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Purpose -The proposed algorithm successfully optimizes complex error functions, which are difficult to differentiate, ill conditioned or discontinuous. It is a benchmark to identify initial solutions in artificial neural network (ANN) training. Design/methodology/approach -A multi-directional ANN training algorithm that needs no derivative information is introduced as constrained one-dimensional problem. A directional search vector examines the ANN error function in weight parameter space. The search vector moves in all possible directions to find minimum function value. The network weights are increased or decreased depending on the shape of the error function hyper surface such that the search vector finds descent directions. The minimum function value is thus determined. To accelerate the convergence of the algorithm a momentum search is designed. It avoids overshooting the local minimum. Findings -The training algorithm is insensitive to the initial starting weights in comparison with the gradient-based methods. Therefore, it can locate a relative local minimum from anywhere of the error surface. It is an important property of this training method. The algorithm is suitable for error functions that are discontinuous, ill conditioned or the derivative of the error function is not readily available. It improves over the standard back propagation method in convergence and avoids premature termination near pseudo local minimum. Research limitations/implications -Classifications problems are efficiently classified when using this method but the complex time series in some instances slows convergence due to complexity of the error surface. Different ANN network structure can further be investigated to find the performance of the algorithm. Practical implications -The search scheme moves along the valleys and ridges of the error function to trace minimum neighborhood. The algorithm only evaluates the error function. As soon as the algorithm detects flat surface of the error function, care is taken to avoid slow convergence. Originality/value -The algorithm is efficient due to incorporation of three important methodologies. The first mechanism is the momentum search. The second methodology is the implementation of directional search vector in coordinate directions. The third procedure is the one-dimensional search in constrained region to identify the self-adaptive learning rates, to improve convergence.
Purpose -The proposed algorithm successfully optimizes complex error functions, which are difficult to differentiate, ill conditioned or discontinuous. It is a benchmark to identify initial solutions in artificial neural network (ANN) training. Design/methodology/approach -A multi-directional ANN training algorithm that needs no derivative information is introduced as constrained one-dimensional problem. A directional search vector examines the ANN error function in weight parameter space. The search vector moves in all possible directions to find minimum function value. The network weights are increased or decreased depending on the shape of the error function hyper surface such that the search vector finds descent directions. The minimum function value is thus determined. To accelerate the convergence of the algorithm a momentum search is designed. It avoids overshooting the local minimum. Findings -The training algorithm is insensitive to the initial starting weights in comparison with the gradient-based methods. Therefore, it can locate a relative local minimum from anywhere of the error surface. It is an important property of this training method. The algorithm is suitable for error functions that are discontinuous, ill conditioned or the derivative of the error function is not readily available. It improves over the standard back propagation method in convergence and avoids premature termination near pseudo local minimum. Research limitations/implications -Classifications problems are efficiently classified when using this method but the complex time series in some instances slows convergence due to complexity of the error surface. Different ANN network structure can further be investigated to find the performance of the algorithm. Practical implications -The search scheme moves along the valleys and ridges of the error function to trace minimum neighborhood. The algorithm only evaluates the error function. As soon as the algorithm detects flat surface of the error function, care is taken to avoid slow convergence. Originality/value -The algorithm is efficient due to incorporation of three important methodologies. The first mechanism is the momentum search. The second methodology is the implementation of directional search vector in coordinate directions. The third procedure is the one-dimensional search in constrained region to identify the self-adaptive learning rates, to improve convergence.
Purpose The purpose of this paper is to introduce new implementations for parallel processing applications using bijective systolic networks and their corresponding carbon-based field emission controlled switching. The developed implementations are performed in the reversible domain to perform the required bijective parallel computing, where the implementations for parallel computations that utilize the presented field-emission controlled switching and their corresponding many-valued (m-ary) extensions for the use in nano systolic networks are introduced. The second part of the paper introduces the implementation of systolic computing using two-to-one controlled switching via carbon-based field emission that were presented in the first part of the paper, and the computational extension to the general case of many-valued (m-ary) systolic networks utilizing many-to-one carbon-based field emission is also introduced. Design/methodology/approach The introduced systolic systems utilize recent findings in field emission and nano applications to implement the functionality of the basic bijective systolic network. This includes many-valued systolic computing via field-emission techniques using carbon-based nanotubes and nanotips. The realization of bijective logic circuits in current and emerging technologies can be very important for various reasons. The reduction of power consumption is a major requirement for the circuit design in future technologies, and thus, the new nano systolic circuits can play an important role in the design of circuits that consume minimal power for future applications such as in low-power signal processing. In addition, the implemented bijective systems can be utilized to implement massive parallel processing and thus obtaining very high processing performance, where the implementation will also utilize the significant size reduction within the nano domain. The extensions of implementations to field emission-based many-valued systolic networks using the introduced bijective nano systolic architectures are also presented. Findings Novel bijective systolic architectures using nano-based field emission implementations are introduced in this paper, and the implementation using the general scheme of many-valued computing is presented. The carbon-based field emission implementation of nano systolic networks is also introduced. This is accomplished using the introduced field-emission carbon-based devices, where field emission from carbon nanotubes and nano-apex carbon fibers is utilized. The implementations of the many-valued bijective systolic networks utilizing the introduced nano-based architectures are also presented. Practical implications The introduced bijective systolic implementations form new important directions in the systolic realizations using the newly emerging nano-based technologies. The 2-to-1 multiplexer is a basic building block in “switch logic,” where in switch logic, a logic circuit is realized as a combination of switches rather than a combination of logic gates as in the gate logic, which proves to be less costly in synthesizing multiplexer-based wide variety of modern circuits and systems since nano implementations exist in very compact space where carbon-based devices switch reliably using much less power than silicon-based devices. The introduced implementations for nano systolic computation are new and interesting for the design in future nanotechnologies that require optimal design specifications of minimum power consumption and minimum size layout such as in low-power control of autonomous robots and in the adiabatic low-power VLSI circuit design for signal processing applications. Originality/value The introduced bijective systolic implementations form new important directions in the systolic realizations utilizing the newly emerging nanotechnologies. The introduced implementations for nano systolic computation are new and interesting for the design in future nanotechnologies that require optimal design specifications of high performance, minimum power and minimum size.
In this first part of the article, basics of field emission will be presented which will be utilized within the second part of the article for the architecture effectuation of new Carbon Nanotube (CNT)-based controlled nano switches. To implement the field emission CNT-based controlled switch, four field emission CNTs that have single carbon nanotubes as the emitters were tested; two with single-walled CNT and two with multiwalled CNT. A tube with a tungsten tip was also used for comparison. The Fowler-Nordheim analysis of the DC current-voltage data provided reasonable values for the sizes and local fields of emitters. It is also shown within the new implementation of the controlled switch that square-wave pulses from a single laser diode with 20 mW power and 658 nm wavelength which is focused on each emitter increased the emitted current by 5.2% with the CNT and 0.19% with the compared tungsten tip.
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