Related papers: Rigid Graph Compression: Motif-based rigidity anal…
The main paradigm of smoothed analysis on graphs suggests that for any large graph $G$ in a certain class of graphs, perturbing slightly the edges of $G$ at random (usually adding few random edges to $G$) typically results in a graph having…
Topological data analysis (TDA) studies the shape patterns of data. Persistent homology is a widely used method in TDA that summarizes homological features of data at multiple scales and stores them in persistence diagrams (PDs). In this…
Graph Neural Networks (GNNs) have achieved remarkable performance in a wide range of graph-related learning tasks. However, explaining their predictions remains a challenging problem, especially due to the mismatch between the graphs used…
The computational analysis of fiber network fracture is an emerging field with application to paper, rubber-like materials, hydrogels, soft biological tissue, and composites. Fiber networks are often described as probabilistic structures of…
Graph neural networks (GNNs) have recently been demonstrated to perform well on a variety of network-based tasks such as decentralized control and resource allocation, and provide computationally efficient methods for these tasks which have…
Detecting the dimensionality of graphs is a central topic in machine learning. While the problem has been tackled empirically as well as theoretically, existing methods have several drawbacks. On the one hand, empirical tools are…
Graph condensation, which reduces the size of a large-scale graph by synthesizing a small-scale condensed graph as its substitution, has immediate benefits for various graph learning tasks. However, existing graph condensation methods rely…
Embedding static graphs in low-dimensional vector spaces plays a key role in network analytics and inference, supporting applications like node classification, link prediction, and graph visualization. However, many real-world networks…
As mobile networks embrace the 5G era, the interest in adopting Reinforcement Learning (RL) algorithms to handle challenges in ultra-low-latency and high throughput scenarios increases. Simultaneously, the advent of packetized fronthaul…
As a granular material is compressed, the particles and forces within the system arrange to form complex heterogeneous structures. Force chains are a prime example and are thought to constrain bulk properties such as mechanical stability…
Data-driven analysis of complex networks has been in the focus of research for decades. An important area of research is to study how well real networks can be described with a small selection of metrics, furthermore how well network models…
While bigger and deeper neural network architectures continue to advance the state-of-the-art for many computer vision tasks, real-world adoption of these networks is impeded by hardware and speed constraints. Conventional model compression…
Several brain disorders can be detected by observing alterations in the brain's structural and functional connectivities. Neurological findings suggest that early diagnosis of brain disorders, such as mild cognitive impairment (MCI), can…
Many complex networks, ranging from social to biological systems, exhibit structural patterns consistent with an underlying hyperbolic geometry. Revealing the dimensionality of this latent space can disentangle the structural complexity of…
Graph convolutional neural networks (GCNs) generalize tradition convolutional neural networks (CNNs) from low-dimensional regular graphs (e.g., image) to high dimensional irregular graphs (e.g., text documents on word embeddings). Due to…
Our goal is to develop a design framework for multifunctional mechanical metamaterials that can tune their rigidity while optimizing other desired properties. Towards this goal, we first demonstrate that underconstrained central force…
Traditional image and video compression algorithms rely on hand-crafted encoder/decoder pairs (codecs) that lack adaptability and are agnostic to the data being compressed. Here we describe the concept of generative compression, the…
Condense phase molecular systems organize in wide range of distinct molecular configurations, including amorphous melt and glass as well as crystals often exhibiting polymorphism, that originate from their intricate intra- and…
Large sparse linear systems of equations are ubiquitous in science and engineering, such as those arising from discretizations of partial differential equations. Algebraic multigrid (AMG) methods are one of the most common methods of…
We investigate how to find generic and globally rigid realizations of graphs in $\mathbb{R}^d$ based on elementary geometric observations. Our arguments lead to new proofs of a combinatorial characterization of the global rigidity of graphs…