A frequency averaging framework is proposed for the solution of complex linear dynamic systems. It is remarkable that, while the mid-frequency region is usually very challenging, a smooth transition from low- through mid- and high-frequency ranges is possible and all ranges can now be considered in a single framework. An interpretation of the frequency averaging in the time domain is presented ...

A simple method for absolute-frequency measurements of molecular transitions in the mid-IR region is reported. The method is based on a cw singly resonant optical parametric oscillator (SRO), which is tunable from 3.2 to 3.45 μm. The mid-IR frequency of the SRO is referenced to an optical frequency comb through its pump and signal beams. Sub-Doppler spectroscopy and absolute-frequency measureme...

We present a new technique suitable for generating broadband phase- and frequency-locked frequency combs in the mid-infrared. Our source is based on a degenerate optical parametric oscillator (OPO) which rigorously both down-converts and augments the spectrum of a pump frequency comb provided by a commercial mode-locked near-IR laser. Low intracavity dispersion, combined with extensive cross-mi...

Children at about age 18 months experience acceleration in word learning. This vocabulary explosion is a robust phenomenon, although the exact shape and timing vary from child to child. One class of explanations, which we term collectively as leveraged learning, posits that knowledge of some words helps with the learning of others. In this framework, the child initially knows no words and so le...

Patterns of word use both reflect and influence a myriad of human activities and interactions. Like other entities that are reproduced and evolve, words rise or decline depending upon a complex interplay between their intrinsic properties and the environments in which they function. Using Internet discussion communities as model systems, we define the concept of a word niche as the relationship...