Related papers: Oral Billiards
We investigate certain word-construction games with variable turn orders. In these games, Alice and Bob take turns on choosing consecutive letters of a word of fixed length, with Alice winning if the result lies in a predetermined target…
We consider the free motion of a point particle inside a circular billiard with periodically moving boundary, with the assumption that the collisions of the particle with the boundary are elastic so that the energy of the particle is not…
A class of Hamiltonian impact systems exhibiting smooth near integrable behavior is presented. The underlying unperturbed model investigated is an integrable, separable, 2 degrees of freedom mechanical impact system with effectively bounded…
We investigate the motion of a hard cylinder rolling down a soft inclined plane. The cylinder is subjected to a viscous drag force and stochastic fluctuations due to the surrounding medium. In a wide range of parameters we observe…
We propose a model of the speech perception of individual words in the presence of mishearings. This phenomenological approach is based on concepts used in linguistics, and provides a formalism that is universal across languages. We put…
We introduce an algebraic formulation of billiards on plane curves over algebraically closed fields, extending Glutsyuk's complex billiards. For any smooth algebraic curve $C$ of degree $d \geq 2$, algebraic billiards is a rational…
We define an alphabet, the IHA, of the 10-D phonetic-prosodic space. The dimensions of this space are perceptual observables, rather than articulatory specifications. Speech is defined as a random chain in time of the 4-D phonetic subspace,…
The article studies a generalization of the elliptic billiard to the complex domain. We show that the billiard orbits also have caustics, and that the number of such caustics is bigger than for the real case. For example, for a given…
We present a model of speech perception which takes into account effects of correlations between sounds. Words in this model correspond to the attractors of a suitably chosen descent dynamics. The resulting lexicon is rich in short words,…
As the most public component of the Supreme Court's decision-making process, oral argument receives an out-sized share of attention in the popular media. Despite its prominence, however, the basic function and operation of oral argument as…
We introduce language-based games, a generalization of psychological games [6] that can also capture reference-dependent preferences [7]. The idea is to extend the domain of the utility function to situations, maximal consistent sets in…
We study finite two dimensional spin lattices with definite geometry (spin billiards) demonstrating the display of collective integrable or chaotic dynamics depending on their shape. We show that such systems can be quantum simulated by…
Human languages evolve continuously, and a puzzling problem is how to reconcile the apparent robustness of most of the deep linguistic structures we use with the evidence that they undergo possibly slow, yet ceaseless, changes. Is the state…
Systems of pinned billiard balls serve as simplified models of collisions, where all particles remain fixed in their positions while their (pseudo-)velocities evolve in accordance with the laws of conservation of energy and momentum. For…
Unsupervised speech representation learning has shown remarkable success at finding representations that correlate with phonetic structures and improve downstream speech recognition performance. However, most research has been focused on…
Prompted models have demonstrated impressive few-shot learning abilities. Repeated interactions at test-time with a single model, or the composition of multiple models together, further expands capabilities. These compositions are…
We construct an autonomous chaotic Hamiltonian ratchet as a channel billiard subdivided by equidistant walls attached perpendicularly to one side of the channel, leaving an opening on the opposite side. A static homogeneous magnetic field…
Rigid bodies collision maps in dimension two, under a natural set of physical requirements, can be classified into two types: the standard specular reflection map and a second which we call, after Broomhead and Gutkin, no-slip. This leads…
We show that the complexity of the billiard in a typical polygon grows cubically and the number of saddle connections grows quadratically along certain subsequences. It is known that the set of points whose first n-bounces hits the same…
Recently, there has been increasing interest in transparency and interpretability in Deep Reinforcement Learning (DRL) systems. Verbal explanations, as the most natural way of communication in our daily life, deserve more attention, since…