Related papers: What's math got to do with patterns in fish?
A variety of computational models have been developed to describe active matter at different length and time scales. The diversity of the methods and the challenges in modeling active matter---ranging from molecular motors and cytoskeletal…
Using high resolution hydrodynamical cosmological simulations, we conduct a comprehensive study of how tidal stripping removes dark matter and stars from galaxies. We find that dark matter is always stripped far more significantly than the…
This is a report on our ongoing research on a combinatorial approach to knot recognition, using coloring of knots by certain algebraic objects called quandles. The aim of the paper is to summarize the mathematical theory of knot coloring in…
Calculations of frequency spectra for organic molecular crystals taking various defects in their structure into account are carried out. It is shown how the presence of the vacancies, orientation disorder, and surface presence affects…
These patterns describe the strategies I use to find novel or unorthodox insights in the area of software design and research. The patterns are driven by inconsistencies between what we say and what we do, and they provide techniques for…
The ocean is filled with microscopic microalgae called phytoplankton, which together are responsible for as much photosynthesis as all plants on land combined. Our ability to predict their response to the warming ocean relies on…
Turing (or double-diffusive) instabilities describe pattern formation in reaction-diffusion systems, and were proposed in 1952 as a potential mechanism behind pattern formation in nature, such as leopard spots and zebra stripes. Because the…
Although Turing pattern is one of the most universal mechanisms for pattern formation, in its standard model the number of stripes changes with the system size, since the wavelength of the pattern is invariant: It fails to preserve the…
We consider the problem of finding a large rainbow matching in a random graph with randomly colored edges. In particular we analyze the performance of two greedy algorithms for this problem. The algorithms we study are colored versions of…
Artificial Intelligence has been developed for decades with the achievement of great progress. Recently, deep learning shows its ability to solve many real world problems, e.g. image classification and detection, natural language…
The torsional oscillation is a well established observational fact and there are theoretical attempts for its description but no final solution has yet been accepted. One of the possible candidates for its cause is the presence of sunspots…
The tidal problem is used to obtain the tidal deformability (or Love number) of stars. The semi-analytical study is usually treated in perturbation theory as a first order perturbation problem over a spherically symmetric background…
Many works have concentrated on visualizing and understanding the inner mechanism of convolutional neural networks (CNNs) by generating images that activate some specific neurons, which is called deep visualization. However, it is still…
We are interested in generating surfaces with arbitrary roughness and forming patterns on the surfaces. Two methods are applied to construct rough surfaces. In the first method, some superposition of wave functions with random frequencies…
Over the last thirty years, numerous consistency conditions for replicated data have been proposed and implemented. Popular examples of such conditions include linearizability (or atomicity), sequential consistency, causal consistency, and…
Graph colouring is a combinatorial optimisation problem with applications in several important domains, including sports scheduling, cartography, street map navigation, and timetabling. It is also of significant theoretical interest and a…
Symmetry can be used to help solve many problems. For instance, Einstein's famous 1905 paper ("On the Electrodynamics of Moving Bodies") uses symmetry to help derive the laws of special relativity. In artificial intelligence, symmetry has…
A perfect matching M in an edge-colored complete bipartite graph K_{n,n} is rainbow if no pair of edges in M have the same color. We obtain asymptotic enumeration results for the number of rainbow matchings in terms of the maximum number of…
It is a well observed phenomenon that natural images are smooth, in the sense that nearby pixels tend to have similar values. We describe a mathematical model of images that makes no assumptions on the nature of the environment that images…
Many natural systems are observed as point patterns in time, space, or space and time. Examples include plant and cellular systems, animal colonies, earthquakes, and wildfires. In practice the locations of the points are not always observed…