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Benjamin F. Maier

Publications and source records attributed to Benjamin F. Maier.

16 recordsLinked to original sources
arXiv2025

LLMs Reproduce Human Purchase Intent via Semantic Similarity Elicitation of Likert Ratings

Consumer research costs companies billions annually yet suffers from panel biases and limited scale. Large language models (LLMs) offer an alternative by simulating synthetic consumers, but produce unrealistic response distributions when asked directly for numerical ratings. We present semantic similarity rating (SSR), a method that elicits textual responses from LLMs and maps these to Likert distributions using embedding similarity to reference statements. Testing on an extensive dataset comprising 57 personal care product surveys conducted by a leading corporation in that market (9,300 human responses), SSR achieves 90% of human test-retest reliability while maintaining realistic response distributions (KS similarity > 0.85). Additionally, these synthetic respondents provide rich qualitative feedback explaining their ratings. This framework enables scalable consumer research simulations while preserving traditional survey metrics and interpretability.

cs.AI↗
arXiv2025

Demography-independent behavioural dynamics influenced the spread of COVID-19 in Denmark

Understanding the factors that impact how a communicable disease like COVID-19 spreads is of central importance to mitigate future outbreaks. Traditionally, epidemic surveillance and forecasting analyses have focused on epidemiological data but recent advancements have demonstrated that monitoring behavioural changes may be equally important. Prior studies have shown that high-frequency survey data on social contact behaviour were able to improve predictions of epidemiological observables during the COVID-19 pandemic. Yet, the full potential of such highly granular survey data remains debated. Here, we utilise daily nationally representative survey data from Denmark collected during 23 months of the COVID-19 pandemic to demonstrate two central use-cases for such high-frequency survey data. First, we show that complex behavioural patterns across demographics collapse to a small number of universal key features, greatly simplifying the monitoring and analysis of adherence to outbreak-mitigation measures. Notably, the temporal evolution of the self-reported median number of face-to-face contacts follows a universal behavioural pattern across age groups, with potential to simplify analysis efforts for future outbreaks. Second, we show that these key features can be leveraged to improve deep-learning-based predictions of daily reported new infections. In particular, our models detect a strong link between aggregated self-reported social distancing and hygiene behaviours and the number of new cases in the subsequent days. Taken together, our results highlight the value of high-frequency surveys to improve our understanding of population behaviour in an ongoing public health crisis and its potential use for prediction of central epidemiological observables.

physics.soc-ph↗
arXiv2024

Decoupling geographical constraints from human mobility

Driven by access to large volumes of movement data, the study of human mobility has grown rapidly over the past decades. The field has shown that human mobility is scale-free, proposed models to generate scale-free moving distance distributions, and explained how the scale-free distribution arises. It has not, however, explicitly addressed how mobility is structured by geographical constraints. How mobility relates to the outlines of landmasses, lakes, and rivers; by the placement of buildings, roadways, and cities. Based on millions of moves, we show how separating the effect of geography from mobility choices, reveals a power law spanning five orders of magnitude. To do so, we incorporate geography via the `pair distribution function' that encapsulates the structure of locations on which mobility occurs. Showing how the spatial distribution of human settlements shapes human mobility, our approach bridges the gap between distance- and opportunity-based models of human mobility.

physics.soc-ph↗
arXiv2023

Maximum-likelihood fits of piece-wise Pareto distributions with finite and non-zero core

We discuss multiple classes of piece-wise Pareto-like power law probability density functions $p(x)$ with two regimes, a non-pathological core with non-zero, finite values for support $0\leq x\leq x_{\mathrm{min}}$ and a power-law tail with exponent $-α$ for $x>x_{\mathrm{min}}$. The cores take the respective shapes (i) $p(x)\propto (x/x_{\mathrm{min}})^β$, (ii) $p(x)\propto\exp(-β[x/x_{\mathrm{min}}-1])$, and (iii) $p(x)\propto [2-(x/x_{\mathrm{min}})^β]$, including the special case $β=0$ leading to core $p(x)=\mathrm{const}$. We derive explicit maximum-likelihood estimators and/or efficient numerical methods to find the best-fit parameter values for empirical data. Solutions for the special cases $α=β$ are presented, as well. The results are made available as a Python package.

stat.ME↗
arXiv2023

Inferring country-specific import risk of diseases from the world air transportation network

Disease propagation between countries strongly depends on their effective distance, a measure derived from the world air transportation network (WAN). It reduces the complex spreading patterns of a pandemic to a wave-like propagation from the outbreak country, i.e. a linear relationship to the arrival time of the unmitigated spread of a disease. However, in the early stage of an outbreak, what matters to countries' decision makers is knowledge about the relative risk of arrival of active cases, i.e. how likely it is that an active case that boarded at the outbreak location will arrive in their country. As accurate mechanistic models to estimate such risks are still lacking, we propose here the ``import risk'' model that defines an import probability by means of the effective-distance framework. The model assumes that airline passengers are distributed along the shortest path tree that starts at the outbreak's origin. In combination with a random walk, we account for all possible paths, thus inferring predominant connecting flights. Our model outperforms other mobility models, such as the radiation and gravity model with varying distance types, and it improves further if additional geographic information is included. The import risk model's precision increases for countries that are more connected within the WAN, and recovers a geographic distance-dependence that suggests a pull- rather than a push- dynamic of the distribution process.

physics.soc-ph↗
arXiv2022

Evidence for positive long- and short-term effects of vaccinations against COVID-19 in wearable sensor metrics -- Insights from the German Corona Data Donation Project

Vaccines are among the most powerful tools used to combat the COVID-19 pandemic. They are highly effective against infection and substantially reduce the risk of severe disease, hospitalization, ICU admission, and death. However, their potential for attenuating long-term effects of a SARS-CoV-2 infection, commonly denoted as Long COVID, remains elusive and is still subject of debate. Such long-term effects can be effectively monitored at the individual level by analyzing physiological data collected by consumer-grade wearable sensors. Here, we investigate changes in resting heart rate, daily physical activity, and sleep duration in response to a SARS-CoV-2 infection stratified by vaccination status. Data was collected over a period of two years in the context of the German Corona Data Donation Project with currently around 190,000 monthly active donors. Compared to their unvaccinated counterparts, we find that vaccinated individuals on average experience smaller changes in their vital data that also return to normal levels more quickly. Likewise, extreme changes in vitals during the acute phase of the disease occur less frequently in vaccinated individuals. Our results solidify evidence that vaccines can mitigate long-term detrimental effects of SARS-CoV-2 infections both in terms of duration and magnitude. Furthermore, they demonstrate the value of large scale, high-resolution wearable sensor data in public health research.

q-bio.QM↗
arXiv2021

Germany's current COVID-19 crisis is mainly driven by the unvaccinated

Vaccines are the most powerful pharmaceutical tool to combat the COVID-19 pandemic. While the majority (about 65%) of the German population were fully vaccinated, incidence started growing exponentially in October 2021 with about 41% of recorded new cases aged twelve or above being symptomatic breakthrough infections, presumably also contributing to the dynamics. At the time, it (i) remains elusive how significant this contribution is and (ii) whether targeted non-pharmaceutical interventions (NPIs) may stop the amplification of the ongoing crisis. Here, we estimate that about 67%-76% of all new infections are caused by unvaccinated individuals, implying that only 24%-33% are caused by the vaccinated. Furthermore, we estimate 38%-51% of new infections to be caused by unvaccinated individuals infecting other unvaccinated individuals. In total, unvaccinated individuals are expected to be involved in 8-9 of 10 new infections. We further show that decreasing the transmissibility of the unvaccinated by, e.g. targeted NPIs, causes a steeper decrease in the effective reproduction number $\mathcal{R}$ than decreasing the transmissibility of vaccinated individuals, potentially leading to temporary epidemic control. Furthermore, reducing contacts between vaccinated and unvaccinated individuals serves to decrease $\mathcal R$ in a similar manner as increasing vaccine uptake. Taken together, our results contribute to the public discourse regarding policy changes in pandemic response and highlight the importance of combined measures, such as vaccination campaigns and contact reduction, to achieve epidemic control and preventing an overload of public health systems.

q-bio.PE↗
arXiv2021

Potential benefits of delaying the second mRNA COVID-19 vaccine dose

Vaccination against COVID-19 with the recently approved mRNA vaccines BNT162b2 (BioNTech/Pfizer) and mRNA-1273 (Moderna) is currently underway in a large number of countries. However, high incidence rates and rapidly spreading SARS-CoV-2 variants are concerning. In combination with acute supply deficits in Europe in early 2021, the question arises of whether stretching the vaccine, for instance by delaying the second dose, can make a significant contribution to preventing deaths, despite associated risks such as lower vaccine efficacy, the potential emergence of escape mutants, enhancement, waning immunity, reduced social acceptance of off-label vaccination, and liability shifts. A quantitative epidemiological assessment of risks and benefits of non-standard vaccination protocols remains elusive. To clarify the situation and to provide a quantitative epidemiological foundation we develop a stochastic epidemiological model that integrates specific vaccine rollout protocols into a risk-group structured infectious disease dynamical model. Using the situation and conditions in Germany as a reference system, we show that delaying the second vaccine dose is expected to prevent deaths in the four to five digit range, should the incidence resurge. We show that this considerable public health benefit relies on the fact that both mRNA vaccines provide substantial protection against severe COVID-19 and death beginning 12 to 14 days after the first dose. The benefits of protocol change are attenuated should vaccine compliance decrease substantially. To quantify the impact of protocol change on vaccination adherence we performed a large-scale online survey. We find that, in Germany, changing vaccination protocols may lead to small reductions in vaccination intention. In sum, we therefore expect the benefits of a strategy change to remain substantial and stable.

q-bio.PE↗
arXiv2020

COVID-19 lockdown induces disease-mitigating structural changes in mobility networks

In the wake of the COVID-19 pandemic many countries implemented containment measures to reduce disease transmission. Studies using digital data sources show that the mobility of individuals was effectively reduced in multiple countries. However, it remains unclear whether these reductions caused deeper structural changes in mobility networks, and how such changes may affect dynamic processes on the network. Here we use movement data of mobile phone users to show that mobility in Germany has not only been reduced considerably: Lockdown measures caused substantial and long-lasting structural changes in the mobility network. We find that long-distance travel was reduced disproportionately strongly. The trimming of long-range network connectivity leads to a more local, clustered network and a moderation of the "small-world" effect. We demonstrate that these structural changes have a considerable effect on epidemic spreading processes by "flattening" the epidemic curve and delaying the spread to geographically distant regions.

physics.soc-ph↗
arXiv2020

Thresholding normally distributed data creates complex networks

Network data sets are often constructed by some kind of thresholding procedure. The resulting networks frequently possess properties such as heavy-tailed degree distributions, clustering, large connected components and short average shortest path lengths. These properties are considered typical of complex networks and appear in many contexts, prompting consideration of their universality. Here we introduce a simple model for correlated relational data and study the network ensemble obtained by thresholding it. We find that some, but not all, of the properties associated with complex networks can be seen after thresholding the correlated data, even though the underlying data are not "complex". In particular, we observe heavy-tailed degree distributions, a large numbers of triangles, and short path lengths, while we do not observe non-vanishing clustering or community structure.

cs.SI↗
arXiv2020

Effective containment explains sub-exponential growth in confirmed cases of recent COVID-19 outbreak in Mainland China

The recent outbreak of COVID-19 in Mainland China is characterized by a distinctive algebraic, sub-exponential increase of confirmed cases during the early phase of the epidemic, contrasting an initial exponential growth expected for an unconstrained outbreak with sufficiently large reproduction rate. Although case counts vary significantly between affected provinces in Mainland China, the scaling law $t^μ$ is surprisingly universal, with a range of exponents $μ=2.1\pm0.3$. The universality of this behavior indicates that despite social, regional, demographical, geographical, and socio-economical heterogeneities of affected Chinese provinces, this outbreak is dominated by fundamental mechanisms that are not captured by standard epidemiological models. We show that the observed scaling law is a direct consequence of containment policies that effectively deplete the susceptible population. To this end we introduce a parsimonious model that captures both, quarantine of symptomatic infected individuals as well as population wide isolation in response to mitigation policies or behavioral changes. For a wide range of parameters, the model reproduces the observed scaling law in confirmed cases and explains the observed exponents. Quantitative fits to empirical data permit the identification of peak times in the number of asymptomatic or oligo-symptomatic, unidentified infected individuals, as well as estimates of local variations in the basic reproduction number. The model implies that the observed scaling law in confirmed cases is a direct signature of effective contaiment strategies and/or systematic behavioral changes that affect a substantial fraction of the susceptible population. These insights may aid the implementation of containment strategies in potential export induced COVID-19 secondary outbreaks elsewhere or similar future outbreaks of other emergent infectious diseases.

q-bio.PE↗
arXiv2020

Thermophoresis in Liquids and its Connection to Equilibrium Quantities

Thermophoresis is the process of particles moving along a temperature gradient in thermodynamic systems. Even though it has been studied for over 150 years, there is neither a complete theoretical description of thermophoresis in liquids nor of the Soret coefficient, the quantifiying measure of the Soret equilibrium. Recent studies connect its nature to equilibrium properties of the system, namely the excess enthalpy and the excess entropy, while there is still a debate over which of both describes the Soret coefficient more accurately and whether it can even be represented using those quantities. In this work I present a theoretical description for both cases based on density analysis by means of Brownian motion and dynamical density functional theory, where I assume local equilibrium. The interpretation of the Brownian stochastic differential equation (SDE) as an Ito or Stratonovich SDE is shown to have an influence on the outcome of the density. I argue that a Soret coefficient proportional to the excess enthalpy is connected to a system in a thermal gradient following its equation of state. Furthermore, I derive that the Boltzmann distribution law for external potentials does not hold for systems in thermal gradients but has to be replaced by a more general quantity. The theoretical predictions are consequently tested by means of BD simulations, where several systems are shown to follow their equation of state. The Soret coefficient of a solute in a toy model solvent is shown to be proportional to the solute's equilibrium solvation enthalpy. I further attempt to verify the theoretic derivations by means of MD simulations of noble gas solutes in SPC/E water. While the Soret equilibrium SPC/E water density follows its equation of state, neither Soret coefficient nor Soret equilibrium solute densitie entail a coherent agreement with any of the theoretical predictions.

cond-mat.soft↗
arXiv2019

Generalization of the small-world effect on a model approaching the Erdős-Rényi random graph

The famous Watts-Strogatz (WS) small-world network model does not approach the Erdős-Rényi (ER) random graph model in the limit of total randomization which can lead to confusion and complicates certain analyses. In this paper we discuss a simple alternative which was first introduced by Song and Wang, where instead of rewiring, edges are drawn between pairs of nodes with a distance-based connection probability. We show that this model is simpler to analyze, approaches the true ER random graph model in the completely randomized limit, and demonstrate that the WS model and the alternative model may yield different quantitative results using the example of a random walk temporal observable. An efficient sampling algorithm for the alternative model is proposed. Analytic results regarding the degree distribution, degree variance, number of two-stars per node, number of triangles per node, clustering coefficient, and random walk mixing time are presented. Subsequently, the small-world effect is illustrated by showing that the clustering coefficient decreases much slower than an upper bound on the message delivery time with increasing long-range connection probability which generalizes the small-world effect from informed searches to random search strategies. Due to its accessibility for analytic evaluations, we propose that this modified model should be used as an alternative reference model for studying the influence of small-world topologies on dynamic systems as well as a simple model to introduce numerous topics when teaching network science.

physics.soc-ph↗
arXiv2018

Modular hierarchical and power-law small-world networks bear structural optima for minimal first passage times and cover time

Networks that are organized as a hierarchy of modules have been the subject of much research, mainly focusing on algorithms that can extract this community structure from data. The question of why modular hierarchical organizations are so ubiquitous in nature, however, has received less attention. One hypothesis is that modular hierarchical topologies may provide an optimal structure for certain dynamical processes. We revisit a modular hierarchical network model that interpolates, using a single parameter, between two known network topologies: from strong hierarchical modularity to an Erdős-Rényi random connectivity structure. We show that this model displays a similar small-world effect as the Kleinberg model, where the connection probability between nodes decays algebraically with distance. We find that there is an optimal structure, in both models, for which the pair-averaged first passage time (FPT) and mean cover time of a discrete-time random walk are minimal, and provide a heuristic explanation for this effect. Finally, we show that analytic predictions for the pair-averaged FPT based on an effective medium approximation fail to reproduce these minima, which implies that their presence is due to a network structure effect.

physics.soc-ph↗
arXiv2018

Cover time for random walks on arbitrary complex networks

We present an analytical method for computing the mean cover time of a random walk process on arbitrary, complex networks. The cover time is defined as the time a random walker requires to visit every node in the network at least once. This quantity is particularly important for random search processes and target localization in network topologies. Based on the global mean first passage time of target nodes we derive an estimate for the cumulative distribution function of the cover time based on first passage time statistics. We show that our result can be applied to various model networks, including Erdős-Rényi and Barabási-Albert networks, as well as various real-world networks. Our results reveal an intimate link between first passage and cover time statistics in networks in which structurally induced temporal correlations decay quickly and offer a computationally efficient way for estimating cover times in network related applications.

cond-mat.stat-mech↗