Related papers: What's math got to do with patterns in fish?
We introduce the notions of arithmetic colorings and arithmetic flows over a graph with labelled edges, which generalize the notions of colorings and flows over a graph. We show that the corresponding arithmetic chromatic polynomial and…
We introduce and investigate a series of matching problems for patterns with variables under Simon's congruence. Our results provide a thorough picture of these problems' computational complexity.
Substances such as chemical compounds are invisible to human eyes, they are usually captured by sensing equipments with their spectral fingerprints. Though spectra of pure chemicals can be identified by visual inspection, the spectra of…
We consider edge colorings of a graph in such a way that each two different triangles have distinct colorings. It is an extension of the well-known idea of distinguishing all maximal stars in a graph. It was introduced in literature in 1985…
Underwater object detection is critical for monitoring marine ecosystems but poses unique challenges, including degraded image quality, imbalanced class distribution, and distinct visual characteristics. Not every species is detected…
Repair and maintenance of underwater structures as well as marine science rely heavily on the results of underwater object detection, which is a crucial part of the image processing workflow. Although many computer vision-based approaches…
Edge-matching problems, also called edge matching puzzles, are abstractions of placement problems with neighborhood conditions. Pieces with colored edges have to be placed on a board such that adjacent edges have the same color. The problem…
In many societies, appearing slim is considered attractive. The fashion industry has been attempting to cater to this trend by designing outfits that can enhance the appearance of slimness. Two anecdotal rules, widespread in the world of…
This paper presents a stochastic differential equation model for describing the process of fish schooling. The model equation always possesses a unique local solution, but global existence can be shown only in some particular cases. Some…
In this letter, we analyze the evolution of physical quantities due to the interaction of strings with background fields. We will obtain the characteristic function for such a string theoretical process. This will be done by generalizing…
Objects moving in fluids experience patterns of stress on their surfaces determined by their motion and the geometry of nearby boundaries. Fish and underwater robots can use these patterns for navigation. This paper extends this…
Recognising and locating image patches or sets of image features is an important task underlying much work in computer vision. Traditionally this has been accomplished using template matching. However, template matching is notoriously…
Biologists have long sought a way to explain how statistical properties of genetic sequences emerged and are maintained through evolution. On the one hand, non-random structures at different scales indicate a complex genome organisation. On…
Ramsey Theory deals with avoiding certain patterns. When constructing an instance that avoids one pattern, it is observed that other patterns emerge. For example, repetition emerges when avoiding arithmetic progression (Van der Waerden…
A tiling is a cover of R^d by tiles such as polygons that overlap only on their borders. A patch is a configuration consisting of finitely many tiles that appears in tilings. From a tiling, we can construct a dynamical system which encodes…
One-dimensional stellar evolution models have been successful at representing the structure and evolution of stars in diverse astrophysical contexts, but complications have been noted in the context of young, magnetically active stars, as…
Spatial distribution of the human population is distinctly heterogeneous, e.g. showing significant difference in the population density between urban and rural areas. In the historical perspective, i.e. on the timescale of centuries, the…
This paper introduces a novel approach to data analysis designed for the needs of specialists in psychology of religion. We detect developmental and cross-cultural patterns in children's drawings of God(s) and other supernatural agents. We…
Structural colors are a result of the scattering of certain frequencies of the incident light on micro- or nanoscale features in a material. This is a quite different phenomenon from that of colors produced by absorption of different…
Pattern matching with wildcards is the problem of finding all factors of a text $t$ of length $n$ that match a pattern $x$ of length $m$, where wildcards (characters that match everything) may be present. In this paper we present a number…