相关论文: Quantization of Complementary ADHM Sigma Model

The alternating direction method of multipliers (ADM or ADMM) breaks a complex optimization problem into much simpler subproblems. The ADM algorithms are typically short and easy to implement yet exhibit (nearly) state-of-the-art…

While Graph Neural Networks (GNNs) are popular in the deep learning community, they suffer from several challenges including over-smoothing, over-squashing, and gradient vanishing. Recently, a series of models have attempted to relieve…

In this paper, we analyze the convergence of Alternating Direction Method of Multipliers (ADMM) on convex quadratic programs (QPs) with linear equality and bound constraints. The ADMM formulation alternates between an equality constrained…

We extend the stochastic quantization method recently developed by Haba and Kleinert to non-autonomous mechanical systems, in the case of the time-dependent harmonic oscillator. In comparison with the autonomous case, the quantization…

Models including two $L^1$ -norm terms have been widely used in image restoration. In this paper we first propose the alternating direction method of multipliers (ADMM) to solve this class of models. Based on ADMM, we then propose the…

We study quantum geometry of Nakajima quiver varieties of two different types - framed A-type quivers and ADHM quivers. While these spaces look completely different we find a surprising connection between equivariant K-theories thereof with…

Embedding randomization procedures in the Alternating Direction Method of Multipliers (ADMM) has recently attracted an increasing amount of interest as a remedy to the fact that the direct multi-block generalization of ADMM is not…

The complementarity experiment reported in Bertet [{\it{et al.}} (2001), {\it{Nature}} {\bf{411}}, 166.] is discussed. The role played by entanglement in reaching the classical limit is pointed out. Dissipative and thermal effects of the…

A simple model is constructed which allows to compute modified dispersion relations with effects from loop quantum gravity. Different quantization choices can be realized and their effects on the order of corrections studied explicitly. A…

The purpose of this work is to present some basic concepts about the non-linear sigma model in a simple and direct way. We start with showing the bosonic model and the Wess-Zumino-Witten term, making some comments about its topological…

I stress how the form of sigma models with (2, 2) supersymmetry differs depending on the number of manifest supersymmetries. The differences correspond to different aspects/formulations of Generalized K\"ahler Geometry.

A method for quantizing the bidimensional N=2 supersymmetric non-linear sigma model is developed. This method is both covariant under coordinate transformations (concerning the order relevant for calculations) and explicitly N=2…

We use semi--classical and perturbation methods to establish the quantum theory of the Neumann model, and explain the features observed in previous numerical computations.

Multi-agent distributed optimization over a network minimizes a global objective formed by a sum of local convex functions using only local computation and communication. We develop and analyze a quantized distributed algorithm based on the…

This paper presents new variants of the averaged alternating modified reflections (AAMR) method for the best approximation problem. Under a mild constraint qualification, we first show its weak convergence and then establish a convergence…

We study the renormalization of an N = 1 supersymmetric Lifshitz sigma model in three dimensions. The sigma model exhibits worldvolume anisotropy in space and time around the high-energy z = 2 Lifshitz point, such that the worldvolume is…

We study a problem of systematical evaluation of the quantum corrections for general 4D supersymmetric K\"ahler sigma models with chiral and antichiral superpotentials. Using manifestly reparametrization covariant techniques (the…

We perform a numerical simulation of the two-dimensional ${\cal N}=(2,2)$ supersymmetric Yang-Mills (SYM) theory on the discretized curved space. The $U(1)_{A}$ anomaly of the continuum theory is maintained also in the discretized theory as…

Nonconvex and structured optimization problems arise in many engineering applications that demand scalable and distributed solution methods. The study of the convergence properties of these methods is in general difficult due to the…

The generalized alternating direction method of multipliers (ADMM) of Xiao et al. [{\tt Math. Prog. Comput., 2018}] aims at the two-block linearly constrained composite convex programming problem, in which each block is in the form of…