arXiv subjects

Lucas Böttcher

Publications and source records attributed to Lucas Böttcher.

54 records · Page 3Linked to original sources

arXiv2020

Incentivizing Narrow-Spectrum Antibiotic Development with Refunding

The rapid rise of antibiotic resistance is a serious threat to global public health. Without further incentives, pharmaceutical companies have little interest in developing antibiotics, since the success probability is low and development costs are huge. The situation is exacerbated by the "antibiotics dilemma": Developing narrow-spectrum antibiotics against resistant bacteria is most beneficial for society, but least attractive for companies since their usage is more limited than for broad-spectrum drugs and thus sales are low. Starting from a general mathematical framework for the study of antibiotic-resistance dynamics with an arbitrary number of antibiotics, we identify efficient treatment protocols and introduce a market-based refunding scheme that incentivizes pharmaceutical companies to develop narrow-spectrum antibiotics: Successful companies can claim a refund from a newly established antibiotics fund that partially covers their development costs. The proposed refund involves a fixed and variable part. The latter (i) increases with the use of the new antibiotic for currently resistant strains in comparison with other newly developed antibiotics for this purpose---the resistance premium---and (ii) decreases with the use of this antibiotic for non-resistant bacteria. We outline how such a refunding scheme can solve the antibiotics dilemma and cope with various sources of uncertainty inherent in antibiotic R\&D. Finally, connecting our refunding approach to the recently established antimicrobial resistance (AMR) action fund, we discuss how the antibiotics fund can be financed.

q-bio.PE↗

arXiv2020

Unifying continuous, discrete, and hybrid susceptible-infected-recovered processes on networks

Waiting times between two consecutive infection and recovery events in spreading processes are often assumed to be exponentially distributed, which results in Markovian (i.e., memoryless) continuous spreading dynamics. However, this is not taking into account memory (correlation) effects and discrete interactions that have been identified as relevant in social, transportation, and disease dynamics. We introduce a framework to model continuous, discrete, and hybrid forms of (non-)Markovian susceptible-infected-recovered (SIR) stochastic processes on networks. The hybrid SIR processes that we study in this paper describe infections as discrete-time Markovian and recovery events as continuous-time non-Markovian processes, which mimic the distribution of cell cycles. Our results suggest that the effective-infection-rate description of epidemic processes fails to uniquely capture the behavior of such hybrid and also general non-Markovian disease dynamics. Providing a unifying description of general Markovian and non-Markovian disease outbreaks, we instead show that the mean transmissibility produces the same phase diagrams independent of the underlying inter-event-time distributions.

physics.soc-ph↗

arXiv2020

Spatio-temporal characteristics of dengue outbreaks

After their re-emergence in the last decades, dengue fever and other vector-borne diseases are a potential threat to the lives of millions of people. Based on a data set of dengue cases in the Brazilian city of Fortaleza, collected from 2011 to 2016, we study the spatio-temporal characteristics of dengue outbreaks to characterize epidemic and non-epidemic years. First, we identify regions that show a high prevalence of dengue cases and mosquito larvae in different years and also analyze their corresponding correlations. Our results show that the characteristic correlation length of the epidemic is of the order of the system size, suggesting that factors such as citizen mobility may play a major role as a drive for spatial spreading of vector-borne diseases. Inspired by this observation, we perform a mean-field estimation of the basic reproduction number and find that our estimated values agree well with the values reported for other regions, pointing towards similar underlying spreading mechanisms. These findings provide insights into the spreading characteristics of dengue in densely populated areas and should be of relevance for the design of improved disease containment strategies.

physics.soc-ph↗

arXiv2020

Learning the Ising Model with Generative Neural Networks

Recent advances in deep learning and neural networks have led to an increased interest in the application of generative models in statistical and condensed matter physics. In particular, restricted Boltzmann machines (RBMs) and variational autoencoders (VAEs) as specific classes of neural networks have been successfully applied in the context of physical feature extraction and representation learning. Despite these successes, however, there is only limited understanding of their representational properties and limitations. To better understand the representational characteristics of RBMs and VAEs, we study their ability to capture physical features of the Ising model at different temperatures. This approach allows us to quantitatively assess learned representations by comparing sample features with corresponding theoretical predictions. Our results suggest that the considered RBMs and convolutional VAEs are able to capture the temperature dependence of magnetization, energy, and spin-spin correlations. The samples generated by RBMs are more evenly distributed across temperature than those generated by VAEs. We also find that convolutional layers in VAEs are important to model spin correlations whereas RBMs achieve similar or even better performances without convolutional filters.

cond-mat.dis-nn↗

arXiv2020

Why case fatality ratios can be misleading: individual- and population-based mortality estimates and factors influencing them

Different ways of calculating mortality ratios during epidemics have yielded very different results, particularly during the current COVID-19 pandemic. We formulate both a survival probability model and an associated infection duration-dependent SIR model to define individual- and population-based estimates of dynamic mortality ratios. The key parameters that affect the dynamics of the different mortality estimates are the incubation period and the time individuals were infected before confirmation of infection. We stress that none of these ratios are accurately represented by the often misinterpreted case fatality ratio (CFR), the number of deaths to date divided by the total number of confirmed infected cases to date. Using data on the recent SARS-CoV-2 outbreaks, we estimate and compare the different dynamic mortality ratios and highlight their differences. Informed by our modeling, we propose more systematic methods to determine mortality ratios during epidemic outbreaks and discuss sensitivity to confounding effects and uncertainties in the data.

q-bio.PE↗

arXiv2020

Diversity in Biology: definitions, quantification, and models

Diversity indices are useful single-number metrics for characterizing a complex distribution of a set of attributes across a population of interest. The utility of these different metrics or sets of metrics depend on the context and application, and whether a predictive mechanistic model exists. In this topical review, we first summarize the relevant mathematical principles underlying heterogeneity in a large population before outlining the various definitions of `diversity' and providing examples of scientific topics in which its quantification plays an important role. We then review how diversity has been a ubiquitous concept across multiple fields including ecology, immunology, cellular barcoding experiments, and socioeconomic studies. Since many of these applications involve sampling of populations, we also review how diversity in small samples is related to the diversity in the entire population. Features that arise in each of these applications are highlighted.

q-bio.PE↗

arXiv2020

The Great Divide: Drivers of Polarization in the US Public

Many democratic societies have become more politically polarized, with the U.S. as the main example. The origins of this phenomenon are still not well-understood and subject to debate. To better understand the mechanisms underlying political polarization, we develop a mathematical framework and employ information-theoretic concepts to analyze empirical data on political polarization that has been collected by Pew Research Center from 1994 to 2017. Our framework can capture the evolution of polarization in the Democratic- and Republican-leaning segments of the U.S. public and allows us to identify its drivers. Our findings provide empirical and quantitative evidence that political polarization in the U.S. is mainly driven by strong and more left-leaning policy/cultural innovations in the Democratic party.

physics.soc-ph↗

arXiv2019

Modeling Deformed Transmission Lines for Continuous Strain Sensing Applications

Transmission lines are essential components in various signal and power distribution systems. In addition to their main use as connecting elements, transmission lines can also be employed as continuous sensors for the measurement and detection of external influences such as mechanical strains and deformations. The measuring principle is based on deformation-induced changes of the characteristic impedance. Reflections of an injected test signal at resulting impedance mismatches can be used to infer applied deformations. To determine the effect of deformations on the characteristic impedance, we develop a numerical framework that allows us to solve Maxwell's equations for any desired transmission-line geometry over a wide frequency range. The proposed framework utilizes a staggered finite-difference Yee method on non-uniform grids to efficiently solve a set of decoupled partial differential equations that we derive from the frequency domain Maxwell equations. To test our framework, we compare simulation results with analytical predictions and corresponding experimental data. Our results suggest that the proposed numerical framework is able to capture experimentally observed deformation effects and may therefore be used in transmission-line-based deformation and strain sensing applications. Furthermore, our framework can also be utilized to simulate and study the electromagnetic properties of complex arrangements of conductor, insulator, and shielding materials.

physics.app-ph↗

arXiv2019

Competing Activists--Political Polarization

Recent empirical findings suggest that societies have become more polarized in various countries. That is, the median voter of today represents a smaller fraction of society compared to two decades ago and yet, the mechanisms underlying this phenomenon are not fully understood. Since interactions between influential actors ("activists") and voters play a major role in opinion formation, e.g. through social media, we develop a macroscopic opinion model in which competing activists spread their political ideas in specific groups of society. These ideas spread further to other groups in declining strength. While unilateral spreading shifts the opinion distribution, competition of activists leads to additional phenomena: Small heterogeneities among competing activists cause them to target different groups in society, which amplifies polarization. For moderate heterogeneities, we obtain target cycles and further amplification of polarization. In such cycles, the stronger activist differentiates himself from the weaker one, while the latter aims to imitate the stronger activist.

physics.soc-ph↗

arXiv2019

Random-Graph Models and Characterization of Granular Networks

Various approaches and measures from network analysis have been applied to granular and particulate networks to gain insights into their structural, transport, failure-propagation and other systems-level properties. In this article, we examine a variety of common network measures and study their ability to characterize various two-dimensional and three-dimensional spatial random-graph models and empirical two-dimensional granular networks. We identify network measures that are able to distinguish between physically plausible and unphysical spatial network models. Our results also suggest that there are significant differences in the distributions of certain network measures in two and three dimensions, hinting at important differences that we also expect to arise in experimental granular networks.

cond-mat.soft↗

arXiv2019

The Impact of Technologies in Political Campaigns

Recent political campaigns have demonstrated how technologies are used to boost election outcomes by microtargeting voters. We propose and analyze a framework which analyzes how political activists use technologies to target voters. Voters are represented as nodes of a network. Political activists reach out locally to voters and try to convince them. Depending on their technological advantage and budget, political activists target certain regions in the network where their activities are able to generate the largest vote-share gains. Analytically and numerically, we quantify vote-share gains and savings in terms of budget and number of activists from employing superior targeting technologies compared to traditional campaigns. Moreover, we demonstrate that the technological precision must surpass a certain threshold in order to lead to a vote-share gain or budget advantage. Finally, by calibrating the technology parameters to the recent U.S. presidential election, we show that a pure targeting technology advantage is consistent with Trump winning against Clinton.

physics.soc-ph↗

arXiv2018

Dynamical universality of the contact process

The dynamical relaxation and scaling properties of three different variants of the contact process in two spatial dimensions are analysed. Dynamical contact processes capture a variety of contagious processes such as the spreading of diseases or opinions. The universality of both local and global two-time correlators of the particle-density and the associated linear responses are tested through several scaling relations of the non-equilibrium exponents and the shape of the associated scaling functions. In addition, the dynamical scaling of two-time global correlators can be used as a tool to improve on the determination of the location of critical points.

cond-mat.stat-mech↗

arXiv2017

Targeted Recovery as an Effective Strategy against Epidemic Spreading

We propose a targeted intervention protocol where recovery is restricted to individuals that have the least number of infected neighbours. Our recovery strategy is highly efficient on any kind of network, since epidemic outbreaks are minimal when compared to the baseline scenario of spontaneous recovery. In the case of spatially embedded networks, we find that an epidemic stays strongly spatially confined with a characteristic length scale undergoing a random walk. We demonstrate numerically and analytically that this dynamics leads to an epidemic spot with a flat surface structure and a radius that grows linearly with the spreading rate.

physics.soc-ph↗

arXiv2017

Temporal dynamics of online petitions

Online petitions are an important avenue for direct political action, yet the dynamics that determine when a petition will be successful are not well understood. Here we analyze the temporal characteristics of online-petition signing behavior in order to identify systematic differences between popular petitions, which receive a high volume of signatures, and unpopular ones. We find that, in line with other temporal characterizations of human activity, the signing process is typically non-Poissonian and non-homogeneous in time. However, this process exhibits anomalously high memory for human activity, possibly indicating that synchronized external influence or contagion play and important role. More interestingly, we find clear differences in the characteristics of the inter-event time distributions depending on the total number of signatures that petitions receive, independently of the total duration of the petitions. Specifically, popular petitions that attract a large volume of signatures exhibit more variance in the distribution of inter-event times than unpopular petitions with only a few signatures, which could be considered an indication that the former are more bursty. However, petitions with large signature volume are less bursty according to measures that consider the time ordering of inter-event times. Our results, therefore, emphasize the importance of accounting for time ordering to characterize human activity.

physics.soc-ph↗

arXiv2017

Critical behaviors in contagion dynamics

We study the critical behavior of a general contagion model where nodes are either active (e.g. with opinion A, or functioning) or inactive (e.g. with opinion B, or damaged). The transitions between these two states are determined by (i) spontaneous transitions independent of the neighborhood, (ii) transitions induced by neighboring nodes and (iii) spontaneous reverse transitions. The resulting dynamics is extremely rich including limit cycles and random phase switching. We derive a unifying mean-field theory. Specifically, we analytically show that the critical behavior of systems whose dynamics is governed by processes (i-iii) can only exhibit three distinct regimes: (a) uncorrelated spontaneous transition dynamics (b) contact process dynamics and (c) cusp catastrophes. This ends a long-standing debate on the universality classes of complex contagion dynamics in mean-field and substantially deepens its mathematical understanding.

physics.soc-ph↗

arXiv2016

Impact of embedding on predictability of failure-recovery dynamics in networks

Failure, damage spread and recovery crucially underlie many spatially embedded networked systems ranging from transportation structures to the human body. Here we study the interplay between spontaneous damage, induced failure and recovery in both embedded and non-embedded networks. In our model the network's components follow three realistic processes that capture these features: (i) spontaneous failure of a component independent of the neighborhood (internal failure), (ii) failure induced by failed neighboring nodes (external failure) and (iii) spontaneous recovery of a component.We identify a metastable domain in the global network phase diagram spanned by the model's control parameters where dramatic hysteresis effects and random switching between two coexisting states are observed. The loss of predictability due to these effects depend on the characteristic link length of the embedded system. For the Euclidean lattice in particular, hysteresis and switching only occur in an extremely narrow region of the parameter space compared to random networks. We develop a unifying theory which links the dynamics of our model to contact processes. Our unifying framework may help to better understand predictability and controllability in spatially embedded and random networks where spontaneous recovery of components can mitigate spontaneous failure and damage spread in the global network.

physics.soc-ph↗

arXiv2015

Disease-induced resource constraints can trigger explosive epidemics

Advances in mathematical epidemiology have led to a better understanding of the risks posed by epidemic spreading and informed strategies to contain disease spread. However, a challenge that has been overlooked is that, as a disease becomes more prevalent, it can limit the availability of the capital needed to effectively treat those who have fallen ill. Here we use a simple mathematical model to gain insight into the dynamics of an epidemic when the recovery of sick individuals depends on the availability of healing resources that are generated by the healthy population. We find that epidemics spiral out of control into "explosive" spread if the cost of recovery is above a critical cost. This can occur even when the disease would die out without the resource constraint. The onset of explosive epidemics is very sudden, exhibiting a discontinuous transition under very general assumptions. We find analytical expressions for the critical cost and the size of the explosive jump in infection levels in terms of the parameters that characterize the spreading process. Our model and results apply beyond epidemics to contagion dynamics that self-induce constraints on recovery, thereby amplifying the spreading process.

physics.soc-ph↗

arXiv2014

Crazy 1d billiards: Behavior of spring-fixated, noisy colliding particles

We study a one-dimensional system of spatially extended particles, which are fixated to regularly spaced locations by means of elastic springs. The particles are assumed to be driven by a Gaussian noise and to have dissipative, energy-conserving or anti-dissipative (flipper-like) interactions, when the particle density exceeds a critical threshold. While each particle in separation shows a wellbehaved behavior characterized by a Gaussian velocity distribution, the interaction of particles at high densities can cause an avalanche-like momentum and energy transfer, which can generate steep power laws without a well-defined variance and mean value. Specifically, the velocity variance increases dramatically towards the free boundaries of the driven-many-particle system. The model might also have some relevance for a better understanding of crowd disasters. Our results suggest that these are most likely caused by passive momentum transfers, and not by active pushing.

cond-mat.stat-mech↗