Related papers: Oral Billiards
Generative Spoken Language Modeling research focuses on optimizing speech Language Models (LMs) using raw audio recordings without accessing any textual supervision. Such speech LMs usually operate over discrete units obtained from…
We describe an exponential Fermi accelerator in a two-dimensional billiard with a moving slit. We have found a mechanism of trapping regions which provides the exponential acceleration for almost all initial conditions with sufficiently…
Machine learning methods have significantly improved in their predictive capabilities, but at the same time they are becoming more complex and less transparent. As a result, explainers are often relied on to provide interpretability to…
The paper presents a language model that develops syntactic structure and uses it to extract meaningful information from the word history, thus enabling the use of long distance dependencies. The model assigns probability to every joint…
We derive an explicit expression for the coupling constants of individual eigenstates of a closed billiard which is opened by attaching a waveguide. The Wigner time delay and the resonance positions resulting from the coupling constants are…
We propose an unsupervised neural model for learning a discrete embedding of words. Unlike existing discrete embeddings, our binary embedding supports vector arithmetic operations similar to continuous embeddings. Our embedding represents…
The classical inner and outer billiards can be formulated in variational terms, with length and area as the respective generating functions. The other two combinations, ``inner with area'' and ``outer with length,'' are more recently…
If language evolved by sexual selection to display superior intelligence, then we require conversational skills, to impress other people, gain high social status, and get a mate. Conversational skills include a Theory of Mind, a sense of…
The Random Language Model (De Giuli 2019) is an ensemble of stochastic context-free grammars, quantifying the syntax of human and computer languages. The model suggests a simple picture of first language learning as a type of annealing in…
This paper presents a modeling study of the way speech motor control can deal with gravity to achieve steady-state tongue positions. It is based on simulations carried out with the 3D biomechanical tongue model developed at ICP, which is…
A billiard is a dynamical system in which a particle alternates between motion in a straight line and specular reflection from a boundary. For billiards in non-convex areas bounded by segments of confocal quadrics are studied. The topology…
We study some statistical properties for the behavior of the average squared velocity -- hence the temperature -- for an ensemble of classical particles moving in a billiard whose boundary is time dependent. We assume the collisions of the…
The notion of a rough two-dimensional (convex) body is introduced, and to each rough body there is assigned a measure on $\TTT^3$ describing billiard scattering on the body. The main result is characterization of the set of measures…
Writing is a universal cultural technology that reuses vision for symbolic communication. Humans display striking resilience: we readily recognize words even when characters are fragmented, fused, or partially occluded. This paper…
We demonstrate that the free motion of any two-dimensional rigid body colliding elastically with two parallel, flat walls is equivalent to a billiard system. Using this equivalence, we analyze the integrable and chaotic properties of this…
We consider the outer billiards map with contraction outside polygons. We construct a 1-parameter family of systems such that each system has an open set in which the dynamics is reduced to that of a piecewise contraction on the interval.…
We study stochastic billiards on general tables: a particle moves according to its constant velocity inside some domain ${\mathcal D} \subset {\mathbb R}^d$ until it hits the boundary and bounces randomly inside according to some reflection…
Multidimensional model describing the cosmological evolution of n Einstein spaces in the theory with l scalar fields and forms is considered. When electro-magnetic composite p-brane ansatz is adopted, and certain restrictions on the…
We study the stability properties of orbits in dispersing billiards in a homogeneous magnetic field by using a modified formalism based on the Bunimovich-Sinai curvature (horocycle method). We identify simple periodic orbits that can be…
We consider the quantum dynamics of a particle in a weakly rough billiard. The Floquet operator for reflection at the boundary is obtained as a unitary band matrix. The resulting dynamics in angular momentum space can be treated in the…