Recent works have demonstrated promising performances of neural networks on hyperbolic spaces and symmetric positive definite (SPD) manifolds. These spaces belong to a family of Riemannian manifolds referred to as symmetric spaces of noncompact type. In this paper, we propose a novel approach for developing neural networks on such spaces. Our approach relies on a unified formulation of the distance from a point to a hyperplane on the considered spaces. We show that some existing formulations of the point-to-hyperplane distance can be recovered by our approach under specific settings. Furthermore, we derive a closed-form expression for the point-to-hyperplane distance in higher-rank symmetric spaces of noncompact type equipped with G-invariant Riemannian metrics. The derived distance then serves as a tool to design fully-connected (FC) layers and an attention mechanism for neural networks on the considered spaces. Our approach is validated on challenging benchmarks for image classification, electroencephalogram (EEG) signal classification, image generation, and natural language inference.
This research presents a Priority-based Energy Management Scheme (PEMS) for a Photovoltaic (PV) and battery-integrated Shunt Active Filter (SAF). It is designed for the energy flow optimization between PV energy, battery, grid and load while ensuring high-power quality on the grid side. The proposed approach effectively mitigates harmonics, which can otherwise adversely deteriorate the power quality and compromise grid stability, hence potentially impacting the distribution equipment, including connected loads. Moreover, a lightweight L-series inductor filter is used for SAF current injection, hence enhancing cost-effectiveness. The novel PEMS strategy, driven by a common control strategy, not only ensures optimal power flow management but also maximizes high SAF performance with maximum PV penetration under dynamic operating conditions. It facilitates quick restoration of the DC bus for enhanced system stability, harmonics mitigation across varying load and PV conditions, maximum PV power generation, and smooth battery operation. The power flow among the grid, PV panels, battery, and load is dynamically controlled and maintained based on the battery’s State of Charge (SoC), available PV power, constraints of the battery, and load requirements. Additionally, the proposed PEMS framework warrants reliable SAF operation while restricting high THD values under various loading conditions well below the IEEE-defined standard of 5 %, achieving a significant reduction from 17.80 % to 0.68 %. Finally, to validate the effectiveness of the proposed strategy, MATLAB-based simulations are conducted, followed by experimental validation in an Industrial lab setup. Therefore allowing and ensuring comprehensive efficiency, reliability, and overall performance.
Controlling dynamical systems, specially high dimensional dynamical networks, is of primary interest. Such a problem is intrinsically related to analyzing the observability of the corresponding state space from measurements, as well as its dual aspect of controllability. An additional constraint can be added by requiring the system to be flat, meaning that its state and actuating signal can be expressed in terms of the measurements and a finite number of its derivatives. Starting from the placement of sensors providing global observability, we address the dual problem of placing the actuators allowing global controllability, and of designing a flat input. Since global observability of a network of y-coupled Rössler systems can be reduced to the observability of each pair of nodes, a step before controlling a network is to design a flat control law for a pair of diffusively y-coupled Rössler systems. It is shown that such a system is flat when a differential delay is inserted.
A flat control law is based on the structural analysis of a controlled system, allowing optimal placement of sensors and actuators. Once designed, any desired dynamics can be imposed onto the system. When the target dynamics comes from a system structurally different from the controlled one, generalized synchronization can be achieved, provided the control gain is sufficiently large. As the gain increases, various relationships emerge between the drive and response systems, depending on differences in their dimensions and dissipation rates. The principal contribution of this work lies in the exploration of drive-response system pairs with varying dimensions (ranging from 2 to 4) and dissipation levels, including combinations of dissipative and conservative systems. We identify several types of generalized synchronization, using a classification based on the thickness of the resulting Lissajous curves and the lack of conjugacy between the first-return maps of the drive and response systems.
This paper examines the nature of the relationship between Financial Sector Development (FSD) and intra-African trade. Using a sample of African countries with available data from 1998 to 2021, and robust estimation techniques that address endogeneity and omitted variables biases, we find a positive significant impact of the composite financial development indicator and cross-border banking flows on intra-African trade. Further analysis reveals that the effects of the financial institution sub-indicators are more pronounced than those of the financial market sub-indicators. The effects are also heterogeneous across the different African Regional Economic Communities (RECs). Finally, our results show that financial sector development affects intra-African trade indirectly through its impact on the services and industrial sectors.
