相关论文: Generalized partitioned local depth

Rough set theory is one of the most widely used and significant approaches for handling incomplete information. It divides the universe in the beginning and uses equivalency relations to produce blocks. Numerous generalized rough set models…

The semantic segmentation task aims at dense classification at the pixel-wise level. Deep models exhibited progress in tackling this task. However, one remaining problem with these approaches is the loss of spatial precision, often produced…

This text provides an introduction to distributed local algorithms -- an area at the intersection of theoretical computer science and discrete mathematics. We collect recent results in the area and demonstrate how they lead to a clean…

In network science, researchers often use mutual information to understand the difference between network partitions produced by community detection methods. Here we extend the use of mutual information to covers, that is, the cases where a…

In this lecture, we review some of the concepts of generalized geometry, as introduced by Hitchin and developed in the speaker's thesis. We also prove a Hodge decomposition for the twisted cohomology of a compact generalized K\"ahler…

The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…

We show that contrary to what it is claimed in Phys. Rev. A \textbf{94}, 022329 (2016), in general the local projective measurement that induces maximal coherence loss is \textit{not} the projection onto the local basis that defines the…

Advances in architectural design, data availability, and compute have driven remarkable progress in semantic segmentation. Yet, these models often rely on relaxed Bayesian assumptions, omitting critical uncertainty information needed for…

One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions can be seen as a special case when the density matrix is restricted to be…

This article presents an in-depth educational overview of the latest mathematical developments in coupled cluster (CC) theory, beginning with Schneider's seminal work from 2009 that introduced the first local analysis of CC theory. We offer…

We generalize recent results of Breuer and Kronholm, and Chern on partitions and overpartitions with bounded differences between largest and smallest parts. We prove our generalization both analytically and combinatorially.

The hierarchical and recursive expressive capability of rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. On the other hand, such hierarchical…

Communities are clusters of nodes with a higher than average density of internal connections. Their detection is of great relevance to better understand the structure and hierarchies present in a network. Modularity has become a standard…

In 1975 John Tukey proposed a multivariate median which is the 'deepest' point in a given data cloud in R^d. Later, in measuring the depth of an arbitrary point z with respect to the data, David Donoho and Miriam Gasko considered…

We extend to general Cartesian categories the idea of Coherent Differentiation recently introduced by Ehrhard in the setting of categorical models of Linear Logic. The first ingredient is a summability structure which induces a partial…

In arXiv:2212.14023 a decomposition of Gaussian measures on finite-dimensional spaces was introduced, which turned out to be a central technical tool to improve currently known bounds on a long standing conjecture in statistical mechanics…

With the recent advances in complex networks theory, graph-based techniques for image segmentation has attracted great attention recently. In order to segment the image into meaningful connected components, this paper proposes an image…

Quantum coherence characterizes the non-classical feature of a single party system with respect to a local basis. Based on a recently introduced resource framework, coherence can be regarded as a resource and be systematically manipulated…

We present a general approach to the study of the local distribution of measures on Euclidean spaces, based on local entropy averages. As concrete applications, we unify, generalize, and simplify a number of recent results on local…

A new general decomposition theory inspired from modular graph decomposition is presented. This helps unifying modular decomposition on different structures, including (but not restricted to) graphs. Moreover, even in the case of graphs,…