Abstract: A derivative spectroscopy system for achieving a tunable resolution of 2 nm or less in resolving spectral components of an input optical signal is provided so as to estimate derivative spectra of the input optical signal based on the resolved spectral components. In the system, a first dispersive-element structure spectrally decomposes the input optical signal into subband signals. A second dispersive-element structure receives part or all of the subband signals and spectrally decomposes the received subband signals to plural spectral components. A material having a temperature-variant refractive index is used to build the second dispersive-element structure, enabling a shift of center wavelength of each spectral component as small as 2 nm of less upon changing a temperature of the second dispersive-element structure.

Abstract: A method for organizing and processing feature based data structures that can be used in linguistic spell checking and auto-correction, comprising: splitting an original dictionary into sub-dictionaries based on different values of a common feature such as high frequency words; receiving an input text that contains errors; determining a sub-dictionary selection feature from the input human-readable text; selecting the sub-dictionary based on the determined sub-dictionary selection feature; executing a first matching in the selected sub-dictionary, wherein a match is found if a similarity between the characters, words, or phrases in proximity of the errors in the input text and a character, word, or phrase in the sub-dictionary is above a threshold; if a unique match is found, the result is returned as an output to correct the errors; otherwise, executing a second matching with a raised threshold, and repeating the second matching until a unique match is found.