Emergence of complex behavior in Memristor Cellular Nonlinear Networks (ECOM)

本项目的目的是深入了解记忆阻元式非线性/纳米级网络(MCNN)的计算能力，因为需要提高最先进的传感器处理器阵列的性能，尽管这些阵列的帧速率高于20 kHz，但由于分辨率较低，其适用范围有限。忆阻器是一种纳米级元件，具有丰富的非线性动力学行为，是神经突触动力学最有效的模拟器。存在许多不同类别的忆阻器，每一类都具有特定的特性。这些类之一包括能够计算和存储数据的元素。另一类对这个项目非常重要的是由元素组成的，这些元素可能表现出局部活跃的行为，从而在基于它们的电子电路中诱导复杂的动力学。非常有趣的是，一些使用Nb氧化物等材料制造的忆阻器属于上述两种类型，因为在这些器件中可能同时存在具有局部活动的存储器开关和阈值开关。在CNN中使用忆阻器可能会导致最先进的传感器-处理器阵列的分辨率极限的扩展。鉴于基于忆阻器的CNN具有广阔的应用前景，该研究项目旨在为这些新型阵列的电路理论特性和非线性动力学行为建立一个稳健的理论框架，以开发新的计算形式，以改进现有硬件解决方案的功能。复杂的图像处理问题可以通过利用阵列内非均匀时空图案的形成来解决。然而，如果整个系统是局部被动的，则网络中不会出现静态或动态模式。因此，本研究最重要的目的是推广局域活性理论，以刻画在满足适当的局域活性准则的条件下，忆阻器CNN中复杂的动力学过程。这一分析将被推广，以适用于一大类忆阻器突触模型。CNN细胞作为局部活性系统的参数域的推导将基于严格的数学处理。总而言之，拟议的研究对于深入了解这些新型生物启发网络的计算功能具有重要意义，这些网络可能为未来的计算机器铺平道路，这些机器具有与人脑性能相似的并行处理能力、大小和能源消耗，以及优于传统阵列的分辨率能力。

The aim of this project is to gain a deep insight into the computational capabilities of memristor Cel-lular Nonlinear/Nanoscale Networks (MCNN) in view of the need to improve the performance of state-of-the art sensorprocessor arrays, which, despite operating at frame rates higher than 20 kHz, have a limited applicability sphere, due to the low resolution. Memristors are nano-scale elements with a rich nonlinear dynamical behavior and represent the most efficient emulators of neural synap-tic dynamics. There exist a number of distinct classes of memristors, each with specific properties. One of such classes include elements capable to compute as well as store data. Another class, very important for this project, is composed of elements, which may exhibit locally-active behavior, and thus induce complex dynamics in electronic circuits based upon them. Very interestingly, some memristors, manufactured using materials such Niobium oxide, belong to both of the mentioned classes, since memory switching and threshold switching with local activity may coexist in these devices. The use of memristors in CNN may lead to the extension of the resolution limits of state-of-the art sensor-processor arrays. In view of the promising perspectives of memristor-based CNNs, the proposed research project aims at deriving a robust theoretical framework on the circuit-theoretic properties as well as on the nonlinear dynamic behaviors of these novel arrays for the development of new forms of computation to improve the functionalities of current hardware solutions. Complex image processing problems may be solved by exploiting the formation of inhomogenous spatio-temporal patterns within the array. However, no static or dynamic pattern may arise in the network if the overall system is locally passive. As a result, the most significant goal of this research is to ex-tend the local activity theory so as to characterize the complex dynamics developing in memristor CNNs under the satisfaction of suitable local activity criteria. The analysis will be generalized so as to apply for a large class of memristor synapse models. The derivation of the parameter domain where a CNN cell acts as a locally-active system will be based on a rigorous mathematical treatment. All in all, the proposed research is of fundamental importance to gain a deeper insight into the com-putational functionalities of these novel bio-inspired networks, which may pave the way towards fu-ture computing machines with parallel processing power, size and energy consumption resembling the performance of the human brain, and resolution capabilities outperforming conventional arrays.