Related papers: Local asymmetry in spatial interactions: A general…
We present a systematic study on a class of nonlocal integral functionals for functions defined on a bounded domain and the naturally induced function spaces. The function spaces are equipped with a seminorm depending on finite differences…
Correctly capturing the symmetry transformations of data can lead to efficient models with strong generalization capabilities, though methods incorporating symmetries often require prior knowledge. While recent advancements have been made…
Nonlinear plant-scale interactions controlling the soil-water balance are generally not valid at larger spatial scales due to spatial heterogeneity in rainfall and vegetation type. The relationships between spatially averaged variables are…
Rapid progress in representation learning has led to a proliferation of embedding models, and to associated challenges of model selection and practical application. It is non-trivial to assess a model's generalizability to new, candidate…
Accurate flood prediction is crucial for disaster prevention and mitigation. Hydrological data exhibit highly nonlinear temporal patterns and encompass complex spatial relationships between rainfall and flow. Existing flood prediction…
Wayfinding behavior and pedestrian movement pattern research relies on objective spatial configuration representation and analysis, such as space syntax, to quantify and control for the difficulty of wayfinding in multi-level buildings and…
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…
This paper describes the systematic application of local topological methods for detecting interfaces and related anomalies in complicated high-dimensional data. By examining the topology of small regions around each point, one can…
Different extended objects can fall in different ways, depending on their internal structures. Some motions are nevertheless impossible, regardless of internal structure. This paper derives universal constraints on extended-body motion,…
Geospatial analysis is very much dominated by a Gaussian way of thinking, which assumes that things in the world can be characterized by a well-defined mean, i.e., things are more or less similar in size. However, this assumption is not…
Multivariate spatially-oriented data sets are prevalent in the environmental and physical sciences. Scientists seek to jointly model multiple variables, each indexed by a spatial location, to capture any underlying spatial association for…
Multivariate measurements taken at different spatial locations occur frequently in practice. Proper analysis of such data needs to consider not only dependencies on-sight but also dependencies in and in-between variables as a function of…
High-dimensional multivariate spatial-temporal data arise frequently in a wide range of applications; however, there are relatively few statistical methods that can simultaneously deal with spatial, temporal and variable-wise dependencies…
Abridged abstract: Inert interactions between randomly moving entities and spatial disorder play a crucial role in quantifying the diffusive properties of a system. These interactions affect only the movement of the entities, and examples…
We introduce and discuss (local) symmetries of geometric structures. These symmetries generalize the classical (locally) symmetric spaces to various other geometries. Our main tools are homogeneous Cartan geometries and their explicit…
Effective learning of asymmetric and local features in images and other data observed on multi-dimensional grids is a challenging objective critical for a wide range of image processing applications involving biomedical and natural images.…
In this paper, we propose a robust end-to-end multi-modal pipeline for place recognition where the sensor systems can differ from the map building to the query. Our approach operates directly on images and LiDAR scans without requiring any…
We propose models and algorithms for learning about random directions in two-dimensional simplex data, and apply our methods to the study of income level proportions and their changes over time in a geostatistical area. There are several…
Complex systems span multiple spatial and temporal scales, making their dynamics challenging to understand and predict. This challenge is especially daunting when one wants to study localized and/or rare events. Advances in dynamical…
Spatial documentation is exponentially increasing given the availability of Big IoT Data, enabled by the devices miniaturization and data storage capacity. Bayesian spatial statistics is a useful statistical tool to determine the dependence…