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Timelines are common visualizations to represent and manipulate temporal data, from historical events storytelling to animation authoring. However, timeline visualizations rarely consider spatio-temporal 3D data (e.g. mesh or volumetric…
In this paper we give some two-dimensional and some three-dimensional examples for the shape of the symmetric solution set of a linear complementarity problem where the given data are not explicitly known but can only be enclosed in…
Visual events in computer vision are studied from the perspective of algebraic geometry. Given a sufficiently general curve or surface in 3-space, we consider the image or contour curve that arises by projecting from a viewpoint.…
Ever since the prevalent use of the LiDARs in autonomous driving, tremendous improvements have been made to the learning on the point clouds. However, recent progress largely focuses on detecting objects in a single 360-degree sweep,…
Discrete event sequences serve as models for numerous real-world datasets, including publications over time, project milestones, and medication dosing during patient treatments. These event sequences typically exhibit bursty behavior, where…
Many materials, processes, and structures in science and engineering have important features at multiple scales of time and/or space; examples include biological tissues, active matter, oceans, networks, and images. Explicitly extracting,…
Point containment queries on trimmed surfaces are fundamental to CAD modeling, solid geometry processing, and surface tessellation. Existing approaches such as ray casting and generalized winding numbers often face limitations in robustness…
Functional data analysis is ubiquitous in most areas of sciences and engineering. Several paradigms are proposed to deal with the dimensionality problem which is inherent to this type of data. Sparseness, penalization, thresholding, among…
We study the apparition of event horizons in accelerated expanding cosmologies. We give a graphical and analytical representation of the horizons using proper distances to coordinate the events. Our analysis is mainly kinematical. We show…
We introduce a new version of dynamic time warping for samples of observed event times that are modeled as time-warped intensity processes. Our approach is devel- oped within a framework where for each experimental unit or subject in a…
This work investigates slant timelike-ruled surfaces and their evolute offsets in Minkowski 3-space $\mathbb{E}_{1}^{3}$. Using the symmetry of evolute curves, we derive a parametric formulation for skew timelike-ruled surfaces and…
Complex networks represent system dynamics through the interactions of a set of anomalous time series. Consider the problem of computing correlations for highly correlated pairs of time series across sliding windows. Efficiently computing…
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…
We describe a geometric method to quantify wave patterns observed in the nervous system, which are non-stationary and with a mixture of spiral, target, plane and irregular waves. The method analyzes fluctuations of the energy angular…
The geometric properties of spacetimes representing expanding impulsive gravitational waves, propagating on a flat background and generated by snapped cosmic strings, are studied. The construction of the line element is reviewed, and…
Mathematical theory of an observer is elaborated upon the basis of A.Poincare's ideas on the nature of geometry and the role of observer's perceptive space. The said theory is generalizing reference frames theory in GR. Physical structure…
A large volume of content generated by online users is geo-tagged and this provides a rich source for querying in various location-based services. An important class of queries within such services involves the association between content…
Temporal alignment is an inherent task in most applications dealing with videos: action recognition, motion transfer, virtual trainers, rehabilitation, etc. In this paper we dive into the understanding of this task from a geometric point of…
The wavelet tree (Grossi et al. [SODA, 2003]) and wavelet matrix (Claude et al. [Inf. Syst., 2015]) are compact data structures with many applications such as text indexing or computational geometry. By continuing the recent research of…
Atmospheric processes involve both space and time. This is why human analysis of atmospheric imagery can often extract more information from animated loops of image sequences than from individual images. Automating such an analysis requires…