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We introduce a novel, geometry-aware distance metric for the family of von Mises-Fisher (vMF) distributions, which are fundamental models for directional data on the unit hypersphere. Although the vMF distribution is widely employed in a…
Complex networks are characterized by latent geometries induced by their topology or by the dynamics on the top of them. In the latter case, different network-driven processes induce distinct geometric features that can be captured by…
The outcome of an epidemic is closely related to the network of interactions between the individuals. Likewise, protein functions depend on the 3D arrangement of their residues and on the underlying energetic interaction network. Borrowing…
An active area of research interest is the inference of ecological models of complex microbial communities. Inferring such ecological models entails understanding the interactions between microbes and how they affect each other's growth.…
As two main focuses of the study of complex networks, the community structure and the dynamics on networks have both attracted much attention in various scientific fields. However, it is still an open question how the community structure is…
Divergence functions are measures of distance or dissimilarity between probability distributions that serve various purposes in statistics and applications. We propose decompositions of Wasserstein and Cram\'er distances$-$which compare two…
Flow and transport in fractured geological media are strongly controlled by aperture heterogeneity and uncertainty in subsurface characterisation, yet most upscaling approaches rely on deterministic representations of fracture permeability.…
Models of disease spreading are critical for predicting infection growth in a population and evaluating public health policies. However, standard models typically represent the dynamics of disease transmission between individuals using…
Distribution-as-response regression problems are gaining wider attention, especially within biomedical settings where observation-rich patient specific data sets are available, such as feature densities in CT scans (Petersen et al., 2021)…
While efficient distribution learning is no doubt behind the groundbreaking success of diffusion modeling, its theoretical guarantees are quite limited. In this paper, we provide the first rigorous analysis on approximation and…
From soil to the gut, communities composed of thousands of microbes perform functions such as carbon sequestration and immune system regulation. Here, we introduce a data-driven approach that explains how community function can be traced to…
Information diffusion, spreading of infectious diseases, and spreading of rumors are fundamental processes occurring in real-life networks. In many practical cases, one can observe when nodes become infected, but the underlying network,…
Regression analysis with probability measures as input predictors and output response has recently drawn great attention. However, it is challenging to handle multiple input probability measures due to the non-flat Riemannian geometry of…
Ongoing advances in microbiome profiling have allowed unprecedented insights into the molecular activities of microbial communities. This has fueled a strong scientific interest in understanding the critical role the microbiome plays in…
In this paper, we consider the problem of propagating an uncertain distribution by a possibly non-linear function and quantifying the resulting uncertainty. We measure the uncertainty using the Wasserstein distance, and for a given input…
Distance measures between graphs are important primitives for a variety of learning tasks. In this work, we describe an unsupervised, optimal transport based approach to define a distance between graphs. Our idea is to derive…
A central problem in data analysis is the low dimensional representation of high dimensional data, and the concise description of its underlying geometry and density. In the analysis of large scale simulations of complex dynamical systems,…
The large-scale collective behavior of biological systems can be characterized by macroscopic transport, which arises from the non-equilibrium microscopic interactions among individual constituents. A prominent example is the formation of…
Accretion occurs across a large range of scales and physical regimes. Despite this diversity in the physics, the observed properties show remarkably similarity. The theory of propagating fluctuations, in which broad-band variability within…
A new method for identifying soft communities in networks is proposed. Reference nodes, either selected using a priori information about the network or according to relevant node measurements, are obtained. Distance vectors between each…