Related papers: Muddy Waters
In this paper we consider the problem of the quantile hedging from the point of view of a better informed agent acting on the market. The additional knowledge of the agent is modelled by a filtration initially enlarged by some random…
Event classification is a common task in gamma-ray astrophysics. It can be treated with rapidly-advancing machine learning algorithms, which have the potential to outperform traditional analysis methods. However, a major challenge for…
This essay considers ways that recent uses of computers in mathematics challenge contemporary views on the nature of mathematical understanding. It also puts these challenges in a historical perspective and offers speculation as to a…
Let $C_1,...,C_{d+1}$ be $d+1$ point sets in $\mathbb{R}^d$, each containing the origin in its convex hull. A subset $C$ of $\bigcup_{i=1}^{d+1} C_i$ is called a colorful choice (or rainbow) for $C_1, \dots, C_{d+1}$, if it contains exactly…
Expanding existing learning systems to provide high-quality customized models for more domains, such as new users, is challenged by the limited labeled data and the data and device heterogeneities. While knowledge distillation methods could…
Symbolic event recognition systems have been successfully applied to a variety of application domains, extracting useful information in the form of events, allowing experts or other systems to monitor and respond when significant events are…
We review some recent results on the Muskat problem modelling multiphase flow in porous media. Furthermore, we prove a new regularity criterion in terms of some norms of the initial data in critical spaces ($\dot{W}^{1,\infty}$ and…
Many questions that we ask about the world do not have a single clear answer, yet typical human annotation set-ups in machine learning assume there must be a single ground truth label for all examples in every task. The divergence between…
To assess the ability of current AI systems to correctly answer research-level mathematics questions, we share a set of ten math questions which have arisen naturally in the research process of the authors. The questions had not been shared…
Argumentation is a major topic in the study of Artificial Intelligence. Since the first edition in 2015, advancements in solving (abstract) argumentation frameworks are assessed in competition events, similar to other closely related…
Our interdisciplinary team Mathematics for Applications in Cultural Heritage (MACH) aims to use mathematical research for the benefit of the arts and humanities. Our ultimate goal is to create user-friendly software toolkits for artists,…
This paper applies machine learning and the mathematics of chaos to the task of designing indoor rock-climbing routes. Chaotic variation has been used to great advantage on music and dance, but the challenges here are quite different,…
Reasoning under uncertainty in Al hats come to mean assessing the credibility of hypotheses inferred from evidence. But techniques for assessing credibility do not tell a problem solver what to do when it is uncertain. This is the focus of…
We describe a new method for computing coherent Lagrangian vortices in two-dimensional flows according to any of the following approaches: black-hole vortices [Haller & Beron-Vera, 2013], objective Eulerian Coherent Structures (OECSs)…
This paper develops a theory of learning under ambiguity induced by the decision maker's beliefs about the collection of data correlated with the true state of the world. Within our framework, two classical results on Bayesian learning…
Volatiles, notably water, are key to the habitability of rocky planets. The presence of water in planetary material can be inferred from the atmospheric oxygen abundances of polluted white dwarfs, but this interpretation is often complex.…
Coloring is a notoriously hard problem, and even more so in the online setting, where each arriving vertex has to be colored immediately and irrevocably. Already on trees, which are trivially two-colorable, it is impossible to achieve…
Solving math word problem (MWP) with AI techniques has recently made great progress with the success of deep neural networks (DNN), but it is far from being solved. We argue that the ability of learning by analogy is essential for an MWP…
In an educational setting, an estimate of the difficulty of multiple-choice questions (MCQs), a commonly used strategy to assess learning progress, constitutes very useful information for both teachers and students. Since human assessment…
Whilst mathematicians assume classical reasoning principles by default they often context switch when working, restricting themselves to various forms of subclassical reasoning. This pattern is especially common amongst logicians and set…