In this lecture series I will give a fundamental insight into configuration space techniques which are of help to calculate a broad class of Feynman diagrams, the sunrisetype diagrams. Applications are shown along with basic concepts and techniques.

The recent proof of the Boij-Söderberg conjectures reveals new structure about Betti diagrams of modules, giving a complete description of the cone of Betti diagrams. We begin to expand on this new structure by investigating the semigroup of Betti diagrams. We prove that this semigroup is finitely generated, and we answer several other fundamental questions about this semigroup.

This note revisits a paper from Velan and Florian [Velan and Florian(2002)] dealing with the entropy condition in traffic flow models. It aims to clarify the application of this condition for non-differentiable fundamental diagrams and then to correct some misunderstandings that appear in the above-mentioned paper. Notably, this note clearly exhibits that the non-smoothness of the fundamental d...

We present experimental results obtained for a one-dimensional pedestrian flow using high precision motion capture. The full pedestrians' trajectories are obtained. In this paper, we focus on the fundamental diagram, and on the relation between the instantaneous velocity and spatial headway (distance to the predecessor). While the latter was found to be linear in previous experiments, we show t...

We present an extended discussion of a macroscopic traffic flow model [18] which includes non-local and relaxation terms for vehicular traffic flow on unidirectional roads. The braking and acceleration forces are based on a behavioural model and on free flow dynamics. The latter are modelled by using different fundamental diagrams. Numerical investigations for different situations illustrate th...

A field experiment in Yokohama (Japan) reveals that a macroscopic fundamental diagram (MFD) linking space-mean flow, density and speed exists on a large urban area. The experiment used a combination of fixed detectors and floating vehicle probes as sensors. It was observed that when the somewhat chaotic scatter-plots of speed vs. density from individual fixed detectors were aggregated the scatt...

Macroscopic models are computationally effective and generate reliable estimates of traffic dynamics based upon the principles of flow conservation and propagation, in which the underlying fundamental diagram (i.e. flow-density relationship) has an important part in capturing the plausible traffic propagation over time and space. This study investigates in practice whether, and in what extent, ...