Biosensor Arrays for Estimating Molecular Concentration in Fluid Flows
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Bibliographic record
Abstract
This paper constructs dynamical models and signal processing-based estimation algorithms for computing the concentration of target molecules in a fluid flow using an array of biosensors. Each biosensor is constructed out of protein molecules embedded in a synthetic cell membrane. The concentration evolves according to an advection-diffusion partial differential equation, which is coupled with chemical reaction equations on the biosensor surface. By using asymptotic analysis and the divergence theorem, an approximate model is constructed that describes the asymptotic behavior of the concentration as a system of ordinary differential equations. The estimate of target molecule concentration is then obtained by solving a nonlinear least squares problem. Then, explicit expressions are obtained for the variance and bias of the estimate using the derived approximate model. These expressions can evaluate the achievable improvement in the estimate based on the number of biosensors. As an example, the results are illustrated for a novel biosensor built out of protein molecules.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it