Related papers: Unfolding Ordered Matrices into BioFabric Motifs

Constructions of directed configuration graphs based on a given bi-degree distribution were introduced in random graph theory some years ago. These constructions lead to graphs where the degrees of two nodes belonging to the same edge are…

We study the problem of determining the minimal genus of a simple finite connected graph. We present an algorithm which, for an arbitrary graph $G$ with $n$ vertices and $m$ edges, determines the orientable genus of $G$ in…

Ordered binary decision diagrams (OBDDs) are an efficient data structure for representing and manipulating Boolean formulas. With respect to different variable orders, the OBDDs' sizes may vary from linear to exponential in the number of…

Hypergraphs provide a powerful framework for modeling complex systems and networks with higher-order interactions beyond simple pairwise relationships. However, graph-based clustering approaches, which focus primarily on pairwise relations,…

In this paper, we develop a novel paradigm, namely hypergraph shift, to find robust graph modes by probabilistic voting strategy, which are semantically sound besides the self-cohesiveness requirement in forming graph modes. Unlike the…

Disordered fibrous matrices, formed by the random assembly of fibers, provide the structural framework for many biological systems and biomaterials. Applied deformation modifies the alignment and stress states of constituent fibers, tuning…

Identifying and understanding the large-scale biodiversity patterns in time and space is vital for conservation and addressing fundamental ecological and evolutionary questions. Network-based methods have proven useful for simplifying and…

The representation of graphs is commonly based on the adjacency matrix concept. This formulation is the foundation of most algebraic and computational approaches to graph processing. The advent of deep learning language models offers a wide…

We consider spectral methods that uncover hidden structures in directed networks. We establish and exploit connections between node reordering via (a) minimizing an objective function and (b) maximizing the likelihood of a random graph…

Deep generative models for graphs have exhibited promising performance in ever-increasing domains such as design of molecules (i.e, graph of atoms) and structure prediction of proteins (i.e., graph of amino acids). Existing work typically…

Robots that arrange household objects should do so according to the user's preferences, which are inherently subjective and difficult to model. We present NeatNet: a novel Variational Autoencoder architecture using Graph Neural Network…

In the past several years, the problem of genome assembly has received considerable attention from both biologists and computer scientists. An important component of current assembly methods is the scaffolding process. This process involves…

Correlative computational microscopy can accelerate imaging and modeling of cellular dynamics by relaxing trade-offs inherent to dynamic imaging. Existing computational microscopy frameworks are either specialized or overly generic,…

We examine ordered graphs, defined as graphs with linearly ordered vertices, from the perspective of homomorphisms (and colorings) and their complexities. We demonstrate the corresponding computational and parameterized complexities, along…

The interactions of users and items in recommender system could be naturally modeled as a user-item bipartite graph. In recent years, we have witnessed an emerging research effort in exploring user-item graph for collaborative filtering…

Despite the recent progress in genome sequencing and assembly, many of the currently available assembled genomes come in a draft form. Such draft genomes consist of a large number of genomic fragments (scaffolds), whose order and/or…

An appropriate visualization of multiobjective non-dominated solutions is a valuable asset for decision making. Although there are methods for visualizing the solutions in the design space, they do not provide any information about their…

Discovering the underlying structure of a given graph is one of the fundamental goals in graph mining. Given a graph, we can often order vertices in a way that neighboring vertices have a higher probability of being connected to each other.…

Over the last two decades, network theory has shown to be a fruitful paradigm in understanding the organization and functioning of real-world complex systems. One technique helpful to this endeavor is identifying functionally influential…

Robotic fabric manipulation is challenging due to the infinite dimensional configuration space, self-occlusion, and complex dynamics of fabrics. There has been significant prior work on learning policies for specific deformable manipulation…