98 citations · 273 across the 11 of their papers we have counts for
11 papers
Generalizing Perron--Frobenius theory and eigenvector-based centralities to networks with complex edge weights
Yu Tian, Mason A. Porter, Lucas Böttcher
A fundamental concept in linear algebra and its applications to network analysis is the Perron--Frobenius (PF) theorem, which underpins eigenvector-based centrality measures such a…
Graph energy as a measure of community detectability in networks
Lucas Böttcher, Mason A. Porter, Santo Fortunato
A key challenge in network science is the detection of communities, which are sets of nodes in a network that are densely connected internally but sparsely connected to the rest of…
A knapsack for collective decision-making
Yurun Ge, Lucas Böttcher, Tom Chou +1
Collective decision-making is the process through which diverse stakeholders reach a joint decision. Within societal settings, one example is participatory budgeting, where constit…
Mathematical Characterization of Private and Public Immune Repertoire Sequences
Lucas Böttcher, Sascha Wald, Tom Chou
Diverse T and B cell repertoires play an important role in mounting effective immune responses against a wide range of pathogens and malignant cells. The number of unique T and B c…
Classical and quantum random-walk centrality measures in multilayer networks
Lucas Böttcher, Mason A. Porter
Multilayer network analysis is a useful approach for studying the structural properties of entities with diverse, multitudinous relations. Classifying the importance of nodes and n…
From classical to quantum walks with stochastic resetting on networks
Sascha Wald, Lucas Böttcher
Random walks are fundamental models of stochastic processes with applications in various fields including physics, biology, and computer science. We study classical and quantum ran…
Competing Activists--Political Polarization
Lucas Böttcher, Pedro Montealegre, Eric Goles +1
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 compar…
Dynamical universality of the contact process
Lucas Böttcher, Hans Jürgen Herrmann, Malte Henkel
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 var…
Critical behaviors in contagion dynamics
Lucas Böttcher, Jan Nagler, Hans J. Herrmann
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 t…
Disease-induced resource constraints can trigger explosive epidemics
Lucas Böttcher, Olivia Woolley-Meza, Nuno A. M. Araújo +2
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 chal…
Crazy 1d billiards: Behavior of spring-fixated, noisy colliding particles
Roman Mani, Lucas Böttcher, Hans J. Herrmann +1
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 driv…