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==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 [[Non-linear function|non-linear functions]], such as [[XOR]]. More complex functions are realizable via Non-Linear CNN (NL-CNN) processors.<ref>E. Gomez-Ramirez, G. Pazienza, X. Vilasis-Cardona, "Polynomial Discrete Time Cellular Neural Networks to solve the XOR Problem", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref>
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]], [[Hexagon|hexagonal]], or any other spatially invariant arrangement. [[Topology|Topologically]], cells can be arranged on an infinite plane or on a [[Torus|toroidal]] space. Cell interconnect is local, meaning that all connections between cells are within a specified radius (with distance measured [[Topology|topologically]]). Connections can also be time-delayed to allow for processing in the temporal ___domain.
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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:Tamás_Roska|Tamas Roska]] and Leon Chua introduced the first algorithmically programmable analog CNN processor in the world.<ref name=":3">{{Cite journal|last=Roska|first=T.|last2=Chua|first2=L.O.|date=1993-03|title=The CNN universal machine: an analogic array computer|url=http://dx.doi.org/10.1109/82.222815|journal=IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing|volume=40|issue=3|pages=163–173|doi=10.1109/82.222815|issn=1057-7130}}</ref> The multi-national effort was funded by the [[Office of Naval Research]], the [[National Science Foundation]], and the [[Hungarian Academy of Sciences]], and researched by the Hungarian Academy of Sciences and the [[University of California, Berkeley|University of California]]. This article proved that CNN processors were producible and provided researchers a physical platform to test their CNN theories. After this article, companies started to invest into larger, more capable processors, based on the same basic architecture as the CNN Universal Processor. Tamas Roska is another key contributor to CNNs. His name is often associated with biologically inspired information processing platforms and algorithms, and he has published numerous key articles and has been involved with companies and research institutions developing CNN technology.
=== Literature ===
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* The proceedings of "The International Workshop on Cellular Neural Networks and Their Applications" provide much CNN literature.
* The proceedings are available online, via [[IEEE Xplore]], for conferences held in 1990, 1992, 1994, 1996, 1998, 2000, 2002, 2005 and 2006.
* There
* For an understanding of the analog [[semiconductor]] based CNN technology, AnaLogic Computers has their product line, in addition to the published articles available on their homepage and their publication list. They also have information on other CNN technologies such as optical computing. Many of the commonly used functions have already been implemented using CNN processors. A good reference point for some of these can be found in image processing libraries for CNN based visual computers such as Analogic’s CNN-based systems.
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=== Reaction-Diffusion ===
CNN processors can be used as [[Reaction–diffusion system|Reaction-Diffusion]] (RD) processors. RD processors are spatially invariant, topologically invariant, analog, parallel processors characterized by reactions, where two agents can combine to create a third agent, and [[diffusion]], the spreading of agents. RD processors are typically implemented through chemicals in a [[Petri dish]] (processor), light (input), and a camera (output) however RD processors can also be implemented through a multi-layer CNN processor. D processors can be used to create [[Voronoi diagrams]] and perform [[Skeletonization|skeletonisation]]. The main difference between the chemical implementation and the CNN implementation is that CNN implementations are considerably faster than their chemical counterparts and chemical processors are spatially continuous whereas the CNN processors are spatially discrete. The most researched RD processor, Belousov-Zhabotinsky (BZ) processors, has already been simulated using a four-layer CNN processors and has been implemented in a semiconductor.<ref>[[Andrew Adamatzky|A. Adamatzky]], B. Costello, T Asai "Reaction-Diffusion Computers", 2005.</ref><ref>F. Gollas and R. Tetzlaff, "Modeling Complex Systems by Reaction-Diffusion Cellular Nonlinear Networks with Polynomial Weight-Functions", Int’l Workshop on Cellular Neural Networks and Their Applications, 2005.</ref><ref>A. Selikhov, "mL-CNN: A CNN Model for Reaction Diffusion Processes in m Component Systems", Int’l Workshop on Cellular Neural Networks and Their Applications, 2005.</ref><ref>B. Shi and T. Luo, "Spatial Pattern Formation via Reaction–Diffusion Dynamics in 32x32x4 CNN Chip", IEEE Trans. On Circuits And Systems-I, 51(5):939-947, 2004.</ref>
=== Boolean functions ===
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==Physical implementations==
There are toy models simulating CNN processors using [[Billiard ball|billiard balls]], but these are used for theoretical studies. In practice, CNN are physically implemented on hardware and current technologies such as [[Semiconductor|semiconductors]]. There are plans to migrate CNN processors to emerging technologies in the future.<ref>R. Carmona, F. Jimenez-Garrido, R. Dominguez-Castro, S. Espejo and A. Rodriguez-Vazquez, "CMOS Realization of a 2-layer CNN Universal Machine", Int’l Workshop on Cellular Neural Networks and Their Applications, 2002.</ref><ref>C. Dominguez-Matas, R. Carmona-Galan, F. Sainchez-Fernaindez, A. Rodriguez-Vazquez, "3-Layer CNN Chip for Focal-Plane Complex Dynamics with Adaptive Image Capture", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref><ref>C. Dominguez-Matas, F. Sainchez-Femaindez, R. Carmona-Galan, and E. Roca-Moreno, "Experiments on Global and Local Adaptation to Illumination Conditions based on Focal Plane Average Computation", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref><ref>S. Xavier-de-Souza, M. Yalcın, J. Suykens, and J. Vandewalle, "Toward CNN Chip-Specific Robustness", IEEE Trans. On Circuits And Systems - I, 51(5): 892-902, 2004.</ref><ref>D. Hillier, S. Xavier de Souza, J. Suykens, J. Vandewalle, "CNNOPT Learning CNN Dynamics and Chip-specific Robustness", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref>
=== 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. 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. ▼
▲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.
=== AnaFocus, AnaLogic ===
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=== 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>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>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> resolution enhancement,<ref>T. Otake, T. Konishi, H. Aomorit, N. Takahashit and M. Tanakat, "Image Resolution Upscaling Via Two-Layered Discrete Cellular Neural Network", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref> image deformations and mapping, image inpainting,<ref>A. Gacsadi and P. Szolgay, "Image Inpainting Methods by Using Cellular Neural Networks", Int’l Workshop on Cellular Neural Networks and Their Applications, 2005.</ref> optical flow,<ref>B. Shi, T. Roska and L. Chua, "Estimating Optical Flow with Cellular Neural Networks," Int’l Journal of Circuit Theory and Applications, 26: 344-364, 1998.</ref> contouring,<ref>Szalka, G. Soos, D. Hillier, L. Kek, G. Andrassy and C. Rekeczky, "Space-time Signature Analysis of 2D Echocardiograms Based on Topographic Cellular Active Contour Techniques", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref><ref>T. Szabot and P. Szolgay, "CNN-UM-Based Methods Using Deformable Contours on Smooth Boundaries", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref> [[moving object detection]],<ref>G. Costantini, D. Casali, and R. Perfetti, "Detection of Moving Objects in a Binocular Video Sequence", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref> axis of symmetry detection,<ref>G Costantini, D. Casafi., and R. Perfetti, "A New CNN-based Method for Detection of the Axis of Symmetry.", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref> and [[image fusion]].<ref>I. Szatmari, P. Foldesy, C. Rekeczky and A. Zarandy, "Image Processing Library for the Aladdin Computer", Int’l Workshop on Cellular Neural Networks and Their Applications, 2005.</ref><ref>I. Szatmari, P. Foldesy, C. Rekeczky and A. Zarandy, "Image processing library for the Aladdin Visual Computer", Int’l Workshop on Cellular Neural Networks and Their Applications, 2002.</ref><ref>K. Wiehler, M. Perezowsky, R. Grigat, "A Detailed Analysis of Different CNN Implementations for a Real-Time Image Processing System", Int’l Workshop on Cellular Neural Networks and Their Applications, 2000.</ref>
Due to their processing capabilities and flexibility, CNN processors have been used and [[Prototype|prototyped]] for novel field applications such as flame analysis for monitoring combustion at a waste [[Incineration|incinerator]],<ref>L. Bertucco, A. Fichaa, G. Nmari and A. Pagano, "A Cellular Neural Networks Approach to Flame Image Analysis for Combustion Monitoring", Int’l Workshop on Cellular Neural Networks and Their Applications, 2000.</ref> mine-detection using [[infrared]] imagery, [[calorimeter]] cluster peak for [[high energy physics]],<ref>C. Baldanza, F. Bisi, M. Bruschi, I. D’Antone, S. Meneghini, M. Riui, M. Zufa, "A Cellular Neural Network For Peak Finding In High-Energy Physics", Int’l Workshop on Cellular Neural Networks and Their Applications, 2000.</ref> anomaly detection in potential field maps for geophysics, laser dot detection, metal inspection for detecting manufacturing defects, and [[Seismology|seismic]] horizon picking. They have also been used to perform [[Biometrics|biometric]] functions<ref>R. Dogaru and I. Dogaru, "Biometric Authentication Based on Perceptual Resonance Between CNN Emergent Patterns and Humans", Int’l Workshop on Cellular Neural Networks and Their Applications, 2002.</ref> such as [[fingerprint recognition]],<ref>T. Su, Y. Du, Y. Cheng, and Y. Su, "A Fingerprint Recognition System Using Cellular Neural Networks", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref> vein feature extraction, face tracking,<ref>S. Xavier-de-Souza, M. Van Dyck, J. Suykens and J. Vandewalle, "Fast and Robust Face Tracking for CNN Chips: Application to Wheelchair Driving", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref> and generating visual stimuli via emergent patterns to gauge perceptual [[Resonance|resonances]].
=== Biology and medicine ===
CNN processors have been used for medical and biological research in performing automated nucleated cell counting for detecting [[hyperplasia]],<ref>Q. Feng, S. Yu and H. Wang, "An New Automatic Nucleated Cell Counting Method With Improved Cellular Neural Networks (ICNN)", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref> segment images into anatomically and [[Pathology|pathologically]] meaningful regions, measure and quantify cardiac function, measure the timing of neurons, and detect brain abnormalities that would lead to seizures.<ref>D. Krug, A. Chernihovskyi, H. Osterhage, C. Elger, and K. Lehnertz, "Estimating Generalized Synchronization in Brain Electrical Activity from Epilepsy Patients with Cellular Nonlinear Networks", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref><ref>C. Niederhoefer and R. Tetzlaff, "Prediction Error Profiles allowing a Seizure Forecasting in Epilepsy?", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref>
One potential future application of CNN microprocessors is to combine them with DNA microarrays to allow for a near-real time DNA analysis of hundreds of thousands of different DNA sequences. Currently, the major bottleneck of DNA [[microarray analysis]] is the amount of time needed to process data in the form of images, and using a CNN microprocessor, researchers have reduced the amount of time needed to perform this calculation to 7ms.
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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 [[Photodetector|photodetectors]] connected to several layers of locally coupled neurons. This makes CNN processors part of an interdisciplinary research area whose goal is to design systems that leverage knowledge and ideas from neuroscience and contribute back via real-world validation of theories. CNN processors have implemented a real-time system that replicates mammalian retinas, validating that the original CNN architecture chosen modeled the correct aspects of the biological neural networks used to perform the task in mammalian life. However, CNN processors are not limited to verifying biological neural networks associated with vision processing; they have been used to simulate dynamic activity seen in mammalian neural networks found in the olfactory bulb and locust [[antennal lobe]], responsible for pre-processing sensory information to detect differences in repeating patterns.<ref>C. Dominguez-Matas, R. Carmona-Galan, F. Sanchez-Fernaindez, J. Cuadri, and A. Rodriguez-Vaizquez, "A Bio-Inspired Vision Front-End Chip with Spatio-Temporal Processing and Adaptive Image Capture", Int’l Workshop on Computer Architecture for Machine Perception and Sensing, 2006.</ref><ref>A. Zarandy and C. Rekeczky, "Bi-i: a standalone ultra high speed cellular vision system", IEEE Circuits and Systems Magazine, 5(2):36-45, 2005.</ref>
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. 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.{{Citation needed|date=December 2015}} 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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*T. Nakaguchi, K. Omiya and M. Tanaka, "Hysteresis Cellular Neural Networks for Solving Combinatorial Optimization Problems", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.
*K. Crounse, C. Wee and L. Chua, "Linear Spatial Filter Design for Implementation on the CNN Universal Machine", Int’l Workshop on Cellular Neural Networks and Their Applications, 2000.
*J. Poikonen1 and A. Paasio, "Mismatch-Tolerant Asynchronous Grayscale Morphological Reconstruction", Int’l Workshop on Cellular Neural Networks and Their Applications, 2005.
*M. Gilli, T. Roska, L. Chua, and P. Civalleri, "CNN Dynamics Represents a Broader Range Class than PDEs", Int’l Journal of Bifurcations and Chaos, 12(10):2051-2068, 2002.
*Fangyue Chen, Guolong He, Xiubin Xu, and [[Chen Guanrong|Guanrong Chen]], "Implementation of Arbitrary Boolean Functions via CNN", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.
*R. Doguru and [[Leon O. Chua|L. Chua]], "CNN Genes for One-Dimensional Cellular Automata: A Multi-Nested Piecewise-Linear Approach", Int’l Journal of Bifurcation and Chaos, 8(10):1987-2001, 1998.
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*T. Roska, "Cellular Wave Computers and CNN Technology – a SoC architecture with xK Processors and Sensor Arrays", Int’l Conference on Computer Aided Design Accepted Paper, 2005.
*K. Karahaliloglu, P. Gans, N. Schemm, and S. Balkir, "Optical sensor integrated CNN for Real-time Computational Applications", IEEE Int’l Symposium on Circuits and Systems, pp. 21–24, 2006.
*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.
*W. Yen, R. Chen and J. Lai, "Design of Min/Max Cellular Neural Networks in CMOS Technology", Int’l Workshop on Cellular Neural Networks and Their Applications, 2002.
*Z. Gallias and M. Ogorzalek, "Influence in System Nonuniformity on Dynamic Phenomenon in Arrays of Coupled Nonlinear Networks", Int’l Workshop on Cellular Neural Networks and Their Applications, 2002
*A. Paasiot and J. Poilkonent, "Programmable Diital Nested CNN", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.
*M. Znggi, R. Dogaru, and L. Chua, "Physical Modeling of RTD-Based CNN Cells", Int’l Workshop on Cellular Neural Networks and Their Applications, 2000.
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*A. Zarandry, S. Espejo, P. Foldesy, L. Kek, G. Linan, C. Rekeczky, A. Rodriguez-Vazquez, T. Roska, I. Szatmari, T. Sziranyi and P. Szolgay, "CNN Technology in Action ", Int’l Workshop on Cellular Neural Networks and Their Applications, 2000.
*L. Chua, S. Yoon and R. Dogaru, "A Nonlinear Dynamics Perspective of Wolfram’s New Kind of Science. Part I: Threshold of Complexity," Int’l Journal of Bifurcation and Chaos, 12(12):2655-2766, 2002.
*P. Ecimovic and J. Wu, "Delay Driven Contrast Enhancement using a Cellular Neural Network with State Dependent Delay", Int’l Workshop on Cellular Neural Networks and Their Applications, 2002.
*G. Cserey, C. Rekeczky and P. Foldesy, "PDE Based Histogram Modification with Embedded Morphological Processing of the Level Sets", Int’l Workshop on Cellular Neural Networks and Their Applications, 2002.
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*H. Kim, H. Son. J. Lee, I. Kim and I. Kim, "An Analog Viterbi Decoder for PRML using Analog Parallel Processing Circuits of the CNN", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.
*S. Chen, M. Kuo and J. Wang, "Image Segmentation Based on Consensus Voting", Int’l Workshop on Cellular Neural Networks and Their Applications, 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.
*P. Korbelt and K. Sloti, "Modeling of Elastic Inter-node Bounds in Cellular Neural Network-based Implementation of the Deformable Grid Paradigm", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.
*D. Vilarino and C. Rekeczky, "Implementation of a Pixel-Level Snake Algorithm on a CNNUM-Based Chip Set Architecture", IEEE Trans. On Circuits And Systems - I, 51(5): 885-891, 2004.
*C. Amenta, P. Arena, S. Baglio, L. Fortuna, D. Richiura, M.Xibilia and L. Vu1, "SC-CNNs for Sensors Data Fusion and Control in Space Distributed Structures", Int’l Workshop on Cellular Neural Networks and Their Applications, 2000.
*E. Bilgili, O. Ucan, A. Albora and I. Goknar, "Potential Anomaly Separation Using Genetically Trained Cellular Neural Networks", Int’l Workshop on Cellular Neural Networks and Their Applications, 2002.
*C. Rekeczky and G. Timar "Multiple Laser Dot Detection and Localization within an Attention Driven Sensor Fusion Framework", Int’l Workshop on Cellular Neural Networks and Their Applications, 2005.
*Z. Szlavikt, R.
*T. Su, Y. Du, Y. Cheng, and Y. Su, "A Fingerprint Recognition System Using Cellular Neural Networks", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.
*M. Bucolo, L. Fortuna, M. Frasca, M. La Rosa, D. Shannahoff-Khalsa, "A CNN Based System to Blind Sources Separation of MEG Signals", Int’l Workshop on Cellular Neural Networks and Their Applications, 2002.
*F. Dohlert, A. Chernihovskyi, F. Mormann, C. Elger, and K. Lehnertz, "Detecting Structural Alterations in the Brain using a Cellular Neural Network based Classification of Magnetic Resonance Images", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.
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*R. Chen and J. Lai, "Data Encryption Using Non-uniform 2-D Von Neumann Cellular Automata", Int’l Workshop on Cellular Neural Networks and Their Applications, 2005.
*A. Chernihovskyi, C. Elger, and K. Lehnertz, "Effect of in Inhibitory Diffusive Coupling on Frequency-Selectivity of Excitable Media Simulated With Cellular Neural Networks", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.
*D. Balya and B. Roska, "A Handy Retina Exploration Device", Workshop on Cellular Neural Networks and Their Applications, 2005.
*P. Arena, M. Bediat, L. Fortuna, D. Lombardo, L. Patane, and M. Velardet, "Spatio-temporal Patterns in CNNs for Classification: the Winnerless Competition Principle", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.
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