# Microscopy as a statistical, R\'enyi-Ulam, half-lie game: a new heuristic search strategy to accelerate imaging

## TL;DR

This paper models the challenge of locating fluorescent targets in microscopy as a Re9nyi-Ulam game with half-lies, developing heuristics that improve search efficiency under deceptive responses.

## Contribution

It introduces a new family of heuristics for microscopy search problems modeled as half-lie Re9nyi-Ulam games, analyzing their efficiency and optimal partitioning strategies.

## Key findings

- Trisectioning with verification is most efficient in most cases.
- Verification incurs a 50% penalty in zero-half-lie bisectioning.
- Optimal search strategies depend on the presence and rate of half-lies.

## Abstract

Finding a fluorescent target in a biological environment is a common and pressing microscopy problem. This task is formally analogous to the canonical search problem. In ideal (noise-free, truthful) search problems, the well-known binary search is optimal. The case of half-lies, where one of two responses to a search query may be deceptive, introduces a richer, R\'enyi-Ulam problem and is particularly relevant to practical microscopy. We analyse microscopy in the contexts of R\'enyi-Ulam games and half-lies, developing a new family of heuristics. We show the cost of insisting on verification by positive result in search algorithms; for the zero-half-lie case bisectioning with verification incurs a 50% penalty in the average number of queries required. The optimal partitioning of search spaces directly following verification in the presence of random half-lies is determined. Trisectioning with verification is shown to be the most efficient heuristic of the family in a majority of cases.