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Computer-Generated Holography (CGH) offers the potential for genuine, high-quality three-dimensional visuals. However, fulfilling this potential remains a practical challenge due to computational complexity and visual quality issues. We…
Let f be a germ of holomorphic diffeomorphism with an irra- tionally indifferent fixed point at the origin in C (i.e. f(0) = 0, f'(0) = e 2pi i alpha, alpha in R - Q). Perez-Marco showed the existence of a unique family of nontrivial…
We use molecular dynamics to study the ordering of a nematic liquid crystal around a spherical particle or droplet. Homeotropic boundary conditions and strong anchoring create a hedgehog director configuration on the particle surface and in…
The evolution of two species with different fitness is investigated on degree-heterogeneous graphs. The population evolves either by one individual dying and being replaced by the offspring of a random neighbor (voter model (VM) dynamics)…
Situated Visualization is an emerging field that unites several areas - visualization, augmented reality, human-computer interaction, and internet-of-things, to support human data activities within the ubiquitous world. Likewise, dashboards…
We propose approaches based on deep learning to localize objects in images when only a small training dataset is available and the images have low quality. That applies to many problems in medical image processing, and in particular to the…
How to extract useful insights from data is always a challenge, especially if the data is multidimensional. Often, the data can be organized according to certain hierarchical structure that are stemmed either from data collection process or…
Hypergraphs, increasingly utilised for modelling complex and diverse relationships in modern networks, gain much attention representing intricate higher-order interactions. Among various challenges, cohesive subgraph discovery is one of the…
In this paper, we are concerned with studying the existence of invariant complex manifolds of two-dimensional holomorphic systems. From the geometric singular perturbation theory we know that if a slow-fast system has associated a normally…
This paper presents a novel method for the reconstruction of high-resolution temporal images in dynamic tomographic imaging, particularly for discrete objects with smooth boundaries that vary over time. Addressing the challenge of limited…
Chaotic dynamics can be quite heterogeneous in the sense that in some regions the dynamics are unstable in more directions than in other regions. When trajectories wander between these regions, the dynamics is complicated. We say a chaotic…
We propose an extension of popular descriptors based on gradient orientation histograms (HOG, computed in a single image) to multiple views. It hinges on interpreting HOG as a conditional density in the space of sampled images, where the…
Homography estimation is an important step in many computer vision problems. Recently, deep neural network methods have shown to be favorable for this problem when compared to traditional methods. However, these new methods do not consider…
One approach to understanding complex data is to study its shape through the lens of algebraic topology. While the early development of topological data analysis focused primarily on static data, in recent years, theoretical and applied…
Cosmography, the study and making of maps of the universe or cosmos, is a field where visual representation benefits from modern three-dimensional visualization techniques and media. At the extragalactic distance scales, visualization is…
We derive the dynamics of several rigid bodies of arbitrary shape in a 2-dimensional inviscid and incompressible fluid, whose vorticity field is given by point vortices. We adopt the idea of Vankerschaver et al. (2009) to derive the…
A finite dimensional system with a quadratic Hamiltonian constraint is Dirac quantized in holomorphic, antiholomorphic and mixed representations. A unique inner product is found by imposing Hermitian conjugacy relations on an operator…
Conceptual design relies on extensive manipulation of morphological properties of real or virtual objects.This study investigates the nature of the perceptual information that could be retrieved from different representation modalities to…
Heterogeneous object modelling is an emerging area where geometric shapes are considered in concert with their internal physically-based attributes. This paper describes a novel theoretical and practical framework for modelling volumetric…
In this paper we consider aspects of geometric observability for hypergraphs, extending our earlier work from the uniform to the nonuniform case. Hypergraphs, a generalization of graphs, allow hyperedges to connect multiple nodes and…