相关论文: Class Cardinality Comparison as a Fermi Problem

It is well known that, under very weak assumptions, multiobjective optimization problems admit $(1+\varepsilon,\dots,1+\varepsilon)$-approximation sets (also called $\varepsilon$-Pareto sets) of polynomial cardinality (in the size of the…

Many machine learning problems require the prediction of multi-dimensional labels. Such structured prediction models can benefit from modeling dependencies between labels. Recently, several deep learning approaches to structured prediction…

This paper reports on an investigation into the correlations between students' understandings of introductory astronomy concepts and the correctness and coherency of their written responses to targeted Lecture-Tutorial questions. We…

Correlations between spacelike separated measurements on entangled quantum systems are stronger than any classical correlations and are at the heart of numerous quantum technologies. In practice, however, spacelike separation is often not…

Cardinality estimation is a fundamental task in database management systems, aiming to predict query results accurately without executing the queries. However, existing techniques either achieve low estimation accuracy or incur high…

Recent work has demonstrated the catastrophic effects of poor cardinality estimates on query processing time. In particular, underestimating query cardinality can result in overly optimistic query plans which take orders of magnitude longer…

This paper contributes to the theory of large cardinals beyond the Kunen inconsistency, or choiceless large cardinal axioms, in the context where the Axiom of Choice is not assumed. The first part of the paper investigates a periodicity…

In many problems of classical analysis extremal configurations appear to exhibit complicated fractal structure. This makes it much harder to describe extremals and to attack such problems. Many of these problems are related to the…

We study two models of the Majority problem. We are given n balls and an unknown coloring of them with two colors. We can ask sets of balls of size k as queries, and in the so-called General Model the answer to a query shows if all the…

Much recent work in cardinal characteristics has focused on generalizing results about $\omega$ to uncountable cardinals by studying analogues of classical cardinal characteristics on the generalized Baire and Cantor spaces $\kappa^\kappa$…

We introduce a new covering property, defined in terms of order types of sequences of open sets, rather than in terms of cardinalities of families. The most general form of this compactness notion depends on two ordinal parameters. In the…

We discuss the problem of separating consistently the total correlations in a bipartite quantum state into a quantum and a purely classical part. A measure of classical correlations is proposed and its properties are explored.

The selection of the best classification algorithm for a given dataset is a very widespread problem. It is also a complex one, in the sense it requires to make several important methodological choices. Among them, in this work we focus on…

Astrophysics spans an enormous range of questions on scales from individual planets to the entire cosmos. To address the richness of 21st century astrophysics requires a corresponding richness of telescopes spanning all bands and all…

We consider N quantum systems initially prepared in pure states and address the problem of unambiguously comparing them. One may ask whether or not all $N$ systems are in the same state. Alternatively, one may ask whether or not the states…

Many topics in introductory astronomy at the college or high-school level rely implicitly on using astronomical photographs and visual data in class. However, students bring many preconceptions to their understanding of these materials that…

Object cross-identification in multiple observations is often complicated by the uncertainties in their astrometric calibration. Due to the lack of standard reference objects, an image with a small field of view can have significantly…

Comparing alternatives in pairs is a well-known method of ranking creation. Experts are asked to perform a series of binary comparisons and then, using mathematical methods, the final ranking is prepared. As experts conduct the individual…

Inferring causal models from observed correlations is a challenging task, crucial to many areas of science. In order to alleviate the computational effort when sifting through possible causal explanations for some given observations, it is…

We show that there are widely-connected spaces of arbitrarily large cardinality, answering a question by David Bellamy.