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This paper is concerned with a class of DC composite optimization problems which, as an extension of the convex composite optimization problem and the DC program with nonsmooth components, often arises from robust factorization models of low-rank matrix recovery. For this class of nonconvex and nonsmooth problems, we propose an inexact linearized proximal algorithm (iLPA) which in each step computes an inexact minimizer of a strongly convex majorization constructed by the partial linearization of their objective functions. The generated iterate sequence is shown to be convergent under the Kurdyka-{\L}ojasiewicz (KL) property of a potential function, and the convergence admits a local R-linear rate if the potential function has the KL property of exponent $1/2$ at the limit point. For the latter assumption, we provide a verifiable condition by leveraging the composite structure, and clarify its relation with the regularity used for the convex composite optimization. Finally, the proposed iLPA is applied to a robust factorization model for matrix completions with outliers, DC programs with nonsmooth components, and $\ell_1$-norm exact penalty of DC constrained programs, and numerical comparison with the existing algorithms confirms the superiority of our iLPA in computing time and quality of solutions.

A significant portion of driving hazards is caused by human error and disregard for local driving regulations; Consequently, an intelligent assistance system can be beneficial. This paper proposes a novel vision-based modular package to ensure drivers' safety by perceiving the environment. Each module is designed based on accuracy and inference time to deliver real-time performance. As a result, the proposed system can be implemented on a wide range of vehicles with minimum hardware requirements. Our modular package comprises four main sections: lane detection, object detection, segmentation, and monocular depth estimation. Each section is accompanied by novel techniques to improve the accuracy of others along with the entire system. Furthermore, a GUI is developed to display perceived information to the driver. In addition to using public datasets, like BDD100K, we have also collected and annotated a local dataset that we utilize to fine-tune and evaluate our system. We show that the accuracy of our system is above 80% in all the sections. Our code and data are available at //github.com/Pandas-Team/Autonomous-Vehicle-Environment-Perception

This paper studies an infinite horizon optimal control problem for discrete-time linear system and quadratic criteria, both with random parameters which are independent and identically distributed with respect to time. In this general setting, we apply the policy gradient method, a reinforcement learning technique, to search for the optimal control without requiring knowledge of statistical information of the parameters. We investigate the sub-Gaussianity of the state process and establish global linear convergence guarantee for this approach based on assumptions that are weaker and easier to verify compared to existing results. Numerical experiments are presented to illustrate our result.

This paper develops several interesting, significant, and interconnected approaches to nonparametric or semi-parametric statistical inferences. The overwhelmingly favoured maximum likelihood estimator (MLE) under parametric model is renowned for its strong consistency and optimality generally credited to Cramer. These properties, however, falter when the model is not regular or not completely accurate. In addition, their applicability is limited to local maxima close to the unknown true parameter value. One must therefore ascertain that the global maximum of the likelihood is strongly consistent under generic conditions (Wald, 1949). Global consistency is also a vital research problem in the context of empirical likelihood (Owen, 2001). The EL is a ground-breaking platform for nonparametric statistical inference. A subsequent milestone is achieved by placing estimating functions under the EL umbrella (Qin and Lawless, 1994). The resulting profile EL function possesses many nice properties of parametric likelihood but also shares the same shortcomings. These properties cannot be utilized unless we know the local maximum at hand is close to the unknown true parameter value. To overcome this obstacle, we first put forward a clean set of conditions under which the global maximum is consistent. We then develop a global maximum test to ascertain if the local maximum at hand is in fact a global maximum. Furthermore, we invent a global maximum remedy to ensure global consistency by expanding the set of estimating functions under EL. Our simulation experiments on many examples from the literature firmly establish that the proposed approaches work as predicted. Our approaches also provide superior solutions to problems of their parametric counterparts investigated by DeHaan (1981), Veall (1991), and Gan and Jiang (1999).

Recent technological advances have made head-mounted displays (HMDs) smaller and untethered, fostering the vision of ubiquitous interaction with information in a digitally augmented physical world. For interacting with such devices, three main types of input - besides not very intuitive finger gestures - have emerged so far: 1) Touch input on the frame of the devices or 2) on accessories (controller) as well as 3) voice input. While these techniques have both advantages and disadvantages depending on the current situation of the user, they largely ignore the skills and dexterity that we show when interacting with the real world: Throughout our lives, we have trained extensively to use our limbs to interact with and manipulate the physical world around us. This thesis explores how the skills and dexterity of our upper and lower limbs, acquired and trained in interacting with the real world, can be transferred to the interaction with HMDs. Thus, this thesis develops the vision of around-body interaction, in which we use the space around our body, defined by the reach of our limbs, for fast, accurate, and enjoyable interaction with such devices. This work contributes four interaction techniques, two for the upper limbs and two for the lower limbs: The first contribution shows how the proximity between our head and hand can be used to interact with HMDs. The second contribution extends the interaction with the upper limbs to multiple users and illustrates how the registration of augmented information in the real world can support cooperative use cases. The third contribution shifts the focus to the lower limbs and discusses how foot taps can be leveraged as an input modality for HMDs. The fourth contribution presents how lateral shifts of the walking path can be exploited for mobile and hands-free interaction with HMDs while walking.

We provide a categorical notion called uncertain bisimilarity, which allows to reason about bisimilarity in combination with a lack of knowledge about the involved systems. Such uncertainty arises naturally in automata learning algorithms, where one investigates whether two observed behaviours come from the same internal state of a black-box system that can not be transparently inspected. We model this uncertainty as a set functor equipped with a partial order which describes possible future developments of the learning game. On such a functor, we provide a lifting-based definition of uncertain bisimilarity and verify basic properties. Beside its applications to Mealy machines, a natural model for automata learning, our framework also instantiates to an existing compatibility relation on suspension automata, which are used in model-based testing. We show that uncertain bisimilarity is a necessary but not sufficient condition for two states being implementable by the same state in the black-box system. To remedy the failure of the one direction, we characterize uncertain bisimilarity in terms of coalgebraic simulations.

We study the error-correction problem of the communication between two vertices in a social network. By applying the concepts of coding theory into the Social Network Analysis (SNA), we develop the code social network model, which can offer an efficient way to ensure the correctness of the message transmission within the social netwoks. The result of this study could apply in vary of social science studies.

In this paper, a sampling-based trajectory planning algorithm for a laboratory-scale 3D gantry crane in an environment with static obstacles and subject to bounds on the velocity and acceleration of the gantry crane system is presented. The focus is on developing a fast motion planning algorithm for differentially flat systems, where intermediate results can be stored and reused for further tasks, such as replanning. The proposed approach is based on the informed optimal rapidly exploring random tree algorithm (informed RRT*), which is utilized to build trajectory trees that are reused for replanning when the start and/or target states change. In contrast to state-of-the-art approaches, the proposed motion planning algorithm incorporates a linear quadratic minimum time (LQTM) local planner. Thus, dynamic properties such as time optimality and the smoothness of the trajectory are directly considered in the proposed algorithm. Moreover, by integrating the branch-and-bound method to perform the pruning process on the trajectory tree, the proposed algorithm can eliminate points in the tree that do not contribute to finding better solutions. This helps to curb memory consumption and reduce the computational complexity during motion (re)planning. Simulation results for a validated mathematical model of a 3D gantry crane show the feasibility of the proposed approach.

The Internet of Things (IoT) is a futuristic technology that promises to connect tons of devices via the internet. As more individuals connect to the internet, it is believed that communication will generate mountains of data. IoT is currently leveraging Wireless Sensor Networks (WSNs) to collect, monitor, and transmit data and sensitive data across wireless networks using sensor nodes. WSNs encounter a variety of threats posed by attackers, including unauthorized access and data security. Especially in the context of the Internet of Things, where small embedded devices with limited computational capabilities, such as sensor nodes, are expected to connect to a larger network. As a result, WSNs are vulnerable to a variety of attacks. Furthermore, implementing security is time-consuming and selective, as traditional security algorithms degrade network performance due to their computational complexity and inherent delays. This paper describes an encryption algorithm that combines the Secure IoT (SIT) algorithm with the Security Protocols for Sensor Networks (SPINS) security protocol to create the Lightweight Security Algorithm (LSA), which addresses data security concerns while reducing power consumption in WSNs without sacrificing performance.

Salient object detection is a problem that has been considered in detail and many solutions proposed. In this paper, we argue that work to date has addressed a problem that is relatively ill-posed. Specifically, there is not universal agreement about what constitutes a salient object when multiple observers are queried. This implies that some objects are more likely to be judged salient than others, and implies a relative rank exists on salient objects. The solution presented in this paper solves this more general problem that considers relative rank, and we propose data and metrics suitable to measuring success in a relative objects saliency landscape. A novel deep learning solution is proposed based on a hierarchical representation of relative saliency and stage-wise refinement. We also show that the problem of salient object subitizing can be addressed with the same network, and our approach exceeds performance of any prior work across all metrics considered (both traditional and newly proposed).