Research ArticleCOMPUTER AND MATERIALS SCIENCES

Pattern recognition with “materials that compute”

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Science Advances  02 Sep 2016:
Vol. 2, no. 9, e1601114
DOI: 10.1126/sciadv.1601114
  • Fig. 1 Two BZ-PZ oscillator units connected with electrical wires.

    Each PZ cantilever consists of two identical layers of a polarized PZ material; the internal and external surfaces are covered with thin electrodes connected in parallel. Periodic volumetric changes in the self-oscillating BZ gels cause rhythmic bending of the PZ plates. The vector of polarization in PZ bending plates is oriented perpendicular to the plate surface (not shown). The colors orange and blue are used to distinguish the two parts of a bimorph PZ plate. The red and black solid lines show the electric wires connected to the external and internal electrodes, respectively. The green cubes depict the BZ gels.

  • Fig. 2 Multiple BZ-PZ oscillator units connected in serial (left) and parallel (right).

    ε1, ε2, …, εn are the force polarities of the n connected units. The orange and blue rectangles depict the two layers of a bimorph PZ plate. The green rectangles depict the self-oscillating BZ gels. The red and black lines show the electrical connections to the respective external and internal electrodes in the PZ plates.

  • Fig. 3 Schematics indicating how to transpose a black-and-white image onto the serially connected network of the BZ-PZ oscillators.

    Here, we store a binary image of the digit “0” that contains 60 pixels. The force polarity of an oscillator is set to +1 for a white pixel and to −1 for a black pixel. The coloring in the BZ-PZ units is the same as in Fig. 2. Note that assigning ε3 = −1 is achieved through flipping the red and black connector wires.

  • Fig. 4 Illustration of the pattern recognition task.

    The three different BZ-PZ oscillator networks, which store the respective images for the digits “0,” “1,” and “2,” are initialized with the same distorted “1” input image. The phase differences of the oscillations in the networks converge to the respective stored patterns in the course of synchronization. The blue and red lines distinguish between the two groups of oscillators that converge to the phase difference of 0 and 0.5, respectively. The convergence is the fastest in the network exhibiting the best match between the input and stored patterns, that is, in the network that stores the digit “1.”

  • Fig. 5 The stored 10 × 10 pattern and an example of the input pattern set used in test 1.

    The set is generated by flipping an increasing number of pixels until the input pattern is transformed into the mirror pattern. The difference between the stored pattern and an image from the set is characterized by the Hamming distance, which is the sum of the element-wise differences between two binary vectors.

  • Fig. 6 The average convergence time obtained in test 1 (blue line) and the Hamming distance between the stored and input images (orange line) as functions of the number of flipped bits.

    The error bars show the range of convergence times obtained from 100 runs at a given number of flipped bits, which were selected at random from all the bits in the system.

  • Fig. 7 An example of the 10 × 10 stored and input patterns used in test 2.

    The input patterns are generated using the same strategy of flipping bits as in test 1.

  • Fig. 8 The average times of convergence to the stored patterns p1 (blue line) and p2 (orange line) obtained in test 2 as functions of the number of flipped bits.

    The error bars are obtained as described in Fig. 6.

  • Fig. 9 The average times of convergence to the stored patterns p1 (blue line) and p2 (orange line) obtained in test 2 as functions of the number of flipped bits.

    The two stored patterns are more similar to each other’s mirror patterns than the stored patterns in Fig. 8. The observed peaks are similar to the one in Fig. 6, the result of test 1.

  • Fig. 10 The images used in test 3.

    (A) Binary images (10 × 6) of the 10 digits used as the stored patterns. (B and C) Distorted images of the digits “3” and “8” that are obtained by flipping 1, 5, 10, 15, 20, 25, and 30 pixels that are randomly selected.

  • Fig. 11 The accuracies of the recognition test 3 for the input patterns of the digits “1,” “3,” “5,” and “7” that are distorted with various levels of noise.

    The bars are colored according to the noise level. The horizontal axis indicates the input patterns.

  • Fig. 12 The difference between the average convergence times of the winner and of the runner-up in all the hit cases in test 3 for the digits shown in Fig. 11.

    The error bars show the SD obtained for each bar. The results indicate how fast the correct, recognized winner leads the runner-up. The other notations are the same as in Fig. 11.

  • Fig. 13 The connection function H(θ) used in the equations of the phase dynamics (Eqs. 8 and 9).

    The connection function is periodic at θ ∈ [0, 1].

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/2/9/e1601114/DC1

    Kinetics of the BZ reaction in a polymer gel.

    Osmotic pressure of the polymer in a gel.

    Properties of a bending PZ bimorph plate.

    Procedure used to map phase dynamics to 0 ≤ ϕ ≤ 0.5.

    Stability of the synchronization mode.

    Complete set of results for test 3.

    The effect of gel heterogeneities on synchronization.

    fig. S1. The phase differences plotted in the ranges [0, 1] and [0, 0.5].

    fig. S2. The phase difference ψ between the two groups of oscillators.

    fig. S3. The accuracies of the recognition test 3 for the input patterns of all 10 digits distorted with various levels of noise.

    fig. S4. The height of the bars represents the average convergence time difference between the winner and the runner-up in all the hit cases in test 3.

    fig. S5. The accuracy in recognizing the digit “7” as a function of the number of flipped pixels in the case where 60 pixels are used to represent the digit.

    fig. S6. The phase dynamics for the uniform distribution ΔT/T0 ∈ [−σ, σ] for various values of σ.

    fig. S7. The convergence time at random ΔT/T0 ∈ [−σ, σ] as a function of the distribution width σ.

    References (2931)

  • Supplementary Materials

    This PDF file includes:

    • Kinetics of the BZ reaction in a polymer gel.
    • Osmotic pressure of the polymer in a gel.
    • Properties of a bending PZ bimorph plate.
    • Procedure used to map phase dynamics to 0 ≤ ϕ ≤ 0.5.
    • Stability of the synchronization mode.
    • Complete set of results for test 3.
    • The effect of gel heterogeneities on synchronization.
    • fig. S1. The phase differences plotted in the ranges 0, 1 and 0, 0.5.
    • fig. S2. The phase difference ψ between the two groups of oscillators.
    • fig. S3. The accuracies of the recognition test 3 for the input patterns of all 10 digits distorted with various levels of noise.
    • fig. S4. The height of the bars represents the average convergence time difference between the winner and the runner-up in all the hit cases in test 3.
    • fig. S5. The accuracy in recognizing the digit “7” as a function of the number of flipped pixels in the case where 60 pixels are used to represent the digit.
    • fig. S6. The phase dynamics for the uniform distribution ΔT/T0 ∈ −σ, σ for various values of σ.
    • fig. S7. The convergence time at random ΔT/T0 ∈ −σ, σ as a function of the distribution width σ.
    • References (2931)

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