Related papers: Construction of k-angle tight frames
In $d$-Scattered Set we are given an (edge-weighted) graph and are asked to select at least $k$ vertices, so that the distance between any pair is at least $d$, thus generalizing Independent Set. We provide upper and lower bounds on the…
Graph neural networks excel at modeling pairwise interactions, but they cannot flexibly accommodate higher-order interactions and features. Topological deep learning (TDL) has emerged recently as a promising tool for addressing this issue.…
Gabor frames have interested many mathematicians and physicists due to their potential applications in time-frequency analysis, in particular, signal processing. A Gabor system is a collection of vectors which is obtained by applying…
We consider two disjoint sets of points. If at least one of the sets can be embedded into an Euclidean space, then we provide sufficient conditions for the two sets to be jointly embedded in one Euclidean space. In this joint Euclidean…
Recent studies on Neural Collapse (NC) reveal that, under class-balanced conditions, the class feature means and classifier weights spontaneously align into a simplex equiangular tight frame (ETF). In long-tailed regimes, however, severe…
Performing density functional theory (DFT) calculations requires a careful choice of computational parameters to ensure convergence and obtain meaningful results. This represents a particularly important problem for high-throughput and…
Many real-world networks are characterized by directionality; however, the absence of an appropriate Fourier basis hinders the effective implementation of graph signal processing techniques. Inspired by discrete signal processing, where…
Many quantities we are interested in predicting are geometric tensors; we refer to this class of problems as geometric prediction. Attempts to perform geometric prediction in real-world scenarios have been limited to approximating them…
Molecular understanding is central to advancing areas such as scientific discovery, yet Large Language Models (LLMs) struggle to understand molecular graphs effectively. Existing graph-LLM bridges often adapt the Q-Former-style connector…
We consider the solution of linear systems with tensor product structure using a GMRES algorithm. In order to cope with the computational complexity in large dimension both in terms of floating point operations and memory requirement, our…
Stochastic and mixed stochastic-deterministic density functional theory (DFT) are promising new approaches for the calculation of the equation-of-state and transport properties in materials under extreme conditions. In the intermediate warm…
Statistical analysis of a graph often starts with embedding, the process of representing its nodes as points in space. How to choose the embedding dimension is a nuanced decision in practice, but in theory a notion of true dimension is…
Deep ensemble is a simple yet powerful way to improve the performance of deep neural networks. Under this motivation, recent works on mode connectivity have shown that parameters of ensembles are connected by low-loss subspaces, and one can…
It was shown recently that the f-diagonal tensor in the T-SVD factorization must satisfy some special properties. Such f-diagonal tensors are called s-diagonal tensors. In this paper, we show that such a discussion can be extended to any…
The three-dimensional Thomas-Fermi (TF) model is used to simulate the variation of the d+d to t + p cross-section at low impact energies, when the target deuterium nucleus is embedded in metallic or insulator environments. Comparison of the…
Finite frame theory has a number of real-world applications. In applications like sparse signal processing, data transmission with robustness to erasures, and reconstruction without phase, there is a pressing need for deterministic…
Message-passing neural networks (MPNN) have shown extremely high efficiency and accuracy in predicting the physical properties of molecules and crystals, and are expected to become the next-generation material simulation tool after the…
Constructing high-quality features is critical to any quantitative data analysis. While feature engineering was historically addressed by carefully hand-crafting data representations based on domain expertise, deep neural networks (DNNs)…
ELM (Extreme Learning Machine) is a single hidden layer feed-forward network, where the weights between input and hidden layer are initialized randomly. ELM is efficient due to its utilization of the analytical approach to compute weights…
This work deals with the construction of networks of topological defects in models described by a single complex scalar field. We take advantage of the deformation procedure recently used to describe kinklike defects in order to build…