# Cellular neural network

**Cellular neural networks (CNN)**are a parallel computing paradigm similar toneural networks , with the difference that communication is allowed between neighbouring units only. Typical applications include image processing, analyzing 3D surfaces, solving partial differential equations, reducing non-visual problems to geometric maps, modelling biological vision and other sensory-motor organs.**CNN Architecture**Due to their number and variety of architectures, it is difficult to give a precise definition for a CNN processor. From an architecture standpoint, CNN processors are a system of a 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 cells. Mathematically, each cell can be modeled as a dissipative, nonlinear dynamical system where information is encoded via its initial state, inputs, and variables used to define its behavior. Dynamics are usually continuous, Continuous-Time CNN (CT-CNN) processors, but can be discrete, Discrete-Time CNN (DT-CNN) processors. Each cell has one output, by which it communicates its state with both other cells and external devices. Output is typically real-valued, but can be complex or even quaternion, i.e. Multi-Valued CNN (MV-CNN). In most CNN processors, processing units are identical, but there are applications that require, Non-Uniform Processor CNN (NUP-CNN) processor, consisting of different types of cells. 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 functions, such as

XOR . If this is a problem, more complex functions are achievable via Non-Linear CNN (NL-CNN) processors.Cells are defined in a normed space, commonly a 2 dimensional euclidean geometry, like a grid. The cells are not limited to 2 dimensional spaces however; they can be defined in arbitrary numbers of dimensions and can be square, triangle, hexagonal, or any other spatially-invariant arrangement. Topologically, cells can be arranged on an infinite plane or on a toroidal space. Cell interconnect is local, meaning that all connections between cells are within a specified radius, where distance is measured topologically. Connections can also be time-delayed to allow for processing in the temporal domain. Most CNN architectures have cells with the same relative interconnect, but there are applications that require, Multiple-Neighborhood-Size CNN (MNS-CNN), consisting of spatially-variant topology. Also, Multiple-Layer CNN (ML-CNN), 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 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 is derived from the interaction between the processing units and not within processing units, and as a result, they exhibit emergent, collective behavior. 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.

**Literature Review**The idea of CNN processors was introduced by

Leon Chua and Lin Yang’s two-part, 1988 article, “Cellular Neural Networks: Theory” and “Cellular Neural Networks: Applications” in IEEE Transactions on Circuits and Systems. Leon Chua is the same professor who pioneered nonlinear-circuit theory and unified it with linear-circuit theory using Kirchhoff laws and element laws. He was also responsible for introducing nonlinear dynamics and chaos theory to Electrical Engineering via Chua Oscillator, a simple, canonical, realizable electrical circuit that exhibit chaotic behavior. In these articles, Leon Chua and Lin Yang’s outline the underlying mathematics behind CNN processors. He uses 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. He then suggests one of the first applications of CNN processors: image processing and pattern recognition, which is still the largest application to this day. 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 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.Another key article is Tamas Roska and Leon Chua’s, 1993 article, “The CNN Universal Machine: An Analogic Array Computer”, where the first algorithmically programmable, analog CNN processor was introduced to the engineering research community. 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. 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 Cellular Neural Networks. 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.

There are several overviews of CNN processors. One of the better references is a paper, “Cellular Neural Networks: A Review” written for the Neural Nets WIRN Vietri 1993, by Valerio Cimagalli and Marco Balsi. This paper is beneficial because it provides definitions, CNN types, dynamics, implementations, and applications in a relatively small, readable document. There is also a book, “Cellular Neural Networks and Visual Computing Foundations and Applications”, written by Leon Chua and Tamas Roska. This reference is valuable because it provides examples and exercise to help illustrates points, which is uncommon in papers and journal articles. This book covers many different aspects of CNN processors and can serve as a textbook for a Masters or PhD course. These two references are invaluable since they manage to organize the vast amount of CNN literature into a coherent framework.

The best place for CNN literature is from the “International Workshop on Cellular Neural Networks and Their Applications” proceedings. The proceedings are available online, via IEEE Xplore, for conferences held in 1990, 1992, 1994, 1996, 1998, 2000, 2002, 2005, and 2006. There is also a workshop being held on July 14-16 in Santiago de Composetela, Spain. Topics include theory, design, applications, algorithms, physical implementations, and programming/training methods. For an understanding of the analog semiconductor based CNN technology, AnaLogic Computers has their product line, in addition to their 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.

**Related Processing Architectures**CNN processors could be thought hybrid between ANN and CA (Continuous Automata). The processing units off CNN and NN are similar. In both cases, the processor units are multi-input, dynamical systems, and the behavior of the overall systems is driven primarily through the weights of the processing unit’s linear interconnect. The main discriminator is that in CNN processors, connections are made locally, whereas in ANN, connections are global. For example neural of one layer are fully connected to another layer in feed-forward NN and all the neurons are fully interconnected in Hopfield networks. In ANN, it the weights contain information on the processing system’s previous state or feedback, but in CNN processors, the weights are used to determine the dynamics of the system. Furthermore, due to the high interconnectivity of ANN, 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 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. 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 has discrete-values. Furthermore the CNN processor cell’s 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 Automata or Continuous Automata are CA with continuous resolution. Depending on how the Continuous Automata is specified, it can also be a CNN. There is also Continuous Spatial Automata, which consists of 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 are more quantitative approach as oppose to a 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 chemical computers. Furthermore, it is conceivable that large CNN processors compared to the resolution of the input and output can be modeled as a Continuous Spatial Automata.

**Model of Computation**The dynamical behaviors of CNN processors can be expressed mathematically as a series of ordinary differential equations, where each equation represents the state of an individual processing unit. The behavior of the entire CNN processor is defined by its initial conditions, the inputs, the cell interconnect (topology and weights), and the cells themselves. One possible use of CNN processors is to generate and respond to signals of specific dynamical properties. For example, CNN processors have been used to generate multi-scroll chaos, synchronize with chaotic systems, and exhibit multi-level hysterisis. CNN processors are designed specifically to solve local, low-level, processor intensive problems expressed as a function of space and time. For example, CNN processors can be used to implement high-pass and low-pass filters and morphological operators. They can also be used to approximate a wide range of Partial Differential Equations (PDE) such as heat dissipation and wave propagation. CNN processors can be used as 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 diffusions, 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 multilayer CNN processor. RD processors can be used to create Voronoi diagrams and perform skeletonisation. The main difference between the chemical implementation and the CNN implementation is that CNN implementations are considerably faster 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.

Like CA, computations can be performed through the generation and propagation of signals that either grow or change over time. Computations can occur within a signal or can occur through the interaction between signals. One type of processing, which uses signals and is gaining momentum is wave processing, which involves the generation, expanding, and eventual collision of waves. Wave processing can be used to measure distances and find optimal paths. Computations can also occur through particles, gliders, solitions, and filterons localized structures that maintain their shape and velocity. Given how these structures interact/collide with each other and with static signals, they can be used to store information as states and implement different Boolean functions. Computations can also occur between complex, potentially growing or evolving localized behavior through worms, ladders, and pixel-snakes. In addition to storing states and performing Boolean functions, these structures can interact, create, and destroy static structures.

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 Machines (UTM), capable of 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, similar to the ANN solution to the problem stated by Marvin Minsky years ago. CNN processors have resulted in the simplest realization of Conway’s Game of Life and Wolfram’s Rule 110, the simplest, known universal 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 emergent behavior never seen before. Any information processing platform that allows the construction of arbitrary Boolean functions is called universal, and as result, this class CNN processors are commonly referred to as universal CNN processors. The original CNN processors can only perform linearly separable Boolean functions. This is essentially the same problem Marvin Minsky introduced with respect to the perceptions of the first neural networks In either case, by translating functions from digital logic or look-up table domains into the CNN domain, some functions can be considerably simplified. For example, the nine-bit, odd parity generation logic, which is typically implemented by eight nested exclusive-or gates, can also be represented by a sum function and four nested absolute value functions. Not only is there a reduction in the function complexity, but the CNN implementation parameters can be represented in the continuous, real-number domain.

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 off 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.

**Technology**An information processing platform remains nothing more than an intellectual exercise unless it can be implemented in hardware and integrated into a system. Although processors based on billiard balls can be interesting, unless their implementation provides advantages for a system, the only purpose they serve is a teaching device. CNN processors have been implemented using current technology and there are plans to implement CNN processors into future technologies. They include the necessary interfaces for programming and interfacing, and have been implemented in a variety of systems. This section will provide a cursory examination of the different types CNN processors available today, their advantages and disadvantages, and the future roadmap for CNN processors.

CNN processors have been implemented and are currently available as semiconductors, and there are plans to migrate CNN processors to emerging technologies in the future. Semiconductor-based CNN processors can be segmented into analog CNN processors, digital CNN processors, and CNN processors emulated using digital processors. Since analog CNN processors were the first to be developed, they will be discussed first. Analog computers were fairly common during the 1950 and 1960’s, but they gradually were replaced by digital computers the 1970’s. 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 algorithmically 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 processors producibility and utility. The CNN concept proved promising and by 2000, there were at least six organizations designing algorithmically programmable, analog CNN processors. This is when AnaFocus, a mixed-signal semiconductor company that was spun off the University of Seville, started with their ACE prototype CNN processor product line. Their first ACE processor contained 20x20 B/W processor units, their next ACE processor increase it to a 48x48 grayscale processor units, and their latest ACE processor contains 128x128 grayscale processor units. As time progressed, not only did the number of processing elements, their speed improved, the number of functions they can performed have increased, and an detector interface was seamlessly integrate into the silicon yielding a considerably improved interface. The ability to embed the detector interface into the CNN processor allows for real-time interaction between the sensing and processing. AnaFocus has a multilayer CASE prototype CNN processors line. The latest CASE processor is a three layer 32x32 CNN processor. Their work in CNN processors is currently culminating in their soon-to-be-released, commercially-available Eye-RIS product line that contains of all the processors, co-processors, software development kits, and support need to program and integrate an analog processor into a system. AnaFocus is working with AnaLogic Computers, to include their CNN processors into visual systems. Founded in 2000, by many of the same researchers behind the first algorithmically programmable CNN Universal Processor, AnaLogic Computers mission is to commercialize high-speed, biologically inspired systems based on CNN processors. In 2003, AnaLogic Computers developed a PCI-X visual processor board that included the ACE 4K processor, with a Texas Instrument DSP module and a high-speed frame-grabber. This allowed CNN processing to be easily included in a desktop computer, considerably improving the usability and capability of CNN analog processors. 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. The product that their developing team is now pursuing is the Bionic Eyeglass. 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 the functions that the Bionic Eyeglass system will perform is route number recognition and color processing. Some researchers are developed their own custom analog CNN processors. For exampole an analog CNN processor was developed from a research team from University degli Studi di Catania, in order to generate gaits for a hexapod robot. Researchers from National Chiao Tung University designed a RM-CNN processor to learn more about pattern learning and recognition and researcher from the National Lien-Ho Institute of Technology developed a Min Max CNN (MMCNN) processor to learn more about CNN dynamics. Given the diversity of CNN processors and the momentum that CNN research has gained, it is plausible that these unique analog CNN development efforts will be fairly common in the near future.

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 processes 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 various will change the trajectory of the system in phase space, resulting a lost of synchronicity or stability. Due to the severity of the problem, there is considerable research being performed in this field. Some researchers are optimizing templates to accommodate more 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. Last, there are researching 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. can not be implemented in a real-time analog CNN processor. Also, the semiconductor real state 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 depicted by Moore’s Law, will only result in minor improvements. For this reason, alternate technologies such as Resonant Tunneling Diodes and Neuron-Bipolar Junction Transistor are being explored. Also, the architecture of CNN processors is being reevaluated. For example, the Star-CNN processors, where one analog multiplier is time-shared between multiple processor units, has been proposed and is expected to result in processor unit reduction size of eighty percent. Although not nearly as fast and energy efficient, digital CNN processors do not share the problems of process variation and feature size as their analog counterparts. This allows digital CNN processors to included nested processor units, non-linearities, etc. In addition, digital CNN are more flexible, cost less and are easier to integrate. The most common implementation of digital CNN processors uses an FPGA. Eutecus, founded in 2002 and operating in Berkley, provides intellectual property that can be synthesized into an Altera FPGA. Their digital 320x280, FPGA-based CNN processors run at 30 frame/s and there are plans to make a fast digital ASIC. Eustecus is a strategic partner of AnaLogic computers, and their FPGA designs can be found in several of AnaLogic’s products. Eutecus is also developing software libraries to perform tasks including but not limited to video analytics for the video security market, feature classification, multi-target tracking, signal and image processing and flow processing. Many of these routines are derived using CNN-like processing. For those wanting to perform CNN simulations for prototyping, low-speed applications, or research, there are several options. First, there are precise CNN emulation software packages like SCNN 2000. If the speed is prohibitive, there are mathematical techniques, such as Jacobi’s Iterative Method or Forward-Backward Recursions that can be used to derive the steady state solution of a CNN processor. These can be performed by any mathematics tool, such as Matlab. Last, digital CNN processors can be emulated on highly-parallel, application-specific processors, specifically graphics processors. Implementing neural networks using graphics processors is an understood by the research community and it would not be a stretch to implement a CNN processor.

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 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, 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 to purchase today and will be in the foreseeable future.

**Applications**The philosophy, interests, and methodologies of CNN researchers are varied. Due to the potential of the CNN architecture, this platform has attracted people from a variety of backgrounds and disciplines. Some are exploring practical implementations of CNN processors, others are using CNN processors to model physical phenomena, and there are even researchers exploring theoretical mathematical, computational, and philosophical ideas through CNN processors. This chapter briefly explores what are CNN processors and what they are being used for. Some applications are engineering related, where some known, understood behavior of CNN processors is exploited to perform a specific task, and some are scientific, where CNN processors are used to explore new and different phenomenon. Hopefully this section will illuminate that CNN processors are versatile platforms that are being used for a variety of applications.

CNN processors were designed to perform image processing; specifically, the original application of CNN processors was to perform real-time ultra-high frame-rate (>10,000 frame/s) processing unachievable by digital processors needed 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, level and gain adjustments, color constancy detection, contrast enhancement, deconvolution, image compression, motion estimation, image encoding, image decoding, image segmentation, orientation preference maps, pattern learning/recognition, multi-target tracking, image stabilization, resolution enhancement, image deformations and mapping, image inpainting, optical flow, contouring, moving object detection, axis of symmetry detection, and image fusion. Due to their processing capabilities and flexibility, CNN processors have been used or has been prototyped for novel field applications such as flame analysis for monitoring combustion at a waste incinerator, mine-detection using infrared imagery, calorimeter cluster peak for high energy physics, anomaly detection in potential field maps for geophysics, laser dot detection, metal inspection for detecting manufacturing defects, and seismic horizon picking. They have also been used to perform biometric functions such as fingerprint recognition, vein feature extraction, face tracking, and generating visual stimuli via emergent patterns to gauge perceptual resonances. CNN processors have been used for medical and biological research in performing automated nucleated cell counting for detecting hyperplasia, segment images into anatomically and pathologically meaningful regions, measuring and quantifying cardiac function, measure the timing of neurons, detecting brain abnormalities that would lead to seizers. One potential future application of CNN microprocessors is to combine them with the DNA microarrays to allow for a near-real time DNA analysis of hundreds of thousands of different DNA sequences. Currently, the major bottleneck of this 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. CNN processors have also been used to generate and analyze patterns and textures. One motivation was to use CNN processors to understand pattern generation in natural systems. They were used to generate Turing Patterns in order to understand the situations in which they form, the different types of patterns which can emerge, and the presence of defects or asymmetries. Also, CNN processors were used to approximate pattern generation systems that create stationary fronts, spatio-temporal patterns oscillating in time, hysteresis, memory, and hetergenity. Furthermore, pattern generation was used to aid high-performance image generation and compression via real-time generation of stochastic and coarse-grained biological patterns, texture boundary detection, and pattern and texture recognition and classification.Control and Actuator Systems

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 that type of system [ ] . These Cellular Machine will eventually create a Sensor-Actuator Network (SAN), 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. The have been used as associate memories, optimize function via genetic algorithm, measuring distances, optimal path finding in a complex, dynamic environment, and theoretically be used to learn and associate complex stimuli. They have also been used to create antonymous gaits and low-level motor for robotic nematodes, spiders, and lamprey gaits using a Central Pattern Generator (CPG). They were able to function using only feedback from the environment, allowing for a robust, flexible, biologically inspired robot motor system. CNN-based systems were able to operate in different environments and still function if some of the processing units were disabled.

The variety of dynamical behavior seen in CNN processors make them intriguing for communication systems. Chaotic communications using CNN processors is being researched due their potential low power consumption, robustness and spread spectrum features. The premise behind chaotic communication is to used a chaotic signal for the carrier way and to use chaotic phase synchronization to reconstruct the message. CNN processors can be used on both the transmitter and receiver end to encode and decode the message. They can also be used for data encryption and decryption, source authentication through watermarking, detecting of complex patterns in spectrogram images (sound processing), and transient spectral signals detection.

CNN processors are neuromorphic processors, meaning that they emulate certain aspects of biological neural networks. The original CNN processors were based on mammalian retinas, which consist of a layer of 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 modeled the correct aspects of biological neural networks used to perform. However, CNN processors are not only 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.

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 for stochastic simulation techniques, which allows scientists to explore spin problems, population dynamics modes, lattice gas models, percolation, etc. Other simulation includes heat transfer, mechanical vibrating systems, protein production, Josephson Transmission Line (JTL), seismic wave propagation, and geothermal structures.

CNN processors have been used to research a variety of mathematical concepts, such as researching non-equilibrium systems, constructing non-linear systems of arbitrary complexity using a collection of simple, well-understood dynamic systems, studying emergent chaotic dynamics, generating chaotic signals, and in general discovering new dynamic behavior. They are often used in researching systemics, a trandisiplinary, scientific field that researches natural systems. Their goal is to develop a conceptual and mathematical framework necessary to analyze, model, and understand systems, including, but are not limited to, atomic, mechanical, molecular, chemical, biological, ecological, social and economic systems. Topics explore are emergences, collective behavior, local activity and its impact on global behavior, and quantifying the complexity of an approximately spatially and topologically invariant system. Although another measure of complexity many not make some people enthusiastic (Seth Lloyd, a professor from Massachusetts Institute of Technology (MIT), has identified 32 different definitions of complexity), it can be potentially be mathematically analyze systems such as economic and social systems.

**References**- L. Chua and L. Yang, “Cellular Neural Networks: Theory,” IEEE Trans. on Circuits and Systems, 35(10):1257-1272, 1988.

- L. Chua and L. Yang, “Cellular Neural Networks: Applications” IEEE Trans. on Circuits and Systems, 35(10):1273:1290, 1988.

- T. Roska, L. Chua, “The CNN Universal Machine: An Analogic Array Computer”, IEEE Trans. on Circuits and Systems-II, 40(3): 163-172, 1993.

- V. Cimagalli, M. Balsi, “Cellular Neural Networks: A Review”, Neural Nets WIRN Vierti, 1993.

- L. Chua, T. Roska, Cellular Neural Networks and Visual Computing: Foundations and Applications, 2005.

- 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.

- H. Harrer and J.Nossek, “Discrete-Time Cellular Neural Networks”, Int'l Journal of Circuit Theory and Applications, 20:453-467, 1992.

- T. Roska and L. Chua, “Cellular Neural Networks with Non-Linear and Delay-Type Template Elements and Non-Uniform Grids”, Int’l Journal of Circuit Theory and Applications, 20:469-481, 1992.

- S. Majorana and L. Chua, “A Unified Framework for Multilayer High Order CNN”, Int’l Journal of Circuit Theory and Applications, 26:567-592, 1998.

- 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.

- D. Balya, G, Tímar, G. Cserey, and T. Roska , “A New Computational Model for CNN-UMsand its Computational Complexity”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2004.

- M. Yalcin, J. Suykens, and J. Vandewalle, Cellular Neural Networks, Multi-Scroll Chaos And Synchronization, 2005.

- K. Yokosawa, Y. Tanji and M. Tanaka, “CNN with Multi-Level Hysteresis Quantization Output” Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

- 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.

- 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.

- M. Brugge, “Morphological Design of Discrete−Time Cellular Neural Networks”, University of Groningen Dissertation, 2005.

- 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.

- A. Adamatzky, B. Costello, T Asai “Reaction-Diffusion Computers”, 2005.

- 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.

- 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.

- 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.

- 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.

- F. Chen, G. He, X. Xu1, and G. Chen, “Implementation of Arbitrary Boolean Functions via CNN”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

- R. Doguru and 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.

- R. Dogaru and L. Chua, “Universal CNN Cells”, Int’l Journal of Bifurcations and Chaos, 9(1):1-48, 1999.

- R. Dogaru and L. O. Chua, “Emergence of Unicellular Organisms from a Simple Generalized Cellular Automata”, Int’l Journal of Bifurcations and Chaos, 9(6):1219-1236, 1999.

- T. Yang, L. Chua, “Implementing Back-Propagation-Through-Time Learning Algorithm Using Cellular Neural Networks”, Int’l Journal of Bifurcations and Chaos, 9(6):1041-1074, 1999.

- 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.

- 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.

- J. Nossek, G. Seiler, T. Roska, and L. Chua, “Cellular Neural Networks: Theory and Circuit Design,” Int’l Journal of Circuit Theory and Applications, 20: 533-553, 1998.

- 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.

- 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, L. Yang, and K. R. Krieg, “Signal Processing Using Cellular Neural Networks”, Journal of VLSI Signal Processing, 3:25-51, 1991.

- T. Roska, L. Chua, “The CNN Universal Machine: An Analogic Array Computer”, IEEE Trans. on Circuits and Systems-II, 40(3): 163-172, 1993.

- T. Roska and A. Rodriguez-Vazquez, “Review of CMOS Implementations of the CNN Universal Machine-Type Visual Microprocessors”, International Symposium on Circuits and Systems, 2000

- 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.

- 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. 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.

- 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.

- 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.

- 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.

- T. Roska, D. Balya, A. Lazar, K. Karacs, R. Wagner and M. Szuhaj, “System Aspects of a Bionic Eyeglass”, IEEE Int’l Symposium on Circuits and Systems, 2006.

- K. Karacst and T. Roskatt, “Route Number Recognition of Pubic Transport Vehicles via the Bionic Eyeglass”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

- R. Wagner and M. Szuhajt, “Color Processing in Wearable Bionic Glasses”

- 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.

- 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

- 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.

- 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.

- 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.

- 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.

- F. Sargeni, V. Bonaiuto and M. Bonifazi, “Multiplexed Star-CNN Architecture”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

- Z. Kincsest, Z. Nagyl, and P. Szolgay, “Implementation of Nonlinear Template Runner Emulated Digital CNN-UM on FPGA”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

- W. Fangt, C. Wang and L. Spaanenburg, “In Search of a Robust Digital CNN System” Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

- Z. Voroshazit, Z. Nagyt, A. Kiss and P. Szolgay, “An Embedded CNN-UM Global Analogic Programming Unit Implementation on FPGA”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

- Eutecus Homepage (http://www.eutecus.com/).

- A. Loncar, R. Kunz and R. Tetzaff, “SCNN 2000 - Part I: Basic Structures and Features of the Simulation System for Cellular Neural Networks”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2000.

- V. Tavsanoglu, “Jacobi’s Iterative Method for Solving Linear Equations and the Simulation of Linear CNN”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

- B. Shi, “Estimating the Steady State using Forward and Backward Recursions”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

- S. Tokes, L. Orzo, and A. Ayoub, “Programmable OASLM as a Novel Sensing Cellular Computer”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

- 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.

- J. Flak, M. Laiho1, and K Halonen, “Programmable CNN Cell Based on SET Transistors”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

- 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.

- 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.

- 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.

- L. Torok and A. Zarandy, “CNN Based Color Constancy Algorithm”, Int’l Workshop on Cellular Neural Networks and Their Applications, 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.

- L. Orzo, “Optimal CNN Templates for Deconvolution”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2006

- P. Venetianer and T. Roska, “Image Compression by Cellular Neural Networks,” IEEE Trans. Circuits Syst., 45(3): 205-215, 1998.

- 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.

- 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.

- H. Aomori, T. Otaket, N. Takahashi, and M. Tanaka, “A Spatial Domain Sigma Delta Modulator Using Discrete Time Cellular Neural Networks”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

- H. Kimt, H. Son. J. Lee, I. Kimt and I. Kimt, “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.

- 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.

- 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.

- 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.

- 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.

- 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.

- 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.

- 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.

- A. Gacsadi and P. Szolgay, “Image Inpainting Methods by Using Cellular Neural Networks”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2005.

- 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.

- 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.

- 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.

- 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.

- 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.

- 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.

- 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.

- 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.

- 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. Tetzlaff1, A. Blug and H. Hoefler, “Visual Inspection of Metal Objects Using Cellular Neural Networks”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

- 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.

- 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.

- S. Malki, Y. Fuqiang, and L. Spaanenburg, “Vein Feature Extraction Using DT-CNNs”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

- 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.

- 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.

- 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.

- 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.

- Z. Szalkat, G. Soost, D. Hilliert, L. Kektt, G. Andrassy and C. Rekeczkytt, “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.

- 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.

- 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.

- 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.

- L. Fortuna, P. Arena, D. Balya, and A. Zarandy, “Cellular Neural Networks: A Paradigm for Nonlinear Spatio-Temporal Processing”, IEEE Circuits and Systems Magazine, 1(4): 6-21, 2001.

- 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.

- A. Slavova and M. Markovat, “Receptor Based CNN Model with Hysteresis for Pattern Generation”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

- L. Komatowskit, K. Slot , P. Dqbiec, and H. Kim, “Generation of Patterns with Predefined Statistical Properties using Cellular Neural Networks”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

- C. Lin and S. Chen, “Biological Visual Processing for Hybrid-Order Texture Boundary Detection with CNN-UM”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

- G. Costantini, D. Casali, and M. Carota, “A Pattern Classification Method Based on a Space-Variant CNN Template”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

- E. David, P. Ungureanu, and L. Goras, “On he Feature Extraction Performances of Gabor-Type Filters in Texture Recognition Applications”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

- C. Lin and Y. Shou, “Texture Classification and Representation by CNN based Feature Extraction”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2005.

- T. Roska and L. O. Chua, “The CNN Universal Machine: 10 Years Later, Journal of Circuits, Systems, and Computers”, Int’l Journal of Bifurcation and Chaos, 12(4):377-388, 2003.

- M. Haenggi, “Mobile Sensor-Actuator Networks: Opportunities and Challenges”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2002.

- R. Bise, N. Takahashi and T. Nishi, “On the Design Method of Cellular Neural Networks for Associate Memories Based on Generalized Eigenvalue Problem”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2002.

- D. Balya and V. Galt, “Analogic Implementation of the Genetic Algorithm”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

- I. Szatmhri, “The Implementation of a Nonlinear Wave Metric for Image Analysis and Classification on the 64x64 I/O CNN-UM Chip”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2000.

- 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.

- I. Gavrilut, V. Tiponut, and A. Gacsadi, “Path Planning of Mobile Robots by Using Cellular Neural Networks”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

- P. Arena, P. Crucitti, L. Fortuna, M. Frasca, D. Lombardo and L. Patane, “Perceptive Patterns For Mobile Robots via RD-CNN and Reinforcement Learning”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

- P. Arena, L. Fortuna, M. Frasca, and L. Patane, “CNN Based Central Pattern Generators with Sensory Feedback”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2005.

- R. Caponetto, L. Fortuna, L. Occhipiniti, and M. G. Xibilii, “SC-CNN Chaotic Signals Generation”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2002.

- 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.

- 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.

- 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.

- 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.

- 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.

- Z. Nagyt, Z. Voroshazi and P. Szolgay, “A Real-time Mammalian Retina Model Implementation on FPGA”, 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.

- V. Perez-Munuzuri, A. P. Munuzuri, M. Gomez-Gesteria, V. Perez-Villar, L. Pivka, and L. Chua, “Nonlinear Waves, Patters, and Spatio-Temporal Chaos in Cellular Neural Networks,” Phil. Trans. R. Soc. Lond. A, (353): 101-113, 1995.

- M. Ercsey-Ravasz, T. Roska and Z. Neda, “Random Number Generator and Monte Carlo type Simulations on the CMM-UM”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

- 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.

- P. Szolgay, T. Hidvegi, Z. Szolgay and P. Kozma, “A Comparison of the Different CNN Implementations in Solving the Problem of Spatiotemporal Dynamics in Mechanical Systems ”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2000.

- 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.

- 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.

- P. Sonkolyt, P. Kozmat, Z. Nagyt and P. Szolgay, “Acoustic Wave Propagation Modeling on CNN-UM Architecture”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

- S. Kocsardit, Z. Nagyt, S. Kostianevt and P. Szolgay, “FPGA Based Implementation of Water Injection in Geothermal Structure”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

- R. Brown and L. Chua, “Chaos or Turbulence”, Int’l Journal of Bifurcation and Chaos, 2(4):1005-1009, 1992.

- P. Arena, L. Fortuna, G. Vagliasindi and A. Basile, “CNN Chip And FPGA To Explore Complexity”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2005.

- E. Gunay, M. Alci and S. Parmaksizoglu , “N-Scroll Generation in SC-CNN via Neuro Fuzzy Based Non-Linear Function”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

- M. Gilli, F. Corinto, and P. Checco, “Periodic Oscillations and Bifurcations in Cellular Nonlinear Networks”, IEEE Trans. on Circuits and Systems – I, 51(5):948-962, 2004.

- K. A. Richardson, “Systems Theory and Complexity: Part 1”, Emergence: Complexity and Organization, 6(3):75-79.

- K. A. Richardson, “Systems Theory and Complexity: Part 2”, Emergence: Complexity and Organization, 6(4):77-82.

- K. A. Richardson, “Systems Theory and Complexity: Part 3”, Emergence: Complexity and Organization, 7(2):104-114.

- P. Anderson, “Emergence”, Proceedings of the Second Int’l Conference on Complex Systems, 2004.

- K. Mainzer, “CNN and the Evolution of Complex Information Systems in Nature and Technology”, Int’l Workshop on Cellular Neural Networks and Their Applications, 2002.

- S. Lloyd, Programming the Universe, 2006.

- L. Chua, “Local Activity is the Origin of Complexity”, Int’l Journal of Bifurcation and Chaos, 15(11):3435-2456, 2005.

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