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This paper presents improvements and novel additions to our recent work on end-to-end optimized hierarchical bi-directional video compression to further advance the state-of-the-art in learned video compression. As an improvement, we…
In this paper, we propose a new graph-based transform and illustrate its potential application to signal compression. Our approach relies on the careful design of a graph that optimizes the overall rate-distortion performance through an…
In this paper we are interested in decomposing a dihypergraph $\mathcal{H} = (V, \mathcal{E})$ into simpler dihypergraphs, that can be handled more efficiently. We study the properties of dihypergraphs that can be hierarchically decomposed…
Deep neural networks (DNNs) have been widely used for medical image analysis. However, the lack of access a to large-scale annotated dataset poses a great challenge, especially in the case of rare diseases, or new domains for the research…
Capturing high-frequency data concerning the condition of complex systems, e.g. by acoustic monitoring, has become increasingly prevalent. Such high-frequency signals typically contain time dependencies ranging over different time scales…
The Dirac operator provides a unified framework for processing signals defined over different order topological domains, such as node and edge signals. Its eigenmodes define a spectral representation that inherently captures cross-domain…
Directed acyclic graphs (DAGs) are commonly used to model causal relationships among random variables. In general, learning the DAG structure is both computationally and statistically challenging. Moreover, without additional information,…
Time-varying graph signals are alternative representation of multivariate (or multichannel) signals in which a single time-series is associated with each of the nodes or vertex of a graph. Aided by the graph-theoretic tools, time-varying…
Directional wavelet dictionaries are hierarchical representations which efficiently capture and segment information across scale, location and orientation. Such representations demonstrate a particular affinity to physical signals, which…
We consider a discrete-time model of continuous-time distributed optimization over dynamic directed-graphs (digraphs) with applications to distributed learning. Our optimization algorithm works over general strongly connected dynamic…
Boundary analysis is developed for a rich class of generally infinite weighted graphs with compact metric completions. These graph completions have totally disconnected boundaries. The classical notion of $\epsilon$-components and the…
The surge in wireless connectivity demand, coupled with the finite nature of spectrum resources, compels the development of efficient spectrum management approaches. Spectrum sharing presents a promising avenue, although it demands precise…
Recent work by Lawrie et al. [PRR 7, 023209 (2025)] introduced a non-diffracting resonant angular filter on a network of thin channels (modelled via quantum graph theory) that exhibits unit transmission of acoustic waves at a discrete,…
In multivariate statistics, acyclic mixed graphs with directed and bidirected edges are widely used for compact representation of dependence structures that can arise in the presence of hidden (i.e., latent or unobserved) variables. Indeed,…
Graph-based transforms have been shown to be powerful tools in terms of image energy compaction. However, when the support increases to best capture signal dependencies, the computation of the basis functions becomes rapidly untractable.…
Surgical instrument segmentation is extremely important for computer-assisted surgery. Different from common object segmentation, it is more challenging due to the large illumination and scale variation caused by the special surgical…
This paper represents a significant leap forward in the problem of enumerating vertex-transitive graphs. Recent breakthroughs on symmetry of Cayley (di)graphs show that almost all finite Cayley (di)graphs have the smallest possible…
A digraph $D=(V,A)$ has a good decomposition if $A$ has two disjoint sets $A_1$ and $A_2$ such that both $(V,A_1)$ and $(V,A_2)$ are strong. Let $T$ be a digraph with $t$ vertices $u_1,\dots , u_t$ and let $H_1,\dots H_t$ be digraphs such…
We define a range of new coarse geometric invariants based on various graph-theoretic measures of complexity for finite graphs, including: treewidth, pathwidth, cutwidth and bandwidth. We prove that, for bounded degree graphs, these…
The rapid progress of Artificial Intelligence research came with the development of increasingly complex deep learning models, leading to growing challenges in terms of computational complexity, energy efficiency and interpretability. In…