Related papers: Exploring Mount Neverest
We provide a list of (mainly unsolved) problems in ordered and orderable groups. These were originally compiled 10 years ago by the last two authors. New problems have been added to the list. Progress on some of these is noted and…
In this article, we study the Euclidean minimum spanning tree problem in an imprecise setup. The problem is known as the \emph{Minimum Spanning Tree Problem with Neighborhoods} in the literature. We study the problem where the neighborhoods…
In classic robust optimization, it is assumed that a set of possible parameter realizations, the uncertainty set, is modeled in a previous step and part of the input. As recent work has shown, finding the most suitable uncertainty set is in…
In this paper we consider a set of travelers, starting from likely different locations towards a common destination within a road network, and propose solutions to find the optimal connecting points for them. A connecting point is a vertex…
Modern statistical software and machine learning libraries are enabling semi-automated statistical inference. Within this context, it appears easier and easier to try and fit many models to the data at hand, reversing thereby the Fisherian…
In incomplete financial markets not every contingent claim can be replicated by a self-financing strategy. The risk of the resulting shortfall can be measured by convex risk measures, recently introduced by F\"ollmer, Schied (2002). The…
We consider optimal design of infinite-dimensional Bayesian linear inverse problems governed by partial differential equations that contain secondary reducible model uncertainties, in addition to the uncertainty in the inversion parameters.…
Given a tree, a set of pebbles initially stationed at some nodes of the tree, and a set of target nodes, the Unlabeled Pebble Motion on Trees problem (UPMT) asks to find a plan to move the pebbles one-at-a-time from the starting nodes to…
One of the actual problems in the field of numerical optimisation, as is well known, is the problem of the search for the global extremum of a multivariate function [1-9,13,14,17-21]. Various versions of the random search methods [6,8,9]…
We study the problem of high-dimensional robust mean estimation in the presence of a constant fraction of adversarial outliers. A recent line of work has provided sophisticated polynomial-time algorithms for this problem with…
Various problems in manifold estimation make use of a quantity called the reach, denoted by $\tau\_M$, which is a measure of the regularity of the manifold. This paper is the first investigation into the problem of how to estimate the…
Prior studies on covert communication with noise uncertainty adopted a worst-case approach from the warden's perspective. That is, the worst-case detection performance of the warden is used to assess covertness, which is overly optimistic.…
The problem of robust utility maximization in an incomplete market with volatility uncertainty is considered, in the sense that the volatility of the market is only assumed to lie between two given bounds. The set of all possible models…
We consider several hill-climbing approaches to clustering as formulated by Fukunaga and Hostetler in the 1970's. We study both continuous-space and discrete-space (i.e., medoid) variants and establish their consistency.
Advances in artificial intelligence (AI) and deep learning have led to neural networks being used to generate lightning-speed answers to complex science questions, paintings in the style of Monet, or stories like those of Twain. Leveraging…
We solve the Dirichlet problem for fully nonlinear elliptic equations on Riemannian manifolds under essentially optimal structure conditions, especially with no restrictions to the curvature of the underlying manifold and the second…
The increasing recognition of the association between adverse human health conditions and many environmental substances as well as processes has led to the need to monitor them. An important problem that arises in environmental statistics…
This study examines the time complexities of the unbalanced optimal transport problems from an algorithmic perspective for the first time. We reveal which problems in unbalanced optimal transport can/cannot be solved efficiently.…
To maximize its success, an AGI typically needs to explore its initially unknown world. Is there an optimal way of doing so? Here we derive an affirmative answer for a broad class of environments.
This paper investigates the consumption and risk taking decision of an economic agent with partial irreversibility of consumption decision by formalizing the theory proposed by Duesenberry (1949). The optimal policies exhibit a type of the…