arXiv research

RODE learns roles to simplify multi-agent tasks.

Bayesian method detects mesoscale structures in pathway data networks.

Knowledge graph is a popular format for representing knowledge, with many applications to semantic search engines, question-answering systems, and recommender systems. Real-world knowledge graphs are usually incomplete, so knowledge graph embedding methods, such as Canonical decomposition/Parallel factorization (CP), D…

Study uses AI agents to improve equity portfolio management.

Random walks are at the heart of many existing network embedding methods. However, such algorithms have many limitations that arise from the use of random walks, e.g., the features resulting from these methods are unable to transfer to new nodes and graphs as they are tied to vertex identity. In this work, we introduce…

Online discussion forums are complex webs of overlapping subcommunities (macrolevel structure, across threads) in which users enact different roles depending on which subcommunity they are participating in within a particular time point (microlevel structure, within threads). This sub-network structure is implicit in m…

Role mining tackles the problem of finding a role-based access control (RBAC) configuration, given an access-control matrix assigning users to access permissions as input. Most role mining approaches work by constructing a large set of candidate roles and use a greedy selection strategy to iteratively pick a small subs…

The paper proposes and discusses semiorthogonal decompositions for moduli spaces of vector bundles.

Intrusion detection systems (IDSs) generate valuable knowledge about network security, but an abundance of false alarms and a lack of methods to capture the interdependence among alerts hampers their utility for network defense. Here, we explore a graph-based approach for fusing alerts generated by multiple IDSs (e.g.,…

The process of exploring and exploiting Oil and Gas (O&G) generates a lot of data that can bring more efficiency to the industry. The opportunities for using data mining techniques in the "digital oil-field" remain largely unexplored or uncharted. With the high rate of data expansion, companies are scrambling to develo…

The paper classifies decompositions of 3-sphere and lens spaces with handlebodies.

Analogues of JSJ decompositions were developed for Poincaré duality pairs in [19]. These decompositions depend only on the group. Our focus will be on describing the edge splittings of these decompositions more precisely. We use our results to compare these decompositions with two other closely related decompositions.

We combine aspects of the notions of finite decomposition complexity and asymptotic property C into a notion that we call finite APC-decomposition complexity. Any space with finite decomposition complexity has finite APC-decomposition complexity and any space with asymptotic property C has finite APC-decomposition comp…

This paper generalizes octahedral decomposition to links in thickened surfaces.

Researchers compute Goeritz groups for all (1,1)-link decompositions.

Study concordance of decompositions from defining sequences in 3-sphere.

Given a Delaunay decomposition of a compact hyperbolic surface, one may record the topological data of the decomposition, together with the intersection angles between the `empty disks' circumscribing the regions of the decomposition. The main result of this paper is a characterization of when a given topological decom…

Study shows OAT decomposition generates unexplained profit and loss, while SU decompositions depend on risk factor order.

A new algorithm speeds up CP decomposition for large tensors.

Paper characterizes optimization landscape of Tucker decomposition.

A double pants decomposition of a 2-dimensional surface is a collection of two pants decomposition of this surface introduced in arXiv:1005.0073v2. There are two natural operations acting on double pants decompositions: flips and handle twists. It is shown in arXiv:1005.0073v2 that the groupoid generated by flips and h…

Smooth 4-manifolds have simple horizontal decompositions.

Let $\mathcal{J}^1$ be the real form of a complex simple Jordan algebra such that the automorphism group is $\mathrm{F}_{4(-20)}$. By using some orbit types of $\mathrm{F}_{4(-20)}$ on $\mathcal{J}^1$, for $\mathrm{F}_{4(-20)}$, explicitly, we give the Iwasawa decomposition, the Oshima--Sekiguchi's $K_ε-$Iwasawa decomp…

We study the topological types of pants decompositions of a surface by associating to any pants decomposition $P,$ in a natural way its pants decomposition graph, $Γ(P).$ This perspective provides a convenient way to analyze the maximum distance in the pants complex of any pants decomposition to a pants decomposition c…

New method uses random decompositions for high-dimensional Bayesian optimization.

New varifold example shows decomposition failure.

Derive new Euler-Ramanujan-type identities and infinite decompositions for zero mean curvature graphs in various spaces.

Decompositions on manifolds appear in various geometric structures. Necessary and sufficient conditions for quotient spaces of decompositions to be manifolds are widely characterized. We characterize necessary and sufficient conditions to be $k$-manifolds $(k = 1, 2)$, which generalize characterizations in the codimens…

Short proof for ideal polygons with near optimal orthogeodesic decomposition.

Paper introduces a new principle for fair redistribution of insurance surplus.

The paper defines and proves the existence of decompositions of integral varifolds.

We give an example of two JSJ decompositions of a group that are not related by conjugation, conjugation of edge-inclusions, and slide moves. This answers the question of Rips and Sela stated in "Cyclic splittings of finitely presented groups and the canonical JSJ decomposition," Ann. of Math. 146 (1997), 53-109. On th…

We consider a union of two pants decompositions of the same orientable 2-dimensional surface of any genus g. Each pants decomposition corresponds to some handlebody bounded by this surface, so two pants decompositions correspond to a Heegaard splitting of a 3-manifold. We introduce a groupoid FT acting on double pants …

We present a novel nonnegative tensor decomposition method, called Legendre decomposition, which factorizes an input tensor into a multiplicative combination of parameters. Thanks to the well-developed theory of information geometry, the reconstructed tensor is unique and always minimizes the KL divergence from an inpu…

Handles decompositions reveal new open book structures.

The aim of this paper is to provide some new tools to aid the study of decomposition complexity, a notion introduced by Guentner, Tessera and Yu. In this paper, three equivalent definitions for decomposition complexity are established. We prove that metric spaces with finite hyperbolic dimension have finite (weak) deco…

Unified algorithm for tensor decomposition supports multiple loss functions and models.

The paper defines and proves stabilization for 3-manifold decompositions with multibranched surface intersections.

To ensure interpretability of extracted sources in tensor decomposition, we introduce in this paper a dictionary-based tensor canonical polyadic decomposition which enforces one factor to belong exactly to a known dictionary. A new formulation of sparse coding is proposed which enables high dimensional tensors dictiona…

Analyzes canonical reductive decomposition of extrinsic homogeneous submanifolds.

Tensor decomposition methods are widely used for model compression and fast inference in convolutional neural networks (CNNs). Although many decompositions are conceivable, only CP decomposition and a few others have been applied in practice, and no extensive comparisons have been made between available methods. Previo…

Examines respectful decompositions of Lie algebras.

In this paper, we study a polynomial decomposition model that arises in problems of system identification, signal processing and machine learning. We show that this decomposition is a special case of the X-rank decomposition --- a powerful novel concept in algebraic geometry that generalizes the tensor CP decomposition…

Formula connects foliated simplicial volume with group cost.

The study examines how different interpolation methods affect the decomposition of life insurance surplus.

The paper uses tensor decompositions to improve neural network models for tree data.

Analyzes vector fields in polytope decompositions, proving curve finiteness.

New surfaces defy traditional pants decompositions.