Related papers: Path-integral representation of diluted pedestrian…
Understanding and modeling the dynamics of pedestrian crowds can help with designing and increasing the safety of civil facilities. A key feature of crowds is its intrinsic stochasticity, appearing even under very diluted conditions, due to…
Quantum walks have emerged as an interesting alternative to the usual circuit model for quantum computing. While still universal for quantum computing, the quantum walk model has very different physical requirements, which lends itself more…
Quantum tunneling in a many-body system is much more non-trivial than that in a one-body system. The most characteristic phenomenon is the mixed tunneling, which has been studied in many fields for decades. For instance, let us consider a…
We develop predictive models of pedestrian dynamics by encoding the coupled nature of multi-pedestrian interaction using game theory, and deep learning-based visual analysis to estimate person-specific behavior parameters. Building…
This paper presents a novel incremental learning algorithm for pedestrian motion prediction, with the ability to improve the learned model over time when data is incrementally available. In this setup, trajectories are modeled as simple…
We follow up the work, where in light of the Picard-Lefschetz thimble approach, we split up the real-time path integral into two parts: the initial density matrix part which can be represented via an ensemble of initial conditions, and the…
We propose a new approach based on the path integral formalism to the calculation of the probability distribution functions of quadratic quantities of the Gaussian polymer chain in d-dimensional space, such as the radius of gyration and…
Two discrete dynamical systems are discussed and analyzed whose trajectories encode significant explicit information about a number of problems in combinatorial probability, including graphical enumeration on Riemann surfaces and random…
The behavior of pedestrians shows certain regularities, which can be described by quantitative (partly stochastic) models. The models are based on the behavior of individual pedestrians, which depends on the pedestrian intentions and on the…
We present the path integral formulation of a broad class of generalized diffusion processes. Employing the path integral we derive exact expressions for the path probability densities and joint probability distributions for the class of…
Understanding pedestrian dynamics is crucial for appropriately designing pedestrian spaces. The pedestrian fundamental diagram (FD), which describes the relationship between pedestrian flow and density within a given space, characterizes…
The path integral approach to quantum mechanics requires a substantial generalisation to describe the dynamics of systems confined to bounded domains. Non-local boundary conditions can be introduced in Feynman's approach by means of…
A quantum measurement model based upon restricted path-integrals allows us to study measurements of generalized position in various one-dimensional systems of phenomenological interest. After a general overview of the method we discuss the…
I assume a universe whereby the speed of light and the planck constant are not constants but instead parameters that vary locally in time-and space. When describing motion, I am able to derive a modified path integral description at the…
For the case of reduction onto the non-zero momentum level, in the problem of the path integral quantization of a scalar particle motion on a smooth compact Riemannian manifold with the given free isometric action of the compact semisimle…
We characterize quantumness of the so-called quantum walks (whose dynamics is governed by quantum mechanics) by introducing two computable measures which are stronger than the variance of the walker's position probability distribution. The…
The goal of this contribution is to introduce the Hamiltonian formalism of theoretical mechanics for analysing motion in generic linear and non-linear dynamical systems, including particle accelerators. This framework allows the derivation…
This paper presents a simple model that mimics quantum mechanics (QM) results in terms of probability fields of free particles subject to self-interference, without using Schr\"{o}dinger equation or wavefunctions. Unlike the standard QM…
A key overall goal of biomolecular simulations is the characterization of "mechanism" -- the pathways through configuration space of processes such as conformational transitions and binding. Some amount of heterogeneity is intrinsic to the…
We demonstrate that the conventional path integral formulations generate inconsistent results exemplified by the geometric Brownian motion under the general stochastic interpretation. We thus develop a novel path integral formulation for…