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

该项目的目的是深入了解忆阻器细胞非线性/纳米尺度网络（MCNN）的计算能力，以提高最先进的传感器处理器阵列的性能，尽管其工作帧速率高于20 kHz，但由于分辨率低，适用范围有限。忆阻器是一种具有丰富非线性动力学行为的纳米级元件，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，每种忆阻器都具有特定的特性。这些类之一包括能够计算以及存储数据的元素。另一类，对这个项目非常重要，是由元素组成的，这些元素可能表现出局部活动行为，从而在基于它们的电子电路中引起复杂的动态。非常有趣的是，一些使用氧化铌等材料制造的忆阻器属于上述两种类型，因为具有局部活性的存储器切换和阈值切换可以共存于这些设备中。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的前景广阔，拟议的研究项目旨在推导出一个关于电路理论特性以及这些新型阵列的非线性动态行为的强大理论框架，用于开发新形式的计算，以改善当前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的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，则在网络中不会出现静态或动态模式。因此，本研究的最重要的目标是扩展局部活性理论，以便在合适的局部活性准则的满足下，描述忆阻器CNN中发展的复杂动力学。分析将被推广，以便适用于一大类忆阻器突触模型。CNN细胞作为局部活动系统的参数域的推导将基于严格的数学处理。总而言之，所提出的研究对于更深入地了解这些新型生物启发网络的计算功能具有根本重要性，这可能为未来的计算机器铺平道路，这些机器具有并行处理能力，尺寸和能耗类似于人脑的性能，分辨率能力优于传统阵列。

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.