相关论文: Octonions and Binocular Mobilevision

Coloured Alexander polynomials form a sequence of non-semisimple quantum invariants coming from the representation theory of the quantum group $U_q(sl(2))$ at roots of unity. This sequence recovers the original Alexander polynomial as the…

In autonomous driving, deep learning enabled motion prediction is a popular topic. A critical gap in traditional motion prediction methodologies lies in ensuring equivariance under Euclidean geometric transformations and maintaining…

In recent years, there is a growing interest in the studying octonions, which are 8-dimensional hypercomplex numbers forming the biggest normed division algebras over the real numbers. In particular, various tools of the classical complex…

Geometrical model for material Dirac wave field and for Maxwell electromagnetic field is suggested where above fields are considered as propagating regions of the space itself with distorted euclidean geometry. It is shown that equations…

Three--dimensional colored triangulations are gluings of tetrahedra whose faces carry the colors 0, 1, 2, 3 and in which the attaching maps between tetrahedra are defined using the colors. This framework makes it possible to generalize the…

The classification of the octonionic realizations of the one-dimensional extended supersymmetries is here furnished. These are non-associative realizations which, albeit inequivalent, are put in correspondence with a subclass of the already…

The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones polynomial and arise in Witten-Chern-Simons…

Recently a study of the first superposed mechanical quantum object ("machine") visible to the naked eye was published. However, as we show, it turns out that if the object would actually be observed, i.e. would interact with an optical…

Classical electromagnetic fields and quantum mechanics -- both obey the principle of superposition alike. This opens up many avenues for simulation of a large variety of phenomena and algorithms, which have hitherto been considered quantum…

A foundation is laid for a theory of combinatorial groupoids, allowing us to use concepts like ``holonomy'', ``parallel transport'', ``bundles'', ``combinatorial curvature'' etc. in the context of simplicial (polyhedral) complexes, posets,…

We describe the time evolution of quantum systems in a classical background space-time by means of a covariant derivative in an infinite dimensional vector bundle. The corresponding parallel transport operator along a timelike curve $\cC$…

Continuous-variables (CV) quantum optics is a natural formalism for neural networks (NNs) due to its ability to reproduce the information processing of such trainable interconnected systems. In quantum optics, Gaussian operators induce…

Learning functions on point clouds has applications in many fields, including computer vision, computer graphics, physics, and chemistry. Recently, there has been a growing interest in neural architectures that are invariant or equivariant…

The paper aims to extend major equations in the electromagnetic and gravitational theories from the flat space into the complex octonion curved space. Maxwell applied simultaneously the quaternion analysis and vector terminology to describe…

Experimental observation of the decoherence of macroscopic objects is of fundamental importance to the study of quantum collapse models and the quantum to classical transition. Optomechanics is a promising field for the study of such models…

Despite the importance of image representations such as histograms of oriented gradients and deep Convolutional Neural Networks (CNN), our theoretical understanding of them remains limited. Aiming at filling this gap, we investigate three…

Quaternion (Q-) mathematics formally contains many fragments of physical laws; in particular, the Hamiltonian for the Pauli equation automatically emerges in a space with Q-metric. The eigenfunction method shows that any Q-unit has an…

In this paper, I propose a project of enlisting quantum information science as a source of task-oriented axioms for use in the investigation of operational theories in a general framework capable of encompassing quantum mechanics, classical…

It is a mystery how the brain decodes color vision purely from the optic nerve signals it receives, with a core inferential challenge being how it disentangles internal perception with the correct color dimensionality from the unknown…

Quantum-to-classical transition is a fundamental open question in physics frontier. Quantum decoherence theory points out that the inevitable interaction with environment is a sink carrying away quantum coherence, which is responsible for…