arXiv subjects

Nora Molkenthin

Publications and source records attributed to Nora Molkenthin.

17 recordsLinked to original sources

arXiv2025

Ride-pooling adoption model for $\mathrm{CO_2}$ emission estimation

With the climate emergency and growing challenges ranging from pollution to congestion, ride-pooling (rp) has been floated as a potential solution for less congested, low-carbon and more space-efficient urban transportation. However, it is unclear which system configurations will enable an economically viable case for shared pooled mobility. To develop a more profound comprehension of the mechanisms underlying this subject, we here develop a simplified model to analyze the switching potential and \coo emissions of ride-pooling systems for a specified number of transport users, road network topology, and other system parameter values. This analysis is conducted across a broad range of switching probability functions (defined as the probability that a car or public transport user switches to ride-pooling) between an upper and lower bound of switching behaviour assumptions. Based on current Berlin parameters and the basic switching probability function, we find that ride-pooling can reduce the carbon emissions resulting from local transportation in Berlin by approximately 39\%. Policies that reduce the time factor - such as the provision of priority lanes - have the greatest effect in encouraging ride-pooling. For the system to be efficient and achieve measurable reductions in carbon emissions, the fleet size must be large enough. Across the range of switching probability functions, our results demonstrate that a fleet of 6,000 to 23,000 minibuses would be optimal to serve Berlin and reduce system-wide emissions.

physics.soc-ph↗

arXiv2024

Instability in Complex Oscillator Networks: Limitations and Potentials of Network Measures and Machine Learning

A central question of network science is how functional properties of systems emerge from their structure. For networked dynamical systems, structure is typically captured through network measures. We investigate the relationship between these measures and stability metrics across non-linear and linear oscillators, as well as real-world power grid topologies and dynamics. We find that this relationship is highly sensitive to the underlying ensemble: minor changes in the networks considered, such as going from mean degree 6 to mean degree 8, can invert the correlation between a network measure and stability. We also investigate network measures as inputs for machine learning, as well as Graph Neural Networks (GNNs) as predictors of stability. Both GNNs and the non-linear combination of many network measures can accurately predict stability within a given ensemble, yet both can fail when the ensemble changes. We conclude that neither approach reliably identifies the underlying structural causes of instability.

nlin.AO↗

arXiv2023

Shared Mobility in Berlin: An Analysis of Ride-Pooling with Car Mobility Data

In face of the threat of a climate catastrophe and the resulting urgent need for decarbonization together with the widespread emergence of the sharing economy, shared pooled mobility has been suggested as an alternative to private vehicle use. However, until now all of its real-life implementations have served a niche market, adjacent to taxi services. To better understand this discrepancy, as well as the potential of pooled mobility, we have here simulated and analyzed pooled mobility on the street network of Berlin with car trip data as input for ride requests. We measure the rate of sharable trips, the relative travel time of passengers, the average occupancy of the vehicles, the relatively driven distance compared to driving with a private vehicle. We observe that for requests in the city center of Berlin it is possible to serve all mobility requests currently done by car, with around 4700 vehicles. The travel time is around 1.34 higher than with a private vehicle, the vehicle's occupancy increases to 2.6. The driven distance is reduced by 65%. In the whole area of Berlin we observe that a ride-pooling system with 10000 vehicles can serve 60% of the trips. The travel time is 1.4 times higher than with a private vehicle, the occupancy gets three and the driven distance is reduced by 40%.

stat.AP↗

arXiv2023

Learning Interpretable Collective Variables for Spreading Processes on Networks

Collective variables (CVs) are low-dimensional projections of high-dimensional system states. They are used to gain insights into complex emergent dynamical behaviors of processes on networks. The relation between CVs and network measures is not well understood and its derivation typically requires detailed knowledge of both the dynamical system and the network topology. In this work, we present a data-driven method for algorithmically learning and understanding CVs for binary-state spreading processes on networks of arbitrary topology. We demonstrate our method using four example networks: the stochastic block model, a ring-shaped graph, a random regular graph, and a scale-free network generated by the Albert-Barab\'asi model. Our results deliver evidence for the existence of low-dimensional CVs even in cases that are not yet understood theoretically.

physics.soc-ph↗

arXiv2022

What geometrically constrained folding models can tell us about real-world protein contact maps

The mechanisms by which a protein's 3D structure can be determined based on its amino acid sequence have long been one of the key mysteries of biophysics. Often simplistic models, such as those derived from geometric constraints, capture bulk real-world 3D protein-protein properties well. One approach is using protein contact maps to better understand proteins' properties. Here, we investigate the emergent behaviour of contact maps for different geometrically constrained models and real-world protein systems. We derive an analytical approximation for the distribution of model amino acid distances, $s$, by means of a mean-field approach. This approximation is then validated for simulations using a 2D and 3D random interaction model, as well as from contact maps of real-world protein data. Using data from the RCSB Protein Data Bank (PDB) and AlphaFold~2 database, the analytical approximation is fitted to protein chain lengths of $L\approx100$, $L\approx200$, and $L\approx300$. While a universal scaling behaviour for protein chains of different lengths could not be deduced, we present evidence that the amino acid distance distributions can be attributed to geometric constraints of protein chains in bulk and amino acid sequences only play a secondary role.

physics.bio-ph↗

arXiv2022

Large population limits of Markov processes on random networks

We consider time-continuous Markovian discrete-state dynamics on random networks of interacting agents and study the large population limit. The dynamics are projected onto low-dimensional collective variables given by the shares of each discrete state in the system, or in certain subsystems, and general conditions for the convergence of the collective variable dynamics to a mean-field ordinary differential equation are proved. We discuss the convergence to this mean-field limit for a continuous-time noisy version of the so-called ``voter model'' on Erd\H{o}s-R\'enyi random graphs, on the stochastic block model, and on random regular graphs. Moreover, a heterogeneous population of agents is studied.

math.PR↗

arXiv2022

Collective dynamics of capacity-constrained ride-pooling fleets

Ride-pooling (or ride-sharing) services combine trips of multiple customers along similar routes into a single vehicle. The collective dynamics of the fleet of ride-pooling vehicles fundamentally underlies the efficiency of these services. In simplified models, the common features of these dynamics give rise to scaling laws of the efficiency that are valid across a wide range of street networks and demand settings. However, it is unclear how constraints of the vehicle fleet impact such scaling laws. Here, we map the collective dynamics of capacity-constrained ride-pooling fleets to services with unlimited passenger capacity and identify an effective fleet size of available vehicles as the relevant scaling parameter characterizing the dynamics. Exploiting this mapping, we generalize the scaling laws of ride-pooling efficiency to capacity-constrained fleets. We approximate the scaling function with a queueing theoretical analysis of the dynamics in a minimal model system, thereby enabling mean-field predictions of required fleet sizes in more complex settings. These results may help to transfer insights from existing ride-pooling services to new settings or service locations.

physics.soc-ph↗

arXiv2021

Moving the epidemic tipping point through topologically targeted social distancing

The epidemic threshold of a social system is the ratio of infection and recovery rate above which a disease spreading in it becomes an epidemic. In the absence of pharmaceutical interventions (i.e. vaccines), the only way to control a given disease is to move this threshold by non-pharmaceutical interventions like social distancing, past the epidemic threshold corresponding to the disease, thereby tipping the system from epidemic into a non-epidemic regime. Modeling the disease as a spreading process on a social graph, social distancing can be modeled by removing some of the graphs links. It has been conjectured that the largest eigenvalue of the adjacency matrix of the resulting graph corresponds to the systems epidemic threshold. Here we use a Markov chain Monte Carlo (MCMC) method to study those link removals that do well at reducing the largest eigenvalue of the adjacency matrix. The MCMC method generates samples from the relative canonical network ensemble with a defined expectation value of $λ_{max}$. We call this the "well-controlling network ensemble" (WCNE) and compare its structure to randomly thinned networks with the same link density. We observe that networks in the WCNE tend to be more homogeneous in the degree distribution and use this insight to define two ad-hoc removal strategies, which also substantially reduce the largest eigenvalue. A targeted removal of 80\% of links can be as effective as a random removal of 90\%, leaving individuals with twice as many contacts.

physics.soc-ph↗

arXiv2021

Relative Canonical Network Ensembles -- (Mis)characterizing Small-World Networks

What do generic networks that have certain properties look like? We define Relative Canonical Network ensembles as the ensembles that realize a property R while being as indistinguishable as possible from a generic network ensemble. This allows us to study the most generic features of the networks giving rise to the property under investigation. To test the approach we apply it first to the network measure "small-world-ness", thought to characterize small-world networks. We find several phase transitions as we go to less and less generic networks in which cliques and hubs emerge. Such features are not shared by typical small-world networks, showing that high "small-world-ness" does not characterize small-world networks as they are commonly understood. On the other hand we see that for embedded networks, the average shortest path length and total Euclidean link length are better at characterizing small-world networks, with hubs that emerge as a defining feature at low genericity. We expect the overall approach to have wide applicability for understanding network properties of real world interest.

physics.soc-ph↗

arXiv2020

Topology dependence of on-demand ride-sharing

Traffic is a challenge in rural and urban areas alike with negative effects ranging from congestion to air pollution. Ride-sharing poses an appealing alternative to personal cars, combining the traffic-reducing ride bundling of public transport with much of the flexibility and comfort of personal cars. Here we study the effects of the underlying street network topology on the viability of ride bundling analytically and in simulations. Using numerical and analytical approaches we find that system performance can be measured in the number of scheduled stops per vehicle. Its scaling with the request rate is approximately linear and the slope, that depends on the network topology, is a measure of the ease of ridesharing in that topology. This dependence is caused by the different growth of the route volume, which we compute analytically for the simplest networks served by a single vehicle.

physics.soc-ph↗

arXiv2019

Topological universality of on-demand ride-sharing efficiency

Ride-sharing may substantially contribute to future-compliant sustainable mobility, both in urban and rural areas. The service quality of ride-sharing fleets jointly depends on the topology of the underlying street networks, the spatio-temporal demand distributions, and the dispatching algorithms. Yet, efficiency of ride-sharing services is typically quantified by economic or ecological ad-hoc measures that do not transfer to new service regions with different characteristics. Here we derive a generic measure of ride-sharing efficiency based on the intrinsic ride-sharing dynamics that follows a universal scaling law across network topologies. We demonstrate that the same scaling holds across street networks of distinct topologies, including cities, islands and rural areas, and is insensitive to modifying request distributions and dispatching criteria. These results further our understanding of the collective dynamics of ride-sharing fleets and may enable quantitative evaluation of conditions towards increasing the feasibility of creating or transferring ride-sharing services to previously unserviced regions.

physics.soc-ph↗

arXiv2018

Geometric constraints in protein folding

The intricate three-dimensional geometries of protein tertiary structures underlie protein function and emerge through a folding process from one-dimensional chains of amino acids. The exact spatial sequence and configuration of amino acids, the biochemical environment and the temporal sequence of distinct interactions yield a complex folding process that cannot yet be easily tracked for all proteins. To gain qualitative insights into the fundamental mechanisms behind the folding dynamics and generic features of the folded structure, we propose a simple model of structure formation that takes into account only fundamental geometric constraints and otherwise assumes randomly paired connections. We find that despite its simplicity, the model results in a network ensemble consistent with key overall features of the ensemble of Protein Residue Networks we obtained from more than 1000 biological protein geometries as available through the Protein Data Base. Specifically, the distribution of the number of interaction neighbors a unit (amino acid) has, the scaling of the structure's spatial extent with chain length, the eigenvalue spectrum and the scaling of the smallest relaxation time with chain length are all consistent between model and real proteins. These results indicate that geometric constraints alone may already account for a number of generic features of protein tertiary structures.

q-bio.BM↗

arXiv2018

Adhesion-induced Discontinuous Transitions and Classifying Social Networks

Transition points mark qualitative changes in the macroscopic properties of large complex systems. Explosive transitions, exhibiting properties of both continuous and discontinuous phase transitions, have recently been uncovered in network growth processes. Real networks not only grow but often also restructure, yet common network restructuring processes, such as small world rewiring, do not exhibit phase transitions. Here, we uncover a class of intrinsically discontinuous transitions emerging in network restructuring processes controlled by \emph{adhesion} -- the preference of a chosen link to remain connected to its end node. Deriving a master equation for the temporal network evolution and working out an analytic solution, we identify genuinely discontinuous transitions in non-growing networks, separating qualitatively distinct phases with monotonic and with peaked degree distributions. Intriguingly, our analysis of heuristic data indicates a separation between the same two forms of degree distributions distinguishing abstract from face-to-face social networks.

physics.soc-ph↗

arXiv2016

Scaling Laws in Spatial Network Formation

Geometric constraints impact the formation of a broad range of spatial networks, from amino acid chains folding to proteins structures to rearranging particle aggregates. How the network of interactions dynamically self-organizes in such systems is far from fully understood. Here, we analyze a class of spatial network formation processes by introducing a mapping from geometric to graph-theoretic constraints. Combining stochastic and mean field analyses yields an algebraic scaling law for the extent (graph diameter) of the resulting networks with system size, in contrast to logarithmic scaling known for networks without constraints. Intriguingly, the exponent falls between that of self-avoiding random walks and that of space filling arrangements, consistent with experimentally observed scaling (of the spatial radius of gyration) for protein tertiary structures.

q-bio.MN↗

arXiv2016

Correlation networks from flows. The case of forced and time-dependent advection-diffusion dynamics

Complex network theory provides an elegant and powerful framework to statistically investigate different types of systems such as society, brain or the structure of local and long-range dynamical interrelationships in the climate system. Network links in climate networks typically imply information, mass or energy exchange. However, the specific connection between oceanic or atmospheric flows and the climate network's structure is still unclear. We propose a theoretical approach for verifying relations between the correlation matrix and the climate network measures, generalizing previous studies and overcoming the restriction to stationary flows. Our methods are developed for correlations of a scalar quantity (temperature, for example) which satisfies an advection-diffusion dynamics in the presence of forcing and dissipation. Our approach reveals that correlation networks are not sensitive to steady sources and sinks and the profound impact of the signal decay rate on the network topology. We illustrate our results with calculations of degree and clustering for a meandering flow resembling a geophysical ocean jet.

physics.flu-dyn↗

arXiv2016

Edge anisotropy and the geometric perspective on flow networks

Spatial networks have recently attracted great interest in various fields of research. While the traditional network-theoretic viewpoint is commonly restricted to their topological characteristics (often disregarding existing spatial constraints), this work takes a geometric perspective, which considers vertices and edges as objects in a metric space and quantifies the corresponding spatial distribution and alignment. For this purpose, we introduce the concept of edge anisotropy and define a class of measures characterizing the spatial directedness of connections. Specifically, we demonstrate that the local anisotropy of edges incident to a given vertex provides useful information about the local geometry of geophysical flows based on networks constructed from spatio-temporal data, which is complementary to topological characteristics of the same flow networks. Taken both structural and geometric viewpoints together can thus assist the identification of underlying flow structures from observations of scalar variables.

physics.flu-dyn↗

arXiv2010

Discrete Nonlinear Schrodinger Equation, Solitons and Organizing Principles for Protein Folding

We introduce a novel generalization of the discrete nonlinear Schrödinger equation. It supports solitons that describe how proteins fold. As an example we scrutinize the villin headpiece HP35, an archetypal protein for testing both experimental and theoretical approaches to protein folding. Using explicit soliton profiles we construct its carbon backbone with an unprecedented accuracy.

physics.bio-ph↗