arXiv research

Maximal knotless graphs have at least 74% of their vertices' edges.

A maximally linkless graph is a graph that can be embedded in $\mathbb{R}^3$ without any links, but cannot be embedded in such a way if any other edge is added to the graph. Recently, a family of maximally linkless graphs was found with $m=3n-3$ edges. We improve upon this by demonstrating a new family of maximally lin…

New bounds on maximal linkless graphs with improved edge-to-vertex ratios.

In Bipartite Correlation Clustering (BCC) we are given a complete bipartite graph $G$ with `+' and `-' edges, and we seek a vertex clustering that maximizes the number of agreements: the number of all `+' edges within clusters plus all `-' edges cut across clusters. BCC is known to be NP-hard. We present a novel approx…

We prove several results about chordal graphs and weighted chordal graphs by focusing on exposed edges. These are edges that are properly contained in a single maximal complete subgraph. This leads to a characterization of chordal graphs via deletions of a sequence of exposed edges from a complete graph. Most interesti…

Edge augmentation connects disconnected graphs by elevating eigenvalues.

We show that the singularities of spacelike maximal surfaces in Lorentz-Minkowski 3-space generically consist of cuspidal edges, swallowtails and cuspidal cross caps. The same result holds for spacelike mean curvature one surfaces in de Sitter 3-space. To prove these, we shall give a simple criterion for a given singul…

New algorithm for competing influence spread in unknown networks.

In matrix factorization, available graph side-information may not be well suited for the matrix completion problem, having edges that disagree with the latent-feature relations learnt from the incomplete data matrix. We show that removing these $\textit{contested}$ edges improves prediction accuracy and scalability. We…

We consider the problem of selecting a seed set to maximize the expected number of influenced nodes in the social network, referred to as the \textit{influence maximization} (IM) problem. We assume that the topology of the social network is prescribed while the influence probabilities among edges are unknown. In order …

Submodular functions have many applications. Matchings have many applications. The bitext word alignment problem can be modeled as the problem of maximizing a nonnegative, monotone, submodular function constrained to matchings in a complete bipartite graph where each vertex corresponds to a word in the two input senten…

Graph pruning improves neural network performance by addressing squashing and smoothing issues.

Hyperideal tetrahedra are the fundamental building blocks of hyperbolic 3-manifolds with geodesic boundary. The study of their geometric properties (in particular, of their volume) has applications also in other areas of low-dimensional topology, like the computation of quantum invariants of 3-manifolds and the use of …

We study the problem of finding the minimal (maximal) genus for a surface where a given four-valent graph with fixed opposite edge structure can be embedded into. We find several partial relations and give new reformulations in combinatorial and knot theoretic languages.

We introduce a principled method for the signed clustering problem, where the goal is to partition a graph whose edge weights take both positive and negative values, such that edges within the same cluster are mostly positive, while edges spanning across clusters are mostly negative. Our method relies on a graph-based …

SWRLDA improves LDA for multi-class classification with edge classes.

We study a game-theoretic variant of the maximum circulation problem. In a flow allocation game, we are given a directed flow network. Each node is a rational agent and can strategically allocate any incoming flow to the outgoing edges. Given the strategy choices of all agents, a maximal circulation that adheres to the…

Existence and uniqueness of discrete Einstein metrics on trees proven.

Network clustering reveals the organization of a network or corresponding complex system with elements represented as vertices and interactions as edges in a (directed, weighted) graph. Although the notion of clustering can be somewhat loose, network clusters or groups are generally considered as nodes with enriched in…

Statistical inference on graphs is a burgeoning field in the applied and theoretical statistics communities, as well as throughout the wider world of science, engineering, business, etc. In many applications, we are faced with the reality of errorfully observed graphs. That is, the existence of an edge between two vert…

Networks are a convenient way to represent complex systems of interacting entities. Many networks contain "communities" of nodes that are more densely connected to each other than to nodes in the rest of the network. In this paper, we investigate the detection of communities in temporal networks represented as multilay…

Graph Neural Networks (GNNs) achieve an impressive performance on structured graphs by recursively updating the representation vector of each node based on its neighbors, during which parameterized transformation matrices should be learned for the node feature updating. However, existing propagation schemes are far fro…

We study the problem of online influence maximization in social networks. In this problem, a learner aims to identify the set of "best influencers" in a network by interacting with it, i.e., repeatedly selecting seed nodes and observing activation feedback in the network. We capitalize on an important property of the i…

We give a new consistent scoring function for structure learning of Bayesian networks. In contrast to traditional approaches to scorebased structure learning, such as BDeu or MDL, the complexity penalty that we propose is data-dependent and is given by the probability that a conditional independence test correctly show…

New framework for online influencer selection considering cost constraints.

In this paper, we study the problem of robust influence maximization in the independent cascade model under a hyperparametric assumption. In social networks users influence and are influenced by individuals with similar characteristics and as such, they are associated with some features. A recent surging research direc…

Until now, the only known maximal surfaces in Minkowski 3-space of finite topology with compact singular set and without branch points were either genus zero or genus one, or came from a correspondence with minimal surfaces in Euclidean 3-space given by the third and fourth authors in a previous paper. In this paper, w…

XGES improves GES by favoring early edge deletion, outperforming GES in finite data settings.

We consider the problem of influence maximization in fixed networks for contagion models in an adversarial setting. The goal is to select an optimal set of nodes to seed the influence process, such that the number of influenced nodes at the conclusion of the campaign is as large as possible. We formulate the problem as…

In this paper, we consider the problem of estimating the underlying graph associated with an Ising model given a number of independent and identically distributed samples. We adopt an \emph{approximate recovery} criterion that allows for a number of missed edges or incorrectly-included edges, in contrast with the widel…

Fold singular points play important roles in the theory of maximal surfaces. For example, if a maximal surface admits fold singular points, it can be extended to a timelike minimal surface analytically. Moreover, there is a duality between conelike singular points and folds. In this paper, we investigate fold singular …

The set of maximal non-integrable structures $(SU(2)\times SU(2),B,I)$, where $B$ is Killing-Cartan metric is described as subset of $\mathbb{CP}^3$. The visualization of complex projective space $\mathbb{CP}^3$ as tetrahedron which edges and faces are $\mathbb{CP}^1$ and $\mathbb{CP}^2$ is used.

We propose a new random pruning method (called "submodular sparsification (SS)") to reduce the cost of submodular maximization. The pruning is applied via a "submodularity graph" over the $n$ ground elements, where each directed edge is associated with a pairwise dependency defined by the submodular function. In each s…

We consider the problem of \emph{influence maximization}, the problem of maximizing the number of people that become aware of a product by finding the `best' set of `seed' users to expose the product to. Most prior work on this topic assumes that we know the probability of each user influencing each other user, or we h…

Herding defines a deterministic dynamical system at the edge of chaos. It generates a sequence of model states and parameters by alternating parameter perturbations with state maximizations, where the sequence of states can be interpreted as "samples" from an associated MRF model. Herding differs from maximum likelihoo…

We study the problem of causal structure learning when the experimenter is limited to perform at most $k$ non-adaptive experiments of size $1$. We formulate the problem of finding the best intervention target set as an optimization problem, which aims to maximize the average number of edges whose directions are resolve…

Consider a finite connected graph possibly with multiple edges and loops. In discrete geometric analysis, Kotani and Sunada constructed the crystal associated to the graph as a standard realization of the maximal abelian covering of the graph. As an application of what the author showed in an earlier paper with Seshadr…

Study of maximal surfaces in a specific Heisenberg group with singularities.

Maximizing energy on flexible curves yields regular or convex polygons.

We propose a number of techniques for obtaining a global ranking from data that may be incomplete and imbalanced -- characteristics almost universal to modern datasets coming from e-commerce and internet applications. We are primarily interested in score or rating-based cardinal data. From raw ranking data, we construc…

Proposes a new sampling method for online learning with cumulative oversampling.

We describe the first-order variations of the angles of Euclidean, spherical or hyperbolic polygons under infinitesimal deformations such that the lengths of the edges do not change. Using this description, we introduce a vector-valued quadratic invariant $b$ on the space of those isometric deformations which, for conv…

A three-dimensional orthoscheme is defined as a tetrahedron whose base is a right-angled triangle and an edge joining the apex and a non-right-angled vertex is perpendicular to the base. A generalization, called complete orthoschemes, of orthoschemes is known in hyperbolic geometry. Roughly speaking, complete orthosche…

New model detects communities in networks with signed, continuous weights.

Latent space models are effective tools for statistical modeling and exploration of network data. These models can effectively model real world network characteristics such as degree heterogeneity, transitivity, homophily, etc. Due to their close connection to generalized linear models, it is also natural to incorporat…

Extends Kelly Criterion to more complex betting scenarios.

Study financial contagion and risk in sparse networks with directed edges.

This paper and its companion arXiv:1002.4564 have been replaced by arXiv:1602.05139. We give a general simple definition of JSJ decompositions by means of a universal maximality property. The JSJ decomposition should not be viewed as a tree (which is not uniquely defined) but as a canonical deformation space of trees. …