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{{short description|Parallel computing paradigm}}
In [[computer science]] and [[machine learning]], '''cellular neural networks''' ('''CNN
CNN is not to be confused with [[
==CNN architecture==
Due to their number and variety of [[Computer architecture|architectures]], it is difficult to give a precise definition for a CNN processor. From an architecture standpoint, CNN processors are a system of finite, fixed-number, fixed-___location, fixed-topology, locally interconnected, multiple-input, single-output, nonlinear processing units. The nonlinear processing units are often referred to as [[neurons]] or [[cell (biology)|cells]]. Mathematically, each cell can be modeled as a [[Dissipation|dissipative]], nonlinear [[dynamical system]] where information is encoded via its initial state, inputs and variables used to define its behavior. Dynamics are usually continuous, as in the case of [[Discrete time and continuous time|Continuous-Time]] CNN (CT-CNN) processors, but can be discrete, as in the case of [[Discrete time and continuous time|Discrete-Time]] CNN (DT-CNN) processors.<ref>S. Malki, Y. Fuqiang, and L. Spaanenburg, "Vein Feature Extraction Using DT-CNNs", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref><ref>H. Harrer and J.Nossek, "Discrete-Time Cellular Neural Networks", [[International Journal of Circuit Theory and Applications]], 20:453-467, 1992.</ref><ref>M. Brugge, "Morphological Design of Discrete−Time Cellular Neural Networks", University of Groningen Dissertation, 2005.</ref>
Each cell has one output, by which it communicates its state with both other cells and external devices. Output is typically [[Real number|real-valued]], but can be [[Complex number|complex]] or even [[quaternion]], i.e. a Multi-Valued CNN (MV-CNN). Most CNN processors, processing units are identical, but there are applications that require non-identical units, which are called Non-Uniform Processor CNN (NUP-CNN) processors, and consist of different types of cells.
=== Chua-Yang CNN ===
In the original '''Chua-Yang CNN''' (CY-CNN) processor, the state of the cell was a weighted sum of the inputs and the output was a [[piecewise linear function]]. However, like the original [[perceptron]]-based neural networks, the functions it could perform were limited: specifically, it was incapable of modeling [[
Cells are defined in a normed gridded space like two-dimensional [[Euclidean geometry]]. However, the cells are not limited to two-dimensional spaces; they can be defined in an [[Arbitrariness|arbitrary]] number of dimensions and can be [[square]], [[triangle]], [[
Most CNN architectures have cells with the same relative interconnects, but there are applications that require a spatially variant topology, i.e. Multiple-Neighborhood-Size CNN (MNS-CNN) processors. Also, Multiple-Layer CNN (ML-CNN) processors, where all cells on the same layer are identical, can be used to extend the capability of CNN processors.
The definition of a system is a collection of independent, interacting entities forming an integrated whole, whose behavior is distinct and [[Qualitative research|qualitatively]] greater than its entities. Although connections are local, [[information exchange]] can happen globally through diffusion. In this sense, CNN processors are systems because their dynamics are derived from the interaction between the processing units and not within processing units. As a result, they exhibit emergent and collective behavior. [[Mathematics|Mathematically]], the relationship between a cell and its neighbors, located within an area of influence, can be defined by a [[coupling]] law, and this is what primarily determines the behavior of the processor. When the coupling laws are modeled by [[fuzzy logic]], it is a fuzzy CNN.<ref>{{Cite journal|last = Yang | first = T. |display-authors=etal |title = The global stability of fuzzy cellular neural network | journal = [[IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications]] | volume = 43 | issue = 10 | pages = 880–883 | publisher = [[IEEE]] | date = October 1996 | doi = 10.1109/81.538999}}</ref> When these laws are modeled by [[
==History==
The idea of CNN processors was introduced by [[Leon Chua]] and Lin Yang in 1988.<ref>https://www.researchgate.net/publication/3183706_Cellular_neural_networks_Theory ("Cellular Neural Networks: Theory" and "Cellular Neural Networks: Applications" in IEEE Transactions on Circuits and Systems)</ref> In these articles, Chua and Yang outline the underlying mathematics behind CNN processors. They use this mathematical model to demonstrate, for a specific CNN implementation, that if the inputs are static, the processing units will converge, and can be used to perform useful calculations. They then suggest one of the first applications of CNN processors: image processing and pattern recognition (which is still the largest application to date). [[Leon O. Chua|Leon Chua]] is still active in CNN research and publishes many of his articles in the [[International Journal of Bifurcation and Chaos]], of which he is an editor. Both [[IEEE Circuits and Systems Society|IEEE Transactions on Circuits and Systems]] and the International Journal of Bifurcation also contain a variety of useful articles on CNN processors authored by other knowledgeable researchers. The former tends to focus on new CNN architectures and the latter more on the dynamical aspects of CNN processors.
In 1993, [[:nl:
=== Literature ===
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==Related processing architectures==
CNN processors could be thought of as a hybrid between [[Artificial neural network|ANN]] and [[Continuous automaton|Continuous Automata]] (CA).
=== Artificial Neural Networks ===
The processing units of CNN and NN are similar. In both cases, the processor units are multi-input, [[
However, in CNN processors, connections are made locally, whereas in ANN, connections are global.
For example, [[
But in CNN processors, the weights are used to determine the dynamics of the system.
Furthermore, due to the high inter-connectivity of ANNs, they tend not exploit locality in either the data set or the processing and as a result, they usually are highly redundant systems that allow for [[Robustness|robust]], fault-tolerant behavior without catastrophic errors.
A cross between an ANN and a CNN processor is a Ratio Memory CNN (RMCNN). In RMCNN processors, the cell interconnect is local and topologically invariant, but the weights are used to store previous states and not to control dynamics. The weights of the cells are modified during some learning state creating long-term memory.<ref>C. Wu and Y. Wu, "The Design of CMOS Non-Self-Feedback Ratio Memory Cellular Nonlinear Network without Elapsed Operation for Pattern Learning and Recognition", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref><ref>C. Wu and C. Cheng, "The Design of Cellular Neural Network with Ratio Memory for Pattern Learning and Recognition", Int’l Workshop on Cellular Neural Networks and Their Applications, 2000.</ref>
=== Continuous Automata ===
The topology and dynamics of CNN processors closely resembles that of CA. Like most CNN processors, CA consists of a fixed-number of identical processors that are spatially discrete and topologically uniform. The difference is that most CNN processors are continuous-valued whereas CA have discrete-values. Furthermore, the CNN processor's cell behavior is defined via some [[non-linear function]] whereas CA processor cells are defined by some state machine.
However, there are some exceptions. Continuous Valued [[Cellular automaton|Cellular Automata]] are CA with continuous resolution. Depending on how a given Continuous Automata is specified, it can also be a CNN.
There are also [[Continuous spatial automaton|Continuous Spatial Automata]], which consist of an infinite number of spatially continuous, continuous-valued automata. There is considerable work being performed in this field since continuous spaces are easier to mathematically model than discrete spaces, thus allowing a more quantitative approach as opposed to an empirical approach taken by some researchers of [[cellular automata]]. Continuous Spatial Automata processors can be physically realized though an unconventional information processing platform such as a [[chemical computer]]. Furthermore, it is conceivable that large CNN processors (in terms of the resolution of the input and output) can be modeled as a Continuous Spatial Automata.
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=== Boolean functions ===
Like CA, computations can be performed through the generation and propagation of signals that either grow or change over time. [[Computation
The applications of CNNs to Boolean functions is discussed in the paper by Fangyue Chen, Guolong He, Xiubin Xu, and [[Chen Guanrong|Guanrong Chen]], "Implementation of Arbitrary Boolean Functions via CNN".<ref name=":1" />
=== Automata and Turing machines ===
Although CNN processors are primarily intended for analog calculations, certain types of CNN processors can implement any Boolean function, allowing simulating CA. Since some CA are [[Universal Turing machine]]s (UTM), capable of [[Simulation|simulating]] any algorithm can be performed on processors based on the [[von Neumann architecture]], that makes this type of CNN processors, universal CNN, a UTM. One CNN architecture consists of an additional layer. CNN processors have resulted in the simplest realization of [[Conway’s Game of Life]] and [[Rule 110|Wolfram’s Rule 110]], the simplest known universal [[Turing machine|Turing Machine]]. This unique, dynamical representation of an old systems, allows researchers to apply techniques and hardware developed for CNN to better understand important CA. Furthermore, the continuous state space of CNN processors, with slight modifications that have no equivalent in [[Cellular Automata]], creates [[Emergence|emergent]] behavior never seen before.<ref name=":0">{{Cite journal|
Any information processing platform that allows the construction of arbitrary [[Boolean function
There are two methods by which to select a CNN processor along with a template or weights. The first is by synthesis, which involves determine the coefficients offline. This can be done by leveraging previous work, i.e. libraries, papers, and articles, or by mathematically deriving co that best suits the problem. The other is through training the processor. Researchers have used [[back-propagation]] and [[genetic algorithms]] to learn and perform functions. Back-propagation algorithms tend to be faster, but genetic algorithms are useful because they provide a mechanism to find a solution in a discontinuous, noisy search space.<ref>T. Kozek, T. Roska, and L. Chua, "Genetic Algorithms for CNN Template Learning," IEEE Trans. on Circuits and Systems I, 40(6):392-402, 1993.</ref><ref>G. Pazienza, E. Gomez-Ramirezt and X. Vilasis-Cardona, "Genetic Programming for the CNN-UM", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref><ref>E. Lopez, M. Balsif, D. Vilarilio and D. Cabello, "Design and Training of Multilayer Discrete Time Cellular Neural Networks for Antipersonnel Mine Detection Using Genetic Algorithms", Int’l Workshop on Cellular Neural Networks and Their Applications, 2000.</ref>
==Physical implementations==
There are toy models simulating CNN processors using [[
=== Semiconductors ===
Semiconductor-based CNN processors can be segmented into analog CNN processors, digital CNN processors, and CNN processors [[Emulator|emulated]] using digital processors. Analog CNN processors were the first to be developed. [[Analog computer]]s were fairly common during the 1950 and 1960s, but they gradually were replaced by digital computers the 1970s. Analog processors were considerably faster in certain applications such as optimizing differential equations and modeling nonlinearities, but the reason why analog computing lost favor was the lack of precision and the difficulty to configure an analog computer to solve a complex equation.
Analog CNN processors share some of the same advantages as their predecessors, specifically speed. The first analog CNN processors were able to perform real-time ultra-high frame-rate (>10,000 frame/s) processing unachievable by digital processors. The analog implementation of CNN processors requires less area and consumes less power than their digital counterparts. Although the accuracy of analog CNN processors does not compare to their digital counterparts, for many applications, noise and process variances are small enough not to perceptually affect the image quality.
The first [[algorithm]]ically programmable, analog CNN processor was created in 1993.<ref name=":3" /> It was named the CNN Universal Processor because its internal controller allowed multiple templates to be performed on the same data set, thus simulating multiple layers and allowing for universal computation. Included in the design was a single layer 8x8 CCN, interfaces, analog memory, switching logic, and software. The processor was developed in order to determine CNN processor producibility and utility. The CNN concept proved promising and by 2000, there were at least six organizations designing algorithmically programmable, analog CNN processors.<ref name=":3" />
=== AnaFocus, AnaLogic ===
In the 2000s, AnaFocus, a mixed-signal semiconductor company from the [[University of Seville]], introduced their ACE prototype CNN processor product line. Their first ACE processor contained 20x20 B/W processor units; and subsequent processors provided 48x48 and 128x128 grayscale processor units, improving the speed and processing elements. AnaFocus also had a multilayer CASE prototype CNN processors line. Their processors allowed real-time interaction between the sensing and processing. In 2014, AnaFocus had been sold to e2v technologies.<ref>{{Cite web|title=Acquisition of AnaFocus: Fast-growing CMOS imaging business to be integrated into High Performance Imaging division|url=https://www.teledyne-e2v.com/news/acquisition-of-anafocus-fast-growing-cmos-imaging-business-to-be-integrated-into-high-performance-imaging-division/|access-date=2020-12-27|website=e2v}}</ref>
Another company, AnaLogic Computers was founded in 2000 by many of the same researchers behind the first algorithmically programmable CNN Universal Processor. In 2003, AnaLogic Computers developed a PCI-X visual processor board that included the ACE 4K processor,<ref>{{Cite web|title=StackPath|url=https://www.vision-systems.com/home/article/16738443/cellular-device-processes-at-ultrafast-speeds|access-date=2020-12-27|website=www.vision-systems.com|date=February 2003 }}</ref> with a [[Texas Instruments|Texas Instrument]] DIP module and a high-speed frame-grabber. This allowed CNN processing to be easily included in a desktop computer. In 2006, AnaLogic Computers developed their Bi-I Ultra High Speed Smart Camera product line, which includes the ACE 4K processor in their high-end models.<ref>A. Rodríguez-Vázquez, G. Liñán-Cembrano, L. Carranza, E. Roca-Moreno, R. Carmona-Galán, F. Jiménez-Garrido, R. Domínguez-Castro, and S. Meana, "ACE16k: The Third Generation of Mixed-Signal SIMD-CNN ACE Chips Toward VSoCs," IEEE Trans. on Circuits and Systems - I, 51(5): 851-863, 2004.</ref>
In 2006, Roska et al. published a paper on designing a Bionic Eyeglass for AnaLogic. The Bionic Eyeglass is a dual-camera, wearable platform, based on the Bi-I Ultra High Speed Smart Camera, designed to provide assistance to blind people. Some of its functions include route number recognition and color processing.<ref>{{Cite
=== Analog CNN processors ===
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* Researchers from the [[National Lien Ho Institute of Technology|National Lien-Ho Institute of Technology]] (W. Yen, R. Chen and J. Lai) developed a Min-Max CNN (MMCNN) processor to learn more about CNN dynamics.<ref>W. Yen, R. Chen and J. Lai, "[https://ieeexplore.ieee.org/document/1035068 Design of Min/Max Cellular Neural Networks in CMOS Technology]" (IEEE), Int’l Workshop on Cellular Neural Networks and Their Applications, 2002.</ref>
Despite their speed and low power consumption, there are some significant drawbacks to analog CNN processors. First, analog CNN processors can potentially create erroneous results due to environment and process variation. In most applications, these errors are not noticeable, but there are situations where minor deviations can result in catastrophic system failures. For example, in chaotic communication, process variation will change the [[trajectory]] of a given system in phase space, resulting in a loss of synchronicity/stability. Due to the severity of the problem, there is considerable research being performed to ameliorate the problem. Some researchers are optimizing templates to accommodate greater variation. Other researchers are improving the semiconductor process to more closely match theoretical CNN performance. Other researchers are investigating different, potentially more robust CNN architectures. Lastly, researchers are developing methods to tune templates to target a specific chip and operating conditions. In other words, the templates are being optimized to match the information processing platform. Not only does process variation limit what can be done with current analog CNN processors, it is also a barrier for creating more complex processing units. Unless this process variation is resolved, ideas such as nested processing units, non-linear inputs, etc. cannot be implemented in a real-time analog CNN processor. Also, the semiconductor "real estate" for processing units limits the size of CNN processors.
Currently the largest AnaVision CNN-based vision processor consists of a 4K detector, which is significantly less than the megapixel detectors found in affordable, consumer cameras. Unfortunately, feature size reductions, as predicted by [[Moore’s Law]], will only result in minor improvements. For this reason, alternate technologies such as Resonant Tunneling Diodes and Neuron-Bipolar Junction Transistors are being explored.<ref>W. Yen and C. Wu, "The Design of Neuron-Bipolar Junction Transistor (vBJT) Cellular Neural Network(CNN) Structure with Multi-Neighborhood-Layer Template", Int’l Workshop on Cellular Neural Networks and Their Applications, 2000.</ref> Also, CNN processor architecture is being re-evaluated. For example, Star-CNN processors, where one analog multiplier is time-shared between multiple processor units, have been proposed and are expected to result in processor unit reduction size of 80%.<ref>F. Sargeni, V. Bonaiuto and M. Bonifazi, "Multiplexed Star-CNN Architecture", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref>
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=== Holography, nanotechnology ===
Researchers are also perusing alternate technologies for CNN processors. Although current CNN processors circumvent some of the problems associated with their digital counterparts, they do share some of the same long-term problems common to all semiconductor-based processors. These include, but are not limited to, speed, reliability, power-consumption, etc. AnaLogic Computers, is developing optical CNN processors, which combine optics, lasers, and biological and [[Holography|holographic]] memories. What initially was technology exploration resulted in a 500x500 CNN processor able to perform 300 giga-operations per second.
Another promising technology for CNN processors is nanotechnology. One [[nanotechnology]] concept being investigated is using single electron tunneling junctions, which can be made into single-electron or high-current transistors, to create McCulloch-Pitts CNN processing units. In summary, CNN processors have been implemented and provide value to their users. They have been able to effectively leverage the advantages and address some of the disadvantages associated with their underling technology, i.e. semiconductors. Researchers are also transitioning CNN processors into emerging technologies. Therefore, if the CNN architecture is suited for a specific information processing system, there are processors available for purchase (as there will be for the foreseeable future).<ref>W. Porod, F. Werblin, L. Chua, T. Roska, A. Rodriguez-Vázquez, B. Roska, R. Faya, G. Bernstein, Y. Huang, and A. Csurgay, "Bio-Inspired Nano-Sensor-Enhanced CNN Visual Computer", Annals of the New York Academy of Sciences, 1013: 92–109, 2004.</ref>
==Applications==
CNN researchers have diverse interests, ranging from physical, engineering, theoretical, mathematical, computational, and philosophical applications.
=== Image processing ===
CNN processors were designed to perform image processing; specifically, real-time ultra-high frame-rate (>10,000 frame/s) processing for applications like particle detection in jet engine fluids and spark-plug detection. Currently, CNN processors can achieve up to 50,000 frames per second, and for certain applications such as missile tracking, flash detection, and spark-plug diagnostics these microprocessors have outperformed a conventional [[supercomputer]]. CNN processors lend themselves to local, low-level, processor intensive operations and have been used in feature extraction,<ref>O. Lahdenoja, M. Laiho and A. Paasio, "Local Binary Pattern Feature Vector Extraction with CNN", Int’l Workshop on Cellular Neural Networks and Their Applications, 2005.</ref> level and gain adjustments, color constancy detection,<ref>L. Torok and A. Zarandy, "CNN Based Color Constancy Algorithm", Int’l Workshop on Cellular Neural Networks and Their Applications, 2002.</ref> contrast enhancement, [[deconvolution]],<ref>L. Orzo, "Optimal CNN Templates for Deconvolution", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006</ref> [[image compression]],<ref>P. Venetianer and T. Roska, "Image Compression by Cellular Neural Networks," IEEE Trans. Circuits Syst., 45(3): 205-215, 1998.</ref><ref>R. Dogarut, R. Tetzlaffl and M. Glesner, "Semi-Totalistic CNN Genes for Compact Image Compression", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref> [[motion estimation]],<ref name="Y. Cheng, J. Chung 2005">Y. Cheng, J. Chung, C. Lin and S. Hsu, "Local Motion Estimation Based On Cellular Neural Network Technology for Image Stabilization Processing", Int’l Workshop on Cellular Neural Networks and Their Applications, 2005.</ref><ref>A. Gacsadi, C. Grava, V. Tiponut, and P. Szolgay, "A CNN Implementation of the Horn & Schunck Motion Estimation Method", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref> image encoding, image decoding, [[image segmentation]],<ref>S. Chen, M. Kuo and J. Wang, "Image Segmentation Based on Consensus Voting", Int’l Workshop on Cellular Neural Networks and Their Applications, 2005.</ref><ref>G. Grassi, E. Sciascio, A. Grieco and P. Vecchio, "A New Object-oriented Segmentation Algorithm based on CNNs - Part II: Performance Evaluation", Int’l Workshop on Cellular Neural Networks and Their Applications, 2005.</ref> orientation preference maps,<ref>J. Wu, Z. Lin and C. Liou, "Formation and Variability of Orientation Preference Maps in Visual Cortex: an Approach Based on Normalized Gaussian Arrays", Int’l Workshop on Cellular Neural Networks and Their Applications, 2005.</ref> pattern learning/recognition,<ref name=":2" /><ref>C. Wu and S. Tsai, "Autonomous Ratio-Memory Cellular Nonlinear Network (ARMCNN) for Pattern Learning and Recognition", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref> multi-target tracking,<ref>G. Timar and C. Rekeczky, "Multitarget Tracking Applications of the Bi-I Platform: Attention-selection, Tracking and Navigation", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref> [[image stabilization]],<ref
Due to their processing capabilities and flexibility, CNN processors have been used and
=== Biology and medicine ===
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There is an ongoing effort to incorporate CNN processors into sensory-computing-actuating machines as part of the emerging field of [[Cellular Machines]]. The basic premise is to create an integrated system that uses CNN processors for the sensory signal-processing and potentially the decision-making and control. The reason is that CNN processors can provide a low power, small size, and eventually low-cost computing and actuating system suited for Cellular Machines. These Cellular Machines will eventually create a Sensor-Actuator Network (SAN),<ref>M. Haenggi, "Mobile Sensor-Actuator Networks: Opportunities and Challenges", Int’l Workshop on Cellular Neural Networks and Their Applications, 2002.</ref> a type of Mobile Ad Hoc Networks (MANET) which can be used for military intelligence gathering, surveillance of inhospitable environments, maintenance of large areas, planetary exploration, etc.
CNN processors have been proven versatile enough for some control functions. They have been used to optimize function via a genetic algorithm,<ref>D. Balya and V. Galt, "Analogic Implementation of the Genetic Algorithm", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref> to measure distances, to perform optimal path-finding in a complex, dynamic environment, and theoretically can be used to learn and associate complex stimuli. They have also been used to create antonymous gaits and low-level motors for robotic [[
=== Communication systems ===
The variety of dynamical behavior seen in CNN processors make them intriguing for communication systems. Chaotic communications using CNN processors is being researched due to their potential low power consumption, robustness and spread spectrum features. The premise behind chaotic communication is to use a chaotic signal for the carrier wave and to use chaotic phase synchronization to reconstruct the original message. CNN processors can be used on both the transmitter and receiver end to encode and decode a given message. They can also be used for data encryption and decryption, source authentication through watermarking,<ref>P. Arena, A. Basile, L. Fortuna, M. E. Yalcin, and J. Vandewalle, "Watermarking for the Authentication of Video on CNN-UM", Int’l Workshop on Cellular Neural Networks and Their Applications, 2002.</ref> detecting of complex patterns in spectrogram images<ref>K. Slot, P. Korbe, M. Gozdzik, and Hyongsuk Kim, "Pattern detection in spectrograms by means of Cellular Neural Networks", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref> ([[sound processing]]), and transient spectral signals detection.
CNN processors are [[Neuromorphic engineering|neuromorphic]] processors, meaning that they emulate certain aspects of [[biological neural network]]s. The original CNN processors were based on mammalian retinas, which consist of a layer of [[
CNN processors are being used to understand systems that can be modeled using simple, coupled units, such as living cells, biological networks, physiological systems, and ecosystems. The CNN architecture captures some of the dynamics often seen in nature and is simple enough to analyze and conduct experiments. They are also being used for [[stochastic]] simulation techniques, which allow scientists to explore spin problems, population dynamics, lattice-based gas models, [[percolation]], and other phenomena. Other simulation applications include heat transfer, mechanical vibrating systems, protein production,<ref>W. Samarrai, J. Yeol, I. Bajis and Y. Ryu, "System Biology Modeling of Protein Process using Deterministic Finite Automata (DFA)", Int’l Workshop on Cellular Neural Networks and Their Applications, 2005.</ref> [[Josephson junction|Josephson Junction]] problems,<ref>V. Mladenovt, and A. Slavoval, "On the Period Solutions in One Dimensional Cellular Neural Networks based on Josephson Junctions", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref> seismic wave propagation,<ref>K. Huang, C. Chang, W. Hsieh, S. Hsieh, L. Wang and F. Tsai, "Cellular Neural Network For Seismic Horizon Picking", Int’l Workshop on Cellular Neural Networks and Their Applications, 2005.</ref> and geothermal structures.<ref>P. Lopez, D. Vilarino, D. Cabello, H. Sahli and M. Balsi, "CNN Based Thermal Modeling of the Soil for Anitpersonnel Mine Detection", Int’l Workshop on Cellular Neural Networks and Their Applications, 2002.</ref> Instances of 3d CNN have been used to prove certain emergent phenomena in complex systems, establishing a link between art, dynamical systems and [[Very Large Scale Integration|VLSI]] technology.<ref>H. Ip, E. Drakakis, and A. Bharath, "Towards Analog VLSI Arrays for Nonseparable 3D Spatiotemporal Filtering", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref><ref>P.Arena, L. Fortuna, M. Frasca, L. Patane, and M. Pollino, "An Autonomous Mini-Hexapod Robot Controller through a CNN Based VLSI Chip", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref><ref>[[Andrew Adamatzky|A. Adamatzky]], P. Arena, A. Basile, R. Carmona-Galán, B. Costello, L. Fortuna, M. Frasca, and A. Rodríguez-Vázquez, "Reaction-Diffusion Navigation Robot Control: From Chemical to VLSI Analogic Processors", IEEE Trans. On Circuits And Systems – I, 51(5):926-938, 2004.</ref><ref>L. Chua, L. Yang, and K. R. Krieg, "Signal Processing Using Cellular Neural Networks", Journal of VLSI Signal Processing, 3:25-51, 1991.</ref>
CNN processors have been used to research a variety of mathematical concepts, such as [[Non-equilibrium statistical mechanics|non-equilibrium systems]], constructing non-linear systems of arbitrary complexity, emergent chaotic dynamics, and discovering new dynamic behavior. They are often used in researching [[systemics]], a trans-disciplinary, scientific field that studies natural systems. The goal of systemics researchers is to develop a conceptual and mathematical framework necessary to analyze, model, and understand systems, including, but not limited to, atomic, mechanical, molecular, chemical, biological, ecological, social and economic systems. Topics explored are emergence, collective behavior, local activity and its impact on global behavior, and quantifying the complexity of an approximately spatial and topologically invariant system.<ref>L. Chua, "Local Activity is the Origin of Complexity", Int’l Journal of Bifurcation and Chaos, 15(11):3435-2456, 2005.</ref> With another definition of complexity (MIT professor [[Seth Lloyd]] has identified 32 different definitions of complexity<ref>S. Lloyd, Programming the Universe, 2006.</ref>), it can potentially be mathematically advantageous when analyzing systems such as economic and social systems.
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* The Chua Lectures: A 12-Part Series with [[Hewlett Packard Labs]] [https://web.archive.org/web/20151211004700/https://www.hpematter.com/event/chua-lectures-first-12-part-series-hp-labs]
*D. Balya, G, Tímar, G. Cserey, and T. Roska, "A New Computational Model for CNN-UMs and its Computational Complexity", Int’l Workshop on Cellular Neural Networks and Their Applications, 2004.
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*S. Chen, M. Kuo and J. Wang, "Image Segmentation Based on Consensus Voting", Int’l Workshop on Cellular Neural Networks and Their Applications, 2005.
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*L. Goras, L. Chua, and D. Leenearts, "Turing Patterns in CNNs – Part I: Once Over Lightly", IEEE Trans. on Circuits and Systems – I, 42(10):602-611, 1995.
*L. Goras, L. Chua, and D. Leenearts, "Turing Patterns in CNNs – Part II: Equations and Behavior", IEEE Trans. on Circuits and Systems – I, 42(10):612-626, 1995.
*L. Goras, L. Chua, and D. Leenearts, "Turing Patterns in CNNs – Part III: Computer Simulation Results", IEEE Trans. on Circuits and Systems – I, 42(10):627-637, 1995.
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* [https://web.archive.org/web/20100306164810/http://www.eutecus.com/ Eutecus Homepage]
{{DEFAULTSORT:Cellular Neural Network}}
[[Category:Artificial neural networks]]
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