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The article provides a pedagogical review aimed at graduate students in materials science, physics, and applied mathematics, focusing on recent developments in the subject. Following a brief summary of concepts from complex analysis, the…
In this paper, we develop several tools to study the degree growth and stabilization of monomial maps. Using these tools, we can classify semisimple three dimensional monomial maps by their dynamical behavior.
Diffusion maps approximate the generator of Langevin dynamics from simulation data. They afford a means of identifying the slowly-evolving principal modes of high-dimensional molecular systems. When combined with a biasing mechanism,…
Many intelligent user interfaces employ application and user models to determine the user's preferences, goals and likely future actions. Such models require application analysis, adaptation and expansion. Building and maintaining such…
State transition algorithm (STA) has been emerging as a novel stochastic method for global optimization in recent few years. To make better understanding of continuous STA, a matlab toolbox for continuous STA has been developed. Firstly,…
Recent improvements in the expressive power of spatio-temporal models have led to performance gains in many real-world applications, such as traffic forecasting and social network modelling. However, understanding the predictions from a…
Motion planning in modified environments is a challenging task, as it compounds the innate difficulty of the motion planning problem with a changing environment. This renders some algorithmic methods such as probabilistic roadmaps less…
Spatial Transcriptomics (ST) enables the measurement of gene expression while preserving spatial information, offering critical insights into tissue architecture and disease pathology. Recent developments have explored the use of…
Vision-language foundation models such as CLIP have achieved tremendous results in global vision-language alignment, but still show some limitations in creating representations for specific image regions. % To address this problem, we…
Data modeling and graphing skill sets are foundational to science learning and careers, yet students regularly struggle to master these basic competencies. Further, although educational researchers have uncovered numerous approaches to…
We introduce Tilt Map, a novel interaction technique for intuitively transitioning between 2D and 3D map visualisations in immersive environments. Our focus is visualising data associated with areal features on maps, for example, population…
Enhancing the fine-grained instance spatiotemporal motion perception capabilities of Video Large Language Models is crucial for improving their temporal and general video understanding. However, current models struggle to perceive detailed…
In many contexts, creating mappings for gestural interactions can form part of an artistic process. Creators seeking a mapping that is expressive, novel, and affords them a sense of authorship may not know how to program it up in a signal…
We derive a sufficient condition for stability in probability of an equilibrium of a randomly perturbed map in ${\mathbb R}^d$. This condition can be used to stabilize weakly unstable equilibria by random forcing. Analytical results on…
IVISIT is a generic interactive visual simulation tool that is based on Python/Numpy and can be used for system simulation, parameter optimization, parameter management, and visualization of system dynamics as required, for example,for…
One key task in environmental science is to map environmental variables continuously in space or even in space and time. Machine learning algorithms are frequently used to learn from local field observations to make spatial predictions by…
Multiscale magnetic simulations, including micromagnetic and atomistic spin dynamics simulations, are widely used in the study of complex magnetic systems over a wide range of spatial and temporal scales. The advances in these simulation…
Motivation: The visualization and analysis of high-dimensional data are essential in biomedical research. There is a need for secure, scalable, and reproducible tools to facilitate data exploration and interpretation. Results: We introduce…
In this work, we begin the study of a new class of dynamical systems determined by interval maps generated by the symbolic action of erasing substitution rules. We do this by discussing in some detail the geometric, analytical, dynamical…
We describe a method of control of chaos that occurs in area-preserving maps. This method is based on small modifications of the original map by addition of a small control term. We apply this control technique to the standard map and to…