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Directed acyclic graphs (DAGs) encode a lot of information about a particular distribution in their structure. However, compute required to infer these structures is typically super-exponential in the number of variables, as inference…
In this paper, we construct a digraph structure on $p$-adic dynamical systems defined by rational functions. We study the conditions under which the functions are measure-preserving, invertible and isometric, ergodic, and minimal on…
Graph Attention Network (GAT) is one of the most popular Graph Neural Network (GNN) architecture, which employs the attention mechanism to learn edge weights and has demonstrated promising performance in various applications. However, since…
In this paper, we introduce a new (constructive) characterization of tight wavelet frames on non-flat domains in both continuum setting, i.e. on manifolds, and discrete setting, i.e. on graphs; discuss how fast tight wavelet frame…
We develop a theory of covering digraphs, similar to the theory of covering spaces. By applying this theory to Cayley digraphs, we build a "bridge" between GLMY-theory and group homology theory, which helps to reduce path homology…
Appearance-based gaze estimation, aiming to predict accurate 3D gaze direction from a single facial image, has made promising progress in recent years. However, most methods suffer significant performance degradation in cross-domain…
Learning-based image compression was shown to achieve a competitive performance with state-of-the-art transform-based codecs. This motivated the development of new learning-based visual compression standards such as JPEG-AI. Of particular…
We show that the properties of the lower part of the spectrum of the Helmholtz equation for an heterogeneous system in a finite region in $d$ dimensions, where the solutions to the homogeneous problems are known, can be systematically…
In this paper, after reviewing the main points of Haar wavelet transform and chaotic trigonometric maps, we introduce a new perspective of Haar wavelet transform. The essential idea of the paper is given linearity properties of the scaling…
Separated graphs provide a powerful combinatorial tool for approximating dynamical systems. This paper details the explicit construction of Bratteli-like separated graphs -- a generalization of classical Bratteli diagrams -- that encode the…
Deep learning-based cardiac MRI reconstruction faces significant domain shift challenges when deployed across multiple clinical centers with heterogeneous scanner configurations and imaging protocols. We propose HierAdaptMR, a hierarchical…
Persistent homology is a tool that can be employed to summarize the shape of data by quantifying homological features. When the data is an object in $\mathbb{R}^d$, the (augmented) persistent homology transform ((A)PHT) is a family of…
Understanding and predicting thermal transport in disordered materials remains a significant challenge due to the absence of periodicity and the complex nature of medium-range structural motifs. In this work, we investigate amorphous…
Graph representation learning has many real-world applications, from super-resolution imaging, 3D computer vision to drug repurposing, protein classification, social networks analysis. An adequate representation of graph data is vital to…
Magnetic texturing on the surface of a topological insulator allows the design of wave guide networks and beam splitters for domain-wall Dirac fermions. Guided by simple analytic arguments we model a Dirac fermion interferometer consisting…
The aim of this paper is to propose distributed strategies for adaptive learning of signals defined over graphs. Assuming the graph signal to be bandlimited, the method enables distributed reconstruction, with guaranteed performance in…
In recent years it has turned out that shearlets have the potential to retrieve directional information so that they became interesting for many applications. Moreover the continuous shearlet transform has the outstanding property to stem…
Weak unit disk contact graphs are graphs that admit representing nodes as a collection of internally disjoint unit disks whose boundaries touch if there is an edge between the corresponding nodes. In this work we focus on graphs without…
Layered hybrid halide compounds offer promising functional properties, particularly tunable band gaps, conductivity, light harvesting thus making them prospective for applications in photovoltaics and optoelectronics. This study exemplifies…
Visual transformers have achieved remarkable performance in image classification tasks, but this performance gain has come at the cost of interpretability. One of the main obstacles to the interpretation of transformers is the…