Related papers: Muddy Waters
The B\"o\"ogg is a large model of a snowman, constructed of inflammable materials and filled with explosives. During the traditional festival of Sechsel\"auten, which takes place each spring in Zurich, Switzerland, the B\"o\"ogg is placed…
Social choice has become a foundational component of modern machine learning systems. From auctions and resource allocation to the alignment of large generative models, machine learning pipelines increasingly aggregate heterogeneous…
The advent of large reasoning models, such as OpenAI o1 and DeepSeek R1, has significantly advanced complex reasoning tasks. However, their capabilities in multilingual complex reasoning remain underexplored, with existing efforts largely…
Chain-of-thought (CoT) prompting enables large language models (LLMs) to solve complex reasoning tasks by generating an explanation before the final prediction. Despite it's promising ability, a critical downside of CoT prompting is that…
These informal notes are based on the author's lecture at the National Academies of Science, Engineering, and Mathematics workshop on "AI to Assist Mathematical Reasoning" in June 2023. The goal is to think through a path by which we might…
Facts are subject to contingencies and can be true or false in different circumstances. One such contingency is time, wherein some facts mutate over a given period, e.g., the president of a country or the winner of a championship.…
Effective teaching relies on knowing what students know-or think they know. Revealing student thinking is challenging. Often used because of their ease of grading, even the best multiple choice (MC) tests, those using research based…
This paper treat determinacy of strong moment problems in part I and indeterminacy of strong moment problems in part II. This paper is a summary of the following papers: [1] Ald\'en. E., Determinacy of Strong Moment Problems. [2] On…
Notes from lectures given at the Autumn School on Algebraic and Arithmetic Geometry at the Johannes Gutenberg-Universit\"at Mainz in October 2017.
Scientific discoveries are often made by finding a pattern or object that was not predicted by the known rules of science. Oftentimes, these anomalous events or objects that do not conform to the norms are an indication that the rules of…
A covering system is a finite collection of arithmetic progressions whose union is the set of integers. The study of these objects was initiated by Erd\H{o}s in 1950, and over the following decades he asked many questions about them. Most…
During natural disasters and conflicts, information about what happened is often confusing, messy, and distributed across many sources. We would like to be able to automatically identify relevant information and assemble it into coherent…
Everything has already been said about the Monty Hall problem, to the point of attracting attention of the high school mathematics program. The purpose of this text is therefore not to add more, but rather to to sort it out while clarifying…
Existing recommender systems tend to prioritize items closely aligned with users' historical interactions, inevitably trapping users in the dilemma of ``filter bubble''. Recent efforts are dedicated to improving the diversity of…
Automatic headline generation enables users to comprehend ongoing news events promptly and has recently become an important task in web mining and natural language processing. With the growing need for news headline generation, we argue…
In this lecture notes we present the equations and the physics involved in the dynamic of incompressible fluids. We present the mathematical techniques needed in order to prove the existence and uniqueness result for the case where we…
There are many extremely challenging problems about existence of monochromatic arithmetic progressions in colorings of groups. Many theorems hold only for abelian groups as results on non-abelian groups are often much more difficult to…
We study colored coverage and clustering problems. Here, we are given a colored point set where the points are covered by (unknown) $k$ clusters, which are monochromatic (i.e., all the points covered by the same cluster, have the same…
Math word problems form a natural abstraction to a range of quantitative reasoning problems, such as understanding financial news, sports results, and casualties of war. Solving such problems requires the understanding of several…
In this paper we present an approach to extract ordered timelines of events, their participants, locations and times from a set of multilingual and cross-lingual data sources. Based on the assumption that event-related information can be…