Related papers: Modular links: Bunch algorithm and upper volume bo…
This paper explores the problem of clustering ensemble, which aims to combine multiple base clusterings to produce better performance than that of the individual one. The existing clustering ensemble methods generally construct a…
Agglomerative clustering is a well established strategy for identifying communities in networks. Communities are successively merged into larger communities, coarsening a network of actors into a more manageable network of communities. The…
We introduce a new method for speeding up the inference of deep neural networks. It is somewhat inspired by the reduced-order modeling techniques for dynamical systems.The cornerstone of the proposed method is the maximum volume algorithm.…
We discuss the possibility of the existence of finite algorithms that may give distinct knot classes. In particular we present two attempts for such algorithms which seem promising, one based on knot projections on a plane, the other on…
We show that the volumes of certain hyperbolic A-adequate links can be bounded (above and) below in terms of two diagrammatic quantities: the twist number and the number of certain alternating tangles in an A-adequate diagram. We then…
The algebraic zigzag construction has recently been introduced as a combinatorial foundation for a higher dimensional notion of string diagram. For use in a proof assistant, a layout algorithm is required to determine the optimal rendering…
In $d$-dimensional space (over any field), given a set of lines, a joint is a point passed through by $d$ lines not all lying in some hyperplane. The joints problem asks to determine the maximum number of joints formed by $L$ lines, and it…
The modular structure of brain networks supports specialized information processing, complex dynamics, and cost-efficient spatial embedding. Inter-individual variation in modular structure has been linked to differences in performance,…
Achieving robust networks is a challenging problem due to its NP-hard nature and complex solution space. Current methods, from handcrafted feature extraction to deep learning, have made progress but remain rigid, requiring manual design and…
Lattices are a popular field of study in mathematical research, but also in more practical areas like cryptology or multiple-input/multiple-output (MIMO) transmission. In mathematical theory, most often lattices over real numbers are…
Clustering is an important part of many modern data analysis pipelines, including network analysis and data retrieval. There are many different clustering algorithms developed by various communities, and it is often not clear which…
Large language models (LLMs) have demonstrated remarkable capabilities across a variety of tasks. One of the main challenges towards the successful deployment of LLMs is memory management, since they typically involve billions of…
We propose an algorithm for detecting communities of links in networks which uses local information, is based on a new evaluation function, and allows for pervasive overlaps of communities. The complexity of the clustering task requires the…
Large Language Models (LLMs) demonstrate exceptional reasoning abilities, enabling strong generalization across diverse tasks such as commonsense reasoning and instruction following. However, as LLMs scale, inference costs become…
The mixed volume counts the roots of generic sparse polynomial systems. Mixed cells are used to provide starting systems for homotopy algorithms that can find all those roots, and track no unnecessary path. Up to now, algorithms for that…
We present new lower bounds for the size of perfect and separating hash families ensuring their existence. Such new bounds are based on the algorithmic Cluster expansion improved version of the Lov\'asz Local Lemma, which also implies that…
The modularity of a network quantifies the extent, relative to a null model network, to which vertices cluster into community groups. We define a null model appropriate for bipartite networks, and use it to define a bipartite modularity.…
Compositionality is a key strategy for addressing combinatorial complexity and the curse of dimensionality. Recent work has shown that compositional solutions can be learned and offer substantial gains across a variety of domains, including…
We introduce the \emph{submodular objectives chasing problem}, which generalizes many natural and previously-studied problems: a sequence of constrained submodular maximization problems is revealed over time, with both the objective and…
We study a category of Whittaker modules over a complex semisimple Lie algebra by realizing it as a category of twisted D-modules on the associated flag variety using Beilinson-Bernstein localization. The main result of this paper is the…