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Compositional observations are an increasingly prevalent data source in spatial statistics. Analysis of such data is typically done on log-ratio transformations or via Dirichlet regression. However, these approaches often make unnecessarily…
Mutualisms are key for structuring ecological communities, but they are sensitive to environmental change and fluctuations in population size. Consequently, how mutualisms achieve stability remains an open question in ecological theory.…
This paper investigates the modeling of an important class of degradation data, which are collected from a spatial domain over time; for example, the surface quality degradation. Like many existing time-dependent stochastic degradation…
Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…
Recently, evolving networks are becoming a suitable form to model many real-world complex systems, due to their peculiarities to represent the systems and their constituting entities, the interactions between the entities and the…
Sociotechnological and geospatial processes exhibit time varying structure that make insight discovery challenging. This paper proposes a new statistical model for such systems, modeled as dynamic networks, to address this challenge. It…
Structural change detection problems are often encountered in analytics and econometrics, where the performance of a model can be significantly affected by unforeseen changes in the underlying relationships. Although these problems have a…
Self-organization, the ability of a system of microscopically interacting entities to shape macroscopically ordered structures, is ubiquitous in Nature. Spatio-temporal patterns are abundantly observed in a large plethora of applications,…
Pattern formation often occurs in confined systems, yet how boundaries shape patterning dynamics is unclear. We develop techniques to analyze confinement effects in nonlocal advection-diffusion equations, which generically capture the…
Discovering the underlying relationships among variables from temporal observations has been a longstanding challenge in numerous scientific disciplines, including biology, finance, and climate science. The dynamics of such systems are…
Time series prediction is a widespread and well studied problem with applications in many domains (medical, geoscience, network analysis, finance, econometry etc.). In the case of multivariate time series, the key to good performances is to…
Systems of dynamical interactions between competing species can be used to model many complex systems, and can be mathematically described by {\em random} networks. Understanding how patterns of activity arise in such systems is important…
Understanding the relationship between complexity and stability in large dynamical systems -- such as ecosystems -- remains a key open question in complexity theory which has inspired a rich body of work developed over more than fifty…
End-to-end learning of dynamical systems with black-box models, such as neural ordinary differential equations (ODEs), provides a flexible framework for learning dynamics from data without prescribing a mathematical model for the dynamics.…
Accurately forecasting urban development and its environmental and climate impacts critically depends on realistic models of the spatial structure of the built environment, and of its dependence on key factors such as population and…
Nonlinear and non-stationary processes are prevalent in various natural and physical phenomena, where system dynamics can change qualitatively due to bifurcation phenomena. Traditional machine learning methods have advanced our ability to…
Spatial pattern formation is a key feature of many natural systems in physics, chemistry and biology. The essential theoretical issue in understanding pattern formation is to explain how a spatially homogeneous initial state can undergo…
Characterizing structural and dynamic properties of proteins and large macromolecular assemblies is crucial to understand the molecular mechanisms underlying biological functions. In the field of Structural Biology, no single method…
Graph-based spatio-temporal neural networks are effective to model the spatial dependency among discrete points sampled irregularly from unstructured grids, thanks to the great expressiveness of graph neural networks. However, these models…
Evolutionary dynamics are shaped by a variety of fundamental, generic drivers, including spatial structure, ecology, and selection pressure. These drivers impact the trajectory of evolution, and have been hypothesized to influence…