A Framework for Computing Discrete-Time Systems and Functions using DNA

University of Minnesota Ph.D. dissertation. July 2017. Major: Electrical/Computer Engineering. Advisors: Keshab Parhi, Marc Riedel. 1 computer file (PDF); xvii, 216 pages.Due to the recent advances in the field of synthetic biology, molecular computing has emerged as a non-conventional computing technology. A broad range of computational processes has been considered for molecular implementation. In this dissertation, we investigate the development of molecular systems for performing the following computations: signal processing, Markov chains, polynomials, and mathematical functions. First, we present a \textit{fully asynchronous} framework to design molecular signal processing algorithms. The framework maps each delay unit to two molecular types, i.e., first-type and second-type, and provides a 4-phase scheme to synchronize data flow for any multi-input/multi-output signal processing system. In the first phase, the input signal and values stored in all delay elements are consumed for computations. Results of computations are stored in the first-type molecules corresponding to the delay units and output variables. During the second phase, the values of the first-type molecules are transferred to the second-type molecules for the output variable. In the third phase, the concentrations of the first-type molecules are transferred to the second-type molecules associated with each delay element. Finally, in the fourth phase, the output molecules are collected. The method is illustrated by synthesizing a simple finite-impulse response (FIR) filter, an infinite-impulse response (IIR) filter, and an 8-point real-valued fast Fourier transform (FFT). The simulation results show that the proposed framework provides faster molecular signal processing systems compared to prior frameworks. We then present an overview of how continuous-time, discrete-time and digital signal processing systems can be implemented using molecular reactions. We also present molecular sensing systems where molecular reactions are used to implement analog-to-digital converters (ADCs) and digital-to-analog converters (DACs). These converters can be used to design mixed-signal processing molecular systems. A complete example of the addition of two molecules using digital implementation is described where the concentrations of two molecules are converted to digital by two 3-bit ADCs, and the 4-bit output of the digital adder is converted to analog by a 4-bit DAC. Furthermore, we describe implementation of other forms of molecular computation. We propose an approach to implement any first-order Markov chain using molecular reactions in general and DNA in particular. The Markov chain consists of two parts: a set of states and state transition probabilities. Each state is modeled by a unique molecular type, referred to as a data molecule. Each state transition is modeled by a unique molecular type, referred to as a control molecule, and a unique molecular reaction. Each reaction consumes data molecules of one state and produces data molecules of another state. The concentrations of control molecules are initialized according to the probabilities of corresponding state transitions in the chain. The steady-state probability of the Markov chain is computed by the equilibrium concentration of data molecules. We demonstrate our method for the Gambler’s Ruin problem as an instance of the Markov chain process. We analyze the method according to both the stochastic chemical kinetics and the mass-action kinetics model. Additionally, we propose a novel {\em unipolar molecular encoding} approach to compute a certain class of polynomials. In this molecular encoding, each variable is represented using two molecular types: a \mbox{type-0} and a \mbox{type-1}. The value is the ratio of the concentration of type-1 molecules to the sum of the concentrations of \mbox{type-0} and \mbox{type-1} molecules. With the new encoding, CRNs can compute any set of polynomial functions subject only to the limitation that these polynomials can be expressed as linear combinations of Bernstein basis polynomials with positive coefficients less than or equal to 1. The proposed encoding naturally exploits the expansion of a power-form polynomial into a Bernstein polynomial. We present molecular encoders for converting any input in a standard representation to the fractional representation, as well as decoders for converting the computed output from the fractional to a standard representation. Lastly, we expand the unipolar molecular encoding for bipolar molecular encoding and propose simple molecular circuits that can compute multiplication and scaled addition. Using these circuits, we design molecular circuits to compute more complex mathematical functions such as $e^{-x}$, $\sin (x)$, and sigmoid$(x)$. According to this approach, we implement a molecular perceptron as a simple artificial neural network

The Logic of Random Pulses: Stochastic Computing.

Recent developments in the field of electronics have produced nano-scale devices whose operation can only be described in probabilistic terms. In contrast with the conventional deterministic computing that has dominated the digital world for decades, we investigate a fundamentally different technique that is probabilistic by nature, namely, stochastic computing (SC). In SC, numbers are represented by bit-streams of 0's and 1's, in which the probability of seeing a 1 denotes the value of the number. The main benefit of SC is that complicated arithmetic computation can be performed by simple logic circuits. For example, a single (logic) AND gate performs multiplication. The dissertation begins with a comprehensive survey of SC and its applications. We highlight its main challenges, which include long computation time and low accuracy, as well as the lack of general design methods. We then address some of the more important challenges. We introduce a new SC design method, called STRAUSS, that generates efficient SC circuits for arbitrary target functions. We then address the problems arising from correlation among stochastic numbers (SNs). In particular, we show that, contrary to general belief, correlation can sometimes serve as a resource in SC design. We also show that unlike conventional circuits, SC circuits can tolerate high error rates and are hence useful in some new applications that involve nondeterministic behavior in the underlying circuitry. Finally, we show how SC's properties can be exploited in the design of an efficient vision chip that is suitable for retinal implants. In particular, we show that SC circuits can directly operate on signals with neural encoding, which eliminates the need for data conversion.PhDComputer Science and EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113561/1/alaghi_1.pd

Self-tuning digital controllers for servo systems

Adaptive self-tuning systems have been the subject of a great deal of research effort in recent years. Practical applications have lagged behind such work, in the main being applied in the process industries. Few serve applications have been reported, the wide bandwidths and demanding performance specifications raising problems not found in the process world. The research project described here is concerned with the use of self-tuning digital controllers applied to servo systems, specifically an electro-mechanical actuation unit. Practical limitations, such as stiction, friction and velocity saturation effects are taken into account. [Continues.

Fault-tolerant quantum computer architectures using hierarchies of quantum error-correcting codes

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.Includes bibliographical references (p. 221-238).Quantum computers have been shown to efficiently solve a class of problems for which no efficient solution is otherwise known. Physical systems can implement quantum computation, but devising realistic schemes is an extremely challenging problem largely due to the effect of noise. A quantum computer that is capable of correctly solving problems more rapidly than modern digital computers requires some use of so-called fault-tolerant components. Code-based fault-tolerance using quantum error-correcting codes is one of the most promising and versatile of the known routes for fault-tolerant quantum computation. This dissertation presents three main, new results about code-based fault-tolerant quantum computer architectures. The first result is a large new family of quantum codes that go beyond stabilizer codes, the most well-studied family of quantum codes. Our new family of codeword stabilized codes contains all known codes with optimal parameters. Furthermore, we show how to systematically find, construct, and understand such codes as a pair of codes: an additive quantum code and a classical (nonlinear) code. Second, we resolve an open question about universality of so-called transversal gates acting on stabilizer codes. Such gates are universal for classical fault-tolerant computation, but they were conjectured to be insufficient for universal fault-tolerant quantum computation. We show that transversal gates have a restricted form and prove that some important families of them cannot be quantum universal. This is strong evidence that so-called quantum software is necessary to achieve universality, and, therefore, fault-tolerant quantum computer architecture is fundamentally different from classical computer architecture. Finally, we partition the fault-tolerant design problem into levels of a hierarchy of concatenated codes and present methods, compatible with rigorous threshold theorems, for numerically evaluating these codes.(cont.) The methods are applied to measure inner error-correcting code performance, as a first step toward elucidation of an effective fault-tolerant quantum computer architecture that uses no more than a physical, inner, and outer level of coding. Of the inner codes, the Golay code gives the highest pseudothreshold of 2 x 10-3. A comparison of logical error rate and overhead shows that the Bacon-Shor codes are competitive with Knill's C₄/C₆ scheme at a base error rate of 10⁻⁴.by Andrew W. Cross.Ph.D

Image-based EUVL Aberration Metrology

A significant factor in the degradation of nanolithographic image fidelity is optical wavefront aberration. As resolution of nanolithography systems increases, effects of wavefront aberrations on aerial image become more influential. The tolerance of such aberrations is governed by the requirements of features that are being imaged, often requiring lenses that can be corrected with a high degree of accuracy and precision. Resolution of lithographic systems is driven by scaling wavelength down and numerical aperture (NA) up. However, aberrations are also affected from the changes in wavelength and NA. Reduction in wavelength or increase in NA result in greater impact of aberrations, where the latter shows a quadratic dependence. Current demands in semiconductor manufacturing are constantly pushing lithographic systems to operate at the diffraction limit; hence, prompting a need to reduce all degrading effects on image properties to achieve maximum performance. Therefore, the need for highly accurate in-situ aberration measurement and correction is paramount. In this work, an approach has been developed in which several targets including phase wheel, phase disk, phase edges, and binary structures are used to generate optical images to detect and monitor aberrations in extreme ultraviolet (EUV) lithographic systems. The benefit of using printed patterns as opposed to other techniques is that the lithography system is tested under standard operating conditions. Mathematical models in conjunction with iterative lithographic simulations are used to determine pupil phase wavefront errors and describe them as combinations of Zernike polynomials