Related papers: Dyonic Objects and Tensor Network Representation

3D shape representation and its processing have substantial effects on 3D shape recognition. The polygon mesh as a 3D shape representation has many advantages in computer graphics and geometry processing. However, there are still some…

General formulas of the two-electron operator representing either atomic or effective interactions are given in a coupled tensorial form in relativistic approximation. The alternatives of using uncoupled, coupled and antisymmetric…

We present a graphical approach to understanding the degeneracy, density of states, and cumulative state number for some simple quantum systems. By taking advantage of basic computing operations we define a straightforward procedure for…

The success of tensor network approaches in simulating strongly correlated quantum systems crucially depends on whether the many body states that are relevant for the problem can be encoded in a local tensor network. Despite numerous…

A graph theoretic perspective is taken for a range of phenomena in continuum physics in order to develop representations for analysis of large scale, high-fidelity solutions to these problems. Of interest are phenomena described by partial…

Efficient electronic structure methods can be built around efficient tensor representations of the wavefunction. Here we describe a general view of tensor factorization for the compact representation of electronic wavefunctions. We use…

A theory of self-propelled particles is developed in two dimensions assuming that the particles can be deformed from a circular shape when the propagating velocity is increased. A coupled set of equations in terms of the velocity and a…

Dynamics of a free point particle on a multi world-line is presented and shown to reduce to that of a bosonic string theory at the appropriate limit. Other higher dimensional extended objects are argued to appear at other regions of the…

We construct effective hydrodynamics for composite particles in (2+1) dimensions carrying a magnetic flux by employing a holographic approach. The hydrodynamics is obtained by perturbation of the dyonic black brane solutions in the…

Mechanistic interpretability aims to understand how models store representations by breaking down neural networks into interpretable units. However, the occurrence of polysemantic neurons, or neurons that respond to multiple unrelated…

This paper is part of a study whose goal is to show the effciency of using Bayes networks to carry out model based vision calculations. [Binford et al. 1987] Recognition proceeds by drawing up a network model from the object's geometric and…

In this paper, we study the problem of large-strain consolidation in poromechanics with deep neural networks (DNN). Given different material properties and different loading conditions, the goal is to predict pore pressure and settlement.…

Deep neural networks (DNNs) are widely used in real-world applications, yet they remain vulnerable to errors and adversarial attacks. Formal verification offers a systematic approach to identify and mitigate these vulnerabilities, enhancing…

This work studies the problem of high-dimensional data (referred to as tensors) completion from partially observed samplings. We consider that a tensor is a superposition of multiple low-rank components. In particular, each component can be…

Tensor networks are factorisations of high rank tensors into networks of lower rank tensors and have primarily been used to analyse quantum many-body problems. Tensor networks have seen a recent surge of interest in relation to supervised…

In the framework of the Density Functional Theory for superconductors, we study the restoration of the particle number symmetry by means of the projection technique. Conceptual problems are outlined and numerical difficulties are discussed.…

Tensor methods have become a promising tool to solve high-dimensional problems in the big data era. By exploiting possible low-rank tensor factorization, many high-dimensional model-based or data-driven problems can be solved to facilitate…

I describe the foundation of a Density Functional Theory approach to include pairing correlations, which was applied to a variety of systems ranging from dilute fermions, to neutron stars and finite nuclei. Ground state properties as well…

It is often desirable to assess how well a given dataset is described by a given model. In network science, for instance, one often wants to say that a given real-world network appears to come from a particular network model. In statistical…

Hadronization is a non-perturbative process, which theoretical description can not be deduced from first principles. Modeling hadron formation requires several assumptions and various phenomenological approaches. Utilizing state-of-the-art…