experiments demonstrate our approach on several hypergraph topologies and a hypergraph representations of neural networks within the mouse hypothalamus.

math.DS

TransferD2: Automated Defect Detection Approach in Smart Manufacturing using Transfer Learning Techniques

Quality assurance is crucial in the smart manufacturing industry as it identifies the presence of defects in finished products before they are shipped out. Modern machine learning techniques can be leveraged to provide rapid and accurate detection of these imperfections. We, therefore, propose a transfer learning approach, namely TransferD2, to correctly identify defects on a dataset of source objects and extend its application to new unseen target objects. We present a data enhancement technique to generate a large dataset from the small source dataset for building a classifier. We then integrate three different pre-trained models (Xception, ResNet101V2, and InceptionResNetV2) into the classifier network and compare their performance on source and target data. We use the classifier to detect the presence of imperfections on the unseen target data using pseudo-bounding boxes. Our results show that ResNet101V2 performs best on the source data with an accuracy of 95.72%. Xception performs best on the target data with an accuracy of 91.00% and also provides a more accurate prediction of the defects on the target images. Throughout the experiment, the results also indicate that the choice of a pre-trained model is not dependent on the depth of the network. Our proposed approach can be applied in defect detection applications where insufficient data is available for training a model and can be extended to identify imperfections in new unseen data.

cs.CV

Hypergraph Analysis Toolbox for Chromosome Conformation

Recent advances in biological technologies, such as multi-way chromosome conformation capture (3C), require development of methods for analysis of multi-way interactions. Hypergraphs are mathematically tractable objects that can be utilized to precisely represent and analyze multi-way interactions. Here we present the Hypergraph Analysis Toolbox (HAT), a software package for visualization and analysis of multi-way interactions in complex systems.

q-bio.QM

Fault Detection in Ball Bearings

Ball bearing joints are a critical component in all rotating machinery, and detecting and locating faults in these joints is a significant problem in industry and research. Intelligent fault detection (IFD) is the process of applying machine learning and other statistical methods to monitor the health states of machines. This paper explores the construction of vibration images, a preprocessing technique that has been previously used to train convolutional neural networks for ball bearing joint IFD. The main results demonstrate the robustness of this technique by applying it to a larger dataset than previously used and exploring the hyperparameters used in constructing the vibration images.

eess.SP

Efficient Set-Based Approaches for the Reliable Computation of Robot Capabilities

To reliably model real robot characteristics, interval linear systems of equations allow to describe families of problems that consider sets of values. This allows to easily account for typical complexities such as sets of joint states and design parameter uncertainties. Inner approximations of the solutions to the interval linear systems can be used to describe the common capabilities of a robotic manipulator corresponding to the considered sets of values. In this work, several classes of problems are considered. For each class, reliable and efficient polytope, n-cube, and n-ball inner approximations are presented. The interval approaches usually proposed are inefficient because they are too computationally heavy for certain applications, such as control. We propose efficient new inner approximation theorems for the considered classes of problems. This allows for usage with real-time applications as well as rapid analysis of potential designs. Several applications are presented for a redundant planar manipulator including locally evaluating the manipulator's velocity, acceleration, and static force capabilities, and evaluating its future acceleration capabilities over a given time horizon.

cs.RO