arXiv subjects

Nathaniel D. Osgood

Publications and source records attributed to Nathaniel D. Osgood.

6 recordsLinked to original sources

arXiv2025

Compositional System Dynamics: The Higher Mathematics Underlying System Dynamics Diagrams & Practice

This work establishes a robust mathematical foundation for compositional System Dynamics modeling, leveraging category theory to formalize and enhance the representation, analysis, and composition of system models. Here, System Dynamics diagrams, such as stock & flow diagrams, system structure diagrams, and causal loop diagrams, are formulated as categorical constructs, enabling scalable, transparent, and systematic reasoning. By encoding these diagrams as data using attributed C-sets and utilizing advanced categorical tools like structured cospans, pushouts, pullbacks, and functor mappings, the framework supports modular composition, stratification, and seamless mapping between syntax and semantics. The approach underwrites traditional practice with firm mathematical structure, facilitates the identification of certain forms of pathways and feedback loops, the detection of simple patterns within complex diagrams, common structure between diagrams, and structure-preserving mappings between diverse diagram types. Additionally, this framework supports alternative semantics, such as stochastic transition dynamics, extending beyond traditional ordinary differential equation (ODE) representations. Applications in compositional modeling, modularity, and team-based collaboration demonstrate the practical advantages of this advanced framework. Future directions include integrating dimensional annotations, supporting hybrid and agent-based modeling paradigms, and expanding the framework's applicability to global and local temporal reasoning through temporal sheaves. By revealing and formalizing the hidden mathematical structure of System Dynamics diagrams, this work empowers practitioners to tackle complex systems with clarity, scalability, and rigor.

eess.SY↗

arXiv2023

Compositional Modeling with Stock and Flow Diagrams

Stock and flow diagrams are widely used in epidemiology to model the dynamics of populations. Although tools already exist for building these diagrams and simulating the systems they describe, we have created a new package called StockFlow, part of the AlgebraicJulia ecosystem, which uses ideas from category theory to overcome notable limitations of existing software. Compositionality is provided by the theory of decorated cospans: stock and flow diagrams can be composed to form larger ones in an intuitive way formalized by the operad of undirected wiring diagrams. Our approach also cleanly separates the syntax of stock and flow diagrams from the semantics they can be assigned. We consider semantics in ordinary differential equations, although others are possible. As an example, we explain code in StockFlow that implements a simplified version of a COVID-19 model used in Canada.

cs.LO↗

arXiv2023

Agent-Based Modeling and its Tradeoffs: An Introduction & Examples

Agent-based modeling is a computational dynamic modeling technique that may be less familiar to some readers. Agent-based modeling seeks to understand the behaviour of complex systems by situating agents in an environment and studying the emergent outcomes of agent-agent and agent-environment interactions. In comparison with compartmental models, agent-based models offer simpler, more scalable and flexible representation of heterogeneity, the ability to capture dynamic and static network and spatial context, and the ability to consider history of individuals within the model. In contrast, compartmental models offer faster development time with less programming required, lower computational requirements that do not scale with population, and the option for concise mathematical formulation with ordinary, delay or stochastic differential equations supporting derivation of properties of the system behaviour. In this chapter, basic characteristics of agent-based models are introduced, advantages and disadvantages of agent-based models, as compared with compartmental models, are discussed, and two example agent-based infectious disease models are reviewed.

cs.MA↗

arXiv2023

A Categorical Framework for Modeling with Stock and Flow Diagrams

Stock and flow diagrams are already an important tool in epidemiology, but category theory lets us go further and treat these diagrams as mathematical entities in their own right. In this chapter we use communicable disease models created with our software, StockFlow.jl, to explain the benefits of the categorical approach. We first explain the category of stock-flow diagrams and note the clear separation between the syntax of these diagrams and their semantics, demonstrating three examples of semantics already implemented in the software: ODEs, causal loop diagrams, and system structure diagrams. We then turn to two methods for building large stock-flow diagrams from smaller ones in a modular fashion: composition and stratification. Finally, we introduce the open-source ModelCollab software for diagram-based collaborative modeling. The graphical user interface of this web-based software lets modelers take advantage of the ideas discussed here without any knowledge of their categorical foundations.

cs.LO↗

arXiv2020

DNA Methylation Data to Predict Suicidal and Non-Suicidal Deaths: A Machine Learning Approach

The objective of this study is to predict suicidal and non-suicidal deaths from DNA methylation data using a modern machine learning algorithm. We used support vector machines to classify existing secondary data consisting of normalized values of methylated DNA probe intensities from tissues of two cortical brain regions to distinguish suicide cases from control cases. Before classification, we employed Principal component analysis (PCA) and t-distributed Stochastic Neighbor Embedding (t-SNE) to reduce the dimension of the data. In comparison to PCA, the modern data visualization method t-SNE performs better in dimensionality reduction. t-SNE accounts for the possible non-linear patterns in low-dimensional data. We applied four-fold cross-validation in which the resulting output from t-SNE was used as training data for the Support Vector Machine (SVM). Despite the use of cross-validation, the nominally perfect prediction of suicidal deaths for BA11 data suggests possible over-fitting of the model. The study also may have suffered from 'spectrum bias' since the individuals were only studied from two extreme scenarios. This research constitutes a baseline study for classifying suicidal and non-suicidal deaths from DNA methylation data. Future studies with larger sample size, while possibly incorporating methylation data from living individuals, may reduce the bias and improve the accuracy of the results.

q-bio.GN↗

arXiv2019

Cough Detection Using Hidden Markov Models

Respiratory infections and chronic respiratory diseases impose a heavy health burden worldwide. Coughing is one of the most common symptoms of many such infections, and can be indicative of flare-ups of chronic respiratory diseases. Whether at a clinical or public health level, the capacity to identify bouts of coughing can aid understanding of population and individual health status. Developing health monitoring models in the context of respiratory diseases and also seasonal diseases with symptoms such as cough has the potential to improve quality of life, help clinicians and public health authorities with their decisions and decrease the cost of health services. In this paper, we investigated the ability to which a simple machine learning approach in the form of Hidden Markov Models (HMMs) could be used to classify different states of coughing using univariate (with a single energy band as the input feature) and multivariate (with a multiple energy band as the input features) binned time series using both of cough data. We further used the model to distinguish cough events from other events and environmental noise. Our Hidden Markov algorithm achieved 92% AUR (Area Under Receiver Operating Characteristic Curve) in classifying coughing events in noisy environments. Moreover, comparison of univariate with multivariate HMMs suggest a high accuracy of multivariate HMMs for cough event classifications.

cs.SD↗