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Accurate velocity estimation of surrounding moving objects and their trajectories are critical elements of perception systems in Automated/Autonomous Vehicles (AVs) with a direct impact on their safety. These are non-trivial problems due to the diverse types and sizes of such objects and their dynamic and random behaviour. Recent point cloud based solutions often use Iterative Closest Point (ICP) techniques, which are known to have certain limitations. For example, their computational costs are high due to their iterative nature, and their estimation error often deteriorates as the relative velocities of the target objects increase (>2 m/sec). Motivated by such shortcomings, this paper first proposes a novel Detection and Tracking of Moving Objects (DATMO) for AVs based on an optical flow technique, which is proven to be computationally efficient and highly accurate for such problems. \textcolor{black}{This is achieved by representing the driving scenario as a vector field and applying vector calculus theories to ensure spatiotemporal continuity.} We also report the results of a comprehensive performance evaluation of the proposed DATMO technique, carried out in this study using synthetic and real-world data. The results of this study demonstrate the superiority of the proposed technique, compared to the DATMO techniques in the literature, in terms of estimation accuracy and processing time in a wide range of relative velocities of moving objects. Finally, we evaluate and discuss the sensitivity of the estimation error of the proposed DATMO technique to various system and environmental parameters, as well as the relative velocities of the moving objects.

Underlying data distributions of natural language, programming code, and mathematical symbols vary vastly, presenting a complex challenge for large language models (LLMs) that strive to achieve high performance across all three domains simultaneously. Achieving a very high level of proficiency for an LLM within a specific domain often requires extensive training with relevant corpora, which is typically accompanied by a sacrifice in performance in other domains. In this paper, we propose to fuse models that are already highly-specialized directly. The proposed fusing framework, UltraFuser, consists of three distinct specialists that are already sufficiently trained on language, coding, and mathematics. A token-level gating mechanism is introduced to blend the specialists' outputs. A two-stage training strategy accompanied by balanced sampling is designed to ensure stability. To effectively train the fused model, we further construct a high-quality supervised instruction tuning dataset, UltraChat 2, which includes text, code, and mathematical content. This dataset comprises approximately 300,000 instructions and covers a wide range of topics in each domain. Experiments show that our model could simultaneously achieve mastery of the three crucial domains.

We develop an implementable stochastic proximal point (SPP) method for a class of weakly convex, composite optimization problems. The proposed stochastic proximal point algorithm incorporates a variance reduction mechanism and the resulting SPP updates are solved using an inexact semismooth Newton framework. We establish detailed convergence results that take the inexactness of the SPP steps into account and that are in accordance with existing convergence guarantees of (proximal) stochastic variance-reduced gradient methods. Numerical experiments show that the proposed algorithm competes favorably with other state-of-the-art methods and achieves higher robustness with respect to the step size selection.

We introduce a new method for extracting structured threat behaviors from threat intelligence text. Our method is based on a multi-stage ranking architecture that allows jointly optimizing for efficiency and effectiveness. Therefore, we believe this problem formulation better aligns with the real-world nature of the task considering the large number of adversary techniques and the extensive body of threat intelligence created by security analysts. Our findings show that the proposed system yields state-of-the-art performance results for this task. Results show that our method has a top-3 recall performance of 81\% in identifying the relevant technique among 193 top-level techniques. Our tests also demonstrate that our system performs significantly better (+40\%) than the widely used large language models when tested under a zero-shot setting.

We propose a predictor-corrector adaptive method for the simulation of hyperbolic partial differential equations (PDEs) on networks under general uncertainty in parameters, initial conditions, or boundary conditions. The approach is based on the stochastic finite volume (SFV) framework that circumvents sampling schemes or simulation ensembles while also preserving fundamental properties, in particular hyperbolicity of the resulting systems and conservation of the discrete solutions. The initial boundary value problem (IBVP) on a set of network-connected one-dimensional domains that represent a pipeline is represented using active discretization of the physical and stochastic spaces, and we evaluate the propagation of uncertainty through network nodes by solving a junction Riemann problem. The adaptivity of our method in refining discretization based on error metrics enables computationally tractable evaluation of intertemporal uncertainty in order to support decisions about timing and quantity of pipeline operations to maximize delivery under transient and uncertain conditions. We illustrate our computational method using simulations for a representative network.

Gaussian graphical models provide a powerful framework to reveal the conditional dependency structure between multivariate variables. The process of uncovering the conditional dependency network is known as structure learning. Bayesian methods can measure the uncertainty of conditional relationships and include prior information. However, frequentist methods are often preferred due to the computational burden of the Bayesian approach. Over the last decade, Bayesian methods have seen substantial improvements, with some now capable of generating accurate estimates of graphs up to a thousand variables in mere minutes. Despite these advancements, a comprehensive review or empirical comparison of all recent methods has not been conducted. This paper delves into a wide spectrum of Bayesian approaches used for structure learning and evaluates their efficacy through a simulation study. We also demonstrate how to apply Bayesian structure learning to a real-world data set and provide directions for future research. This study gives an exhaustive overview of this dynamic field for newcomers, practitioners, and experts.

We propose a novel differentially private algorithm for online federated learning that employs temporally correlated noise to improve the utility while ensuring the privacy of the continuously released models. To address challenges stemming from DP noise and local updates with streaming noniid data, we develop a perturbed iterate analysis to control the impact of the DP noise on the utility. Moreover, we demonstrate how the drift errors from local updates can be effectively managed under a quasi-strong convexity condition. Subject to an $(\epsilon, \delta)$-DP budget, we establish a dynamic regret bound over the entire time horizon that quantifies the impact of key parameters and the intensity of changes in dynamic environments. Numerical experiments validate the efficacy of the proposed algorithm.

Two algorithms for computing the rational univariate representation of zero-dimensional ideals with parameters are presented in the paper. Different from the rational univariate representation of zero-dimensional ideals without parameters, the number of zeros of zero-dimensional ideals with parameters under various specializations is different, which leads to choosing and checking the separating element, the key to computing the rational univariate representation, is difficult. In order to pick out the separating element, by partitioning the parameter space we can ensure that under each branch the ideal has the same number of zeros. Subsequently with the help of the extended subresultant theorem for parametric cases, two ideas are given to conduct the further partition of parameter space for choosing and checking the separating element. Based on these, we give two algorithms for computing rational univariate representations of zero-dimensional ideals with parameters. Furthermore, the two algorithms have been implemented on the computer algebra system Singular. Experimental data show that the second algorithm has the better performance in contrast to the first one.

Models for the dynamics of congestion control generally involve systems of coupled differential equations. Universally, these models assume that traffic sources saturate the maximum transmissions allowed by the congestion control method. This is not suitable for studying congestion control of intermittent but bursty traffic sources. In this paper, we present a characterization of congestion control for arbitrary time-varying traffic that applies to rate-based as well as window-based congestion control. We leverage the capability of network calculus to precisely describe the input-output relationship at network elements for arbitrary source traffic. We show that our characterization can closely track the dynamics of even complex congestion control algorithms.

As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.