How to take an exam if you must: Decision under Deadline

This paper uses the example of an exam to model multi-dimensional search under a deadline. When the dimension is two, an order-invariance property allows simple characterization of the optimal search policy. Behavior is shown to be highly sensitive to changes in the deadline, and a wide variety of policies can be rationalized (as being optimal) as the length of the deadline increases. This is contrasted with behavior under the traditional case of geometric discounting, in which a similar sensitivity to changes in the discount factor cannot hold. For dimensions higher than two, the invariance principle does not hold; this increases complexity of the problem of finding the optimal search policy.Deadline, search, invariance

How to take an exam if you must: Decision under Deadline

This paper uses the example of an exam to model multi-dimensional search under a deadline. When the dimension is two, an order-invariance property allows simple characterization of the optimal search policy. Behavior is shown to be highly sensitive to changes in the deadline, and a wide variety of policies can be rationalized (as being optimal) as the length of the deadline increases. This is contrasted with behavior under the traditional case of geometric discounting, in which a similar sensitivity to changes in the discount factor cannot hold. For dimensions higher than two, the invariance principle does not hold; this increases complexity of the problem of finding the optimal search policy

Laws of Trigonometry in Symmetric Spaces

This paper consists of two parts. In the first part, we reformulate the work of E. Leuzinger on trigonometry in noncompact symmetric spaces. In the second part, we outline an alternative method using invariants of the isotropy group representation. Appropriately formulated, these methods apply to both compact and noncompact symmetric spaces. This work is contained in the Ph.D. dissertation of H.-L. Huynh

Laws of Trigonometry of SU(3) and SL(3,C)/SU(3)

We use a method outlined in the Ph.D. dissertation of H.-L. Huynh to derive laws of trigonometry of SU(3) and SL(3, C)/SU(3). This gives a unified alternative to the earlier results of H. Aslaksen and E. Leuzinger. This method also gives laws of trigonometry for n-tuples

Imaging PD-L1 Expression with ImmunoPET

High sensitivity imaging tools could provide a more holistic view of target antigen expression to improve the identification of patients who might benefit from cancer immunotherapy. We developed for immunoPET a novel recombinant human IgG1 (termed C4) that potently binds an extracellular epitope on human and mouse PD-L1 and radiolabeled the antibody with zirconium-89. Small animal PET/CT studies showed that ⁸⁹Zr-C4 detected antigen levels on a patient derived xenograft (PDX) established from a non-small-cell lung cancer (NSCLC) patient before an 8-month response to anti-PD-1 and anti-CTLA4 therapy. Importantly, the concentration of antigen is beneath the detection limit of previously developed anti-PD-L1 radiotracers, including radiolabeled atezolizumab. We also show that ⁸⁹Zr-C4 can specifically detect antigen in human NSCLC and prostate cancer models endogenously expressing a broad range of PD-L1. ⁸⁹Zr-C4 detects mouse PD-L1 expression changes in immunocompetent mice, suggesting that endogenous PD-1/2 will not confound human imaging. Lastly, we found that ⁸⁹Zr-C4 could detect acute changes in tumor expression of PD-L1 due to standard of care chemotherapies. In summary, we present evidence that low levels of PD-L1 in clinically relevant cancer models can be imaged with immunoPET using a novel recombinant human antibody