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Phylogenetic networks extend phylogenetic trees to allow for modeling reticulate evolutionary processes such as hybridization. They take the shape of a rooted, directed, acyclic graph, and when parameterized with evolutionary parameters,…
Given the ubiquitous nature of numbers in text, reasoning with numbers to perform simple calculations is an important skill of AI systems. While many datasets and models have been developed to this end, state-of-the-art AI systems are…
Chinese paleography, the study of ancient Chinese writing, is undergoing a computational turn powered by artificial intelligence. This position paper charts the trajectory of this emerging field, arguing that it is evolving from automating…
In special coordinates (codon position--specific nucleotide frequencies) bacterial genomes form two straight lines in 9-dimensional space: one line for eubacterial genomes, another for archaeal genomes. All the 348 distinct bacterial…
This paper aims to give a brief account of the mathematical work of the 7th-century Armenian polymath and natural philosopher Anania Shirakatsi. The three sections of Anania's ``Book of Arithmetic'' -- tables of arithmetic operations, a…
Humans have the ability to reason about geometric patterns in images and scenes from a young age. However, developing large multimodal models (LMMs) capable of similar reasoning remains a challenge, highlighting the need for robust…
By c. 3000 BC, in the late Neolithic, there had been a significant change in the way people materialized their cosmology across Scotland with the introduction of free-standing stones. These were erected almost until the end of the Bronze…
A novel model, devised to describe spontaneous chirality synchronization in complex liquids and liquid crystals, is proposed and studied. Segments of ribbon-like molecular columns with left- or right-handed 180degree twist lie on the bonds…
We study pairwise Ising models for describing the statistics of multi-neuron spike trains, using data from a simulated cortical network. We explore efficient ways of finding the optimal couplings in these models and examine their…
Ice cores provide insight into the past climate over many millennia. Due to ice compaction, the raw data for any single core are irregular in time. Multiple cores have different irregularities; jointly these series are misaligned. After…
The study of knot mosaics is based upon representing knot diagrams using a set of tiles on a square grid. This branch of knot theory has many unanswered questions, especially regarding the efficiency with which we draw knots as mosaics.…
Die analysis is an essential numismatic method, and an important tool of ancient economic history. Yet, manual die studies are too labor-intensive to comprehensively study large coinages such as those of the Roman Empire. We address this…
A systematic procedure to numerically compute a horseshoe map is presented. This new method uses piecewise functions and expresses the required operations by means of elementary transformations, such as translations, scalings, projections…
Discrete rearranging patterns include cellular patterns, for instance liquid foams, biological tissues, grains in polycrystals; assemblies of particles such as beads, granular materials, colloids, molecules, atoms; and interconnected…
Talk 1: Open problems in knot theory that everyone can try to solve. Knot theory is more than two hundred years old; the first scientists who considered knots as mathematical objects were A.Vandermonde (1771) and C.F.Gauss (1794). However,…
A desarrangement is a permutation whose first ascent is even. Desarrangements were introduced in the 1980s by Jacques D\'{e}sarm\'{e}nien, who proved that they are in bijection with derangements. We revisit the study of desarrangements,…
Polynomial partitioning techniques have recently led to improved geometric data structures for a variety of fundamental problems related to semialgebraic range searching and intersection searching in 3D and higher dimensions (e.g., see…
A consistent interpretation is provided for Neolithic Gobekli Tepe and Catalhoyuk as well as European Palaeolithic cave art. It appears they all display the same method for recording dates based on precession of the equinoxes, with animal…
When algorithmic skeletons were first introduced by Cole in late 1980 the idea had an almost immediate success. The skeletal approach has been proved to be effective when application algorithms can be expressed in terms of skeletons…
We describe a sketch interpretation system that detects and classifies clock numerals created by subjects taking the Clock Drawing Test, a clinical tool widely used to screen for cognitive impairments (e.g., dementia). We describe how it…