arXiv subjects

Sebastian Gartzke

Publications and source records attributed to Sebastian Gartzke.

5 recordsLinked to original sources

arXiv2024

Correlations in Motion: A Simple Response-Based Analysis of Traffic Flow

Why does a traffic jams form out of nowhere, and why does it stretch for kilometers even after the initial cause is passed? This study examines how congestion moves and spreads across motorways using a surprisingly simple method: response functions. These functions are based purely on data and show how changes in traffic flow, density, and velocity are connected over time and space. Using real-world data from German motorways, we track how traffic reacts to earlier disturbances, capturing the waves of slowing and accelerating that drivers experience in stop-and-go traffic. The results demonstrate how congestion propagates and how its rhythm can be measured and predicted. Unlike complex traffic models, this approach requires no simulations or assumptions about driver behavior. It works directly from the information provided by the road. The goal is clear: to understand congestion better so that we can manage it more effectively and perhaps spend less time stuck in it.

physics.soc-ph↗

arXiv2021

Spatial Correlation Analysis of Traffic Flow on Parallel Motorways in Germany

With the widely used method of correlation matrix analysis, this study reveals the change of traffic states on parallel motorways in North Rhine-Westphalia, Germany. In terms of the time series of traffic flow and velocity, we carry out a quantitative analysis in correlations and reveal a high level of strongly positive traffic flow correlation and rich structural features in the corresponding correlation matrices. The strong correlation is mainly ascribed to the daily time evolution of traffic flow during the periods of rush hours and non-rush hours. In terms of free flow and congestion, the structural features are able to capture the average traffic situation we derive from our data. Furthermore, the structural features in correlation matrices for individual time periods corroborate our results from the correlation matrices regarding a whole day. The average correlations in traffic flows and velocities over all pairwise sections disclose the traffic behavior during each individual time period. Our contribution uncovers the potential application of correlation analysis on the study of traffic networks as a complex system.

physics.soc-ph↗

arXiv2021

Collective behavior in the North Rhine-Westphalia motorway network

To understand the dynamics on complex networks, measurement of correlations is indispensable. In a motorway network, it is not sufficient to collect information on fluxes and velocities on all individual links, i.e. parts of the freeways between ramps and highway crosses. The interdependencies and mutual connections are also of considerable interest. We analyze correlations in the complete motorway network in North Rhine-Westphalia, the most populous state in Germany. We view the motorway network as a complex system consisting of road sections which interact via the motion of vehicles, implying structures in the corresponding correlation matrices. In particular, we focus on collective behavior, i.e. coherent motion in the whole network or in large parts of it. To this end, we study the eigenvalue and eigenvector statistics and identify significant sections in the motorway network. We find collective behavior in these significant sections and further explore its causes. We show that collectivity throughout the network cannot directly be related to the traffic states (free, synchronous and congested) in Kerner's three-phase theory. Hence, the degree of collectivity provides a new, complementary observable to characterize the motorway network.

physics.soc-ph↗

arXiv2020

Quasi-stationary states in temporal correlations for traffic systems: Cologne orbital motorway as an example

Traffic systems are complex systems that exhibit non-stationary characteristics. Therefore, the identification of temporary traffic states is significant. In contrast to the usual correlations of time series, here we study those of position series, revealing structures in time, i.e. the rich non-Markovian features of traffic. Considering the traffic system of the Cologne orbital motorway as a whole, we identify five quasi-stationary states by clustering reduced rank correlation matrices of flows using the $k$-means method. The five quasi-stationary states with nontrivial features include one holiday state, three workday states and one mixed state of holidays and workdays. In particular, the workday states and the mixed state exhibit strongly correlated time groups shown as diagonal blocks in the correlation matrices. We map the five states onto reduced-rank correlation matrices of velocities and onto traffic states where free or congested states are revealed in both space and time. Our study opens a new perspective for studying traffic systems. This contribution is meant to provide a proof of concept and a basis for further study.

physics.soc-ph↗

arXiv2017

Generalized W-state of four qubits with exclusively threetangle

We single out a class of states possessing only threetangle but distributed all over four qubits. This is a three-site analogue of states from the $W$-class, which only possess globally distributed pairwise entanglement as measured by the concurrence. We perform an analysis for four qubits, showing that such a state indeed exists. To this end we analyze specific states of four qubits that are not convexly balanced as for $SL$ invariant families of entanglement, but only affinely balanced. For these states all possible $SL$-invariants vanish, hence they are part of the $SL$ null-cone. Instead, they will possess at least a certain unitary invariant. As an interesting byproduct it is demonstrated that the exact convex roof is reached in the rank-two case of a homogeneous polynomial $SL$-invariant measure of entanglement of degree $2m$, if there is a state which corresponds to a maximally $m$-fold degenerate solution in the zero-polytope that can be combined with the convexified minimal characteristic curve to give a decomposition of $ρ$. If more than one such state does exist in the zero polytope, a minimization must be performed. A better lower bound than the lowest convexified characteristic curve is obtained if no decomposition of $ρ$ is obtained in this way.

quant-ph↗