Related papers: A Chaotic Dynamical System that Paints
This paper presents an algorithm that transforms color visual images, like photographs or paintings, into tactile graphics. In the algorithm, the edges of objects are detected and colors of the objects are estimated. Then, the edges and the…
Dynamical networks are important models for the behaviour of complex systems, modelling physical, biological and societal systems, including the brain, food webs, epidemic disease in populations, power grids and many other. Such dynamical…
We present an approach to learn the dynamics of multiple objects from image sequences in an unsupervised way. We introduce a probabilistic model that first generate noisy positions for each object through a separate linear state-space…
By analysing an n-dimensional generalisation of Thomas's cyclically symmetric attractor we find that this chaotic dynamical system behaves like a random walk constrained onto the surface of a hypersphere. The growth of error is limited,…
Monte Carlo algorithms, such as Markov chain Monte Carlo (MCMC) and Hamiltonian Monte Carlo (HMC), are routinely used for Bayesian inference in generalized linear models; however, these algorithms are prohibitively slow in massive data…
Inpainting is the technique of reconstructing unknown or damaged portions of an image in a visually plausible way. Inpainting algorithm automatically fills the damaged region in an image using the information available in undamaged region.…
Paint marbling refers to techniques for creating intricate designs in colored paints floating on a liquid surface. If the marbling motions are executed slowly, then this layer of paints can be modeled as a two-dimensional incompressible…
Optomechanical systems attract a lot of attention because they provide a novel platform for quantum measurements, transduction, hybrid systems, and fundamental studies of quantum physics. Their classical nonlinear dynamics is surprisingly…
We construct a data-driven dynamical system model for a macroscopic variable the Reynolds number of a high-dimensionally chaotic fluid flow by training its scalar time-series data. We use a machine-learning approach, the reservoir computing…
Identification of nonlinear systems is a challenging problem. Physical knowledge of the system can be used in the identification process to significantly improve the predictive performance by restricting the space of possible mappings from…
Leveraging recent work on data-driven methods for constructing a finite state space Markov process from dynamical systems, we address two problems for obtaining further reduced statistical representations. The first problem is to extract…
A panoramic image mosaic is an attractive visualization for viewing many overlapping photos, but its images must be both captured and processed correctly to produce an acceptable composite. We propose Swipe Mosaics, an interactive…
Sequence modeling with neural networks has lead to powerful models of symbolic music data. We address the problem of exploiting these models to reach creative musical goals, by combining with human input. To this end we generalise previous…
The problem of representative selection amounts to sampling few informative exemplars from large datasets. This paper presents MOSAIC, a novel representative selection approach from high-dimensional data that may exhibit non-linear…
The emergence of hydrodynamics is one of the deepest phenomena in many-body systems. Arguably, the hydrodynamic equations are also the most important tools for predicting large-scale behaviour. Understanding how such equations emerge from…
We study the dynamical properties of a broad class of high-dimensional random dynamical systems exhibiting chaotic as well as fixed point and periodic attractors. We consider cases in which attractors can co-exists in some regions of the…
Exploring chaotic systems via Poincar\'e sections has proven essential in dynamical systems, yet measuring their characteristics poses challenges to identify the various dynamical regimes considered. In this paper, we propose a new approach…
Many large scale problems in computational fluid dynamics such as uncertainty quantification, Bayesian inversion, data assimilation and PDE constrained optimization are considered very challenging computationally as they require a large…
We study the problem of synthesizing a number of likely future frames from a single input image. In contrast to traditional methods that have tackled this problem in a deterministic or non-parametric way, we propose to model future frames…
In various fields of natural science, the chaotic systems of differential equations are considered more than 50 years. The correct prediction of the behaviour of solutions of dynamical model equations is important in understanding of…