Microscopic traffic models serve as indispensable tools in tasks such as constructing test scenarios for autonomous vehicles (AVs), predicting trajectories, and analyzing traffic flow dynamics. However, a significant proportion of these models rely on assumptions of normal behaviors. Yet, the validity of these assumptions is dubious given the heterogeneous nature of traffic flow and existence of abnormal driving behaviors. These limitations impede the efficacy of conventional microscopic models in crucial tasks like constructing AV test scenarios with specified risk levels, analyzing abnormal behaviors, etc. To address these challenges, this study contributes by proposing a model tailored to accommodate two-dimensional abnormal driving behaviors in microscopic traffic framework. The proposed approach have the following innovations: 1) it incorporates assumptions concerning abnormal behaviors in both the longitudinal and lateral dimensions; 2) abnormality at each dimension is captured by a combination of certain terms; 3) stochastic control barrier method is applied to customize the risk levels of the resulting traffic flow dynamics. Additionally, we present a method for retrieving vehicular maneuver information, enabling the extraction of detailed vehicle body gestures and driver control inputs, which would benefit the analysis of abnormal behavior. Our findings demonstrate that the proposed model yields longitudinal and lateral dynamics consistent with empirical observations, and various abnormal behavior patterns can be simulated.

Learning a decent representation from unlabeled time series is a challenging task, especially when the time series data is derived from diverse channels at different sampling rates. Our motivation stems from the financial domain, where sparsely labeled covariates are commonly collected at different frequencies, *e.g.*, daily stock market index, monthly unemployment rate and quarterly net revenue of a certain listed corporation. This paper presents **M**ulti-**F**requency **C**ontrastive **L**earning **R**epresentation (MF-CLR), aimed at learning a good representation of multi-frequency time series in a self-supervised paradigm by leveraging the ability of contrastive learning. MF-CLR introduces a hierarchical mechanism that spans across different frequencies along the feature dimension. Within each contrastive block, two groups of subseries with adjacent frequencies are embedded based on our proposed cross-frequency consistency. To validate the effectiveness of MF-CLR, we conduct extensive experiments on five downstream tasks, including long-term and short-term forecasting, classification, anomaly detection and imputation. Experimental evidence shows that MF-CLR delivers a leading performance in all the downstream tasks and keeps consistent performance across different target dataset scales in the transfer learning scenario.

Digital twin (DT) technology integrates the physical world with its digitalized counterpart and suggests significant potential for intelligent transportation system development, such as CAV test and development. In the foreseeable near future, human-driven vehicles (HDVs) will continue to predominate, and a digital replica of the transportation system should reflect their behavioral patterns for enhanced simulation realism purposes. As such, stochastic driver behavior and vehicle dynamics should be respected. The observations serving as DT input, often captured at discrete moments (e.g., the roadside units and cameras are only installed at certain locations), result in discontinuously captured vehicle trajectories. The stochastic generation of behaviorally consistent vehicle trajectories conditional on such incomplete information becomes important. Current conditional approaches include modified Brownian bridge (MBB) and guided proposal bridge (GPB) may not be able to output realistic results. To fill this gap, we propose conditional generation methods of behaviorally consistent trajectories, employing the stochastic bridge approach for the first time. First, a vehicular dynamics model that encapsulates the stochasticity of the human–vehicle system is employed, and then we prove that MBB and GPB fail to generate satisfactory results. Then, a forward–backward method is proposed based on the backward Markov process, which takes the vehicular dynamics model as behavioral input. The proposed method is validated against real-world data and mainstream simulation platforms, showing that the forward–backward generation method provides consistent and realistic results. Its time consumption has also been proven to be promising for real-time DT applications.

There has been significant recent interest in a class of three-player leader-follower game models in many important cybersecurity scenarios. In such a tri-level hierarchical structure, a defender usually serves as a leader, dominating the decision process by the Stackelberg equilibrium (SE) strategy. However, such a leader-follower scheme may not always work, and the Nash equilibrium (NE) strategy may provide an alternative choice. Thus, we need to reveal the consistency between SE and NE in the three-player model to help the leader evaluate its strategy impact and avoid a choice dilemma. To this end, we first provide a necessary and sufficient condition such that each SE is an NE, which not only provides access to seek a satisfactory SE but also makes a criterion for an obtained SE. Then, we apply the results for case studies with a unique SE or with at least one SE being an NE. Moreover, when the consistency condition falls short, we give an upper bound of the deviation between SE and NE to help the leader tolerably adopt an SE strategy. Finally, we apply our consistency analysis to practical scenarios, including secure wireless transmission and advanced persistent threat defense.

In this article, we aim to design a distributed approximate algorithm for seeking Nash equilibria (NE) of an aggregative game. Due to the local set constraints of each player, projection-based algorithms have been widely employed for solving such problems actually. Since it may be quite hard to get the exact projection in practice, we utilize inscribed polyhedrons to approximate local set constraints, which yields a related approximate game model. We first prove that the NE of the approximate game is the ϵ -NE of the original game and then propose a distributed algorithm to seek the ϵ -NE, where the projection is then of a standard form in quadratic optimization with linear constraints. With the help of the existing developed methods for solving quadratic optimization, we show the convergence of the proposed algorithm and also discuss the computational cost issue related to the approximation. Furthermore, based on the exponential convergence of the algorithm, we estimate the approximation accuracy related to ϵ . In addition, we investigate the computational cost saved by approximation in numerical simulation.

The microscopic behavior of the vehicle can be decomposed into car following and lane changing, and can be described by the longitudinal and lateral movement. The longitudinal movement has long been studied, while the lateral counterpart, especially the stochastic lateral movement, has rarely been investigated. The lacking of an understanding of the lateral behavior makes current microscopic simulation results deviate from real-world observations. Besides, many behavior identification algorithms which rely on lateral displacement are not robust, if the lateral stochastic nature is not well studied. To fill in this gap, a stochastic differential equation approach is employed. Firstly, the lateral noise is modeled by a transformed Brownian motion. Then the noise is embedded into a differential lateral movement model. The parameters in the lateral noise and movement models all have clear physical meaning. The Fokker-Planck equation, which describes the distribution evolution of the lateral displacement, is derived. A parameters calibration procedure is derived using the Euler discretization scheme. The model is calibrated using real world data. The results show that the proposed model can well describe the lateral movement distribution.

Road intersections play an important role in the operation of an urban road transportation system. However, channelized segment (C-segment) spillovers frequently occur during peak hours, making the vehicle queue on a lane spatially and temporally interact with the queue on another lane. Intersection traffic efficiency is thus largely degraded. Unfortunately, most of the existing models cannot capture the spatial-temporal queue interactions and thus are incapable of developing efficient intersection optimization plans. To fill this gap, the paper proposes a highly efficient approach traffic flow model to capture C-segment spillovers. An optimization problem that takes C-segment spillovers into account is formulated as a nonlinear programming model, and it is solved by using a Markov chain Monte Carlo method. The proposed model and solution are tested in several scenarios with various intersection settings, and the effectiveness of the proposed models is demonstrated. This study is beneficial to understanding C-segment spillovers and the models can be applied to improve traffic efficiency at recurrently-congested intersections.

Given a static logical network, partition-based solutions are investigated. Easily verifiable necessary and sufficient conditions are obtained, and the corresponding formulas are presented to provide all types of the partition-based solutions. Then, the results are extended to mix-valued logical networks. Finally, two applications are presented: 1) an implicit function (IF) theorem of logical equations, which provides necessary and sufficient condition for the existence of IF and 2) converting the difference-algebraic network into a standard difference network.

This paper proposes and investigates a Boolean gossip model as a simplified but non-trivial probabilistic Boolean network. With positive node interactions, in view of standard theories from Markov chains, we prove that the node states asymptotically converge to an agreement at a binary random variable, whose distribution is characterized for large-scale networks by mean-field approximation. Using combinatorial analysis, we also successfully count the number of communication classes of the positive Boolean network explicitly in terms of the topology of the underlying interaction graph, where remarkably minor variation in local structures can drastically change the number of network communication classes. With general Boolean interaction rules, emergence of absorbing network Boolean dynamics is shown to be determined by the network structure with necessary and sufficient conditions established regarding when the Boolean gossip process defines absorbing Markov chains. Particularly, it is shown that for the majority of the Boolean interaction rules, except for nine out of the total 216- 1 possible nonempty sets of binary Boolean functions, whether the induced chain is absorbing has nothing to do with the topology of the underlying interaction graph, as long as connectivity is assumed. These results illustrate the possibilities of relating dynamical properties of Boolean networks to graphical properties of the underlying interactions.

The evolutionarily stable strategy (ESS) of networked evolutionary games (NEGs) is studied. Analyzing the ESS of infinite popular evolutionary games and comparing it with networked games, a new verifiable definition of ESS for NEGs is proposed. Then, the fundamental evolutionary equation (FEE) is investigated and used to construct the strategy profile dynamics (SPDs) of homogeneous NEGs. Two ways for verifying the ESS are proposed: 1) using the SPDs to verify it directly. The SPDs provides complete information about the NEGs, and then necessary and sufficient conditions are revealed. It can be used for NEGs with small size and 2) some sufficient conditions are proposed to verify the ESS of NEGs via their FEEs. This method is particularly suitable for large scale networks. Some illustrative examples are included to demonstrate the theoretical results.

In this paper, a set of data is assumed to be obtained from an experiment that satisfies a Boolean dynamic process. For instance, the dataset can be obtained from the diagnosis of describing the diffusion process of cancer cells. With the observed datasets, several methods to construct the dynamic models for such Boolean networks are proposed. Instead of building the logical dynamics of a Boolean network directly, its algebraic form is constructed first and then is converted back to the logical form. Firstly, a general construction technique is proposed. To reduce the size of required data, the model with the known network graph is considered. Motivated by this, the least in-degree model is constructed that can reduce the size of required data set tremendously. Next, the uniform network is investigated. The number of required data points for identification of such networks is independent of the size of the network. Finally, some principles are proposed for dealing with data with errors.

This paper provides a comprehensive framework for the state-space approach to Boolean networks. First, it surveys the authors' recent work on the topic: Using semitensor product of matrices and the matrix expression of logic, the logical dynamic equations of Boolean (control) networks can be converted into standard discrete-time dynamics. To use the state-space approach, the state space and its subspaces of a Boolean network have been carefully defined. The basis of a subspace has been constructed. Particularly, the regular subspace, Y-friendly subspace, and invariant subspace are precisely defined, and the verifying algorithms are presented. As an application, the indistinct rolling gear structure of a Boolean network is revealed.