Related papers: Signal Processing on Product Spaces
Medical images are often acquired in different settings, requiring harmonization to adapt to the operating point of algorithms. Specifically, to standardize the physical spacing of imaging voxels in heterogeneous inference settings, images…
A dynamical system framework is used to describe transport processes in plasmas embedded in a magnetic field. For periodic systems with one degree of freedom the Poincar\'e map provides a splitting of the phase space into regions where…
We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…
Neural networks are able to extract information from the timing of spikes. Here we provide new results on the behavior of the simplest neuronal model which is able to decode information embedded in temporal spike patterns, the so called…
Let $V$ be a quasi-conformal grading-restricted vertex algebra, $W$ be its module, and $\W_{z_1, \ldots, z_n}$ be the space of rational differential forms with complex parameters $(z_1, \ldots, z_n)$ for $n \ge 0$. Using geometric…
In this paper we propose a product space reformulation to transform monotone inclusions described by finitely many operators on a Hilbert space into equivalent two-operator problems. Our approach relies on Pierra's classical reformulation…
Rapid developments in streaming data technologies have enabled real-time monitoring of human activity that can deliver high-resolution data on health variables over trajectories or paths carved out by subjects as they conduct their daily…
The approximation of matrices to the sum of tensor products of Hermitian matrices is studied. A minimum decomposition of matrices on tensor space $H_1\otimes H_2$ in terms of the sum of tensor products of Hermitian matrices on $H_1$ and…
The dynamical phase-space of axisymmetric Canham-Helfrich (CH) cells is constructed from a Hamiltonian field recapitulating membrane curvature-elasticity and systemic restrictions. Guiding principles are reparametrization to convert a…
This is the same version that was previously only on my home page. We give a description of geometric realization which makes it evident that it commutes with products. A similar approach is used to treat cyclic sets. Our approach is…
A simple pseudo-Hamiltonian formulation is proposed for the linear inhomogeneous systems of ODEs. In contrast to the usual Hamiltonian mechanics, our approach is based on the use of non-stationary Poisson brackets, i.e. corresponding…
We study the mixed formulation of the abstract Hodge Laplacian on axisymmetric domains with general data through Fourer-finite-element-methods in weighted functions spaces. Closed Hilbert complexes and commuting projectors are used through…
Symbolic encoding has been used in multi-operator learning as a way to embed additional information for distinct time-series data. For spatiotemporal systems described by time-dependent partial differential equations, the equation itself…
Simplicial complexes capture the underlying network topology and geometry of complex systems ranging from the brain to social networks. Here we show that algebraic topology is a fundamental tool to capture the higher-order dynamics of…
A unified simulator that can model diverse physical phenomena without solver-specific redesign is a long-standing goal across simulation science. We present a learning-based particle simulator built on a single transformer architecture to…
Biological and artificial systems encode information through several complex nonlinear operations, making their exact study a formidable challenge. These internal mechanisms often take place across multiple timescales and process external…
On general symplectic manifolds we describe a correspondence between symplectic transformations and their phase functions. On the quantum level, this is a correspondence between unitary operators and phase functions of the…
Spline interpolation is a widely used class of methods for solving interpolation problems by constructing smooth interpolants that minimize a regularized energy functional involving the Laplacian operator. While many existing approaches…
Topological simplification is the process of reducing complexity of a function while maintaining its essential features. Its goal is to find a new filter function, which reorders cells of the input complex in a way which eliminates some…
Complex systems are fascinating because their rich macroscopic properties emerge from the interaction of many simple parts. Understanding the building principles of these emergent phenomena in nature requires assessing natural complex…