Related papers: Additive index and Carlitz rank
Smallish large cardinals $\kappa$ are often characterized by the existence of a collection of filters on $\kappa$, each of which is an ultrafilter on the subsets of $\kappa$ of some transitive $\mathrm{ZFC}^-$-model of size $ \kappa$. We…
In recent decades, a number of centrality metrics describing network properties of nodes have been proposed to rank the importance of nodes. In order to understand the correlations between centrality metrics and to approximate a…
Rademacher complexity is often used to characterize the learnability of a hypothesis class and is known to be related to the class size. We leverage this observation and introduce a new technique for estimating the size of an arbitrary…
In this paper, we introduce relative LS category of a map and study some of its properties. Then we introduce `higher topological complexity' of a map, a homotopy invariant. We give a cohomological lower bound and compare it with previously…
We study the asymptotic rank of adjacency matrices of a large class of edge-weighted configuration models. Here, the weight of a (multi-)edge can be any fixed non-zero element from an arbitrary field, as long as it is independent of the…
We introduce the coherent algebra of a compact metric measure space by analogy with the corresponding concept for a finite graph. As an application we show that upon topologizing the collection of isomorphism classes of compact metric…
In scenarios where training data is limited due to observation costs or data scarcity, enriching the label information associated with each instance becomes crucial for building high-accuracy classification models. In such contexts, it is…
Journal ranking is becoming more important in assessing the quality of academic research. Several indices have been suggested for this purpose, typically on the basis of a citation graph between the journals. We follow an axiomatic approach…
Shrub-depth and rank-depth are dense analogues of the tree-depth of a graph. It is well known that a graph has large tree-depth if and only if it has a long path as a subgraph. We prove an analogous statement for shrub-depth and rank-depth,…
We study the complexity of locally checkable labeling (LCL) problems on $\mathbb{Z}^n$ from the point of view of descriptive set theory, computability theory, and factors of i.i.d. Our results separate various complexity classes that were…
This paper classifies the complexity of various teaching models by their position in the arithmetical hierarchy. In particular, we determine the arithmetical complexity of the index sets of the following classes: (1) the class of uniformly…
List-wise learning to rank methods are considered to be the state-of-the-art. One of the major problems with these methods is that the ambiguous nature of relevance labels in learning to rank data is ignored. Ambiguity of relevance labels…
We count subrings of small index of $\mathbb{Z}^n$, where the addition and multiplication are defined componentwise. Let $f_n(k)$ denote the number of subrings of index $k$. For any $n$, we give a formula for this quantity for all integers…
We compute characteristic functionals of Dirichlet-Ferguson measures over a locally compact Polish space and prove continuous dependence of the random measure on the parameter measure. In finite dimension, we identify the dynamical symmetry…
Chatterjee (2021)'s ingenious approach to estimating a measure of dependence first proposed by Dette et al. (2013) based on simple rank statistics has quickly caught attention. This measure of dependence has the unusual property of being…
We use the notions of reflexivity and of reflexive dimensions in order to introduce probability measures for lattice polytopes and initiate the investigation of their statistical properties. Examples of applications to discrete geometry…
Cardinal functions provide valuable insight into the topological properties of spaces, helping to analyze and compare spaces in terms of their covering, convergence and separation properties. This paper focuses on investigating cardinal…
The linear complexity is a measure for the unpredictability of a sequence over a finite field and thus for its suitability in cryptography. In 2012, Diem introduced a new figure of merit for cryptographic sequences called expansion…
One of the consequences of the Compactness Principle in structural Ramsey theory is that the small Ramsey degrees cannot exceed the corresponding big Ramsey degrees, thereby justifying the choice of adjectives. However, it is unclear what…
The coincidence rank, introduced by Barge and Kwapisz, measures the regularity of the maximal equicontinuous factor of minimal dynamical systems. We provide a characterization of the finiteness of coincidence rank using a multivariate…