Structural characterization of classical and memristive circuits with purely imaginary eigenvalues

The hyperbolicity problem in circuit theory concerns the existence of purely imaginary eigenvalues (PIEs) in the linearization of the time-domain description of the circuit dynamics. In this paper we characterize the circuit configurations which, in a strictly passive setting, yield purely imaginary eigenvalues for all values of the capacitances and inductances. Our framework is based on branch-oriented, semistate (differential-algebraic) circuit models which capture explicitly the circuit topology, and uses several notions and results from digraph theory. So-called P-structures arising in the analysis turn out to be the key element supporting our results. The analysis is shown to hold not only for classical (RLC) circuits but also for nonlinear circuits including memristors and other mem-devices

Memristor Platforms for Pattern Recognition Memristor Theory, Systems and Applications

In the last decade a large scientific community has focused on the study of the memristor. The memristor is thought to be by many the best alternative to CMOS technology, which is gradually showing its flaws. Transistor technology has developed fast both under a research and an industrial point of view, reducing the size of its elements to the nano-scale. It has been possible to generate more and more complex machinery and to communicate with that same machinery thanks to the development of programming languages based on combinations of boolean operands. Alas as shown by Moore’s law, the steep curve of implementation and of development of CMOS is gradually reaching a plateau. It is clear the need of studying new elements that can combine the efficiency of transistors and at the same time increase the complexity of the operations. Memristors can be described as non-linear resistors capable of maintaining memory of the resistance state that they reached. From their first theoretical treatment by Professor Leon O. Chua in 1971, different research groups have devoted their expertise in studying the both the fabrication and the implementation of this new promising technology. In the following thesis a complete study on memristors and memristive elements is presented. The road map that characterizes this study departs from a deep understanding of the physics that govern memristors, focusing on the HP model by Dr. Stanley Williams. Other devices such as phase change memories (PCMs) and memristive biosensors made with Si nano-wires have been studied, developing emulators and equivalent circuitry, in order to describe their complex dynamics. This part sets the first milestone of a pathway that passes trough more complex implementations such as neuromorphic systems and neural networks based on memristors proving their computing efficiency. Finally it will be presented a memristror-based technology, covered by patent, demonstrating its efficacy for clinical applications. The presented system has been designed for detecting and assessing automatically chronic wounds, a syndrome that affects roughly 2% of the world population, through a Cellular Automaton which analyzes and processes digital images of ulcers. Thanks to its precision in measuring the lesions the proposed solution promises not only to increase healing rates, but also to prevent the worsening of the wounds that usually lead to amputation and death

Chemical Wave Computing from Labware to Electrical Systems

Unconventional and, specifically, wave computing has been repeatedly studied in laboratory based experiments by utilizing chemical systems like a thin film of Belousov–Zhabotinsky (BZ) reactions. Nonetheless, the principles demonstrated by this chemical computer were mimicked by mathematical models to enhance the understanding of these systems and enable a more detailedinvestigation of their capacity. As expected, the computerized counterparts of the laboratory based experiments are faster and less expensive. A further step of acceleration in wave-based computingis the development of electrical circuits that imitate the dynamics of chemical computers. A key component of the electrical circuits is the memristor which facilitates the non-linear behavior of the chemical systems. As part of this concept, the road-map of the inspiration from wave-based computing on chemical media towards the implementation of equivalent systems on oscillating memristive circuits was studied here. For illustration reasons, the most straightforward example was demonstrated, namely the approximation of Boolean gates

MACHINE LEARNING AUGMENTATION MICRO-SENSORS FOR SMART DEVICE APPLICATIONS

Novel smart technologies such as wearable devices and unconventional robotics have been enabled by advancements in semiconductor technologies, which have miniaturized the sizes of transistors and sensors. These technologies promise great improvements to public health. However, current computational paradigms are ill-suited for use in novel smart technologies as they fail to meet their strict power and size requirements. In this dissertation, we present two bio-inspired colocalized sensing-and-computing schemes performed at the sensor level: continuous-time recurrent neural networks (CTRNNs) and reservoir computers (RCs). These schemes arise from the nonlinear dynamics of micro-electro-mechanical systems (MEMS), which facilitates computing, and the inherent ability of MEMS devices for sensing. Furthermore, this dissertation addresses the high-voltage requirements in electrostatically actuated MEMS devices using a passive amplification scheme. The CTRNN architecture is emulated using a network of bistable MEMS devices. This bistable behavior is shown in the pull-in, the snapthrough, and the feedback regimes, when excited around the electrical resonance frequency. In these regimes, MEMS devices exhibit key behaviors found in biological neuronal populations. When coupled, networks of MEMS are shown to be successful at classification and control tasks. Moreover, MEMS accelerometers are shown to be successful at acceleration waveform classification without the need for external processors. MEMS devices are additionally shown to perform computing by utilizing the RC architecture. Here, a delay-based RC scheme is studied, which uses one MEMS device to simulate the behavior of a large neural network through input modulation. We introduce a modulation scheme that enables colocalized sensing-and-computing by modulating the bias signal. The MEMS RC is tested to successfully perform pure computation and colocalized sensing-and-computing for both classification and regression tasks, even in noisy environments. Finally, we address the high-voltage requirements of electrostatically actuated MEMS devices by proposing a passive amplification scheme utilizing the mechanical and electrical resonances of MEMS devices simultaneously. Using this scheme, an order-of-magnitude of amplification is reported. Moreover, when only electrical resonance is used, we show that the MEMS device exhibits a computationally useful bistable response. Adviser: Dr. Fadi Alsalee

Bifurcation and Chaos in Fractional-Order Systems

This book presents a collection of seven technical papers on fractional-order complex systems, especially chaotic systems with hidden attractors and symmetries, in the research front of the field, which will be beneficial for scientific researchers, graduate students, and technical professionals to study and apply. It is also suitable for teaching lectures and for seminars to use as a reference on related topics

Novel Computing Paradigms using Oscillators

This dissertation is concerned with new ways of using oscillators to perform computational tasks. Specifically, it introduces methods for building finite state machines (for general-purpose Boolean computation) as well as Ising machines (for solving combinatorial optimization problems) using coupled oscillator networks.But firstly, why oscillators? Why use them for computation?An important reason is simply that oscillators are fascinating. Coupled oscillator systems often display intriguing synchronization phenomena where spontaneous patterns arise. From the synchronous flashing of fireflies to Huygens' clocks ticking in unison, from the molecular mechanism of circadian rhythms to the phase patterns in oscillatory neural circuits, the observation and study of synchronization in coupled oscillators has a long and rich history. Engineers across many disciplines have also taken inspiration from these phenomena, e.g., to design high-performance radio frequency communication circuits and optical lasers. To be able to contribute to the study of coupled oscillators and leverage them in novel paradigms of computing is without question an interesting andfulfilling quest in and of itself.Moreover, as Moore's Law nears its limits, new computing paradigms that are different from mere conventional complementary metal–oxide–semiconductor (CMOS) scaling have become an important area of exploration. One broad direction aims to improve CMOS performance using device technology such as fin field-effect transistors (FinFET) and gate-all-around (GAA) FETs. Other new computing schemes are based on non-CMOS material and device technology, e.g., graphene, carbon nanotubes, memristive devices, optical devices, etc.. Another growing trend in both academia and industry is to build digital application-specific integrated circuits (ASIC) suitable for speeding up certain computational tasks, often leveraging the parallel nature of unconventional non-von Neumann architectures. These schemes seek to circumvent the limitations posed at the device level through innovations at the system/architecture level.Our work on oscillator-based computation represents a direction that is different from the above and features several points of novelty and attractiveness. Firstly, it makes meaningful use of nonlinear dynamical phenomena to tackle well-defined computational tasks that span analog and digital domains. It also differs from conventional computational systems at the fundamental logic encoding level, using timing/phase of oscillation as opposed to voltage levels to represent logic values. These differences bring about several advantages. The change of logic encoding scheme has several device- and system-level benefits related to noise immunity and interference resistance. The use of nonlinear oscillator dynamics allows our systems to address problems difficult for conventional digital computation. Furthermore, our schemes are amenable to realizations using almost all types of oscillators, allowing a wide variety of devices from multiple physical domains to serve as the substrate for computing. This ability to leverage emerging multiphysics devices need not put off the realization of our ideas far into the future. Instead, implementations using well-established circuit technology are already both practical and attractive.This work also differs from all past work on oscillator-based computing, which mostly focuses on specialized image preprocessing tasks, such as edge detection, image segmentation and pattern recognition. Perhaps its most unique feature is that our systems use transitions between analog and digital modes of operation --- unlike other existing schemes that simply couple oscillators and let their phases settle to a continuum of values, we use a special type of injection locking to make each oscillator settle to one of the several well-defined multistable phase-locked states, which we use to encode logic values for computation. Our schemes of oscillator-based Boolean and Ising computation are built upon this digitization of phase; they expand the scope of oscillator-based computing significantly.Our ideas are built on years of past research in the modelling, simulation and analysis of oscillators. While there is a considerable amount of literature (arguably since Christiaan Huygens wrote about his observation of synchronized pendulum clocks in the 17th century) analyzing the synchronization phenomenon from different perspectives at different levels, we have been able to further develop the theory of injection locking, connecting the dots to find a path of analysis that starts from the low-level differential equations of individual oscillators and arrives at phase-based models and energy landscapes of coupled oscillator systems. This theoretical scaffolding is able not only to explain the operation of oscillator-based systems, but also to serve as the basis for simulation and design tools. Building on this, we explore the practical design of our proposed systems, demonstrate working prototypes, as well as develop the techniques, tools and methodologies essential for the process

Continuous-time Algorithms and Analog Integrated Circuits for Solving Partial Differential Equations

Analog computing (AC) was the predominant form of computing up to the end of World War II. The invention of digital computers (DCs) followed by developments in transistors and thereafter integrated circuits (IC), has led to exponential growth in DCs over the last few decades, making ACs a largely forgotten concept. However, as described by the impending slow-down of Moore’s law, the performance of DCs is no longer improving exponentially, as DCs are approaching clock speed, power dissipation, and transistor density limits. This research explores the possibility of employing AC concepts, albeit using modern IC technologies at radio frequency (RF) bandwidths, to obtain additional performance from existing IC platforms. Combining analog circuits with modern digital processors to perform arithmetic operations would make the computation potentially faster and more energy-efficient. Two AC techniques are explored for computing the approximate solutions of linear and nonlinear partial differential equations (PDEs), and they were verified by designing ACs for solving Maxwell\u27s and wave equations. The designs were simulated in Cadence Spectre for different boundary conditions. The accuracies of the ACs were compared with finite-deference time-domain (FDTD) reference techniques. The objective of this dissertation is to design software-defined ACs with complementary digital logic to perform approximate computations at speeds that are several orders of magnitude greater than competing methods. ACs trade accuracy of the computation for reduced power and increased throughput. Recent examples of ACs are accurate but have less than 25 kHz of analog bandwidth (Fcompute) for continuous-time (CT) operations. In this dissertation, a special-purpose AC, which has Fcompute = 30 MHz (an equivalent update rate of 625 MHz) at a power consumption of 200 mW, is presented. The proposed AC employes 180 nm CMOS technology and evaluates the approximate CT solution of the 1-D wave equation in space and time. The AC is 100x, 26x, 2.8x faster when compared to the MATLAB- and C-based FDTD solvers running on a computer, and systolic digital implementation of FDTD on a Xilinx RF-SoC ZCU1275 at 900 mW (x15 improvement in power-normalized performance compared to RF-SoC), respectively