Related papers: Generating minimal boundary maps
Matrices arising in scientific applications frequently admit linear low-rank approximations due to smoothness in the physical and/or temporal domain of the problem. In large-scale problems, computing an optimal low-rank approximation can be…
Graph clustering aims at discovering a natural grouping of the nodes such that similar nodes are assigned to a common cluster. Many different algorithms have been proposed in the literature: for simple graphs, for graphs with attributes…
We present the `Basic S*' algorithm for computing shortest path through a metric simplicial complex. In particular, given a metric graph, $G$, which is constructed as a discrete representation of an underlying configuration space (a larger…
In this paper, we present a novel data structure, called the Mixture Graph. This data structure allows us to compress, render, and query segmentation histograms. Such histograms arise when building a mipmap of a volume containing…
Random networks are increasingly used to analyse complex transportation networks, such as airline routes, roads and rail networks. So far, this research has been focused on describing the properties of the networks with the help of random…
Limited data availability in machine learning significantly impacts performance and generalization. Traditional augmentation methods enhance moderately sufficient datasets. GANs struggle with convergence when generating diverse samples.…
Images with shared characteristics naturally form sets. For example, in a face verification benchmark, images of the same identity form sets. For generative models, the standard way of dealing with sets is to represent each as a one hot…
We propose a new framework for generating cross-sectional synthetic datasets via disjoint generative models. In this paradigm, a dataset is partitioned into disjoint subsets that are supplied to separate instances of generative models. The…
Generating scene graph to describe all the relations inside an image gains increasing interests these years. However, most of the previous methods use complicated structures with slow inference speed or rely on the external data, which…
Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…
Combinatorial topology is used in distributed computing to model concurrency and asynchrony. The basic structure in combinatorial topology is the simplicial complex, a collection of subsets called simplices of a set of vertices, closed…
Matrix completion aims to reconstruct a data matrix based on observations of a small number of its entries. Usually in matrix completion a single matrix is considered, which can be, for example, a rating matrix in recommendation system.…
Various specifiable combinatorial structures, with d extensive parameters, can be exactly sampled both by the recursive method, with linear arithmetic complexity if a heavy preprocessing is performed, or by the Boltzmann method, with…
Graph generation is integral to various engineering and scientific disciplines. Nevertheless, existing methodologies tend to overlook the generation of edge attributes. However, we identify critical applications where edge attributes are…
We propose a new approach to train the Generative Adversarial Nets (GANs) with a mixture of generators to overcome the mode collapsing problem. The main intuition is to employ multiple generators, instead of using a single one as in the…
Thin and elongated filamentous structures, such as microtubules and actin filaments, often play important roles in biological systems. Segmenting these filaments in biological images is a fundamental step for quantitative analysis. Recent…
Graphs from complex systems often share a partial underlying structure across domains while retaining individual features. Thus, identifying common structures can shed light on the underlying signal, for instance, when applied to scientific…
The problem of map enumeration concerns counting connected spatial graphs, with a specified number $j$ of vertices, that can be embedded in a compact surface of genus $g$ in such a way that its complement yields a cellular decomposition of…
Population synthesis is a critical task that involves generating synthetic yet realistic representations of populations. It is a fundamental problem in agent-based modeling (ABM), which has become the standard to analyze intelligent…
We study entanglement properties of mixed density matrices obtained from combinatorial Laplacians. This is done by introducing the notion of the density matrix of a graph. We characterize the graphs with pure density matrices and show that…