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Many statistical models are algebraic in that they are defined by polynomial constraints or by parameterizations that are polynomial or rational maps. This opens the door for tools from computational algebraic geometry. These tools can be…
The ability to map the cosmological expansion has developed enormously, spurred by the turning point one decade ago of the discovery of cosmic acceleration. The standard model of cosmology has shifted from a matter dominated, standard…
Thomas Schelling proposed an influential simple spatial model to illustrate how, even with relatively mild assumptions on each individual's nearest neighbor preferences, an integrated city would likely unravel to a segregated city, even if…
Scaling has been proposed as a powerful tool to analyze the properties of complex systems, and in particular for cities where it describes how various properties change with population. The empirical study of scaling on a wide range of…
In real-world applications, observations are often constrained to a small fraction of a system. Such spatial subsampling can be caused by the inaccessibility or the sheer size of the system, and cannot be overcome by longer sampling.…
Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…
Urban scaling laws relate socio-economic, behavioral, and physical variables to the population size of cities and allow for a new paradigm of city planning, and an understanding of urban resilience and economies. Independently of culture…
Shape inference is classically ill-posed, because it involves a map from the (2D) image domain to the (3D) world. Standard approaches regularize this problem by either assuming a prior on lighting and rendering or restricting the domain,…
The use of geospatially dependent information, which has been stipulated as a law in geography, to model geographic patterns forms the cornerstone of geostatistics, and has been inherited in many data science based techniques as well, such…
Based on the cosmological principle only, the method of describing the evolution of the Universe, called cosmography, is in fact a kinematics of cosmological expansion. The effectiveness of cosmography lies in the fact that it allows, based…
The research field of spatial scientometrics is dedicated to measuring and analyzing science with spatial components (e.g., location, place, mapping). Because of the dynamic nature of this field, researchers from multidisciplinary domains…
We discuss the relevance of studying ecology within the framework of Complexity Science from a statistical mechanics approach. Ecology is concerned with understanding how systems level properties emerge out of the multitude of interactions…
The failure of roughness parameters to predict surface properties stems from their inherent scale-dependence; in other words, the measured value depends on the way it was measured. Here we take advantage of this scale-dependence to develop…
In light of the emergence of big data, I have advocated and argued for a paradigm shift from Tobler's law to scaling law, from Euclidean geometry to fractal geometry, from Gaussian statistics to Paretian statistics, and - more importantly -…
Stochastic methods are a crucial area in contemporary climate research and are increasingly being used in comprehensive weather and climate prediction models as well as reduced order climate models. Stochastic methods are used as…
This review is intended to give a pedagogical and unified view on the subject of the statistics and scaling of physical quantities in disordered electron systems at very low temperatures. Quantum coherence at low temperatures and randomness…
Poverty mapping is a powerful tool to study the geography of poverty. The choice of the spatial resolution is central as poverty measures defined at a coarser level may mask their heterogeneity at finer levels. We introduce a small area…
Deep learning (DL) creates impactful advances following a virtuous recipe: model architecture search, creating large training data sets, and scaling computation. It is widely believed that growing training sets and models should improve…
Compositional understanding is crucial for human intelligence, yet it remains unclear whether contemporary vision models exhibit it. The dominant machine learning paradigm is built on the premise that scaling data and model sizes will…
Many aggregate distributions of urban activities such as city sizes reveal scaling but hardly any work exists on the properties of spatial distributions within individual cities, notwithstanding considerable knowledge about their fractal…