arXiv research

Study classifies graphs with positive curvature without quadrilaterals.

Line graph transformation aids graph isomorphism tests by excluding challenging graph properties.

The paper explores graphons of line graphs from sparse finite graphs.

Proper proximality proved for various groups on non-positive curvature spaces.

We define a pseudo-inverse for line graphs using linear integer programming.

LineMVGNN improves AML detection by integrating multi-view graph learning.

In this paper, we study curvature dimension conditions on birth-death processes which correspond to linear graphs, i.e., weighted graphs supported on the infinite line or the half line. We give a combinatorial characterization of Bakry and Émery's $CD(K,n)$ condition for linear graphs and prove the triviality of edge w…

We construct Hodge filtered function spaces associated to infinite loop spaces. For Brown-Peterson cohomology, we show that the corresponding Hodge filtered spaces satisfy an analog of Wilson's unstable splitting. As a consequence, we obtain an analog of Quillen's theorem for Hodge filtered Brown-Peterson cohomology fo…

Study of Poincaré-Reeb graphs for algebraic domains.

A new algorithm tackles graph-based contextual bandits with efficient regret bounds.

Graphs with maximum degree Δ have at most O(1) equiangular lines for λ < 3/sqrt(2).

Study geodesics on graphs with random lengths, proving bi-infinite paths exist.

Proves existence and uniqueness of Killing graphs with prescribed curvature.

Classifies solitons for surface diffusion flow of graphs.

Study minimal graphs on non-negative Ricci curvature manifolds.

A new hypergraph expansion method treats vertices and hyperedges equally, improving node classification.

This paper is first-line research expanding GANs into graph topology analysis. By leveraging the hierarchical connectivity structure of a graph, we have demonstrated that generative adversarial networks (GANs) can successfully capture topological features of any arbitrary graph, and rank edge sets by different stages a…

The paper provides a converse to linking theorems for graphs in 3-space and higher dimensions.

It is proved the existence and uniqueness of graphs with prescribed mean curvature in Riemannian submersions fibered by flow lines of a vertical Killing vector field.

Examples of area-minimizing graphs with low regularity in a specific group.

The fundamental group of the complement of a hyperplane arrangement plays an important role in studying the corresponding arrangements. In particular, for large families of hyperplane arrangements, this fundamental group, being isomorphic to the fundamental group of a complement of a line arrangement, has some remarkab…

A meander of order n is a simple closed curve in the plane which intersects a horizontal line transversely at 2n points. (Meanders which differ by an isotopy of the line and plane are considered equivalent.) Let Gamma_n be the Cayley graph of the symmetric group S_n as generated by all (n choose 2) transpositions. Let …

LG algorithm finds profitable trading paths in decentralized exchanges.

Graphs are general and powerful data representations which can model complex real-world phenomena, ranging from chemical compounds to social networks; however, effective feature extraction from graphs is not a trivial task, and much work has been done in the field of machine learning and data mining. The recent advance…

New algorithm reduces regret in multi-agent bandits over undirected graphs.

Hop Sampling improves GNNs in non-stationary environments by preventing overfitting.

We construct a series of finitely presented semigroups. The centers of these semigroups encode uniquely up to rigid ambient isotopy in 3-space all non-oriented spatial graphs. This encoding is obtained by using three-page embeddings of graphs into the product of the line with the cone on three points. By exploiting thr…

Consider a surface $S$ immersed in the Lorentz-Minkowski 3-space $\boldsymbol R^3_1$. A complete light-like line in $\boldsymbol R^3_1$ is called an entire null line on the surface $S$ in $\boldsymbol R^3_1$ if it lies on $S$ and consists of only null points with respect to the induced metric. In this paper, we show th…

Generative model captures hubs and dense communities in social networks.

The study proves properties of capillary graphs in half-spaces.

Modern intelligent transportation systems provide data that allow real-time dynamic demand prediction, which is essential for planning and operations. The main challenge of prediction of dynamic Origin-Destination (O-D) demand matrices is that demands cannot be directly measured by traffic sensors; instead, they have t…

Optimizing the execution time of tensor program, e.g., a convolution, involves finding its optimal configuration. Searching the configuration space exhaustively is typically infeasible in practice. In line with recent research using TVM, we propose to learn a surrogate model to overcome this issue. The model is trained…

In many physical, statistical, biological and other investigations it is desirable to approximate a system of points by objects of lower dimension and/or complexity. For this purpose, Karl Pearson invented principal component analysis in 1901 and found 'lines and planes of closest fit to system of points'. The famous k…

In trying to provide explicit deformations of quadrics the starting point of our investigation is to use Bianchi's link between real deformations of totally real regions of real paraboloids and various totally real forms of the sine-Gordon equation coupled with Bianchi's simple observation that the vacuum soliton of th…

The splitting number is effective to distinguish the embedded topology of plane curves, and it is not determined by the fundamental group of the complement of the plane curve. In this paper, we give a generalization of the splitting number, called the splitting graph. By using the splitting graph, we classify the embed…

Traditionally, community detection in graphs can be solved using spectral methods or posterior inference under probabilistic graphical models. Focusing on random graph families such as the stochastic block model, recent research has unified both approaches and identified both statistical and computational detection thr…

Graph Neural Networks (GNNs) have achieved much success on graph-structured data. In light of this, there have been increasing interests in studying their expressive power. One line of work studies the capability of GNNs to approximate permutation-invariant functions on graphs, and another focuses on the their power as…

Power system studies require the topological structures of real-world power networks; however, such data is confidential due to important security concerns. Thus, power grid synthesis (PGS), i.e., creating realistic power grids that imitate actual power networks, has gained significant attention. In this letter, we cas…

In this article we consider surfaces in the product space $\h^2\times \r$ of the hyperbolic plane $\h^2$ with the real line. The main results are: a description of some geometric properties of minimal graphs; new examples of complete minimal graphs; the classification of umbilical surfaces.

We introduce the notion of a conjugation-free geometric presentation for a fundamental group of a line arrangement's complement, and we show that the fundamental groups of the following family of arrangements have a conjugation-free geometric presentation: A real arrangement L, whose graph of multiple points is a union…

Graphs and networks are a key research tool for a variety of science fields, most notably chemistry, biology, engineering and social sciences. Modeling and generation of graphs with efficient sampling is a key challenge for graphs. In particular, the non-uniqueness, high dimensionality of the vertices and local depende…

Survey of graph adversarial learning tasks and their attacks and defenses.

We show that Caratheodory's conjecture, on umbilical points of closed convex surfaces, may be reformulated in terms of the existence of at least one umbilic in the graphs of functions f: R^2-->R whose gradient decays uniformly faster than 1/r. The divergence theorem then yields a pair of integral equations for the norm…

Researchers find explicit Bäcklund transforms for specific quadrics.

We construct potentially new manifolds homeomorphic but not diffeomorphic to $\mathbb{CP}^{2} \# 8 \overline{\mathbb{CP}^{2}}$ and $\mathbb{CP}^{2} \# 9 \overline{\mathbb{CP}^{2}}$ via rational blowdown surgery along certain $4$-valent plumbing graphs. This way all the graph classes from \cite{weighted} have a represen…

Simpler algorithms for morphing planar and toroidal graphs.

New method determines arrangement combinatorics from Milnor fiber boundary.

This paper proposes a method to reveal task relationships in multi-task learning models using sparse graphs.