Quantum algorithm for tree size estimation, with applications to backtracking and 2-player games

We study quantum algorithms on search trees of unknown structure, in a model where the tree can be discovered by local exploration. That is, we are given the root of the tree and access to a black box which, given a vertex $v$, outputs the children of $v$. We construct a quantum algorithm which, given such access to a search tree of depth at most $n$, estimates the size of the tree $T$ within a factor of $1\pm \delta$ in $\tilde{O}(\sqrt{nT})$ steps. More generally, the same algorithm can be used to estimate size of directed acyclic graphs (DAGs) in a similar model. We then show two applications of this result: a) We show how to transform a classical backtracking search algorithm which examines $T$ nodes of a search tree into an $\tilde{O}(\sqrt{T}n^{3/2})$ time quantum algorithm, improving over an earlier quantum backtracking algorithm of Montanaro (arXiv:1509.02374). b) We give a quantum algorithm for evaluating AND-OR formulas in a model where the formula can be discovered by local exploration (modeling position trees in 2-player games). We show that, in this setting, formulas of size $T$ and depth $T^{o(1)}$ can be evaluated in quantum time $O(T^{1/2+o(1)})$. Thus, the quantum speedup is essentially the same as in the case when the formula is known in advance.Comment: Fixed some typo

A Randomized Trial Comparing Digital and Live Lecture Formats

Problem Statement and Background – Medical education is increasingly being conducted in community-based teaching sites making it difficult to provide a consistent curriculum. We conducted a randomized trial to assess whether digital lectures could replace live lectures. Methods – Students were randomized to either attending a lecture series at our main campus or viewing digital versions of the same lectures at community sites. Both groups completed an examination based on the lectures and the group viewing the digital lectures completed a feedback form. Results – The group who viewed the digital lectures performed slightly better than the live lecture group however the differences were not statistically significant. Despite technical problems the students who viewed the digital lectures overwhelmingly felt the digital lectures could replace live lectures. Conclusions – Digital lectures appear to be a viable alternative to live lectures as a means of delivering didactic presentations in a community-based setting

Conferences & Lectures

Dean Haddon shares global vision for law school and legal education. Navigating new spheres of international law. Distinguished visiting professors offer new perspectives. SEC Inspector General lectures on Madoff Scandal

CfA Plasma Talks

Notes from a series of 13 one hour (or more) lectures on Plasma Physics given to Ramesh Narayan' research group at the Harvard-Smithsonian Center for Astrophysics, between January and July 2012. Lectures 1 to 5 cover various key Plasma Physics themes. Lectures 6 to 12 mainly go over the Review Paper on "Multidimensional electron beam-plasma instabilities in the relativistic regime" [\emph{Physics of Plasmas} \textbf{17}, 120501 (2010)]. Lectures 13 talks about the so-called Biermann battery and its ability to generate magnetic fields from scratch.Comment: 58 pages, 21 figure

Quantum Gravity

General lectures on quantum gravity.Comment: Lectures given at Karpacz. 40 pages, submitted to Lecture Notes in Physics. Bigger figure

John F. Sonnett Memorial Lecture Series: List of Lectures

A list of lectures in the John F. Sonnett Memorial Lectures Series organized by topic. Document has handwritten notes.https://ir.lawnet.fordham.edu/events_programs_sonnett_miscellaneous/1008/thumbnail.jp