arXiv research

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

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

In many video coding systems, separable transforms (such as two-dimensional DCT-2) have been used to code block residual signals obtained after prediction. This paper proposes a parametric approach to build graph-based separable transforms (GBSTs) for video coding. Specifically, a GBST is derived from a pair of line gr…

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

Sp(n)-instantons linked to complex Lagrangian graphs via Fourier-Mukai transform.

Study of line congruences for Appell's rank-4 hypergeometric functions.

We prove that the Fourier--Laplace--Nahm transform for connections on the projective line is a hyper-Kähler isometry.

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

Defines state sum models with defects in 3-manifolds.

The paper tackles matching a desired mean in causal systems through shift interventions.

Since the invention of word2vec, the skip-gram model has significantly advanced the research of network embedding, such as the recent emergence of the DeepWalk, LINE, PTE, and node2vec approaches. In this work, we show that all of the aforementioned models with negative sampling can be unified into the matrix factoriza…

Inverts rank m symmetric tensor fields using line integrals.

The asymptotic lattices and their transformations are studied within the line geometry approach. It is shown that the discrete asymptotic nets are represented by isotropic congruences in the Plucker quadric. On the basis of the Lelieuvre-type representation of asymptotic lattices and of the discrete analog of the Mouta…

A special group of transformations of the real line cannot act effectively on it.

Harmonic maps from $\BR^2$ or one-connected domain $Ø\subset \BR^2$ into $GL(m, \BC)$ and $U(m)$ are treated. The GBDT version of the Bäcklund-Darboux transformation is applied to the case of the harmonic maps. A new general formula on the GBDT transformations of the Sym-Tafel immersions is derived. A class of the harm…

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…

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

We give an explicit description of rational curves in the product of three copies of complex projective lines, which are transformed into twistor lines in M. Nagata's example of non-projective complete algebraic variety, viewed as the twistor space of Eguchi-Hanson metric. In particular, we show that there exist two fa…

PatchGT uses non-trainable graph patches to improve graph representation learning.

We present graph wavelet neural network (GWNN), a novel graph convolutional neural network (CNN), leveraging graph wavelet transform to address the shortcomings of previous spectral graph CNN methods that depend on graph Fourier transform. Different from graph Fourier transform, graph wavelet transform can be obtained …

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

Graph transformers outperform graph convolutions by preserving community information.

Study of Poincaré-Reeb graphs for algebraic domains.

The mirror of a projective toric manifold $X_Σ$ is given by a Landau-Ginzburg model $(Y,W)$. We introduce a class of Lagrangian submanifolds in $(Y,W)$ and show that, under the SYZ mirror transformation, they can be transformed to torus-invariant hermitian metrics on holomorphic line bundles over $X_Σ$. Through this ge…

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…

New methods create full discretized isothermic tori in Euclidean spaces.

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

We give a full description of Darboux transformations of any order for arbitrary (nondegenerate) differential operators on the superline. We show that every Darboux transformation of such operators factorizes into elementary Darboux transformations of order one. Similar statement holds for operators on the ordinary lin…

We study the hyperholomorphic line bundle on a hyperkaehler manifold with circle action introduced by A Haydys, and in particular show how it transforms under a hyperkaehler quotient. Applications include ALE spaces and coadjoint orbits.

It is shown that there exist non-singular cubic surfaces in CP^3 containing 5 twistor lines. This is the maximum number of twistor fibres that a non-singular cubic can contain. Cubic surfaces in CP^3 with 5 twistor lines are classified up to transformations preserving the conformal structure of S^4.

The paper studies surfaces with spherical curvature lines and their generation by constrained elastic curves.

Many signals on Cartesian product graphs appear in the real world, such as digital images, sensor observation time series, and movie ratings on Netflix. These signals are "multi-dimensional" and have directional characteristics along each factor graph. However, the existing graph Fourier transform does not distinguish …

Transformer learns graph structure better with subgraph info.

Maps asymptotically embed conic transforms from circle bundles.

The paper explores a B-field transform of complex structures on complex tori.

Transformer adapts to graphs with adaptive attention and auto-regressive decoding.

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

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…

Study classifies graphs with positive curvature without quadrilaterals.

This thesis explores GNNs, categorizing them into local and global approaches.

RP-GFRFT unifies fractional order and rotation control for graph signals.

We continue the investigation of the correspondence between systems of conservation laws and congruences of lines in projective space. Relationship between "additional" conservation laws and hypersurfaces conjugate to a congruence is established. This construction allows us to introduce, in a purely geometric way, the …

Deep Graph Neural Networks (GNNs) are useful models for graph classification and graph-based regression tasks. In these tasks, graph pooling is a critical ingredient by which GNNs adapt to input graphs of varying size and structure. We propose a new graph pooling operation based on compressive Haar transforms -- HaarPo…

Scattering transforms are non-trainable deep convolutional architectures that exploit the multi-scale resolution of a wavelet filter bank to obtain an appropriate representation of data. More importantly, they are proven invariant to translations, and stable to perturbations that are close to translations. This stabili…

New mappings in Minkowski spacetime classified under mild conditions.

An analogue of the correspondence between GL(k)-conjugacy classes of matricial polynomials and line bundles is given for K-conjugacy classes, where K is one of the following: maximal parabolic, maximal torus, GL(k-1) embedded diagonally. The generalised Legendre transform construction of hyperkaehler metrics is studied…

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

IGT learns graph representations without supervision.