Related papers: Combining Grassmann algebra with entanglement reno…
The exact renormalization group (ERG) for $O(N)$ vector models (at large $N$) on flat Euclidean space can be interpreted as the bulk dynamics corresponding to a holographically dual higher spin gauge theory on $AdS_{d+1}$. This was…
The use of adaptive mesh refinement (AMR) techniques is crucial for accurate and efficient simulation of higher dimensional spacetimes. In this work we develop an adaptive algorithm tailored to the integration of finite difference…
We consider the problem of efficiently approximating and encoding high-dimensional data sampled from a probability distribution $\rho$ in $\mathbb{R}^D$, that is nearly supported on a $d$-dimensional set $\mathcal{M}$ - for example…
The particular structure of Galileon interactions allows for higher-derivative terms while retaining second order field equations for scalar fields and Abelian $p$-forms. In this work we introduce an index-free formulation of these…
The Ryu-Takayanagi (RT) formula is a crucial concept in current theory of gauge-gravity duality and emergent phenomena of geometry. Recent reinterpretation of this formula in terms of a set of "bit threads" is an interesting effort in…
We use computational algorithms recently developed by us to study completely four index divergence free quadratic in Riemann tensor polynomials in GR. Some results are new and some other reproduce and/or correct known ones. The algorithms…
We introduce a tensor renormalization group scheme for coarse-graining a two-dimensional tensor network that can be successfully applied to both classical and quantum systems on and off criticality. The key innovation in our scheme is to…
This paper constructs a semi-discrete tight frame of tensor needlets associated with a quadrature rule for tangent vector fields on the unit sphere $\mathbb{S}^2$ of $\mathbb{R}^3$ --- tensor needlets. The proposed tight tensor needlets…
Machine learning (ML) models can effectively optimize a multi-cell wireless network by designing the beamforming vectors and association decisions. Existing ML designs, however, often needs to approximate the integer association variables…
Exploiting symmetries in tensor network algorithms plays a key role for reducing the computational and memory costs. Here we explain how to incorporate the Hermitian symmetry in double-layer tensor networks, which naturally arise in methods…
We present an application of deep generative models in the context of partial-differential equation (PDE) constrained inverse problems. We combine a generative adversarial network (GAN) representing an a priori model that creates subsurface…
Traditional network analysis focuses on single-layer networks, real-world systems often form multilayer networks with multiple relationship types. However, existing methods typically fail to capture complex inter-layer dependencies by…
We propose a simple modification of the density matrix renormalization group (DMRG) method in order to tackle strongly disordered quantum spin chains. Our proposal, akin to the idea of the adaptive time-dependent DMRG, enables us to reach…
Generative Adversarial Network (GAN) and its variants exhibit state-of-the-art performance in the class of generative models. To capture higher-dimensional distributions, the common learning procedure requires high computational complexity…
We propose a framework for calculating two-loop Feynman diagrams which appear within a renormalizable theory in the general mass case and at finite external momenta. Our approach is a combination of analytical results and of high accuracy…
We revisit the renormalisation group equations (RGE) for general renormalisable gauge theories at one- and two-loop accuracy. We identify and correct various mistakes in the literature for the $\beta$-functions of the dimensionful…
Magnetic Resonance Angiography (MRA) has become an essential MR contrast for imaging and evaluation of vascular anatomy and related diseases. MRA acquisitions are typically ordered for vascular interventions, whereas in typical scenarios,…
The optimization of structural parameters, such as mass(m), stiffness(k), and damping coefficient(c), is critical for designing efficient, resilient, and stable structures. Conventional numerical approaches, including Finite Element Method…
Among many types of quantum entanglement properties, the entanglement spectrum provides more abundant information than other observables. Exact diagonalization and density matrix renormalization group method could handle the system in…
We introduce randomized algorithms to Clifford's Geometric Algebra, generalizing randomized linear algebra to hypercomplex vector spaces. This novel approach has many implications in machine learning, including training neural networks to…