Related papers: Probing the Geometry of Data with Diffusion Fr\'ec…
Human social behavior is organized in stratified, hierarchical networks, with a support group with about 5 members, expanding proportionally at each layer up to a maximum of approximately 150 frequent interactions per individual. This is…
In this paper, the statistical properties of Newton s method algorithm output in a specific case have been studied. The relative frequency density of this sample converges to a well-defined function, prompting us to explore its…
Distribution networks -- from vasculature to urban transportation systems -- are prevalent in both the natural and consumer worlds. These systems are intrinsically physical in composition and are embedded into real space, properties that…
Describing networks geometrically through low-dimensional latent metric spaces has helped design efficient learning algorithms, unveil network symmetries and study dynamical network processes. However, latent space embeddings are limited to…
We study diffusion of (fluorescently) tagged hard-core interacting particles of finite size in a finite one-dimensional system. We find an exact analytical expression for the tagged particle probability density using a coordinate…
Graph-based machine learning methods are useful tools in the identification and prediction of variation in genetic data. In particular, the comprehension of phenotypic effects at the cellular level is an accelerating research area in…
Ecosystems tend to fluctuate around stable equilibria in response to internal dynamics and environmental factors. Occasionally, they enter an unstable tipping region and collapse into an alternative stable state. Our understanding of how…
We consider two statistical problems at the intersection of functional and non-Euclidean data analysis: the determination of a Fr\'echet mean in the Wasserstein space of multivariate distributions; and the optimal registration of deformed…
Two crucial elements facilitate the understanding and control of communicable disease spread within a social setting. These components are, the underlying contact structure among individuals that determines the pattern of disease…
Because diffusion typically involves symmetric interactions, scant attention has been focused on studying asymmetric cases. However, important networked systems underlain by diffusion (e.g. cortical networks and WWW) are inherently…
We introduce diffusion geometry as a new framework for geometric and topological data analysis. Diffusion geometry uses the Bakry-Emery $\Gamma$-calculus of Markov diffusion operators to define objects from Riemannian geometry on a wide…
A new methodology is proposed for generating realizations of a random vector with values in a finite-dimensional Euclidean space that are statistically consistent with a data set of observations of this vector. The probability distribution…
The availability of new data sources on human mobility is opening new avenues for investigating the interplay of social networks, human mobility and dynamical processes such as epidemic spreading. Here we analyze data on the time-resolved…
We introduce a community detection algorithm (Fluid Communities) based on the idea of fluids interacting in an environment, expanding and contracting as a result of that interaction. Fluid Communities is based on the propagation…
The contact structure between hosts has a critical influence on disease spread. However, most networkbased models used in epidemiology tend to ignore heterogeneity in the weighting of contacts. This assumption is known to be at odds with…
Graph embedding provides a feasible methodology to conduct pattern classification for graph-structured data by mapping each data into the vectorial space. Various pioneering works are essentially coding method that concentrates on a…
Communication and coordination play a major role in the ability of bacterial cells to adapt to ever changing environments and conditions. Recent work has shown that such coordination underlies several aspects of bacterial responses…
In eukaryotic cells, mitochondria form networks that range from highly fused interconnected structures to fragmented populations of individual organelles that undergo transient interactions. These structures can be described as temporal…
When propagating uncertainty in the data of differential equations, the probability laws describing the uncertainty are typically themselves subject to uncertainty. We present a sensitivity analysis of uncertainty propagation for…
The diffusion of information and behaviors over social networks is of considerable interest in research fields ranging from sociology to computer science and application domains such as marketing, finance, human health, and national…