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1. An Oscillatory Neural Network Based Local Processing Unit for Pattern Recognition Applications

   https://doi.org/10.3390/electronics8010064  

   Zhang, Ting; Haider, Mohammad; Massoud, Yehia; Alexander, J. (January 2019, Electronics)

   Prolific growth of sensors and sensor technology has resulted various applications in sensing, monitoring, assessment and control operations. Owing to the large number of sensing units the the aggregate data volume creates a burden to the central data processing unit. This paper demonstrates an analog computational platform using weakly coupled oscillator neural network for pattern recognition applications. The oscillator neural network (ONN) has been studied over the last couple of decades for it’s increasing computational efficiency. The coupled ONN can realize the classification and pattern recognition functionalities based on its synchronization phenomenon. The convergence time and frequency of synchronization are considered as the indicator of recognition. For hierarchical sensing, the synchronization is detected in the first layer, and then the classification is accomplished in the second layer. In this work, a Kuramoto model based frequency synchronization approach is utilized, and simulation results indicate less than 160 ms convergence time and close frequency match for a simplified pattern recognition application. An array of 10 sensors is considered to affect the coupling weights of the oscillating nodes, and demonstrate network level computation. Based on MATLAB simulations, the proposed ONN architecture can successfully detect the close-in-match pattern through synchronization, and differentiate the far-out-match pattern through loss of synchronization in the oscillating nodes. 

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2. Experimental Forced Response Analysis of Two-Degree-of-Freedom Piecewise-Linear Systems With a Gap

   https://doi.org/10.1115/DETC2020-22289  

   Saito, Akira; Umemoto, Junta; Noguchi, Kohei; Tien, Meng-Hsuan; D’Souza, Kiran (August 2020, ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference)

   null (Ed.)

   Abstract In this paper, an experimental forced response analysis for a two degree of freedom piecewise-linear oscillator is discussed. First, a mathematical model of the piecewise linear oscillator is presented. Second, the experimental setup developed for the forced response study is presented. The experimental setup is capable of investigating a two degree of freedom piecewise linear oscillator model. The piecewise linearity is achieved by attaching mechanical stops between two masses that move along common shafts. Forced response tests have been conducted, and the results are presented. Discussion of characteristics of the oscillators are provided based on frequency response, spectrogram, time histories, phase portraits, and Poincaré sections. Period doubling bifurcation has been observed when the excitation frequency changes from a frequency with multiple contacts between the masses to a frequency with single contact between the masses occurs. 

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3. Teachers’ responses to instances of student mathematical thinking with varied potential to support student learning

   https://doi.org/10.1007/s13394-020-00334-x  

   Stockero, Shari L.; Van Zoest, Laura R.; Freeburn, Ben; Peterson, Blake E.; Leatham, Keith R. (January 2020, Mathematics Education Research Journal)

   null (Ed.)

   Teacher responses to student mathematical thinking (SMT) matter because the way in which teachers respond affects student learning. Although studies have provided important insights into the nature of teacher responses, little is known about the extent to which these responses take into account the potential of the instance of SMT to support learning. This study investigated teachers’ responses to a common set of instances of SMT with varied potential to support students’ mathematical learning, as well as the productivity of such responses. To examine variations in responses in relation to the mathematical potential of the SMT to which they are responding, we coded teacher responses to instances of SMT in a scenario-based interview. We did so using a scheme that analyzes who interacts with the thinking (Actor), what they are given the opportunity to do in those interactions (Action), and how the teacher response relates to the actions and ideas in the contributed SMT (Recognition). The study found that teachers tended to direct responses to the student who had shared the thinking, use a small subset of actions, and explicitly incorporate students’ actions and ideas. To assess the productivity of teacher responses, we first theorized the alignment of different aspects of teacher responses with our vision of responsive teaching. We then used the data to analyze the extent to which specific aspects of teacher responses were more or less productive in particular circumstances. We discuss these circumstances and the implications of the findings for teachers, professional developers, and researchers. 

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4. Parity–time symmetric optical neural networks

   https://doi.org/10.1364/OPTICA.435525  

   Deng, Haoqin; Khajavikhan, Mercedeh (October 2021, Optica)

   Optical neural networks (ONNs), implemented on an array of cascaded Mach–Zehnder interferometers (MZIs), have recently been proposed as a possible replacement for conventional deep learning hardware. They potentially offer higher energy efficiency and computational speed when compared to their electronic counterparts. By utilizing tunable phase shifters, one can adjust the output of each of MZI to enable emulation of arbitrary matrix–vector multiplication. These phase shifters are central to the programmability of ONNs, but they require a large footprint and are relatively slow. Here we propose an ONN architecture that utilizes parity–time (PT) symmetric couplers as its building blocks. Instead of modulating phase, gain–loss contrasts across the array are adjusted as a means to train the network. We demonstrate that PT symmetric ONNs (PT-ONNs) are adequately expressive by performing the digit-recognition task on the Modified National Institute of Standards and Technology dataset. Compared to conventional ONNs, the PT-ONN achieves a comparable accuracy (67% versus 71%) while circumventing the problems associated with changing phase. Our approach may lead to new and alternative avenues for fast training in chip-scale ONNs. 

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5. Equation Attention Relationship Network (EARN) : A Geometric Deep Metric Framework for Learning Similar Math Expression Embedding

   https://doi.org/10.1109/ICPR48806.2021.9412619  

   Ahmed, Saleem; Davila, Kenny; Setlur, Srirangaraj; Govindaraju, Venu (May 2021, 2020 25th International Conference on Pattern Recognition (ICPR))

   null (Ed.)

   Representational Learning in the form of high dimensional embeddings have been used for multiple pattern recognition applications. There has been a significant interest in building embedding based systems for learning representations in the mathematical domain. At the same time, retrieval of structured information such as mathematical expressions is an important need for modern IR systems. In this work, our motivation is to introduce a robust framework for learning representations for similarity based retrieval of mathematical expressions. Given a query by example, the embedding can find the closest matching expression as a function of euclidean distance between them. We leverage recent advancements in image-based and graph-based deep learning algorithms to learn our similarity embeddings. We do this first, by using unimodal encoders in graph space and image space and then, a multi-modal combination of the same. To overcome the lack of training data, we force the networks to learn a deep metric using triplets generated with a heuristic scoring function. We also adopt a custom strategy for mining hard samples to train our neural networks. Our system produces rankings similar to those generated by the original scoring function, but using only a fraction of the time. Our results establish the viability of using such a multi-modal embedding for this task. 

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