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We propose a method for unsupervised reconstruction of a temporally-consistent sequence of surfaces from a sequence of time-evolving point clouds. It yields dense and semantically meaningful correspondences between frames. We represent the…
Event sequence data record series of discrete events in the time order of occurrence. They are commonly observed in a variety of applications ranging from electronic health records to network logs, with the characteristics of large-scale,…
In this paper, we discuss the global aspect of the geometric dynamics of volumetric expansion and its application to the problem of the existence in the space-time of compact and complete spacelike hypersurface.
A temporal graph is a data structure, consisting of nodes and edges in which the edges are associated with time labels. To analyze the temporal graph, the first step is to find a proper graph dataset/benchmark. While many temporal graph…
We study the convex-hull problem in a probabilistic setting, motivated by the need to handle data uncertainty inherent in many applications, including sensor databases, location-based services and computer vision. In our framework, the…
Event-based sensors offer high temporal resolution and low latency by generating sparse, asynchronous data. However, converting this irregular data into dense tensors for use in standard neural networks diminishes these inherent advantages,…
This paper evaluates several improvements to the memory layout of convex hulls to improve computation times for support point queries. The support point query is a fundamental part of common collision algorithms, and the work presented…
In this paper, we analyze timed systems with data structures, using a rich interplay of logic and properties of graphs. We start by describing behaviors of timed systems using graphs with timing constraints. Such a graph is called…
A data structure is presented for point location in connected planar subdivisions when the distribution of queries is known in advance. The data structure has an expected query time that is within a constant factor of optimal. More…
In this paper I present several novel, efficient, algorithmic techniques for solving some multidimensional geometric data management and analysis problems. The techniques are based on several data structures from computational geometry…
We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.
Geometric deep learning has gained tremendous attention in both academia and industry due to its inherent capability of representing arbitrary structures. Due to exponential increase in interest towards renewable sources of energy,…
The global time in Geometrodynamics is defined in a covariant under diffeomorphisms form. An arbitrary static background metric is taken in the tangent space. The global intrinsic time is identified with the mean value of the logarithm of…
This paper presents expression of mutual information that defines the information gain in planning of sensing resources, when the goal is to reduce the forecast uncertainty of some quantities of interest and the system dynamics is described…
Orienting surface normals correctly and consistently is a fundamental problem in geometry processing. Applications such as visualization, feature detection, and geometry reconstruction often rely on the availability of correctly oriented…
We study Lie point symmetry structure of generalized nonlinear wave equations in the $(n+1)$-dimensional space-time.
The real world and its geographic objects are modeled and represented in different spatial databases. Each of these databases provides only a partial description (in space and time) of the geographic objects represented. Sometimes,…
It is known that statistical model selection as well as identification of dynamical equations from available data are both very challenging tasks. Physical systems behave according to their underlying dynamical equations which, in turn, can…
We define an almost--cosymplectic--contact structure which generalizes cosymplectic and contact structures of an odd dimensional manifold. Analogously, we define an almost--coPoisson--Jacobi structure which generalizes a Jacobi structure.…
Given a set $P$ of coloured points on the real line, we study the problem of answering range $\alpha$-majority (or "heavy hitter") queries on $P$. More specifically, for a query range $Q$, we want to return each colour that is assigned to…