D-modules and projective stacks

We study twisted D-modules on the weighted projective stacks. We determine for which values of the twist and the weight the global section functor is an equivalence, thus, proving a version of Beilinson-Bernstein Localisation Theorem.Comment: 22 pages, minor updates to the previous versio

Smooth projective stacks : ample bundles and D-affinity

This thesis is on the study of sheaves of O-modules and D-modules on projective stacks. In chapter 1, a historical perspective is given on the main fidings that have shaped and influenced the study carried out and exposed in this thesis. In chapter 2, the principal definitions and results used in the forthcoming sections are recalled. An appendix is added at the end of this chapter exposing self-containedly why quotient singularities and orbifolds are two equivalent notions. In chapter 3, the property of ampleness of vector bundles on projective stacks is generalised and studied. Basic properties are given; in particular it is proved that weighted projective stacks have ample tangent vector bundle. In chapter 4, D-modules on projective stacks are studied. General conditions on the weights and the shift guaranteeing a weighted projective stack to be D-affine are given. Thus, proving a version of the Beilinson-Bernstein Localisation Theorem. In particular, a weighted projective stack is D-affine if and only if the greatest common divisor of its weights is one. A theorem of Kashiwara is extended to smooth projective stacks, it is shown that the category of D-modules on a smooth closed projective substack [X] is equivalent to the category of D-modules on the ambient smooth projective stack [Y ] supported on [X]

Low-complexity channel estimation for V2X systems using feed-forward neural networks

Research on machine learning for channel estimation, especially neural network solutions for wireless communications, is attracting significant current interest. This is because conventional methods cannot meet the present demands of the high speed communication. In the paper, we deploy a general residual convolutional neural network to achieve channel estimation for the orthogonal frequency-division multiplexing (OFDM) signals in a downlink scenario. Our method also deploys a simple interpolation layer to replace the transposed convolutional layer used in other networks to reduce the computation cost. The proposed method is more easily adapted to different pilot patterns and packet sizes. Compared with other deep learning methods for channel estimation, our results for 3GPP channel models suggest improved mean squared error performance for our approach

A novel detection approach of unknown cyber-attacks for intra-vehicle networks using recurrence plots and neural networks

Proliferation of connected services in modern vehicles could make them vulnerable to a wide range of cyber-attacks through intra-vehicle networks that connect various vehicle systems. Designers usually equip vehicles with predesigned counter-measures, but these may not be effective against novel cyber-attacks. Intrusion Detection Systems (IDSs) serve as an additional layer of defence when conventional measures that are implemented by the designers fail. Several intrusion detection techniques have been proposed in the literature but these techniques have limited capability in detecting novel cyber-attacks. This paper proposes a new Machine Learning (ML)-based IDS for detecting novel cyber-attacks in intra-vehicle networks, specifically in Controller Area Networks (CANs). The proposed IDS generates high-level representations of CAN messages transmitted on the bus exploiting their temporal properties as well as the intra and inter message dependencies through the use of Recurrence Plot (RP), which are then fed into a bespoke Neural Network, designed and trained to detect novel intrusions. Evaluation of the performance of the proposed IDS in comparison with that of the state-of-the-art existing IDS schemes demonstrates the superiority of the proposed IDS

State-of-the-art in PHY layer deep learning for future wireless communication systems and networks

Ongoing activities by several standardization bodies, experimental demonstrations in research projects, and recent trends and investments by the telecommunication sector reveal that the next generation of wireless communication systems will offer a multitude of unprecedented use cases, such as enhanced mobile broadband for ultra-high-speed railways, augmented reality, and 3d connectivity involving unmanned aerial vehicles (UAVs) and intelligent reflecting surfaces. Furthermore, well-established and verified mathematical models, such as those utilised for channel equalization, link adaptation, and symbol detection, will likely fall short once applied in wireless systems operating in higher frequencies and deployed in challenging environments. Fortunately, recent advancements in data collection and storage, together with breakthroughs in artificial intelligence (AI) and machine learning (ML), will allow communication engineers to construct data-driven solutions for optimising the performance of envisioned future networks. Motivated by these potentials, in this chapter, we provide the interested readers with a comprehensive analysis and review of the most recent progress in using data-driven and ML-based approaches at the PHY layer of modern communications. We review the performance of purely data-driven auto-encoders and put an emphasis on model-aided transfer learning schemes for PHY layer operation. Key studies reveal that embedding ML into traditional model-based schemes can significantly enhance the performance of various PHY layer functions. Nevertheless, the explicability of neural networks remains an open issue and is expected to be an active area of research in the coming years, lying at the intersection of computer science and PHY layer communications