Related papers: Math and Dance: Notes from emerging interaction
Face-to-face interactions reveal recurring patterns, suggesting the possibility of shared underlying mechanisms. More specifically, inter-contact durations, contact durations and number of contacts per edge share similar heavy-tail…
Human action is naturally compositional: humans can easily recognize and perform actions with objects that are different from those used in training demonstrations. In this paper, we study the compositionality of action by looking into the…
When two pedestrians approach each other on the sidewalk head-on, they sometimes engage in an awkward interaction, both deviating to the same side (repeatedly) to avoid a collision. This phenomenon is known as the sidewalk salsa. Although…
Choreography extraction deals with the generation of a choreography (a global description of communication behaviour) from a set of local process behaviours. In this work, we implement a previously proposed theory for extraction and show…
We put forward a conjecture of recurrence for a gas of hard spheres that collide elastically in a finite volume. The dynamics consists of a sequence of instantaneous binary collisions. We study how the numbers of collisions of different…
In this paper, for the spatial Newtonian $2n$-body problem with equal masses, by proving the minimizers of the action functional under certain symmetric, topological and monotone constraints are collision-free, we found a family of spatial…
There has been an everlasting discussion around the concept of form in music. This work is motivated by such debate by using a complex systems framework in which we study the form as an emergent property of rhythm. Such a framework…
The space-time (s-t) algebra provides a mathematical model for communication and computation using values encoded as events in discretized linear (Newtonian) time. Consequently, the input-output behavior of s-t algebra and implemented…
We consider interacting dark matter-dark energy models arising out of a general interaction term $Q=f(\rho_{m},\rho_{d},\dot{\rho}_{m},\dot{\rho}_{d}).$ Here $f$ is a functional relation connecting the energy densities $\rho_{m}$ and…
This essay provides a critical overview of the mathematical kinetic theory of active particles, which is used to model and study collective systems consisting of interacting living entities, such as those involved in behavior and evolution.…
Mechanics studies the relationships between space, time, and matter, which can be expressed in terms of the dimensions of length $\mathcal{L}$, time $\mathcal{T}$, and mass $\mathcal{M}$. Each dimension broadens the scope of mechanics, from…
The dynamical history of most merging galaxies is not well understood. Correlations between galaxy interaction and star formation have been found in previous studies, but require the context of the physical history of merging systems for…
Early research in aerodynamics and biological propulsion was dramatically advanced by the analytical solutions of Theodorsen, von K\'{a}rm\'{a}n, Wu and others. While these classical solutions apply only to isolated swimmers, the flow…
This research extends a method previously applied to music and philosophy,representing the evolution of art as a time-series where relations like dialectics are measured quantitatively. For that, a corpus of paintings of 12 well-known…
We describe DANCE^2, an interactive dance performance in which audience members channel their collective agency into a dancer-robot duet by voting on the behavior of a wearable robot affixed to the dancer's body. At key moments during the…
This work presents computational methods for transferring body movements from one person to another with videos collected in the wild. Specifically, we train a personalized model on a single video from the Internet which can generate videos…
Physicists have recently begun doing research in finance, and even though this movement is less than five years old, interesting and useful contributions have already emerged. This article reviews these developments in four areas, including…
Mathematicians occasionally discover interesting truths even when they are playing with mathematical ideas with no thoughts about possible consequences of their actions. This paper describes two specific instances of this phenomenon. The…
This article describes a project called ReShape in which we created and designed a crowdsourced art initiative, inspired and powered by mathematics.
Human activity, which usually consists of several actions, generally covers interactions among persons and or objects. In particular, human actions involve certain spatial and temporal relationships, are the components of more complicated…