Related papers: New class of spin projection operators for 3D mode…
The convergence rate of a multigrid method depends on the properties of the smoother and the so-called grid transfer operator. In this paper we define and analyze new grid transfer operators with a generic cutting size which are applicable…
We study the relation between the frame-like and metric-like formulation of higher-spin gauge theories in three space-time dimensions. We concentrate on the theory that is described by an SL(3) x SL(3) Chern-Simons theory in the frame-like…
Many integrable systems can be reformulated as holomorphic vector bundles on twistor space. This is a powerful organizing principle in the theory of integrable systems. One shortcoming is that it is formulated at the level of the equations…
This paper considers an extension of origami geometry to the case of "folding" a three dimensional (3D) space along a plane. First, all possible incidence constraints between given points, lines and planes are analyzed by using the geometry…
The level-k U(1) Chern-Simons theory is a spin topological quantum field theory for k odd. Its dynamics is captured by the 2d CFT of a compact boson with a certain radius. Recently it was recognized that a dependence on the 2d spin…
This paper presents an experimental study on the application of quaternions in several machine learning algorithms. Quaternion is a mathematical representation of rotation in three-dimensional space, which can be used to represent complex…
We introduce a class of 3d theories consisting of strongly-coupled ${\mathcal N}=4$ systems coupled to ${\mathcal N}=3$ Chern-Simons gauge multiplets, which exhibit ${\mathcal N}=4$ enhancements when a peculiar condition on the Chern-Simons…
We investigate the Chern-Simons-like formulation of exotic general massive gravity models within the framework of third-way to three-dimensional gravity. We classify our construction into two main approaches: one using torsional…
New extended interpolating operators made of quenched three dimensional fermions are introduced in the context of lattice QCD. The mass of the 3D fermions can be tuned in a controlled way to find a better overlap of the extended operators…
Projected gradient descent has been proved efficient in many optimization and machine learning problems. The weighted $\ell_1$ ball has been shown effective in sparse system identification and features selection. In this paper we propose…
In quantum computing, knowing the symmetries a given system or state obeys or disobeys is often useful. For example, Hamiltonian symmetries may limit allowed state transitions or simplify learning parameters in machine learning…
We propose a new family of neural networks to predict the behaviors of physical systems by learning their underpinning constraints. A neural projection operator lies at the heart of our approach, composed of a lightweight network with an…
A new way of orthogonalizing ensembles of vectors by "lifting" them to higher dimensions is introduced. This method can potentially be utilized for solving quantum decision and computing problems.
Here I will review the theoretical results that have been obtained for spin glasses. I will concentrate my attention on the predictions of the mean field approach in three dimensional systems and on its numerical and experimental…
A wide class of three-dimensional gravity models can be put into "Chern-Simons-like" form. We perform a Hamiltonian analysis of the general model and then specialise to Einstein-Cartan Gravity, General Massive Gravity, the recently proposed…
The convergence of a new general variable metric algorithm based on compositions of averaged operators is established. Applications to monotone operator splitting are presented.
Recent results on the construction and applications of the transmutation (transformation) operators are discussed. Three new representations for solutions of the one-dimensional Schr\"odinger equation are considered. Due to the fact that…
The physical meaning of the operators is not reducible to the intrinsic relations of the quantum system, since unitary transformations can find other operators satisfying the exact same relations. The physical meaning is determined…
The construction of baryonic operators for determining the N* excitation spectrum is discussed. The operators are designed with one eye towards maximizing overlaps with the low-lying states of interest, and the other eye towards minimizing…
We explore a novel method to perceive and manipulate 3D articulated objects that generalizes to enable a robot to articulate unseen classes of objects. We propose a vision-based system that learns to predict the potential motions of the…