Secure and Trustworthy Artificial Intelligence-Extended Reality (AI-XR) for Metaverses

Metaverse is expected to emerge as a new paradigm for the next-generation Internet, providing fully immersive and personalised experiences to socialize, work, and play in self-sustaining and hyper-spatio-temporal virtual world(s). The advancements in different technologies like augmented reality, virtual reality, extended reality (XR), artificial intelligence (AI), and 5G/6G communication will be the key enablers behind the realization of AI-XR metaverse applications. While AI itself has many potential applications in the aforementioned technologies (e.g., avatar generation, network optimization, etc.), ensuring the security of AI in critical applications like AI-XR metaverse applications is profoundly crucial to avoid undesirable actions that could undermine users' privacy and safety, consequently putting their lives in danger. To this end, we attempt to analyze the security, privacy, and trustworthiness aspects associated with the use of various AI techniques in AI-XR metaverse applications. Specifically, we discuss numerous such challenges and present a taxonomy of potential solutions that could be leveraged to develop secure, private, robust, and trustworthy AI-XR applications. To highlight the real implications of AI-associated adversarial threats, we designed a metaverse-specific case study and analyzed it through the adversarial lens. Finally, we elaborate upon various open issues that require further research interest from the community.Comment: 24 pages, 11 figure

WKB analysis of edge states in graphene in a strong magnetic field

We investigate the fine structure of the edge states energy spectrum for zigzag and armchair ribbons of graphene in a strong magnetic field. At low energy, the spectra can be described by an effective Schrodinger Hamiltonian with a double well potential, symmetric in the zigzag case and asymmetric in the armchair case. We develop a semiclassical formalism based on the WKB approximation to calculate analytically the energy spectrum for the two types of edges, including regions which were not studied earlier. Our results are in very good quantitative agreement with numerical calculations. This approach leads to a qualitative description of the spectra in terms of the quantization of unusual classical orbits in the real space.Comment: 20 pages, 25 figure

On the computation of rational points of a hypersurface over a finite field

We design and analyze an algorithm for computing rational points of hypersurfaces defined over a finite field based on searches on "vertical strips", namely searches on parallel lines in a given direction. Our results show that, on average, less than two searches suffice to obtain a rational point. We also analyze the probability distribution of outputs, using the notion of Shannon entropy, and prove that the algorithm is somewhat close to any "ideal" equidistributed algorithm.Comment: 31 pages, 5 table

On the Covariance of ICP-based Scan-matching Techniques

This paper considers the problem of estimating the covariance of roto-translations computed by the Iterative Closest Point (ICP) algorithm. The problem is relevant for localization of mobile robots and vehicles equipped with depth-sensing cameras (e.g., Kinect) or Lidar (e.g., Velodyne). The closed-form formulas for covariance proposed in previous literature generally build upon the fact that the solution to ICP is obtained by minimizing a linear least-squares problem. In this paper, we show this approach needs caution because the rematching step of the algorithm is not explicitly accounted for, and applying it to the point-to-point version of ICP leads to completely erroneous covariances. We then provide a formal mathematical proof why the approach is valid in the point-to-plane version of ICP, which validates the intuition and experimental results of practitioners.Comment: Accepted at 2016 American Control Conferenc

A "metric" semi-Lagrangian Vlasov-Poisson solver

We propose a new semi-Lagrangian Vlasov-Poisson solver. It employs elements of metric to follow locally the flow and its deformation, allowing one to find quickly and accurately the initial phase-space position $Q(P)$ of any test particle $P$, by expanding at second order the geometry of the motion in the vicinity of the closest element. It is thus possible to reconstruct accurately the phase-space distribution function at any time $t$ and position $P$ by proper interpolation of initial conditions, following Liouville theorem. When distorsion of the elements of metric becomes too large, it is necessary to create new initial conditions along with isotropic elements and repeat the procedure again until next resampling. To speed up the process, interpolation of the phase-space distribution is performed at second order during the transport phase, while third order splines are used at the moments of remapping. We also show how to compute accurately the region of influence of each element of metric with the proper percolation scheme. The algorithm is tested here in the framework of one-dimensional gravitational dynamics but is implemented in such a way that it can be extended easily to four or six-dimensional phase-space. It can also be trivially generalised to plasmas.Comment: 32 pages, 14 figures, accepted for publication in Journal of Plasma Physics, Special issue: The Vlasov equation, from space to laboratory plasma

Parallizable manifolds and the fundamental group

ntroduction. Low-dimensional topology is dominated by the fundamental group. However, since every finitely presented group is the fundamental group of some closed 4-manifold, it is often stated that the effective influence of π1 ends in dimension three. This is not quite true, however, and there are some interesting border disputes. In this paper, we show that, by imposing the extra condition of parallelizability on the tangent bundle, the dominion of π1 is extended by an extra dimension