Related papers: Nested Head-Tail Vlasov Solver

Dynamics of solitons is considered in the framework of an extended nonlinear Schrodinger equation (NLSE), which is derived from a system of the Zakharov's type for the interaction between high- and low-frequency (HF and LF) waves. The…

Novel view synthesis (NVS) seeks to render photorealistic, 3D-consistent images of a scene from unseen camera poses given only a sparse set of posed views. Existing deterministic networks render observed regions quickly but blur unobserved…

Solving nonlinear algebraic equations is a fundamental but challenging problem in scientific computations and also has many applications in system engineering. Though traditional iterative methods and modern optimization algorithms have…

Recently, Vision Transformer (ViT) has achieved promising performance in image recognition and gradually serves as a powerful backbone in various vision tasks. To satisfy the sequential input of Transformer, the tail of ViT first splits…

This is a review of the main ideas of the inverse scattering method (ISM) for solving nonlinear evolution equations (NLEE), known as soliton equations. As a basic tool we use the fundamental analytic solutions (FAS) of the Lax operator L.…

With the rise of Transformer models in NLP and CV domain, Multi-Head Attention has been proven to be a game-changer. However, its expensive computation poses challenges to the model throughput and efficiency, especially for the long…

This paper develops the numerical inverse scattering transform (NIST) framework for the coupled modified Korteweg-de Vries (mKdV) equation based on its associated Riemann-Hilbert problem. The coupled system gives rise to a $3\times3$…

This paper presents new results in the theory of number theoretic Hilbert (NHT) transforms. New polymorphic solutions have been found for the 14-point and 16-point transforms. Several transform pairs are computed and solutions found for…

Nonconvex sparse learning plays an essential role in many areas, such as signal processing and deep network compression. Iterative hard thresholding (IHT) methods are the state-of-the-art for nonconvex sparse learning due to their…

One of the crucial challenges taken in document analysis is mathematical expression recognition. Unlike text recognition which only focuses on one-dimensional structure images, mathematical expression recognition is a much more complicated…

We describe a thermodynamic-inspired computing paradigm based on oscillatory neural networks (ONNs). While ONNs have been widely studied as Ising machines for tackling complex combinatorial optimization problems, this work investigates…

In this work we start with an introductory review of the relatively recently discovered type of liquid crystals, twist-bend nematics N_{TB}. Then we describe a more detailed account of recent developments in the field. Namely: (i) Landau…

Tensors with unit Frobenius norm are fundamental objects in many fields, including scientific computing and quantum physics, which are able to represent normalized eigenvectors and pure quantum states. While the tensor train decomposition…

In recent years, Transformer has achieved good results in Natural Language Processing (NLP) and has also started to expand into Computer Vision (CV). Excellent models such as the Vision Transformer and Swin Transformer have emerged. At the…

A thermostat of the Nose-Hoover type, based on relative velocities and a local definition of the temperature, is presented. The thermostat is momentum-conserving and Galilean-invariant, which should make it suitable for use in Dissipative…

The recent increase in computational resources and data availability has led to a significant rise in the use of Machine Learning (ML) techniques for data analysis in physics. However, the application of ML methods to solve differential…

Turbulence is notoriously difficult to model due to its multi-scale nature and sensitivity to small perturbations. Classical solvers of turbulence simulation generally operate on finer grids and are computationally inefficient. In this…

Designing hardware accelerators for deep neural networks (DNNs) has been much desired. Nonetheless, most of these existing accelerators are built for either convolutional neural networks (CNNs) or recurrent neural networks (RNNs). Recently,…

Deep learning has shown a tremendous growth in hashing techniques for image retrieval. Recently, Transformer has emerged as a new architecture by utilizing self-attention without convolution. Transformer is also extended to Vision…

Transformers excel at sequence modeling but face quadratic complexity, while linear attention offers improved efficiency but often compromises recall accuracy over long contexts. In this work, we introduce Native Hybrid Attention (NHA), a…