Related papers: What's math got to do with patterns in fish?
We revisit the game in which each of several players chooses a pattern and then a coin is flipped repeatedly until one of these patterns is generated. In particular, we demonstrate how to compute the probability of any one player winning…
The problem of neural coding is to understand how sequences of action potentials (spikes) are related to sensory stimuli, motor outputs, or (ultimately) thoughts and intentions. One clear question is whether the same coding rules are used…
Do fish respond to the presence of underwater vehicles, potentially biasing our estimates about them? If so, are there strategies to measure and mitigate this response? This work provides a theoretical and practical framework towards…
This paper is about the design of an automated machine to cut turbot fish specimens. Machine vision is a key part of this project as it is used to compute a cutting curve for the specimen head. This task is impossible to be carried out by…
Rainbows and boat wakes may seem unrelated, but they share deep mathematical connections through ray folding, caustics, and Airy interference. This paper explores these principles, which are also relevant for explaining phenomena such as…
Popularized explanations of the color of the sea often prove to be incomplete or oversimplified, and hence inadequate to become acquainted with the phenomenon in its whole. In this paper, after a historical review of the investigations on…
Data classification is present in different real problems, such as recognizing patterns in images, differentiating defective parts in a production line, classifying benign and malignant tumors, among many others. Many of these problems have…
Jigsaw puzzle solving is an intriguing problem which has been explored in computer vision for decades. This paper focuses on a specific variant of the problem - solving puzzles with eroded boundaries. Such erosion makes the problem…
One of the most highly debated questions in the field of animal swarming and social behaviour, is the collective random patterns and chaotic behaviour formed by some animal species, in particular if there is a danger. Is such a behaviour…
A graph is a data structure composed of dots (i.e. vertices) and lines (i.e. edges). The dots and lines of a graph can be organized into intricate arrangements. The ability for a graph to denote objects and their relationships to one…
Social behavior across animal species ranges from simple pairwise interactions to thousands of individuals coordinating goal-directed movements. Regardless of the scale, these interactions are governed by the interplay between multimodal…
A Markovian lattice model for photoreceptor cells is introduced to describe the growth of mosaic patterns on fish retina. The radial stripe pattern observed in wild-type zebrafish is shown to be selected naturally during the retina growth,…
NP-complete problems should be hard on some instances but those may be extremely rare. On generic instances many such problems, especially related to random graphs, have been proven easy. We show the intractability of random instances of a…
Artists spent a great deal of time studying anatomy for precise rendering of the human body as well as light, shadows, and perspective for convincing representation of the three-dimensional world. But in many paintings, they also had to…
Symmetry is a key feature observed in nature (from flowers and leaves, to butterflies and birds) and in human-made objects (from paintings and sculptures, to manufactured objects and architectural design). Rotational, translational, and…
Coral bleaching is a major concern for marine ecosystems; more than half of the world's coral reefs have either bleached or died over the past three decades. Increasing sea surface temperatures, along with various spatiotemporal…
Given a graph on $n$ vertices and an assignment of colours to the edges, a rainbow Hamilton cycle is a cycle of length $n$ visiting each vertex once and with pairwise different colours on the edges. Similarly (for even $n$) a rainbow…
Statistical pattern recognition methods based on the Coherence Length Diagram (CLD) have been proposed for medical image analyses, such as quantitative characterisation of human skin textures, and for polarized light microscopy of liquid…
Suppose one desires to randomly sample a pair of objects such as socks, hoping to get a matching pair. Even in the simplest situation for sampling, which is sampling with replacement, the innocent phrase "the distribution of the color of a…
Can the cross product be generalized? Why are the trace and determinant so important in matrix theory? What do all the coefficients of the characteristic polynomial represent? This paper describes a technique for `doodling' equations from…