Random Fourier Features for Asymmetric Kernels

The random Fourier features (RFFs) method is a powerful and popular technique in kernel approximation for scalability of kernel methods. The theoretical foundation of RFFs is based on the Bochner theorem that relates symmetric, positive definite (PD) functions to probability measures. This condition naturally excludes asymmetric functions with a wide range applications in practice, e.g., directed graphs, conditional probability, and asymmetric kernels. Nevertheless, understanding asymmetric functions (kernels) and its scalability via RFFs is unclear both theoretically and empirically. In this paper, we introduce a complex measure with the real and imaginary parts corresponding to four finite positive measures, which expands the application scope of the Bochner theorem. By doing so, this framework allows for handling classical symmetric, PD kernels via one positive measure; symmetric, non-positive definite kernels via signed measures; and asymmetric kernels via complex measures, thereby unifying them into a general framework by RFFs, named AsK-RFFs. Such approximation scheme via complex measures enjoys theoretical guarantees in the perspective of the uniform convergence. In algorithmic implementation, to speed up the kernel approximation process, which is expensive due to the calculation of total mass, we employ a subset-based fast estimation method that optimizes total masses on a sub-training set, which enjoys computational efficiency in high dimensions. Our AsK-RFFs method is empirically validated on several typical large-scale datasets and achieves promising kernel approximation performance, which demonstrate the effectiveness of AsK-RFFs

A survey on cyber security of CAV

With the ever fast developments of technologies in science and engineering, it is believed that CAV (connected and autonomous vehicles) will come into our daily life soon. CAV could be used in many different aspects in our lives such as public transportation and agriculture, and so on. Although CAV will bring huge benefits to our lives and society, issues such as cyber security threats, which may reveal drivers’ private information or even pose threat to driver’s life, present significant challenges before CAV can be utilised in our society. In computer science, there is a clear category of cyber security attacks while there is no specific survey on cyber security of CAV. This paper overviews different passive and active cyber security attacks which may be faced by CAV. We also present solutions of each of these attacks based on the current state-of-the-art, and discuss future improvements in research on CAV cyber security

Towards a Severity Assessment Method for Potential Cyber Attacks to Connected and Autonomous Vehicles

CAV (connected and autonomous vehicle) is a crucial part of intelligent transportation systems. CAVs utilize both sensors and communication components to make driving decisions. A large number of companies, research organizations, and governments have researched extensively on the development of CAVs. The increasing number of autonomous and connected functions however means that CAVs are exposed to more cyber security vulnerabilities. Unlike computer cyber security attacks, cyber attacks to CAVs could lead to not only information leakage but also physical damage. According to the UK CAV Cyber Security Principles, preventing CAVs from cyber security attacks need to be considered at the beginning of CAV development. In this paper, a large set of potential cyber attacks are collected and investigated from the aspects of target assets, risks, and consequences. Severity of each type of attacks is then analysed based on clearly defined new set of criteria. The levels of severity for the attacks can be categorized as critical, important, moderate, and minor. Mitigation methods including prevention, reduction, transference, acceptance, and contingency are then suggested. It is found that remote control, fake vision on cameras, hidden objects to LiDAR and Radar, spoofing attack to GNSS, and fake identity in cloud authority are the most dangerous and of the highest vulnerabilities in CAV cyber security

Lorentz transformation of three dimensional gravitational wave tensor

Recently there are more and more interest on the gravitational wave of moving sources. This introduces a Lorentz transformation problem of gravitational wave. Although Bondi-Metzner-Sachs (BMS) theory has in principle already included the Lorentz transformation of gravitational wave, the transformation of the three dimensional gravitational wave tensor has not been explicitly calculated before. Within four dimensional spacetime, gravitational wave have property of `boost weight zero' and `spin weight 2'. This fact makes the Lorentz transformation of gravitational wave difficult to understand. In the current paper we adopt the traditional three dimensional tensor description of gravitational wave. Such a transverse-traceless tensor describes the gravitational wave freedom directly. We derive the explicit Lorentz transformation of the gravitational wave tensor. The transformation is similar to the Lorentz transformation for electric field vector and magnetic field vector which are three dimensional vectors. Based on the deduced Lorentz transformation of the gravitational wave three dimensional tensor, we can construct the gravitational waveform of moving source with any speed if only the waveform of the corresponding rest waveform is given. As an example, we apply our method to the effect of kick velocity of binary black hole. The adjusted waveform by the kick velocity is presented.Comment: 17 pages, 8 figure

Structural biology of glycoprotein hormones and their receptors: insights to signaling.

Abstract This article reviews the progress made in the field of glycoprotein hormones (GPH) and their receptors (GPHR) by several groups of structural biologists including ourselves aiming to gain insight into GPH signaling mechanisms. The GPH family consists of four members, with follicle-stimulating hormone (FSH) being the prototypic member. GPH members belong to the cystine-knot growth factor superfamily, and their receptors (GPHR), possessing unusually large N-terminal ectodomains, belong to the G-protein coupled receptor Family A. GPHR ectodomains can be divided into two subdomains: a high-affinity hormone binding subdomain primarily centered on the N-terminus, and a second subdomain that is located on the C-terminal region of the ectodomain that is involved in signal specificity. The two subdomains unexpectedly form an integral structure comprised of leucine-rich repeats (LRRs). Following the structure determination of hCG in 1994, the field of FSH structural biology has progressively advanced. Initially, the FSH structure was determined in partially glycosylated free form in 2001, followed by a structure of FSH bound to a truncated FSHR ectodomain in 2005, and the structure of FSH bound to the entire ectodomain in 2012. Comparisons of the structures in three forms led a proposal of a two-step monomeric receptor activation mechanism. First, binding of FSH to the FSHR high-affinity hormone-binding subdomain induces a conformational change in the hormone to form a binding pocket that is specific for a sulfated-tyrosine found as sTyr 335 in FSHR. Subsequently, the sTyr is drawn into the newly formed binding pocket, producing a lever effect on a helical pivot whereby the docking sTyr provides as the 'pull & lift' force. The pivot helix is flanked by rigid LRRs and locked by two disulfide bonds on both sides: the hormone-binding subdomain on one side and the last short loop before the first transmembrane helix on the other side. The lift of the sTyr loop frees the tethered extracellular loops of the 7TM domain, thereby releasing a putative inhibitory influence of the ectodomain, ultimately leading to the activating conformation of the 7TM domain. Moreover, the data lead us to propose that FSHR exists as a trimer and to present an FSHR activation mechanism consistent with the observed trimeric crystal form. A trimeric receptor provides resolution of the enigmatic, but important, biological roles played by GPH residues that are removed from the primary FSH-binding site, as well as several important GPCR phenomena, including negative cooperativity and asymmetric activation. Further reflection pursuant to this review process revealed additional novel structural characteristics such as the identification of a 'seat' sequence in GPH. Together with the 'seatbelt', the 'seat' enables a common heteodimeric mode of association of the common α subunit non-covalently and non-specifically with each of the three different β subunits. Moreover, it was possible to establish a dimensional order that can be used to estimate LRR curvatures. A potential binding pocket for small molecular allosteric modulators in the FSHR 7TM domain has also been identified