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Topological Deep Learning seeks to enhance the predictive performance of neural network models by harnessing topological structures in input data. Topological neural networks operate on spaces such as cell complexes and hypergraphs, that…
We investigate networks of automata that synchronise over common action labels. A graph synchronisation topology between the automata is defined in such a way that two automata are connected iff they can synchronise over an action. We show…
Image matting refers to the estimation of the opacity of foreground objects. It requires correct contours and fine details of foreground objects for the matting results. To better accomplish human image matting tasks, we propose the Cascade…
Computers and algorithms play an ever-increasing role in obtaining new results in graph theory. In this survey, we present a broad range of techniques used in computer-assisted graph theory, including the exhaustive generation of all…
Maintaining a $k$-core decomposition quickly in a dynamic graph has important applications in network analysis. The main challenge for designing efficient exact algorithms is that a single update to the graph can cause significant global…
State-of-the-art machine-learning methods for event cameras treat events as dense representations and process them with conventional deep neural networks. Thus, they fail to maintain the sparsity and asynchronous nature of event data,…
We introduce cellular automata whose cell spaces are left homogeneous spaces and prove a uniform as well as a topological variant of the Curtis-Hedlund-Lyndon theorem. Examples of left homogeneous spaces are spheres, Euclidean spaces, as…
We study an extension of the classical graph cut problem, wherein we replace the modular (sum of edge weights) cost function by a submodular set function defined over graph edges. Special cases of this problem have appeared in different…
We present an efficient algorithm designed for and capable of detecting elongated, thin features such as lines and curves in astronomical images, and its application to the automatic detection of gravitational arcs. The algorithm is…
We present a framework to use recently introduced Capsule Networks for solving the problem of Optical Flow, one of the fundamental computer vision tasks. Most of the existing state of the art deep architectures either uses a correlation…
This paper studies complexity of recognition of classes of bounded configurations by a generalization of conventional cellular automata (CA) -- finite dynamic cellular automata (FDCA). Inspired by the CA-based models of biological and…
We extend a previously introduced semi-analytical representation of a decomposition of CA dynamics in arbitrary dimensions and neighborhood schemes via the use of certain universal maps in which CA rule vectors are derivable from the…
We present applications of a cellular automaton approach to pedestrian dynamics introduced in [1,2]. It is shown that the model is able to reproduce collective effects and self-organization phenomena encountered in pedestrian traffic, e.g.…
Cellular automata are a set of computational models in discrete space that have a discrete time evolution defined by neighbourhood rules. They are used to simulate many complex systems in physics and science in general. In this work,…
In recent years, there has been considerable interest in developing machine learning models on graphs to account for topological inductive biases. In particular, recent attention has been given to Gaussian processes on such structures since…
Geometric, topological and graph theory modeling and analysis of biomolecules are of essential importance in the conceptualization of molecular structure, function, dynamics, and transport. On the one hand, geometric modeling provides…
This study focuses on an extended model of a standard cellular automaton (CA) that includes an extra index consisting of a radius that defines a perception area for each cell in addition to the radius defined by the CA rule. Extended…
Cell formation is a critical step in the design of cellular manufacturing systems. Recently, it was tackled using a cut-based-graph-partitioning model. This model meets real-life production systems requirements as it uses the actual amount…
This is a motivating tutorial introduction to a semantic analysis of programming languages using a graphical language as the representation of terms, and graph rewriting as a representation of reduction rules. We show how the graphical…
Enhancement is an important step in post-processing digital images for personal use, in medical imaging, and for object recognition. Most existing manual techniques rely on region selection, similarity, and/or thresholding for editing,…