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Using deep learning techniques to process 3D objects has achieved many successes. However, few methods focus on the representation of 3D objects, which could be more effective for specific tasks than traditional representations, such as…

In this paper we study the topological properties of wireless communication maps and their usability in algorithmic design. We consider the SINR model, which compares the received power of a signal at a receiver against the sum of strengths…

Ubiquitous geometric objects can be precisely and efficiently represented as polyhedra. The transformation of a polyhedron into a vector, known as polyhedra representation learning, is crucial for manipulating these shapes with mathematical…

Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections,…

Mapping the environment has been an important task for robot navigation and Simultaneous Localization And Mapping (SLAM). LIDAR provides a fast and accurate 3D point cloud map of the environment which helps in map building. However,…

Many computer vision challenges require continuous outputs, but tend to be solved by discrete classification. The reason is classification's natural containment within a probability $n$-simplex, as defined by the popular softmax activation…

Spatial ecological networks are widely used to model interactions between georeferenced biological entities (e.g., populations or communities). The analysis of such data often leads to a two-step approach where groups containing similar…

Information dissemination is a fundamental and frequently occurring problem in large, dynamic, distributed systems. In order to solve this, there has been an increased interest in creating efficient overlay networks that can maintain…

The loss surface of deep neural networks has recently attracted interest in the optimization and machine learning communities as a prime example of high-dimensional non-convex problem. Some insights were recently gained using spin glass…

Understanding the spatial networks formed by the trajectories of mobile users can be beneficial to applications ranging from epidemiology to local search. Despite the potential for impact in a number of fields, several aspects of human…

This paper uses the theory of point processes and stochastic geometry to quantify the sky visibility experienced by users located in an urban environment. The general idea is to represent the buildings of this environment as a stationary…

In human spatial awareness, 3-D projective geometry structures information integration and action planning through perspective taking within an internal representation space. The way different perspectives are related and transform a world…

We study the effects of spatial constraints on the structural properties of networks embedded in one or two dimensional space. When nodes are embedded in space, they have a well defined Euclidean distance $r$ between any pair. We assume…

Many biological and medical tasks require the delineation of 3D curvilinear structures such as blood vessels and neurites from image volumes. This is typically done using neural networks trained by minimizing voxel-wise loss functions that…

Traffic forecasting is significant for urban traffic management, intelligent route planning, and real-time flow monitoring. Recent advances in spatial-temporal models have markedly improved the modeling of intricate spatial-temporal…

A spatial surface is a compact surface embedded in the $3$-sphere. We assume that a spatial surface is oriented and that each connected component of a spatial surface is neither a disk nor without a boundary. A diagram of a spatial surface…

Spatial networks, in which nodes and edges are embedded in space, play a vital role in the study of complex systems. For example, many social networks attach geo-location information to each user, allowing the study of not only topological…

In this paper we investigate the problem of inducing a distribution over three-dimensional structures given two-dimensional views of multiple objects taken from unknown viewpoints. Our approach called "projective generative adversarial…

The functional features of spatial networks depend upon a non-trivial relationship between the topological and physical structure. Here, we explore that relationship for spatial networks with radial symmetry and disordered fractal…

This paper presents an online informative path planning approach for active information gathering on three-dimensional surfaces using aerial robots. Most existing works on surface inspection focus on planning a path offline that can provide…