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Traffic prediction, an essential component for intelligent transportation systems, endeavours to use historical data to foresee future traffic features at specific locations. Although existing traffic prediction models often emphasize…
The objective of this paper is to describe a development of an innovative approach to enable students studying science, technology, engineering, and mathematics (STEM) to apply the concepts learned in physics and mathematics to engineering…
Due to the increasing heterogeneity and deployment density of emerging cellular networks, new flexible and scalable approaches for their modeling, simulation, analysis and optimization are needed. Recently, a new approach has been proposed:…
Long Short-Term Memory (LSTM) networks are often used to capture temporal dependency patterns. By stacking multi-layer LSTM networks, it can capture even more complex patterns. This paper explores the effectiveness of applying stacked LSTM…
Network performance modeling is a field that predates early computer networks and the beginning of the Internet. It aims to predict the traffic performance of packet flows in a given network. Its applications range from network planning and…
Instead of assuming fully loaded cells in the analysis on cache-enabled networks with tools of stochastic geometry, we focus on the dynamic traffic in this letter. With modeling traffic dynamics of request arrivals and departures,…
Steady-state solutions for a variety of relevant queueing systems are known today, e.g., from queueing theory, effective bandwidths, and network calculus. The behavior during transient phases, on the other hand, is understood to a much…
Network calculus is an elegant theory which uses envelopes to determine the worst-case performance bounds in a network. Statistical network calculus is the probabilistic version of network calculus, which strives to retain the simplicity of…
The goal of these notes is to provide an introduction to rough partial differential equations. For this purpose, we will present the theory of rough paths to the extend as it is required. Applications to stochastic partial differential…
Stochastic mathematical models are essential tools for understanding and predicting complex phenomena. The purpose of this work is to study the exit times of a stochastic dynamical system-specifically, the mean exit time and the…
Transport-based techniques for signal and data analysis have received increased attention recently. Given their abilities to provide accurate generative models for signal intensities and other data distributions, they have been used in a…
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…
Robust estimates for the performance of complicated queueing networks can be obtained by showing that the number of jobs in the network is stochastically comparable to a simpler, analytically tractable reference network. Classical coupling…
Recently, it has been recognized that phase transitions play an important role in the probabilistic analysis of combinatorial optimization problems. However, there are in fact many other relations that lead to close ties between computer…
We report on a course project in which students submit weekly probabilistic forecasts of two weather variables and one financial variable. This real-time format allows students to engage in practical forecasting, which requires a diverse…
Representations of sequential data are commonly based on the assumption that observed sequences are realizations of an unknown underlying stochastic process, where the learning problem includes determination of the model parameters. In this…
We describe stochastic calculus in the context of processes that are driven by an adapted point process of locally finite intensity and are differentiable between jumps. This includes Markov chains as well as non-Markov processes. By…
These are the notes for a set of lectures delivered by the two authors at the Les Houches Summer School on `Complex Systems' in July 2006. They provide an introduction to the basic concepts in modern (probabilistic) coding theory,…
The aim of this textbook is to bridge in regard of quantum computation what proves to be a considerable threshold even to the usual science trained readership between the level of science popularization, and on the other hand, the presently…
Models for predicting aircraft motion are an important component of modern aeronautical systems. These models help aircraft plan collision avoidance maneuvers and help conduct offline performance and safety analyses. In this article, we…