Related papers: A dominance tree approach to systems of cities
High-dimensional systems that have a low-dimensional dominant behavior allow for model reduction and simplified analysis. We use differential analysis to formalize this important concept in a nonlinear setting. We show that dominance can be…
Humans recognize object structure from both their appearance and motion; often, motion helps to resolve ambiguities in object structure that arise when we observe object appearance only. There are particular scenarios, however, where…
Networks and graphs provide a simple but effective model to a vast set of systems which building blocks interact throughout pairwise interactions. Unfortunately, such models fail to describe all those systems which building blocks interact…
We introduce a site-wise domination criterion for local percolation models, which enables the comparison of one-arm probabilities even in the absence of stochastic domination. The method relies on a local-to-global principle: if, at each…
We investigate higher-order Voronoi diagrams in the city metric. This metric is induced by quickest paths in the L1 metric in the presence of an accelerating transportation network of axis-parallel line segments. For the structural…
The spread of infectious disease in a human community or the proliferation of fake news on social media can be modeled as a randomly growing tree-shaped graph. The history of the random growth process is often unobserved but contains…
We develop an analysis pipeline for characterizing the topology of large scale structure and extracting cosmological constraints based on persistent homology. Persistent homology is a technique from topological data analysis that quantifies…
Fiber tractography on diffusion imaging data offers rich potential for describing white matter pathways in the human brain, but characterizing the spatial organization in these large and complex data sets remains a challenge. We show that…
Understanding urban form is crucial for sustainable urban planning and enhancing quality of life. This study presents a data-driven framework to systematically identify and compare urban typologies across geographically and culturally…
Community structure is one of the key properties of complex networks and plays a crucial role in their topology and function. While an impressive amount of work has been done on the issue of community detection, very little attention has…
Model-free forecasting of the temporal evolution of chaotic systems is crucial but challenging. Existing solutions require hyperparameter tuning, significantly hindering their wider adoption. In this work, we introduce a tree-based approach…
Structure identification in cosmological simulations plays an important role in analysing simulation outputs. The definition of these structures directly impacts the inferred properties derived from these simulations. This paper proposes a…
The description of the Internet topology is an important open problem, recently tackled with the introduction of scale-free networks. In this paper we focus on the topological and dynamical properties of real Internet maps in a three years…
The spatial distribution of income shapes the structure and organisation of cities and its understanding has broad societal implications. Despite an abundant literature, many issues remain unclear. In particular, all definitions of…
We consider the well-studied pattern counting problem: given a permutation $\pi \in \mathbb{S}_n$ and an integer $k > 1$, count the number of order-isomorphic occurrences of every pattern $\tau \in \mathbb{S}_k$ in $\pi$. Our first result…
We investigate the statistics of trees grown from some initial tree by attaching links to preexisting vertices, with attachment probabilities depending only on the valence of these vertices. We consider the asymptotic mass distribution that…
Decision trees are widely used for non-linear modeling, as they capture interactions between predictors while producing inherently interpretable models. Despite their popularity, performing inference on the non-linear fit remains largely…
Easy and intuitive navigability is of central importance in cities. The actual scale-free networking of urban street networks in their topological space, where navigation information is encoded by mapping roads to nodes and junctions to…
Staged trees are a relatively recent class of probabilistic graphical models that extend Bayesian networks to formally and graphically account for non-symmetric patterns of dependence. Machine learning algorithms to learn them from data…
We study the probabilistic behavior of persistence-based statistics and propose a novel nonparametric framework for detecting structural changes in high-dimensional random point clouds. We establish moment bounds and tightness results for…