Related papers: Kirkman Equiangular Tight Frames and Codes

The ensemble Kalman filter (EnKF) is a method for combining a dynamical model with data in a sequential fashion. Despite its widespread use, there has been little analysis of its theoretical properties. Many of the algorithmic innovations…

Fusion frames consist of a sequence of subspaces from a Hilbert space and corresponding positive weights so that the sum of weighted orthogonal projections onto these subspaces is an invertible operator on the space. Given a spectrum for a…

Equivariant Graph Neural Networks (GNNs) have significantly advanced the modeling of 3D molecular structure by leveraging group representations. However, their message passing, heavily relying on Clebsch-Gordan tensor product convolutions,…

Finite tight frames for polynomial subspaces are constructed using monic Hahn polynomials and Krawtchouk polynomials of several variables. Based on these polynomial frames, two methods for constructing tight frames for the Euclidean spaces…

We develop an Effective Field Theory (EFT) formalism to solve for the conservative dynamics of binary systems in gravity via Post-Minkowskian (PM) scattering data. Our framework combines a systematic EFT approach to compute the deflection…

We show that much of the theory of finite tight frames can be generalised to vector spaces over the quaternions. This includes the variational characterisation, group frames, and the characterisations of projective and unitary equivalence.…

The ensemble Kalman filter (EnKF) is a recursive filter suitable for problems with a large number of variables, such as discretizations of partial differential equations in geophysical models. The EnKF originated as a version of the Kalman…

Ensemble Kalman Inversion (EKI) methods are a family of iterative methods for solving weighted least-squares problems, especially those arising in scientific and engineering inverse problems in which unknown parameters or states are…

The Bootstrap Particle Filter (BPF) and the Ensemble Kalman Filter (EnKF) are two widely used methods for sequential Bayesian filtering: the BPF is asymptotically exact but can suffer from weight degeneracy, while the EnKF scales well in…

We introduce a class of Parity-Time symmetric elastodynamic metamaterials (Ed-MetaMater) whose Hermitian counterpart exhibits a frequency spectrum with unfolding (fractal) symmetries. Our study reveals a scale-free formation of exceptional…

The task of shape space learning involves mapping a train set of shapes to and from a latent representation space with good generalization properties. Often, real-world collections of shapes have symmetries, which can be defined as…

Hilbert space frames generalize orthonormal bases to allow redundancy in representations of vectors while keeping good reconstruction properties. A frame comes with an associated frame operator encoding essential properties of the frame. We…

We consider the trial wavefunctions for the Fractional Quantum Hall Effect (FQHE) that are given by conformal blocks, and construct their associated edge excited states in full generality. The inner products between these edge states are…

Condensed matter physics increasingly focuses on exploiting the magnetic order parameter orientation n as a tuning knob for properties of collinear magnetic materials, but a general method for constructing effective Hamiltonians with…

Angle encoding has emerged as a popular feature map for embedding classical data into quantum models, naturally generating truncated Fourier series with universal function approximation capabilities. Despite this expressive capability,…

We study the rigidity properties of Grassmannian frames: basis-like sets of unit vectors that correspond to optimal Grassmannian line packings. It is known that Grassmannian frames characterized by the Welch bound must satisfy the…

A finite-dimensional Hilbert space is usually described in terms of an orthonormal basis, but in certain approaches or applications a description in terms of a finite overcomplete system of vectors, called a finite tight frame, may offer…

Periodically driven quantum systems can exhibit subharmonic response, usually characterized through physical observables and often discussed in interacting settings. Here we show that a sharp subharmonic signature already appears in the…

Equivariant Graph Neural Networks (EGNNs) have become a widely used approach for modeling 3D atomistic systems. However, mainstream architectures face critical scalability bottlenecks due to the explicit construction of geometric features…

Modeling sparse and dense image matching within a unified functional correspondence model has recently attracted increasing research interest. However, existing efforts mainly focus on improving matching accuracy while ignoring its…