Related papers: What's math got to do with patterns in fish?
Circular coloring is a constraints satisfaction problem where colors are assigned to nodes in a graph in such a way that every pair of connected nodes has two consecutive colors (the first color being consecutive to the last). We study…
The field of robotics faces inherent challenges in manipulating deformable objects, particularly in understanding and standardising fabric properties like elasticity, stiffness, and friction. While the significance of these properties is…
We consider pattern formation using reaction-diffusion equation on various non-uniformly curved surfaces. We explore how, in general, curvature and, in particular the domain shape would affect the pattern formation in these geometries. As…
A first step in investigating colour symmetries of periodic and nonperiodic patterns is determining the number of colours which allow perfect colourings of the pattern under consideration. A perfect colouring is one where each symmetry of…
Knot colorings are one of the simplest ways to distinguish knots, dating back to Reidemeister, and popularized by Fox. In this mostly expository article, we discuss knot invariants like colorability, knot determinant and number of…
Real-world systems are often complex, dynamic, and nonlinear. Understanding the dynamics of a system from its observed time series is key to the prediction and control of the system's behavior. While most existing techniques tacitly assume…
Empirical data reveals a broad variety of hull shapes among the different ship categories. We present a minimal theoretical approach to address the problem of ship hull optimisation. We show that optimal hull aspect ratios result -- at…
We consider a certain tiling problem of a planar region in which there are no long horizontal or vertical strips consisting of copies of the same tile. Intuitively speaking, we would like to create a dappled pattern with two or more kinds…
In his 1952 paper "The chemical basis of morphogenesis", Alan M. Turing presented a model for the formation of skin patterns. While it took several decades, the model has been validated by finding corresponding natural phenomena, e.g. in…
We present some results on the proportion of permutations of length $n$ containing certain mesh patterns as $n$ grows large, and give exact enumeration results in some cases. In particular, we focus on mesh patterns where entire rows and…
Patterns and nonlinear waves, such as spots, stripes, and rotating spirals, arise prominently in many natural processes and in reaction-diffusion models. Our goal is to compute boundaries between parameter regions with different prevailing…
Many species of phytoplankton migrate vertically near the surface of the ocean, either in search of light or nutrients. These motile organisms are affected by ocean waves at the surface. We derive a set of wave-averaged equations to…
The recognition of coral species based on underwater texture images pose a significant difficulty for machine learning algorithms, due to the three following challenges embedded in the nature of this data: 1) datasets do not include…
In this paper, we present a simplified framework to represent competition, coordination and bargaining in fisheries when they operate under financial and technological constraints. Competition within constraints leads to a particular type…
By means of the direct numerical simulation of directional waves on the surface of deep water it is shown that extreme waves can exhibit such asymmetry that the occurrence of deeper troughs is several times more likely on the wave rear…
Numerical simulations of starlight that is reflected by Earth-like exoplanets predict habitability signatures that can be searched for with future telescopes. We explore signatures of water oceans in the flux and polarization spectra of…
The goal of this paper is to present a generic multi-region nonlinear age-size structured fish population model, and to assess its mathematical well-posedness. An initial-boundary-value problem is formulated. Existence and uniqueness of a…
An edge-coloring of a graph $G$ with consecutive integers $c_{1},\ldots,c_{t}$ is called an \emph{interval $t$-coloring} if all colors are used, and the colors of edges incident to any vertex of $G$ are distinct and form an interval of…
A classical question in combinatorial number theory asks whether an equation has a solution inside a particular subset of its domain. The Rado's Theorem gives a set of necessary and sufficient conditions for a systems of linear equations to…
In the W-streaming model, an algorithm is given $O(n \mathrm{polylog} n)$ space and must process a large graph of up to $O(n^2)$ edges. In this short note we give two algorithms for edge colouring under the W-streaming model. For edge…