Related papers: Two kinds of parametric piecewise rational interpo…
We consider nearly-perfect cuboids (NPC), where the only irrational is one of the face diagonals. Obtained are three rational parametrizations for NPC with one parameter.
We study both canonical reproducing kernels and constructive reproducing kernels for holomorphic functions in $\CC^1$ and $\CC^n$. We compare and contrast the two, and also develop important relations between the two types of kernels. We…
This paper proposes the paradigm of large convolutional kernels in designing modern Convolutional Neural Networks (ConvNets). We establish that employing a few large kernels, instead of stacking multiple smaller ones, can be a superior…
Implicit neural representations (INRs) are a powerful paradigm for modeling data, offering a continuous alternative to discrete signal representations. Their ability to compactly encode complex signals has led to strong performance in many…
Complex interval arithmetic is a powerful tool for the analysis of computational errors. The naturally arising rectangular, polar, and circular (together called primitive) interval types are not closed under simple arithmetic operations,…
In CAGD the design of a surface that interpolates an arbitrary quadrilateral mesh is definitely a challenging task. The basic requirement is to satisfy both criteria concerning the regularity of the surface and aesthetic concepts. With…
Quantum-inspired neural network is one of the interesting researches at the junction of the two fields of quantum computing and deep learning. Several models of quantum-inspired neurons with real parameters have been proposed, which are…
We present a methodology to recover cosmic microwave background (CMB) polarization in which the quantity $P = Q+ iU$ is linearly combined at different frequencies using complex coefficients. This is the most general linear combination of…
It is believed that neural information representation and processing relies on the neural population instead of a single neuron. In neuromorphic photonics, photonic neurons in the form of nonlinear responses have been extensively studied in…
Quantum photonic neural networks are variational photonic circuits that can be trained to implement high-fidelity quantum operations. However, work-to-date has assumed idealized components, including a perfect $\pi$ Kerr nonlinearity. Here,…
Let $\mathbb F_{q^2}$ be the finite field with $q^2$ elements. We provide a simple and effective method, using reciprocal polynomials, for the construction of algebraic curves over $\mathbb F_{q^2}$ with many rational points. The curves…
Photonic platforms represent a promising technology for the realization of several quantum communication protocols and for experiments of quantum simulation. Moreover, large-scale integrated interferometers have recently gained a relevant…
We study the consistency of minimum-norm interpolation in reproducing kernel Hilbert spaces corresponding to bounded kernels. Our main result give lower bounds for the generalization error of the kernel interpolation measured in a…
Hermitian cubic norm structures were recently introduced in order to study the class of skew-dimension one structurable algebras (which are typically only defined over fields of characteristic different from $2$ and $3$) over arbitrary…
A novel search method for large polarization kernels is proposed. The algorithm produces a kernel with given partial distances by employing the depth-first search combined with the computation of coset leaders weight tables and sufficient…
Image convolution with complex kernels is a fundamental operation in photography, scientific imaging, and animation effects, yet direct dense convolution is computationally prohibitive on resource-limited devices. Existing approximations,…
The purpose of this work is to explore the existence and properties of reproducing kernel Hilbert subspaces of $L^2(\C, \, d^2z/\pi)$ based on subsets of complex Hermite polynomials. The resulting coherent states (CS) form a family…
Object proposals are an ensemble of bounding boxes with high potential to contain objects. In order to determine a small set of proposals with a high recall, a common scheme is extracting multiple features followed by a ranking algorithm…
This paper proposes a 4X4 Census Transform (4X4CT) to encourage further research in computer vision and visual computing. Unlike the traditional 3X3 CT which uses a nine pixels kernel, the proposed 4X4CT uses a sixteen pixels kernel with…
Ng and Schauenburg proved that the kernel of a $(2+1)$-dimensional topological quantum field theory representation of $\mathrm{SL}(2, \mathbb{Z})$ is a congruence subgroup. Motivated by their result, we explore when the kernel of an…