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The integration of Diffusion Models into Intelligent Transportation Systems (ITS) is a substantial improvement in the detection of accidents. We present a novel hybrid model integrating guidance classification with diffusion techniques. By…
Models for vehicle dynamics play an important role in maneuver planning for automated driving. They are used to derive trajectories from given control inputs, or to evaluate a given trajectory in terms of constraint violation or optimality…
Truncated Levy flights are stochastic processes which display a crossover from a heavy-tailed Levy behavior to a faster decaying probability distribution function (pdf). Putting less weight on long flights overcomes the divergence of the…
The promotion work 'The Estimation of Transport Logistic Processes Models on the Base of Intensive Computer Methods of Statistics' has been worked out by Helen Afanasyeva to obtain the scientific degree of 'Doctor of Science Engineering in…
We study stochastic tree fluid networks driven by a multidimensional Levy process. We are interested in (the joint distribution of) the steady-state content in each of the buffers, the busy periods, and the idle periods. To investigate…
V2V technologies bridge two infrastructures: the communications infrastructure and the transportation infrastructure. These infrastructures are interconnected and interdependent. On the one hand, the communications network enables V2V…
The complex driving environment brings great challenges to the visual perception of autonomous vehicles. It's essential to extract clear and explainable information from the complex road and traffic scenarios and offer clues to decision and…
A linear singularly perturbed convection-diffusion problem with characteristic layers is considered in three dimensions. Sharp bounds for the associated Green's function and its derivatives are established in the $L_1$ norm. The dependence…
In this article we study certain ultradiffusion equations connected with energy landscapes of exponential type. These equations are connected with the p-adic models of complex systems introduced by Avetisov et al. We show that the…
We investigate the application of artificial neural networks to stabilize proper orthogonal decomposition based reduced order models for quasi-stationary geophysical turbulent flows. An extreme learning machine concept is introduced for…
We propose a fast and scalable algorithm to project a given density on a set of structured measures defined over a compact 2D domain. The measures can be discrete or supported on curves for instance. The proposed principle and algorithm are…
Autonomous driving is a major paradigm shift in transportation, with the potential to enhance safety, optimize traffic congestion, and reduce fuel consumption. Although autonomous vehicles rely on advanced sensors and on-board computing…
Autonomous vehicles (AVs) are expected to revolutionize transportation by improving efficiency and safety. Their success relies on 3D vision systems that effectively sense the environment and detect traffic agents. Among sensors AVs use to…
Deep generative models such as diffusion and flow matching are powerful machine learning tools capable of learning and sampling from high-dimensional distributions. They are particularly useful when the training data appears to be…
The equation with the time fractional substantial derivative and space fractional derivative describes the distribution of the functionals of the L\'evy flights; and the equation is derived as the macroscopic limit of the continuous time…
The two-dimensional elastodynamic Green tensor is the primary building block of solutions of linear elasticity problems dealing with nonuniformly moving rectilinear line sources, such as dislocations. Elastodynamic solutions for these…
Intelligent Transportation Systems (ITS) are vital in modern traffic management and optimization, significantly enhancing traffic efficiency and safety. Recently, diffusion models have emerged as transformative tools for addressing complex…
We generalize Einstein's probabilistic method for the Brownian motion to study compressible fluids in porous media. The multi-dimensional case is considered with general probability distribution functions. By relating the expected…
We consider a car-following model described by a delay difference equation and give its exact solutions that present propagation of a traffic jam. This model is a discrete-time version of the delayed optimal-velocity model; in the continuum…
This paper provides a detailed theoretical analysis of methods to approximate the solutions of high-dimensional (>10^6) linear Bayesian problems. An optimal low-rank projection that maximizes the information content of the Bayesian…