Semidefinite relaxations in optimal experiment design with application\n to substrate injection for hyperpolarized MRI
Bibliographic record
Abstract
We consider the problem of optimal input design for estimating uncertain\nparameters in a discrete-time linear state space model, subject to simultaneous\namplitude and l1/l2-norm constraints on the admissible inputs. We formulate\nthis problem as the maximization of a (non-concave) quadratic function over the\nspace of inputs, and use semidefinite relaxation techniques to efficiently find\nthe global solution or to provide an upper bound. This investigation is\nmotivated by a problem in medical imaging, specifically designing a substrate\ninjection profile for in vivo metabolic parameter mapping using magnetic\nresonance imaging (MRI) with hyperpolarized carbon-13 pyruvate. In the\nl2-norm-constrained case, we show that the relaxation is tight, allowing us to\nefficiently compute a globally optimal injection profile. In the\nl1-norm-constrained case the relaxation is no longer tight, but can be used to\nprove that the boxcar injection currently used in practice achieves at least\n98.7% of the global optimum.\n
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.012 | 0.022 |
| Meta-epidemiology (narrow) | 0.003 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.004 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".