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)
Systems without Koopman-invariant subspaces that explicitly span the state For any system with multiple fixed points, periodic orbits, or atrracting/repelling structures, there is no finite-dimensional Koopman invariant subspace that explicitly includes the state. This follows from the fact that these systems cannot be topologically conjugate to a(More)