相关论文: Generalized spiral transformation for high-resolut…
The closure of a Diximier sheet is the image of a generalized Grothendieck's simultaneous resolution. We show that the associated variety of simple affine vertex algebras is contained in the closure of the Diximier sheet when a…
Many domains, from deep learning to finance, require compounding real numbers over long sequences, often leading to catastrophic numerical underflow or overflow. We introduce generalized orders of magnitude (GOOMs), a principled extension…
We shall investigate randomized algorithms for solving large-scale linear inverse problems with general regularizations. We first present some techniques to transform inverse problems of general form into the ones of standard form, then…
We introduce a new spin-fermion mapping, for arbitrary spin $S$ generating the SU(2) group algebra, that constitutes a natural generalization of the Jordan-Wigner transformation for $S=1/2$. The mapping, valid for regular lattices in any…
Panoramic distortion poses a significant challenge in 360 depth estimation, particularly pronounced at the north and south poles. Existing methods either adopt a bi-projection fusion strategy to remove distortions or model long-range…
We present modular and optimal architectures for implementing arbitrary discrete unitary transformations on light. These architectures are based on systematically combining smaller M-mode linear optical interferometers together to implement…
We demonstrate a new versatile method for 3D super-resolution microscopy by using a deformable mirror to shape the point spread function of our microscope in a continuous and controllable way. We apply this for 3D STORM imaging of…
Achieving efficient and accurate simulation of the radiative transfer has long been a research challenge. Here we introduce the general synthetic iterative scheme as an easy-to-implement approach to address this issue. First, a macroscopic…
Blending schemes based on circles provide smooth `fair' interpolations between series of points. Here we demonstrate a simple, robust set of algorithms for performing circle blends for a range of cases. An arbitrary level of G-continuity…
Let $f\colon X \to \mathbb{A}^1_t$ be an affine flat morphism of finite type, and let $V = f^{-1}(0)$. Then, we obtain a morphism of log schemes $f\colon (X|V) \to (\mathbb{A}^1_t|0)$. In this article, we develop algorithmic tools to study…
The affine Weyl groups with their corresponding four types of orbit functions are considered. Two independent admissible shifts, which preserve the symmetries of the weight and the dual weight lattices, are classified. Finite subsets of the…
We consider the problem of direction finding using partly calibrated arrays, a distributed subarray with position errors between subarrays. The key challenge is to enhance angular resolution in the presence of position errors. To achieve…
Recovering 3D structure and camera motion from images has been a long-standing focus of computer vision research and is known as Structure-from-Motion (SfM). Solutions to this problem are categorized into incremental and global approaches.…
When integrating the radiative transfer equation for polarized light, the necessity of high-order numerical methods is well known. In fact, well-performing high-order formal solvers enable higher accuracy and the use of coarser spatial…
We designed a metallic programmable mirror for optical wavelengths made up of a large number of discrete steps which can be moved independently by actuators. The device is able to easily reshape an incident beam, imprinting on it an optical…
Shape analysis is ubiquitous in problems of pattern and object recognition and has developed considerably in the last decade. The use of shapes is natural in applications where one wants to compare curves independently of their…
The linearly constrained convex composite programming problems whose objective function contains two blocks with each block being the form of nonsmooth+smooth arises frequently in multiple fields of applications. If both of the smooth terms…
In this paper, to solve a broad class of complex symmetric linear systems, we recast the complex system in a real formulation and apply the generalized successive overrelaxation (GSOR) iterative method to the equivalent real system. We then…
In optics, mode conversion is an elegant way to switch between Hermite Gaussian and Laguerre Gaussian beam profiles and thereby impart orbital angular momentum onto the beam and to create vortices. In optics such vortex beams can be…
This paper introduces a reformulation of the classical convergence theorem for spectral sequences of filtered complexes which provides an algorithm to effectively compute the induced filtration on the total (co)homology, as soon as the…