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Predicting the ancestral sequences of a group of homologous sequences related by a phylogenetic tree has been the subject of many studies, and numerous methods have been proposed to this purpose. Theoretical results are available that show…
We introduce and study methods for inferring and learning from correspondences among neurons. The approach enables alignment of data from distinct multiunit studies of nervous systems. We show that the methods for inferring correspondences…
This paper explores a novel mathematical approach to extract archaeological insights from ensembles of similar artifact shapes. We show that by considering all the shape information in a find collection, it is possible to identify shape…
Hitomezashi patterns, which originate from traditional Japanese embroidery, are intricate arrangements of unit-length line segments called stitches. The stitches connect to form hitomezashi strands and hitomezashi loops, which divide the…
A codon table is a useful tool for mapping codons to amino acids as they have been assigned by nature. It has become a scientific icon because of the way it embodies our understanding of this natural process and the way it immediately…
A major task of evolutionary biology is the reconstruction of phylogenetic trees from molecular data. The evolutionary model is given by a Markov chain on a tree. Given samples from the leaves of the Markov chain, the goal is to reconstruct…
The question of whether a given region can be successfully filled by a finite set of tiles has been commonly studied, and there are many available arguments for whether a given finite region can be tiled. We can show that there is no domino…
Phylogenetic placement refers to a family of tools and methods to analyze, visualize, and interpret the tsunami of metagenomic sequencing data generated by high-throughput sequencing. Compared to alternative (e. g., similarity-based)…
The stability of social relationships is important to animals living in groups, and social network analysis provides a powerful tool to help characterize and understand their (in)stability and the consequences at the group level. However,…
The analyses of ancient coins, and especially the identification of those struck with the same die, provides invaluable information for archaeologists and historians. Nowadays, these die links are identified manually, which makes the…
Icosoku is a challenging and interesting puzzle that exhibits highly symmetrical and combinatorial nature. In this paper, we pose the questions derived from the puzzle, but with more difficulty and generality. In addition, we also present a…
Phase transitions are a central theme of statistical mechanics, and of probability more generally. Lattice spin models represent a general paradigm for phase transitions in finite dimensions, describing ferromagnets and even some fluids…
Structural stability is a necessary condition for successful construction of an assembly. However, designing a stable assembly requires a non-trivial effort since a slight variation in the design could significantly affect the structural…
Craniofacial reconstruction in forensic science is crucial for the identification of the victims of crimes and disasters. The objective is to map a given skull to its corresponding face in a corpus of faces with known identities using…
Evolomino is a pencil-and-paper logic puzzle published by the Japanese company Nikoli, renowned for culture-independent puzzles such as Sudoku, Kakuro, and Slitherlink. Its name reflects the core mechanic: the polyomino-like blocks drawn by…
This paper presents a survey of the khipu-based enumeration system of the Incas. In this system, different knots are tied together and they are attached to a primary cord. The numerical basis of the khipu system is well understood but more…
We take the occasion of this article to review one hundred years of the physical and mathematical study of the Ising model. The model, introduced by Lenz in 1920, has been at the cornerstone of many major revolutions in statistical…
The investigation of the relation among the distances of an arbitrary point in the Euclidean space $\mathbb{R}^n$ to the vertices of a regular $n$-simplex in that space has led us to the study of simplices having a regular facet. Calling an…
The study of cultural artifact provenance, tracing ownership and preservation, holds significant importance in archaeology and art history. Modern technology has advanced this field, yet challenges persist, including recognizing evidence…
In this article we study domino tilings of a family of finite regions called Aztec diamonds. Every such tiling determines a partition of the Aztec diamond into five sub-regions; in the four outer sub-regions, every tile lines up with nearby…