1,314 research outputs found
Exploring an Infinite Space with Finite Memory Scouts
Consider a small number of scouts exploring the infinite -dimensional grid
with the aim of hitting a hidden target point. Each scout is controlled by a
probabilistic finite automaton that determines its movement (to a neighboring
grid point) based on its current state. The scouts, that operate under a fully
synchronous schedule, communicate with each other (in a way that affects their
respective states) when they share the same grid point and operate
independently otherwise. Our main research question is: How many scouts are
required to guarantee that the target admits a finite mean hitting time?
Recently, it was shown that is an upper bound on the answer to this
question for any dimension and the main contribution of this paper
comes in the form of proving that this bound is tight for .Comment: Added (forgotten) acknowledgement
Deep Learning Reconstruction of Ultra-Short Pulses
Ultra-short laser pulses with femtosecond to attosecond pulse duration are
the shortest systematic events humans can create. Characterization (amplitude
and phase) of these pulses is a key ingredient in ultrafast science, e.g.,
exploring chemical reactions and electronic phase transitions. Here, we propose
and demonstrate, numerically and experimentally, the first deep neural network
technique to reconstruct ultra-short optical pulses. We anticipate that this
approach will extend the range of ultrashort laser pulses that can be
characterized, e.g., enabling to diagnose very weak attosecond pulses
Solitons in Nonlinear Media with an Infinite Range of Nonlocality: First Observation of Coherent Elliptic Solitons and of Vortex-Ring Solitons
We present an experimental study on wave propagation in highly nonlocal optically nonlinear media, for which far-away boundary conditions significantly affect the evolution of localized beams. As an example, we set the boundary conditions to be anisotropic and demonstrate the first experimental observation of coherent elliptic solitons. Furthermore, exploiting the natural ability of such nonlinearities to eliminate azimuthal instabilities, we perform the first observation of stable vortex-ring solitons. These features of highly nonlocal nonlinearities affected by far-away boundary conditions open new directions in nonlinear science by facilitating remote control over soliton propagation
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