arXiv subjects

Malte Schröder

Publications and source records attributed to Malte Schröder.

At least 19 recordsLinked to original sources

arXiv2026

Higher-order interactions reveal synergistic backbones of cycling infrastructure networks

Infrastructure networks essentially underlie human mobility and transport. Improving the quality of single links increases network performance locally. However, efficient transport requires high-quality connected corridors across multi-link paths that do not emerge from independent single-link upgrades. Here, we introduce a framework for evaluating the impact of jointly upgrading multiple links as inherently higher-order interactions, enabling us to quantify link synergies in complex transport networks. Two links are synergistic if an upgrade of one increases the benefit of upgrading the other, promoting upgrades of topologically complementary links along the same path while discouraging upgrades of redundant parallel links. By expressing these synergies as second-order derivatives of overall network performance, we develop an efficient computational framework to identify synergistic links that form a connected network backbone. We apply our theoretical framework by combining empirical street network and cycling demand data for Hamburg, Germany, with a perturbed utility route choice model for urban bicycle traffic. Our results reveal synergies from higher-order interactions, thereby enabling strategic infrastructure planning that goes beyond local link importance in complex transport and flow networks.

physics.soc-ph↗

arXiv2025

Robust design of bicycle infrastructure networks

Promoting active mobility like cycling relies on the availability of well-connected, high-quality bicycle networks. However, expanding these networks over an extended planning horizon presents one of the most complex challenges in transport science. This complexity arises from the intricate interactions between infrastructure availability and usage, such as network spillover effects and mode choice substitutions. In this paper, we approach the problem from two perspectives: direct optimization methods, which generate near-optimal solutions using operations research techniques, and conceptual heuristics, which offer intuitive and scalable algorithms grounded in network science. Specifically, we compare direct welfare optimization with an inverse network percolation approach to planning cycle superhighway extensions in Copenhagen. Interestingly, while the more complex optimization models yield better overall welfare results, the improvements over simpler methods are small. More importantly, we demonstrate that the increased complexity of planning approaches generally makes them more vulnerable to input uncertainty, reflecting the bias-variance tradeoff. This issue is particularly relevant in the context of long-term planning, where conditions change during the implementation of the planned infrastructure expansions. Therefore, while planning bicycle infrastructure is important and renders exceptionally high benefit-cost ratios, considerations of robustness and ease of implementation may justify the use of more straightforward network-based methods.

physics.soc-ph↗

arXiv2024

Complexified Synchrony

The Kuramoto model and its generalizations have been broadly employed to characterize and mechanistically understand various collective dynamical phenomena, especially the emergence of synchrony among coupled oscillators. Despite almost five decades of research, many questions remain open, in particular for finite-size systems. Here, we generalize recent work [Phys. Rev. Lett. 130, 187201 (2023)] on the finite-size Kuramoto model with its state variables analytically continued to the complex domain and also complexify its system parameters. Intriguingly, systems of two units with purely imaginary coupling do not actively synchronize even for arbitrarily large magnitudes of the coupling strengths, $|K| \rightarrow \infty$, but exhibit conservative dynamics with asynchronous rotations or librations for all $|K|$. For generic complex coupling, both, traditional phase-locked states and asynchronous states generalize to complex locked states, fixed points off the real subspace that exist even for arbitrarily weak coupling. We analyze a new collective mode of rotations exhibiting finite, yet arbitrarily large rotation numbers. Numerical simulations for large networks indicate a novel form of discontinuous phase transition. We close by pointing to a range of exciting questions for future research.

nlin.AO↗

arXiv2024

Synchrony for weak coupling in the complexified Kuramoto model

We present the finite-size Kuramoto model analytically continued from real to complex variables and analyze its collective dynamics. For strong coupling, synchrony appears through locked states that constitute attractors, as for the real-variable system. However, synchrony persists in the form of \textit{complex locked states} for coupling strengths $K$ below the transition $K^{(\text{pl})}$ to classical \textit{phase locking}. Stable complex locked states indicate a locked sub-population of zero mean frequency in the real-variable model and their imaginary parts help identifying which units comprise that sub-population. We uncover a second transition at $K'<K^{(\text{pl})}$ below which complex locked states become linearly unstable yet still exist for arbitrarily small coupling strengths.

nlin.AO↗

arXiv2023

Formation of trade networks by economies of scale and product differentiation

Understanding the structure and formation of networks is a central topic in complexity science. Economic networks are formed by decisions of individual agents and thus not properly described by established random graph models. In this article, we establish a model for the emergence of trade networks that is based on rational decisions of individual agents. The model incorporates key drivers for the emergence of trade, comparative advantage and economic scale effects, but also the heterogeneity of agents and the transportation or transaction costs. Numerical simulations show three macroscopically different regimes of the emerging trade networks. Depending on the specific transportation costs and the heterogeneity of individual preferences, we find centralized production with a star-like trade network, distributed production with all-to-all trading or local production and no trade. Using methods from statistical mechanics, we provide an analytic theory of the transitions between these regimes and estimates for critical parameters values.

physics.soc-ph↗

arXiv2023

Exponential Adoption of Battery Electric Cars

The adoption of battery electric vehicles (BEVs) may significantly reduce greenhouse gas emissions caused by road transport. However, there is wide disagreement as to how soon battery electric vehicles will play a major role in overall transportation. Focusing on battery electric passenger cars, we here analyze BEV adoption across 17 individual countries, Europe, and the World, and consistently find exponential growth trends. Modeling-based estimates of future adoption given past trends suggests system-wide adoption substantially faster than typical economic analyses have proposed so far. For instance, we estimate the majority of passenger cars in Europe to be electric by about 2031. Within regions, the predicted times of mass adoption are largely insensitive to model details. Despite significant differences in current electric fleet sizes across regions, their growth rates consistently indicate fast doubling times of approximately 15 months, hinting at radical economic and infrastructural consequences in the near future.

physics.soc-ph↗

arXiv2023

Taming Travel Time Fluctuations through Adaptive Stop Pooling

Ride sharing services combine trips of multiple users in the same vehicle and may provide more sustainable transport than private cars. As mobility demand varies during the day, the travel times experienced by passengers may substantially vary as well, making the service quality unreliable. We show through model simulations that such travel time fluctuations may be drastically reduced by stop pooling. Having users walk to meet at joint locations for pick-up or drop-off allows buses to travel more direct routes by avoiding frequent door-to-door detours, especially during high demand. We in particular propose adaptive stop pooling by adjusting the maximum walking distance to the temporally and spatially varying demand. The results highlight that adaptive stop pooling may substantially reduce travel time fluctuations while even improving the average travel time of ride sharing services, especially for high demand. Such quality improvements may in turn increase the acceptance and adoption of ride sharing services.

physics.soc-ph↗

arXiv2023

Identifying the threshold to sustainable ridepooling

Ridepooling combines trips of multiple passengers in the same vehicle and may thereby provide a more sustainable option than transport by private cars. The efficiency and sustainability of ridepooling is typically quantified by key performance indicators such as the average vehicle occupancy or the total distance driven by all ridepooling vehicles relative to individual transport. However, even if the average occupancy is high and rides are shared, ridepooling services may increase the total distance driven due to additional detours and deadheading. Moreover, these key performance indicators are difficult to predict without large-scale simulations or actual ridepooling operation. Here, we propose a dimensionless parameter to estimate the sustainability of ridepooling by quantifying the load on a ridepooling service, relating characteristic timescales of demand and supply. The load bounds the relative distance driven and uniquely marks the break-even point above which the total distance driven by all vehicles of a ridepooling service falls below that of motorized individual transport. Detailed event-based simulations and a comparison with empirical observations from a ridepooling pilot project in a rural area of Germany validate the theoretical prediction. Importantly, the load follows directly from a small set of aggregate parameters of the service setting and is thus predictable a priori. The load may thus complement standard key performance indicators and simplify planning, operation and evaluation of ridepooling services.

physics.soc-ph↗

arXiv2022

Explosive Transitions in Epidemic Dynamics

Standard epidemic models exhibit one continuous, second order phase transition to macroscopic outbreaks. However, interventions to control outbreaks may fundamentally alter epidemic dynamics. Here we reveal how such interventions modify the type of phase transition. In particular, we uncover three distinct types of explosive phase transitions for epidemic dynamics with capacity-limited interventions. Depending on the capacity limit, interventions may (i) leave the standard second order phase transition unchanged but exponentially suppress the probability of large outbreaks, (ii) induce a first-order discontinuous transition to macroscopic outbreaks, or (iii) cause a secondary explosive yet continuous third-order transition. These insights highlight inherent limitations in predicting and containing epidemic outbreaks. More generally our study offers a cornerstone example of a third order explosive phase transition in complex systems.

physics.soc-ph↗

arXiv2022

Phase separation induces congestion waves in electric vehicle charging

Electric vehicles may dominate motorized transport in the next decade, yet the impact of the collective dynamics of electric mobility on long-range traffic flow is still largely unknown. We demonstrate a type of congestion that arises if charging infrastructure is limited or electric vehicle density is high. This congestion emerges solely through indirect interactions at charging infrastructure by queue-avoidance behavior that - counterintuitively - induces clustering of occupied charging stations and phase separation of the flow into free and congested stations. The resulting congestion waves always propagate forward in the direction of travel, in contrast to typically backward-propagating congestion waves known from traditional traffic jams. These results may guide the planning and design of charging infrastructure and decision support applications in the near future.

nlin.AO↗

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↗

arXiv2022

Demand-driven design of bicycle infrastructure networks for improved urban bikeability

Cycling is a crucial part of sustainable urban transportation. Promoting cycling critically relies on a sufficiently developed bicycle infrastructure. However, designing efficient bike path networks constitutes a complex problem that requires balancing multiple constraints while still supporting all cycling demand. Here, we propose a framework to create families of efficient bike path networks by explicitly taking into account the demand distribution and cyclists' route choices based on safety preferences. By reversing the network formation process and iteratively removing bike paths from an initially complete bike path network and continually updating cyclists' route choices, we create a sequence of networks that is always adapted to the current cycling demand. We illustrate the applicability of this demand-driven planning scheme for two cities. A comparison of the resulting bike path networks with those created for homogenized demand enables us to quantify the importance of the demand distribution for network planning. The proposed framework may thus enable quantitative evaluation of the structure of current and planned bike path networks and support the demand-driven design of efficient infrastructures.

physics.soc-ph↗

arXiv2022

Spontaneous symmetry breaking in ride-sharing adoption dynamics

Symmetry breaking ubiquitously occurs across complex systems, from phase transition in statistical physics to self-organized lane formation in pedestrian dynamics. Here, we uncover spontaneous symmetry breaking in a simple model of ride-sharing adoption. We analyze how collective interactions among ride-sharing users to avoid detours in shared rides give rise to spontaneous symmetry breaking and pattern formation in the adoption dynamics. These dynamics result in bistability of high homogeneous and partial heterogeneous adoption states, potentially limiting the population-wide adoption of ride-sharing. Our results provide a framework to understand real-world adoption patterns of ride-sharing in complex urban settings and support the (re)design of ride-sharing services and incentives for sustainable shared mobility.

physics.soc-ph↗

arXiv2022

Dynamic stop pooling for flexible and sustainable ride sharing

Ride sharing - the bundling of simultaneous trips of several people in one vehicle - may help to reduce the carbon footprint of human mobility. However, standard door-to-door ride sharing services trade reduced route length for increased user travel times and come with the burden of many stops and detours to pick up individual users. Requiring some users to walk to nearby shared stops reduces detours, but could become inefficient if spatio-temporal demand patterns do not well fit the stop locations. Here, we present a simple computational model of dynamic stop pooling with flexible stop positions, and analyze its influence on the performance of ride sharing services. We find that dynamic stop pooling does a-priori not save route length, but occupancy. Intriguingly, it also reduces the travel time although users walk parts of their trip. Together, dynamic stop pooling may break the trade-off between route lengths and travel time in door-to-door ride sharing, thus enabling higher sustainability and service quality.

physics.soc-ph↗

arXiv2021

Obscuring digital route choice information prevents delay-induced congestion

Although routing applications increasingly affect individual mobility choices, their impact on collective traffic dynamics remains largely unknown. Smart communication technologies provide accurate traffic data for choosing one route over other alternatives, yet inherent delays undermine the potential usefulness of such information. Here we introduce and analyze a simple model of collective traffic dynamics which result from route choice relying on outdated traffic information. We find for sufficiently small information delays that traffic flows are stable against perturbations. However, delays beyond a bifurcation point induce self-organized flow oscillations of increasing amplitude -- congestion arises. Providing delayed information averaged over sufficiently long periods of time or, more intriguingly, reducing the number of vehicles adhering to the route recommendations may prevent such delay-induced congestion. We reveal the fundamental mechanisms underlying these phenomena in a minimal two-road model and demonstrate their generality in microscopic, agent-based simulations of a road network system. Our findings provide a way to conceptually understand system-wide traffic dynamics caused by broadly used non-instantaneous routing information and suggest how resulting unintended collective traffic states could be avoided.

physics.soc-ph↗

arXiv2021

Disentangling Scaling Arguments to Empower Complex Systems Analysis

Scaling arguments provide valuable analysis tools across physics and complex systems yet are often employed as one generic method, without explicit reference to the various mathematical concepts underlying them. A careful understanding of these concepts empowers us to unlock their full potential.

physics.gen-ph↗

arXiv2021

Asymmetry in repeated isotropic rotations

Random operators constitute fundamental building blocks of models of complex systems yet are far from fully understood. Here, we explain an asymmetry emerging upon repeating identical isotropic (uniformly random) operations. Specifically, in two dimensions, repeating an isotropic rotation twice maps a given point on the two-dimensional unit sphere (the unit circle) uniformly at random to any point on the unit sphere, reflecting a statistical symmetry as expected. In contrast, in three and higher dimensions, a point is mapped more often closer to the original point than a uniform distribution predicts. Curiously, in the limit of the dimension $d \rightarrow \infty$, a symmetric distribution is approached again. We intuitively explain the emergence of this asymmetry and why it disappears in higher dimensions by disentangling isotropic rotations into a sequence of partial actions. The asymmetry emerges in two qualitatively different forms and for a wide range of general random operations relevant in complex systems modeling, including repeated continuous and discrete rotations, roto-reflections and general orthogonal transformations

cond-mat.stat-mech↗

arXiv2021

Dynamic perturbation spreading in networks

Understanding how local perturbations induce the transient dynamics of a network of coupled units is essential to control and operate such systems. Often a perturbation initiated in one unit spreads to other units whose dynamical state they transiently alter. The maximum state changes at those units and the timings of these changes constitute key characteristics of such transient response dynamics. However, even for linear dynamical systems it is not possible to analytically determine time and amplitude of the maximal response of a unit to a perturbation. Here, we propose to extract approximate peak times and amplitudes from effective expectation values used to characterize the typical time and magnitude of the response of a unit by interpreting the system's response as a probability distribution over time. We derive analytic estimators for the peak response based on these expectation value measures in linearized systems operating close to a stable fixed point. These estimators can be expressed in terms of the inverse of the system's Jacobian. We obtain identical results with different approximations for the response dynamics, indicating that these estimators become exact in the limit of weak coupling. Furthermore, the results suggest that perturbations spread ballistically in networks with diffusive coupling.

physics.soc-ph↗