Related papers: Verifying an algorithm computing Discrete Vector F…

Vector field design on surfaces was originally motivated by applications in graphics such as texture synthesis and rendering. In this paper, we consider the idea of vector field design with a new motivation from computational topology. We…

We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse…

The Dolbeault resolution of the sheaf of holomorphic vector fields $Lie$ on a complex manifold $M$ relates $Lie$ to a sheaf of differential graded Lie algebras, known as the Fr\"olicher-Nijenhuis algebra $g$. We establish - following B. L.…

A privacy-preserving support vector machine (SVM) computing scheme is proposed in this paper. Cloud computing has been spreading in many fields. However, the cloud computing has some serious issues for end users, such as the unauthorized…

The rapid growth of visual data under stringent storage and bandwidth constraints makes extremely low-bitrate image compression increasingly important. While Vector Quantization (VQ) offers strong structural fidelity, existing methods lack…

In this paper, we study the discrete differential calculus on hypergraphs by using the Kouzul complexes. We define the constrained (co)homology for hypergraphs and give the corresponding Mayer-Vietoris sequences. We prove the functoriality…

We present a general theorem which computes the cohomology of a homological vector field on global sections of vector bundles over smooth affine supervarieties. The hypotheses and results have the clear flavor of a localization theorem.

We report an algorithm, based on quantum optics formulation, where a coherent state is used as the elementary quantum resource for the image representation. We provide an architecture with constituent optical elements in linear order with…

We describe an essential improvement of our recent algorithm for computing cohomology of Lie (super)algebra based on partition of the whole cochain complex into minimal subcomplexes. We replace the arithmetic of rational numbers or integers…

Complex vector modes have become topical of late due to their fascinating properties and the many applications they have found across a broad variety of research fields. Even though such modes can be generated in a wide variety of ways,…

In recent time there has been an increasing amount of interest in developing novel techniques for the generation of complex vector light beams. Amongst these, digital holography stands out as one of the most flexible and versatile with…

With the rapid progress in quantum hardware and software, the need for verification of quantum systems becomes increasingly crucial. While model checking is a dominant and very successful technique for verifying classical systems, its…

Topological physics desires stable methods to measure the polarization singularities in optical vector fields. Here a periodic plasmonic metasurface is proposed to perform divergence computation of vectorial paraxial beams. We design such…

We show that Horrock's criterion for the splitting of vector bundles on $\PP^n$ can be extended to vector bundles on multiprojective spaces and to smooth projective varieties with the weak CM property (see Definition 3.11). As a main tool…

The non-separability between the spatial and polarisation Degrees of Freedom (DoFs) of complex vector light fields has drawn significant attention in recent time. Key to this are its remarkable similarities with quantum entanglement, with…

Discretized techniques for vector tomographic reconstructions are prone to producing artifacts in the reconstructions. The quality of these reconstructions may further deteriorate as the amount of noise increases. In this work, we instead…

We present Channel-wise Vector Quantization (CVQ), a novel image tokenization paradigm that replaces patch-wise tokens with channel-wise tokens. Unlike conventional vector quantization, which assigns a discrete token to each patch feature…

Features play a crucial role in computer vision. Initially designed to detect salient elements by means of handcrafted algorithms, features are now often learned by different layers in Convolutional Neural Networks (CNNs). This paper…

Accurately simulating photon transport is crucial for non-destructive testing and medical diagnostic applications using X-ray radiography and computed tomography (CT). Solving a discretized form of the linear Boltzmann equation is a…

High-throughput approximations of quantum mechanics calculations and combinatorial experiments have been traditionally used to reduce the search space of possible molecules, drugs and materials. However, the interplay of structural and…