Anomalous Paths Research Articles

Secure multi-path routing for Internet of Things based on trust evaluation.

In the realm of the Internet of Things (IoT), ensuring the security of communication links and evaluating the safety of nodes within these links remains a significant challenge. The continuous threat of anomalous links, harboring malicious switch nodes, poses risks to data transmission between edge nodes and between edge nodes and cloud data centers. To address this critical issue, we propose a novel trust evaluation based secure multi-path routing (TESM) approach for IoT. Leveraging the software-defined networking (SDN) architecture in the data transmission process between edge nodes, TESM incorporates a controller comprising a security verification module, a multi-path routing module, and an anomaly handling module. The security verification module ensures the ongoing security validation of data packets, deriving trust scores for nodes. Subsequently, the multi-path routing module employs multi-objective reinforcement learning to dynamically generate secure multiple paths based on node trust scores. The anomaly handling module is tasked with handling malicious switch nodes and anomalous paths. Our proposed solution is validated through simulation using the Ryu controller and P4 switches in an SDN environment constructed with Mininet. The results affirm that TESM excels in achieving secure data forwarding, malicious node localization, and the secure selection and updating of transmission paths. Notably, TESM introduces a minimal 12.4% additional forwarding delay and a 5.46% throughput loss compared to traditional networks, establishing itself as a lightweight yet robust IoT security defense solution.

Outlier Vehicle Trajectory Detection Using Deep Autoencoders in Santiago, Chile.

In the last decade, a large amount of data from vehicle location sensors has been generated due to the massification of GPS systems to track them. This is because these sensors usually include multiple variables such as position, speed, angular position of the vehicle, etc., and, furthermore, they are also usually recorded in very short time intervals. On the other hand, routes are often generated so that they do not correspond to reality, due to artifacts such as buildings, bridges, or sensor failures and where, due to the large amount of data, visual analysis of human expert is unable to detect genuinely anomalous routes. The presence of such abnormalities can lead to faulty sensors being detected which may allow sensor replacement to reliably track the vehicle. However, given the reliability of the available sensors, there are very few examples of such anomalies, which can make it difficult to apply supervised learning techniques. In this work we propose the use of unsupervised deep neural network models based on stacked autoencoders to detect anomalous routes in vehicles within Santiago de Chile. The results show that the proposed model is capable of effectively detecting anomalous paths in real data considering validation given by an expert user, reaching a performance of 82.1% on average. As future work, we propose to incorporate the use of Long Short-Term Memory (LSTM) and attention-based networks in order to improve the detection of anomalous trajectories.

A Sequential Pattern Mining Based Approach to Adaptively Detect Anomalous Paths in Floating Vehicle Trajectories

The detection of anomalous paths from floating vehicle trajectories plays an increasingly important role in dynamic path planning because of its ability to identify fraudulent transport behaviors, unexpected traffic accidents, and traffic restriction areas. Existing studies mostly emphasize the significant deviations based on global shape metrics and cannot manage trajectories with missing segments. To address these problems, this study proposes a new sequential pattern mining based method for detecting anomalous paths (SPDAP) in floating vehicle trajectories. First, discrete trajectory points were transformed into consecutive road segment sequences using map matching and essential empirical information. Focusing on these segment sequences, this method constructs a directed graph and calculates the conditional occurrence probabilities of multi-order sub-paths on the graph. On this basis, we designed a sequential pattern mining algorithm by estimating kernel density distributions to adaptively extract multi-order frequent sub-paths. Finally, these anomalous paths can be identified by matching the operations with frequent paths. Comparative experiments on simulated trajectories demonstrated that SPDAP could accurately, adequately, and adaptively detect anomalous paths. Additionally, using real-life taxi trajectories, we conducted semantic analysis by considering travel time and charges to further derive four patterns from the detected anomalous paths. These patterns are expected to support the identification of fraudulent taxi trips and the discovery of candidate driving routes with a preference for saving time or charge. In the future, we will focus on tracing the intrinsic causes of anomalous paths by introducing multisource information and performing real-time anomalous path detection using adaptive time intervals.

Time-Extremal Navigation in Arbitrary Winds on Conformally Flat Riemannian Manifolds

This paper aims at solving Zermelo’s navigation problem on conformally flat Riemannian manifolds admitting a ship’s variable self-speed, under the action of arbitrary winds including space and time dependence for both perturbation and ship’s speed. Our approach is a variational one under application of the Euler–Lagrange equations with reference to the initial studies of this problem. First of all, we distinguish the navigation cases in non-critical, i.e. weak or strong, and critical winds, which are then unified into an arbitrary wind. After having considered the second variation of a given functional, we obtain the conditions for both time-minimal, i.e. the typical solutions to Zermelo’s problem, and time-maximal extremals. The anomalous paths are also emphasized. Moreover, some classification results are presented with respect to the kinds of perturbation considered separately and under an arbitrary wind. This study is illustrated at its end by a two-dimensional example including a prolate ellipsoid in the presence of a rotational vector field, wherein the solution types are being compared.

Visual Analytic Method for Metro Anomaly Detection and Diffusion

With the rapid development of urbanization in recent years, thousands of people have flooded into the city, which has brought tremendous pressure on the supervision and operation of relevant traffic management departments. In particular, the unexpected events in the urban rail transit system have caused great troubles for city managers. Aiming at the problem of abnormal passenger flow in the metro, this paper proposes a visual analytic method to support the abnormal passenger flow detection, verification, and diffusion analysis in the metro system. The method provides an intuitive visual metaphor and allows users to perform simple interactive operations to verify abnormal passenger flow. In addition, the method reveals the diffusion law of abnormal passenger flow in time and space in a two-dimensional diffusion view. The Beijing Rail Transit AFC data are used to validate the developed system, and two reliable analysis cases are presented. The system can help users quickly grasp the abnormal propagation rules and help them to develop different scheduling strategies for different anomalous propagation paths.

On spectral analysis of the Internet delay space and detecting anomalous routing paths

Latency is one of the most critical performance metrics for a wide range of applications. Therefore, it is important to understand the underlying mechanisms that give rise to the observed latency values and diagnose the ones that are unexpectedly high. In this paper, we study the Internet delay space via robust principal component analysis (RPCA). Using RPCA, we show that the delay space, i.e. the matrix of measured round trip times between end hosts, can be decomposed into two components: the estimated latency between end hosts with respect to the current state of the Internet and the inflation on the paths between the end hosts. Using this decomposition, first we study the well- known low-dimensionality phenomena of the delay space and ask what properties of the end hosts define the dimensions. Second, using the decomposition, we develop a filtering method to detect the paths that experience unexpected latencies and identify routing anomalies. We show that our filter successfully identifies an anomalous route even when its observed latency is not obviously high in magnitude.

Structured Features in Naive Bayes Classification

We propose the structured naive Bayes (SNB) classifier, which augments the ubiquitous naive Bayes classifier with structured features. SNB classifiers facilitate the use of complex features, such as combinatorial objects (e.g., graphs, paths and orders) in a general but systematic way. Underlying the SNB classifier is the recently proposed Probabilistic Sentential Decision Diagram (PSDD), which is a tractable representation of probability distributions over structured spaces. We illustrate the utility and generality of the SNB classifier via case studies. First, we show how we can distinguish players of simple games in terms of play style and skill level based purely on observing the games they play. Second, we show how we can detect anomalous paths taken on graphs based purely on observing the paths themselves.

Anomalous paths in quantum mechanical path-integrals

We investigate modifications of the discrete-time lattice action, for a quantum mechanical particle in one spatial dimension, that vanish in the naïve continuum limit but which, nevertheless, induce non-trivial effects due to quantum fluctuations. These effects are seen to modify the geometry of the paths contributing to the path-integral describing the time evolution of the particle, which we investigate through numerical simulations. In particular, we demonstrate the existence of a modified lattice action resulting in paths with any fractal dimension, df, between one and two. We argue that df=2 is a critical value, and we exhibit a type of lattice modification where the fluctuations in the position of the particle becomes independent of the time step, in which case the paths are interpreted as superdiffusive Lévy flights. We also consider the jaggedness of the paths, and show that this gives an independent classification of lattice theories.

On Distributions of Functionals of Anomalous Diffusion Paths

Functionals of Brownian motion have diverse applications in physics, mathematics, and other fields. The probability density function (PDF) of Brownian functionals satisfies the Feynman-Kac formula, which is a Schrodinger equation in imaginary time. In recent years there is a growing interest in particular functionals of non-Brownian motion, or anomalous diffusion, but no equation existed for their PDF. Here, we derive a fractional generalization of the Feynman-Kac equation for functionals of anomalous paths based on sub-diffusive continuous-time random walk. We also derive a backward equation and a generalization to Levy flights. Solutions are presented for a wide number of applications including the occupation time in half space and in an interval, the first passage time, the maximal displacement, and the hitting probability. We briefly discuss other fractional Schrodinger equations that recently appeared in the literature.

Joint inversion of normal mode and body wave data for inner core anisotropy 2. Possible complexities

In this study we focus on inner core sensitive body wave data to investigate lateral and radial heterogeneity within the inner core. Normal mode data are used to constrain a global model and to monitor if complexities introduced by body wave data are compatible with mode measurements. In particular, we investigate the possibilities of an isotropic layer near the inner core boundary and large‐scale variations in anisotropy such as hemispheric dependence proposed in studies based upon differential travel time data. Travel time data from distances between 130° and 140° require anisotropy near the inner core boundary. This evidence is supported by differential travel time data based upon diffracted waves, contrasting the previous inferences of isotropy at the surface of the inner core. Our experiments also show that variations at a hemispheric scale are not necessary and that the sources of apparent hemispheric differences can be localized. A comparison of differential and absolute travel time data suggests that differences in inferred inner core anisotropy models arise mainly from a few anomalous paths. These paths are responsible for the strong anisotropy which is characteristic of models based upon differential data. Assuming constant anisotropy in the inner core, we investigate the distribution of residual differential travel times at the entry and exit points of rays turning within the outer core. The results are consistent with existing models of structure near the core‐mantle boundary. Placing the source of the difference between differential and absolute travel time data in the lowermost mantle gives a more satisfactory result than attempting to model it with a complex inner core.

Investigations into the diver method of particle size analysis

Divers constructed from polythene incorporating a thin copper coil have been used to investigate the accuracy of the diver method of particle size analysis. A continuous record of the path of the diver through a suspension was obtained using an electromagnetic technique for locating the diver in conjunction with a high speed pen recorder. Anomalous diver paths were obtained which suggested that powder settlement on to the diver is more serious than expected from accounts of the technique previously published. An explanation for the mechanism of this settlement is suggested and it is shown that this difficulty can be overcome by suitable design of the diver. The implications of these experiments with regard to the use of the techniques for routine analysis are discussed.