Related papers: Knots, Music and DNA
We analyze the connections between the mathematical theory of knots and quantum physics by addressing a number of algorithmic questions related to both knots and braid groups. Knots can be distinguished by means of `knot invariants', among…
This is a report on aspects of the theory and use of monoidal categories. The first section introduces the main concepts through the example of the category of vector spaces. String notation is explained and shown to lead naturally to a…
Sound and movement are closely coupled, particularly in dance. Certain audio features have been found to affect the way we move to music. Is this relationship between sound and movement something which can be modelled using machine…
Knots and knotted fields enrich physical phenomena ranging from DNA and molecular chemistry to the vortices of fluid flows and textures of ordered media. Liquid crystals provide an ideal setting for exploring such topological phenomena…
Initiating a quest to unravel the complexities of musical aesthetics through the lens of information dynamics, our study delves into the realm of musical sequence modeling, drawing a parallel between the sequential structured nature of…
We make use of the 3D nature of knots and links to find savings in computational complexity when computing knot invariants such as the linking number and, in general, most finite type invariants. These savings are achieved in comparison…
We investigate correlations among pitches in several songs and pieces of piano music by mapping them to one-dimensional walks. Two kinds of correlations are studied, one is related to the real values of frequencies while they are treated…
We consider countable linear orders and study the quasi-order of convex embeddability and its induced equivalence relation. We obtain both combinatorial and descriptive set-theoretic results, and further extend our research to the case of…
Studying the history of music may provide a glimpse into the development of human creativity as we examine the evolutionary and revolutionary trends in music and genres. First, a musical influence metric was created to construct a directed…
Much like most of cognition research, music cognition is an interdisciplinary field, which attempts to apply methods of cognitive science (neurological, computational and experimental) to understand the perception and process of composition…
We provide various formulations of knot homology that are predicted by string dualities. In addition, we also explain the rich algebraic structure of knot homology which can be understood in terms of geometric representation theory in these…
We give a number theoretic proof of the integrality of certain BPS invariants of knots. The formulas for these numbers are sums involving binomial coefficients and the M\"obius function. We also prove a conjecture about further divisibility…
All known life forms are based upon a hierarchy of interwoven feedback loops, operating over a cascade of space, time and energy scales. Among the most basic loops are those connecting DNA and proteins. For example, in genetic networks, DNA…
Music segmentation refers to the dual problem of identifying boundaries between, and labeling, distinct music segments, e.g., the chorus, verse, bridge etc. in popular music. The performance of a range of music segmentation algorithms has…
Long, flexible physical filaments are naturally tangled and knotted, from macroscopic string down to long-chain molecules. The existence of knotting in a filament naturally affects its configuration and properties, and may be very stable or…
I present a summary of the recent progress made in field and string theory which has led to a reformulation of quantum-group polynomial invariants for knots and links into new polynomial invariants whose coefficients can be described in…
We consider several classes of knotted objects, namely usual, virtual and welded pure braids and string links, and two equivalence relations on those objects, induced by either self-crossing changes or self-virtualizations. We provide a…
To many people, music is a mystery. It is uniquely human, because no other species produces elaborate, well organized sound for no particular reason. It has been part of every known civilization on earth. It has become a very part of man's…
We show several relations between local moves on 1-dimensional knots and those on high dimensional knots related by products of knots.
Our study delves into the "Embodied Musicking Dataset," exploring the intertwined relationships and correlations between physiological and psychological dimensions during improvisational music performances. The primary objective is to…