Related papers: Signal Processing on Product Spaces
Time dependence is a universal phenomenon in nature, and a variety of mathematical models in terms of dynamical systems have been developed to understand the time-dependent behavior of real-world problems. Originally constructed to analyze…
Cells in natural environments like tissue or soil sense and respond to extracellular ligands with intricately structured and non-monotonic spatial distributions that are sculpted by processes such as fluid flow and substrate adhesion.…
With the recent development of localization and tracking systems for both indoor and outdoor settings, we consider the problem of sensing, representing and analyzing human movement trajectories that we expect to gather in the near future.…
This paper proposes a novel beamforming framework in the reproducing kernel domain, derived from a unified interpretation of directional response as spatial differentiation of the sound field. By representing directional response using…
This paper extends the concept of Laplacian filtered quasi-Helmholtz decompositions we have recently introduced, to the basis-free projector-based setting. This extension allows the discrete analyses of electromagnetic integral operators…
Deductive verification of hybrid systems (HSs) increasingly attracts more attention in recent years because of its power and scalability, where a powerful specification logic for HSs is the cornerstone. Often, HSs are naturally modelled by…
We present a method to simplify expressions in the context of an equational theory. The basic ideas and concepts of the method have been presented previously elsewhere but here we tackle the difficult task of making it efficient in…
The eigenfunctions of the Laplacian are a natural basis of functions for many tasks in computational mathematics. On the circle and sphere, the eigenfunctions are given by complex periodic exponentials and spherical harmonics, respectively,…
Spaceplates have emerged in the context of nonlocal metasurfaces, enabling the compression of optical systems by minimizing the required empty space between their components. In this work, we design and analyze spaceplates that support…
Aspects of the theory of characteristic modes, based on their variational formulation, are presented and an explicit form of a related functional, involving only currents in a spatial domain, is derived. The new formulation leads to deeper…
While many geological and geophysical processes such as the melting of icecaps, the magnetic expression of bodies emplaced in the Earth's crust, or the surface displacement remaining after large earthquakes are spatially localized, many of…
All-optical image processing offers a high-speed, energy-efficient alternative to conventional electronic systems by leveraging the wave nature of light for parallel computation. However, traditional optical processors rely on bulky…
We study the problem of computing the homology of the configuration spaces of a finite cell complex $X$. We proceed by viewing $X$, together with its subdivisions, as a subdivisional space--a kind of diagram object in a category of cell…
This paper introduces a topological framework for interpreting the internal representations of Multilayer Perceptrons (MLPs). We construct a simplicial tower, a sequence of simplicial complexes connected by simplicial maps, that captures…
In this work, a numerical modal decomposition approach is applied to model the optical field of laser light after propagating through a highly multi-mode fiber. The algorithm for the decomposition is based on the reconstruction of measured…
A method is proposed for evaluation of single and double layer potentials of the Laplace and Helmholtz equations on piecewise smooth manifold boundary elements with constant densities. The method is based on a novel two-term decomposition…
This paper addresses the structurally-constrained sparse decomposition of multi-dimensional signals onto overcomplete families of vectors, called dictionaries. The contribution of the paper is threefold. Firstly, a generic spatio-temporal…
Multiscale and inhomogeneous molecular systems are challenging topics in the field of molecular simulation. In particular, modeling biological systems in the context of multiscale simulations and exploring material properties are driving a…
The paper studies processes defined on time domains structured as oriented spatial graphs (or metric graphs, or oriented branched 1-manifolds). This setting can be used, for example, for forecasting models involving branching scenarios. For…
We introduce a new neural architecture and an unsupervised algorithm for learning invariant representations from temporal sequence of images. The system uses two groups of complex cells whose outputs are combined multiplicatively: one that…