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One of basic difficulties of machine learning is handling unknown rotations of objects, for example in image recognition. A related problem is evaluation of similarity of shapes, for example of two chemical molecules, for which direct…
We offer a Maple package {\tt Poincare\_Series} for calculating the Poincar\'e series for the algebras of invariants/covariants of binary forms, for the algebras of joint invariants/covariants of several binary forms, for the kernel of…
We derive a class of cubic interaction vertices for three higher spin fields, with integer spins $\lambda_1$, $\lambda_2$, $\lambda_3$, by closing commutators of the Poincar\'e algebra in four-dimensional flat spacetime. We find that these…
To better understand the dependence of the magnetic field structure in the plasma edge on the plasma boundary shape, in the context of X-point and island divertor designs, we define and develop a class of stellarators called umbilic…
We present a computational method for studying transverse homoclinic orbits for periodic solutions of delay differential equations, a phenomenon that we refer to as the \emph{Poincar\'{e} scenario}. The strategy is geometric in nature, and…
Cosmic-ray acceleration processes in astrophysical plasmas are often investigated with fully-kinetic or hybrid kinetic numerical simulations, which enable us to describe a detailed microphysics of particle energization mechanisms. Tracing…
In 3D point cloud-based visual self-localization, pole landmarks have a great potential as landmarks for accurate and reliable localization due to their long-term stability under seasonal and weather changes. In this study, we aim to…
A challenging and fundamental research problem is the better understanding and control of the turbulent transport of heat in present-day tokamak fusion experiments. Recent developments in numerical methods along with enormous gains in…
The phase space of an integrable Hamiltonian system is foliated by invariant tori. For an arbitrary Hamiltonian H such a foliation may not exist, but we can artificially construct one through a parameterised family of surfaces, with the…
Self-Organising Maps (SOMs) are effective tools in classification problems, and in recent years the even more powerful Dynamic Growing Neural Networks, a variant of SOMs, have been developed. Automatic Classification (also called…
Aiming at obtaining detailed information of surface environment of Earth analogs, Kawahara & Fujii (2011) proposed an inversion technique of annual scattered light curves named the spin-orbit tomography (SOT), which enables one to sketch a…
One of the most intensely studied aspects of magnetic confinement fusion is edge plasma turbulence which is critical to reactor performance and operation. Drift-reduced Braginskii two-fluid theory has for decades been widely applied to…
Controlling and monitoring plasma within a tokamak device is complex and challenging. Plasma off-normal events, such as disruptions, are hindering steady-state operation. For large devices, they can even endanger the machine's integrity and…
Machine learning models are exceptionally effective in capturing complex non-linear relationships of high-dimensional datasets and making accurate predictions. However, their intrinsic ``black-box'' nature makes it difficult to interpret…
Can a machine or algorithm discover or learn the elliptical orbit of Mars from astronomical sightings alone? Johannes Kepler required two paradigm shifts to discover his First Law regarding the elliptical orbit of Mars. Firstly, a shift…
This paper addresses the problem of determining the symmetries of a plane or space curve defined by a rational parametrization. We provide effective methods to compute the involution and rotation symmetries for the planar case. As for space…
Magnetic nulls are ubiquitous in space plasmas, and are of interest as sites of localized energy dissipation or magnetic reconnection. As such, a number of methods have been proposed for detecting nulls in both simulation data and in situ…
General formula describing both the divertor strike point splitting and width of magnetic islands created by resonant magnetic perturbations (RMPs) in a poloidally diverted tokamak equilibrium is derived. Under the assumption that the RMP…
We give an algorithm for deciding whether a planar polynomial differential system has a first integral which factorizes as a product of defining polynomials of curves with only one place at infinity. In the affirmative case, our algorithm…
Nuclear fusion represents one of the best alternatives for a sustainable source of clean energy. Tokamaks allow to confine fusion plasma with magnetic fields and one of the main challenges in the control of the magnetic configuration is the…