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Computational art analysis has, through its reliance on classification tasks, prioritised historical datasets in which the artworks are already well sorted with the necessary annotations. Art produced today, on the other hand, is numerous…
A necklace splitting theorem of Goldberg and West asserts that any k-colored (continuous) necklace can be fairly split using at most k cuts. Motivated by the problem of Erd\H{o}s on strongly nonrepetitive sequences, Alon et al. proved that…
In the early twentieth century, L.E.J. Brouwer pioneered a new philosophy of mathematics, called intuitionism. Intuitionism was revolutionary in many respects but stands out -mathematically speaking- for its challenge of Hilbert's formalist…
The goal of this study was to investigate the translate-ability of creative works into other domains. We tested whether people were able to recognize which works of art were inspired by which pieces of music. Three expert painters created…
The artistic style of a painting is a subtle aesthetic judgment used by art historians for grouping and classifying artwork. The recently introduced `neural-style' algorithm substantially succeeds in merging the perceived artistic style of…
A decomposition principle for nonlinear dynamic compartmental systems is introduced in the present paper. This theory is based on the mutually exclusive and exhaustive, analytical and dynamic, novel system and subsystem partitioning…
For a compact and convex window, Mecke described a process of tessellations which arise from cell divisions in discrete time. At each time step, one of the existing cells is selected according to an equally-likely law. Independently, a line…
One way illustrators engage in disciplined drawing - the process of drawing to improve technical skills - is through studying and replicating reference images. However, for many novice and intermediate digital artists, knowing how to…
Patterns, which are collections of elements arranged in regular or near-regular arrangements, are an important graphic art form and widely used due to their elegant simplicity and aesthetic appeal. When a pattern is encoded as a flat image…
In his Discourse on the Method of Rightly Conducting the Reason, and Seeking Truth in the Sciences, Rene Descartes sought ``clear and certain knowledge of all that is useful in life.'' Almost three centuries later, in ``The foundations of…
When faced with a mathematical model, often the first step is to reduce the complexity of the model by turning variables and parameters into dimensionless quantities. This process is often performed by hand, relying on a skill practiced…
The continuum has been one of the most controversial topics in mathematics since the time of the Greeks. Some mathematicians, such as Euclid and Cantor, held the position that a line is composed of points, while others, like Aristotle, Weyl…
This paper proposes a computational approach for analysis of strokes in line drawings by artists. We aim at developing an AI methodology that facilitates attribution of drawings of unknown authors in a way that is not easy to be deceived by…
Maximal planar graph refers to the planar graph with the most edges, which means no more edges can be added so that the resulting graph is still planar. The Four-Color Conjecture says that every planar graph without loops is 4-colorable.…
Disclinations, first observed in mesomorphic phases, are relevant to a number of ill-ordered condensed matter media, with continuous symmetries or frustrated order. They also appear in polycrystals at the edges of grain boundaries. They are…
Georg Cantor was the genuine discoverer of the Mathematical Infinity, and whatever he claimed, suggested, or even surmised should be taken seriously -- albeit not necessary at its face value. Because alongside his exquisite in beauty…
In this paper we consider the fundamental operations dilation and erosion of mathematical morphology. Many powerful image filtering operations are based on their combinations. We establish homomorphism between max-plus semi-ring of integers…
Image demosaicking and denoising are the first two key steps of the color image production pipeline. The classical processing sequence has for a long time consisted of applying denoising first, and then demosaicking. Applying the operations…
Separating an image into meaningful underlying components is a crucial first step for both editing and understanding images. We present a method capable of selecting the regions of a photograph exhibiting the same material as an…
A modified form of Euclid's algorithm has gained popularity among musical composers following Toussaint's 2005 survey of so-called Euclidean rhythms in world music. We offer a method to easily calculate Euclid's algorithm by hand as a…