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We consider the space-fractional operator with order $0<\alpha<1$ on the metric star graph. The boundary conditions at the vertices of the metric star graph providing the self-adjointness of the operator are derived. The obtained result is…
The area of Data Analytics on graphs promises a paradigm shift as we approach information processing of classes of data, which are typically acquired on irregular but structured domains (social networks, various ad-hoc sensor networks).…
Due to the increasing heterogeneity and deployment density of emerging cellular networks, new flexible and scalable approaches for their modeling, simulation, analysis and optimization are needed. Recently, a new approach has been proposed:…
In this paper, we propose a new approach for building cellular automata to solve real-world segmentation problems. We design and train a cellular automaton that can successfully segment high-resolution images. We consider a colony that…
Topological correctness plays a critical role in many image segmentation tasks, yet most networks are trained using pixel-wise loss functions, such as Dice, neglecting topological accuracy. Existing topology-aware methods often lack robust…
This paper studies infinite graphs produced from a natural unfolding operation applied to finite graphs. Graphs produced via such operations are of finite degree and automatic over the unary alphabet (that is, they can be described by…
Many real world networks are considered temporal networks, in which the chronological ordering of the edges has importance to the meaning of the data. Performing temporal subgraph matching on such graphs requires the edges in the subgraphs…
We present a parallel implementation of cellular automata to simulate chemical reactions on surfaces. The scaling of the computer time with the number of processors for this parallel implementation is quite close to the ideal T/P, where T…
Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections,…
Tabular data are ubiquitous for the widespread applications of tables and hence have attracted the attention of researchers to extract underlying information. One of the critical problems in mining tabular data is how to understand their…
Many computer vision tasks address the problem of scene understanding and are naturally interrelated e.g. object classification, detection, scene segmentation, depth estimation, etc. We show that we can leverage the inherent relationships…
We define the harmonic evolution of states of a graph by iterative application of the harmonic operator (Laplacian over $Z_2$). This provides graphs with a new geometric context and leads to a new tool to analyze them. The digraphs of…
Any algorithm (in the sense of Gurevich's abstract-state-machine axiomatization of classical algorithms) operating over any arbitrary unordered domain can be simulated by a dynamic cellular automaton, that is, by a pattern-directed cellular…
We present a new cellular data processing scheme, a hybrid of existing cellular automata (CA) and gate array architectures, which is optimized for realization at the quantum scale. For conventional computing, the CA-like external clocking…
In this chapter, we show why parallel MATLAB is useful, provide a comparison of the different parallel MATLAB choices, and describe a number of applications in Signal and Image Processing: Audio Signal Processing, Synthetic Aperture Radar…
In this paper, we propose a novel approach to generate images (or other artworks) by using neural cellular automatas (NCAs). Rather than training NCAs based on single images one by one, we combined the idea with variational autoencoders…
Finding the dense regions of a graph and relations among them is a fundamental problem in network analysis. Core and truss decompositions reveal dense subgraphs with hierarchical relations. The incremental nature of algorithms for computing…
Grayscale image colorization is a fascinating application of AI for information restoration. The inherently ill-posed nature of the problem makes it even more challenging since the outputs could be multi-modal. The learning-based methods…
These are the proceedings of the Second Workshop on GRAPH Inspection and Traversal Engineering (GRAPHITE 2013), which took place on March 24, 2013 in Rome, Italy, as a satellite event of the 16th European Joint Conferences on Theory and…
Synthetic Aperture Radar (SAR) imaging systems operate by emitting radar signals from a moving object, such as a satellite, towards the target of interest. Reflected radar echoes are received and later used by image formation algorithms to…