Related papers: Exploring Mount Neverest
The first part of this paper contains an introduction to Bell inequalities and Tsirelson's theorem for the non-specialist. The next part gives an explicit optimum construction for the "hard" part of Tsirelson's theorem. In the final part we…
Borwein et al. (2000) solved a surprise maximization problem by applying results from convex analysis and mathematical programming. Although, their proof is elegant, it requires advanced knowledge from both areas to understand it. Here, we…
We consider the problem of inferring the topology of a network using the measurements available at the end nodes, without cooperation from the internal nodes. To this end, we provide a simple method to obtain path interference which…
Multivariate, heteroscedastic errors complicate statistical inference in many large-scale denoising problems. Empirical Bayes is attractive in such settings, but standard parametric approaches rest on assumptions about the form of the prior…
This paper is motivated by two problems in the theory of Diophantine approximation, namely, Davenport's problem regarding badly approximable points on submanifolds of a Euclidean space and Schmidt's problem regarding the intersections of…
In 1971, Knuth gave an $O(n^2)$-time algorithm for the classic problem of finding an optimal binary search tree. Knuth's algorithm works only for search trees based on 3-way comparisons, while most modern computers support only 2-way…
In the longest plane spanning tree problem, we are given a finite planar point set $\mathcal{P}$, and our task is to find a plane (i.e., noncrossing) spanning tree for $\mathcal{P}$ with maximum total Euclidean edge length. Despite more…
We propose a generative model that achieves minimax-optimal convergence rates for estimating probability distributions supported on unknown low-dimensional manifolds. Building on Fefferman's solution to the geometric Whitney problem, our…
A searcher is tasked with exploring a graph with edge lengths and vertex weights, starting from a designated vertex. Initially, only the starting vertex is considered explored. At each step, the searcher adds an edge to the solution,…
This paper describes ongoing research into planning in an uncertain environment. In particular, it introduces U-Plan, a planning system that constructs quantitatively ranked plans given an incomplete description of the state of the world.…
The tree inclusion problem is, given two node-labeled trees $P$ and $T$ (the ``pattern tree'' and the ``target tree''), to locate every minimal subtree in $T$ (if any) that can be obtained by applying a sequence of node insertion operations…
Sir Arthur Eddington is considered one of the greatest astrophysicist of the twentieth century and yet he gained a stigma when, in the 1930s, he embarked on a quest to develop a unified theory of gravity and quantum mechanics. His attempts…
We consider the problem of computing the Fr\'echet distance between two curves for which the exact locations of the vertices are unknown. Each vertex may be placed in a given uncertainty region for that vertex, and the objective is to place…
In this paper, the authors investigate the Deep Sea Treasure (DST) problem as proposed by Vamplew et al. Through a number of proofs, the authors show the original DST problem to be quite basic, and not always representative of practical…
A recently introduced general-purpose heuristic for finding high-quality solutions for many hard optimization problems is reviewed. The method is inspired by recent progress in understanding far-from-equilibrium phenomena in terms of {\em…
We construct crude estimates for non-optimality of quantum measurements in terms of their violation of Holevo's simplified minimum-error optimality conditions. As an application, we show that a modification of Barnett and Croke's proof of…
We study set selection problems where the weights are uncertain. Instead of its exact weight, only an uncertainty interval containing its true weight is available for each element. In some cases, some solutions are universally optimal;…
Adaptive exploration methods propose ways to learn complex policies via alternating between exploration and exploitation. An important question for such methods is to determine the appropriate moment to switch between exploration and…
This paper proposes an optimal autonomous search framework, namely Dual Control for Exploration and Exploitation (DCEE), for a target at unknown location in an unknown environment. Source localisation is to find sources of atmospheric…
The so-called problem of grue was introduced by Nelson Goodman in 1954 as a "riddle" about induction, a riddle which has been widely thought to cast doubt on the validity and rationality of induction. That unnecessary doubt in turn is…