Joshua L. Proctor

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Extracting governing equations from data is a central challenge in many diverse areas of science and engineering. Data are abundant whereas models often remain elusive, as in climate science, neuroscience, ecology, finance, and epidemiology, to name only a few examples. In this work, we combine sparsity-promoting techniques and machine learning with(More)
The haemozoin crystal continues to be investigated extensively for its potential as a biomarker for malaria diagnostics. In order for haemozoin to be a valuable biomarker, it must be present in detectable quantities in the peripheral blood and distinguishable from false positives. Here, dark-field microscopy coupled with sophisticated image processing(More)
BACKGROUND The development and application of quantitative methods to understand disease dynamics and plan interventions is becoming increasingly important in the push toward eradication of human infectious diseases, exemplified by the ongoing effort to stop the spread of poliomyelitis. METHODS Dynamic mode decomposition (DMD) is a recently developed(More)
—The goal of compressive sensing is efficient reconstruction of data from few measurements, sometimes leading to a categorical decision. If only classification is required, reconstruction can be circumvented and the measurements needed are orders-of-magnitude sparser still. We define enhanced sparsity as the reduction in number of measurements required for(More)
In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in(More)
A model of malaria transmission dynamics is presented that tracks the genetic barcodes of individual Plasmodium falciparum infections using seasonally-driven effective reproduction rates for clonal propagation, external importation , and the outcrossing of strains both within and between infections. We explore quantitatively the relationship between(More)
Currently developing data driven algorithms for performing Koopman Mode Decomposition (KMD) on dynamical systems defined by data rather than equations. KMD is a generalization of the eigenvector/eigenvalue decomposition that is suitable for systems whose evolution is fundamentally nonlinear. The goal is to develop the theoretical and computational tools(More)
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