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We further develop an algorithmic and diagrammatic computational framework for very general exact renormalization groups, where the embedded regularisation scheme, parametrised by a general cutoff function and infinitely many higher point…
This article presents a new approach to the real-time solution of inverse problems on embedded systems. The class of problems addressed corresponds to ordinary differential equations (ODEs) with generalized linear constraints, whereby the…
X-ray Bragg coherent diffraction imaging has been demonstrated as a powerful three-dimensional (3D) microscopy approach for the investigation of sub-micrometer-scale crystalline particles. It is based on the measurement of a series of…
The efficient manipulation, sorting, and measurement of optical modes and single-photon states is fundamental to classical and quantum science. Here, we realise simultaneous and efficient sorting of non-orthogonal, overlapping states of…
We have studied quantum systems on finite-dimensional Hilbert spaces and found that all these systems are connected through local transformations. Actually, we have shown that these transformations give rise to a gauge group that connects…
The paper aims to emphasise how switched systems can be analysed with elementary techniques which require only undergraduate-level linear algebra and differential equations. It is also emphasised how math software can become useful for…
Different from the quasi-static network in the traditional power system, the dynamic network in the power-electronic-dominated power system should be considered due to rapid response of converters' controls. In this paper, a nonlinear…
An efficient systematic procedure is provided for symbolic computation of Lie groups of equivalence transformations and generalized equivalence transformations of systems of differential equations that contain arbitrary elements (arbitrary…
We present recent results from experimental studies of power corrections in the model of Dokshitzer, Marchesini and Webber using data from the process e+e- -> hadrons at several centre-of-mass energies. Fitted O(alpha_S^2)+NLLA QCD…
The modern power system features high penetration of power converters due to the development of renewables, HVDC, etc. Currently, the controller design and parameter tuning of power converters heavily rely on rich engineering experience and…
We experimentally study the infinite-size limit of the Dicke model of quantum optics with a parity-breaking deformation strength that couples the system to an external bosonic reservoir. We focus on the dynamical consequences of such…
We present two related techniques to measure the two-point correlation function and the power spectrum with edge correction in any spatial dimensions. The underlying algorithm uses fast Fourier transforms for calculating the two-point…
We design an algorithm for control of a linear switched system by means of Geometric Algebra. More precisely, we develop a switching path searching algorithm for a two-dimensional linear dynamical switched system with non-singular matrix…
Grid-connected power converters encounter significant stability challenges during weak grid faults, when conventional PI-based controllers exhibit an oscillatory response and poor fault-ride-through performance. This paper addresses this…
A linear algebraic method named the shifted conjugate-orthogonal-conjugate-gradient method is introduced for large-scale electronic structure calculation. The method gives an iterative solver algorithm of the Green's function and the…
Load models have a great impact on voltage behaviors as well as power system transient dynamics. Extensive work has been done on this topic, proposing appropriate load models and capturing better load behaviors during transient. This paper…
Quadratic surfaces gain more and more attention among the Geometric Algebra community and some frameworks were proposed in order to represent, transform, and intersect these quadratic surfaces. As far as the authors know, none of these…
The state of art of electromagnetic integral equations has seen significant growth over the past few decades, overcoming some of the fundamental bottlenecks: computational complexity, low frequency and dense discretization breakdown,…
Matrix computations have become increasingly significant in many data-driven applications. However, Moores law for digital computers has been gradually approaching its limit in recent years. Moreover, digital computers encounter substantial…
In this article we summarize and describe the recently found transforms for theories of connections modulo gauge transformations associated with compact gauge groups. Specifically, we put into a coherent picture the so-called loop…