Microscopy as a statistical, Rényi-Ulam, half-lie game: a new heuristic search strategy to accelerate imaging

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, Rényi-Ulam problem and is particularly relevant to practical microscopy. We analyse microscopy in the contexts of Rényi-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

Pengembangan Algoritma Pencarian Non Interaktif untuk Penyelesaian Permasalahan Ulam dengan Kebohongan Jamak

Pada permasalahan permainan klasik pencarian Ulam dan Rényi, penanya harus mengajukan beberapa pertanyaan iya dan tidak untuk mencari sebuah nilai dalam range pencarian yang sudah disepakati, namun penjawab diperbolehkan berbohong. Sudah ada solusi dari beberapa variasi pada permasalahan pencarian Ulam dan Rényi, yaitu pada jenis query antara rentang atau subset dan jumlah maksimal bohong antara satu, dua, tiga, dan seterusnya. Namun belum ada solusi yang sempurna untuk query yang non interaktif yaitu penjawab hanya boleh menjawab query penanya setelah penanya selesai menanyakan semua querynya. Belum ada penelitian yang menyelesaikan permasalahan ini. Pada paper ini akan dijelaskan solusi sempurna untuk permainan Ulam dan Rényi non interaktif dengan maksimal kebohongan jamak menggunakan kode biner dengan jarak Hamming. Hasil algoritma pada paper ini menunjukkan jumlah query yang jauh lebih sedikit dari algoritma umum repetisi biner dan hasil terbaik pada pengujian online ternama. ============================ On the classic Ulam and Rényi searching problem, the questioner has to ask some yes-no questions to find an unknown value within the agreed search space, but the answerer is allowed to lie. There are already solutions of some variations in the Ulam and Rényi searching problem, i.e. on the type of query between range or subset and the maximum number of lies between one, two, three, and so on. But there is no perfect solution for non-interactive queries which the answerer can only answer the questioner's query after the questioner has finished querying all the queries. No research has resolved this problem yet. In this paper we will describe the perfect solution for non-interactive Ulam and Rényi searching problem with many lies using binary code with Hamming distance. The algorithm results in this paper shows a much smaller number of queries than the common binary repetition algorithm and the best results on a reputable online judge

The Rényi-Ulam Pathological Liar Game with a Fixed Number of Lies

The q-round Rényi-Ulam pathological liar game with k lies on the set [n] := {1,..., n} is a 2-player perfect information zero sum game. In each round Paul chooses a subset A ⊆ [n] and Carole either assigns 1 lie to each element of A or to each element of [n]\A. Paul wins if after q rounds there is at least one element with k or fewer lies. The game is dual to the original Rényi-Ulam liar game for which the winning condition is that at most one element has k or fewer lies. Define F*k(q) to be the minimum n such that Paul can win the q-round pathological liar game with k lies and initial set [n]. For fixed k we prove that F*k (q) is within an absolute constant (depending only on k) of the sphere bound, 2q/(q≤k); this is already known to hold for the original Rényi-Ulam liar game due to a result of J. Spencer

The Rényi-Ulam Pathological Liar Game with a Fixed Number of Lies

The q-round Rényi-Ulam pathological liar game with k lies on the set [n]:= {1,..., n} is a 2-player perfect information zero sum game. In each round Paul chooses a subset A ⊆ [n] and Carole either assigns 1 lie to each element of A or to each element of [n] \ A. Paul wins if after q rounds there is at least one element with k or fewer lies. The game is dual to the original Rényi-Ulam liar game for which the winning condition is that at most one element has k or fewer lies. Define F ∗ k (q) to be the minimum n such that Paul can win the q-round pathological liar game with k lies and initial set [n]. For fixed k we prove that F ∗ k (q) is within an absolute constant (depending only on k) of the sphere bound, 2q / � � q ≤k; this is already known to hold for the original Rényi-Ulam liar game due to a result of J. Spencer. Key words: Rényi-Ulam game, pathological liar game, sphere bound, searching with lies 1991 MSC: 91A46, 05A99, 05B40