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The arithmetic mean is the most commonly used measure of the central tendency of a data set. It is defined as the sum of all the elements constituting the data set, divided by the total number of elements. It is sometimes loosely referred to as the “average.”
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Phasor Arithmetics01:13

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Phasors and their corresponding sinusoids are interrelated, offering unique insights into the behavior of alternating current (AC) circuits. One way to understand this relationship is through the operations of differentiation and integration in both the time and phasor domains.
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In materials that exhibit elastic and plastic behavior, known as elastoplastic materials, residual stresses can accumulate when these materials experience plastic deformation. This deformation arises from either high levels of shearing stress or significant strains. Residual stresses are internal stresses that persist within a material after removing the external force causing deformation. This phenomenon is demonstrated when observing the behavior of a shaft under torque; notably, the...
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Residue number system arithmetic based on integrated nanophotonics.

Jiaxin Peng, Shuai Sun, Vikram K Narayana

    Optics Letters
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    This study introduces an optical hardware for residue number system (RNS) arithmetic using nanophotonics. This photonic RNS processor offers high-speed computation for applications like convolutional neural networks.

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    Area of Science:

    • Photonics
    • Computer Arithmetic
    • Nanotechnology

    Background:

    • The residue number system (RNS) reduces computational complexity by decomposing large numbers into smaller integers.
    • Parallel processing of these smaller integers enhances computational efficiency and speed.
    • Existing RNS hardware implementations face limitations in speed and scalability.

    Purpose of the Study:

    • To demonstrate an optical hardware implementation of the residue number system (RNS) using integrated nanophotonics.
    • To leverage optical signal routing for digit-wise RNS arithmetic operations.
    • To explore the potential of photonic RNS for high-speed computation and specific applications.

    Main Methods:

    • Representing RNS residues via spatial shifting of optical signals in 2x2 hybrid photonic-plasmonic switches.
    • Cascading photonic switches to construct RNS adders and multipliers.
    • Utilizing wavelength-division-multiplexing for inherent optical parallelism.

    Main Results:

    • Successfully designed and demonstrated a photonic RNS adder and multiplier.
    • Achieved computational execution times in the tens of picoseconds due to optical propagation delays.
    • Showcased the integration of RNS processing with optical network parallelism.

    Conclusions:

    • Integrated nanophotonics provides a viable platform for high-speed RNS hardware.
    • Photonic RNS processors offer significant speed advantages over electronic counterparts.
    • This technology is well-suited for accelerating computations in areas such as convolutional neural network analysis.