146

IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 37, NO. 1, JANUARY 2009

First Application of Cellular Nonlinear Network Methods to the Real-Time Identification of Hot Spots in JET Guido Vagliasindi, Student Member, IEEE, Andrea Murari, Paolo Arena, Senior Member, IEEE, Luigi Fortuna, Fellow, IEEE, Gilles Arnoux, Eric Gauthier, and JET EFDA Contributors

Abstract—In order to qualify materials and develop integrated scenarios for ITER, Joint European Torus (JET) is going to operate with a new wall consisting of beryllium in the main chamber and tungsten in the divertor. These new materials will require particular care when the machine operates, considering that they are much more vulnerable than the present combination of graphite and stainless steel. Early detection of hot spots, which are regions of the first wall where the temperature approaches dangerous levels, is considered one essential element in the safety strategy. In this paper, cellular nonlinear networks (CNNs) are applied to the task of detecting hot spots in the infrared images of JET wide-angle camera. The ability of the CNNs to process the pixels of the images in parallel makes this technology a very good candidate for this task. Various algorithms are presented, which can locate the hot regions in any part of the image with a temporal resolution on the order of 60 ms, which is considered adequate for safety purposes at JET. In addition to the frame-by-frame static identification of the hot spots, their evolution in time is also followed to determine if they approach dangerous parts of the vacuum vessel. The potential of the CNNs would therefore allow for the implementation of alternative protection strategies, such as following the increase and displacement of the hot spots inside the entire vacuum vessel and identifying particles dropping into the plasma. Index Terms—Cellular nonlinear networks (CNNs), hot spots, infrared (IR) imaging, tokamak.

I. I NTRODUCTION

I

N THE present generation of magnetic confinement fusion machines, graphite is the most used material for the divertor,

Manuscript received August 3, 2007; revised March 13, 2008 and July 23, 2008. Current version published January 8, 2009. G. Vagliasindi, P. Arena, and L. Fortuna are with the Dipartimento di Ingegneria Elettrica Elettronica e dei Sistemi, Università degli Studi di Catania, 95125 Catania, Italy (e-mail: [email protected]). A. Murari is with the Consorzio RFX, Associazione EURATOM ENEA per la Fusione, 35127 Padua, Italy. G. Arnoux is with the Association EURATOM-CEA, DSMDRFC, CEA Cadarache, 13108 Saint Paul lez Durance, France and also with the Euratom/UKAEA Fusion Association, Culham Science Centre, Oxon OX14 3DB, Abingdon, U.K. E. Gauthier is with the Association EURATOM-CEA, DSMDRFC, CEA Cadarache, 13108 Saint Paul lez Durance, France. JET-EFDA is located at the Culham Science Centre, OX14 3DB, Abingdon, U.K., and JET EFDA Contributors are listed in the annex of M. L.Watkins et al., “Overview of JET results,” in Fusion Energy 2006, Proc. 21st IAEA Conf., Chengdu, 2006. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPS.2008.2005985

where most of the plasma–wall interactions take place, whereas in the main chambers, stainless steel is the typical choice. The main advantage of graphite resides in its high sublimation point of about 2000 ◦ C and low Z. At this temperature, instead of melting, carbon evaporates and leads to increased radiation in the plasma edge, hence reducing the peak loads on the wall without increasing the radiation losses in the core. On the Joint European Torus (JET), the main chamber plasma facing components are in carbon fiber composite, whose heat conductivity is about 200 W/m · K. Despite its great advantages, carbon is not considered a realistic candidate for the long-term future due to excessive fuel retention [1]. Therefore, alternative wall materials have to be identified. The ITER design foresees a beryllium (Be) wall and a tungsten (W) divertor, with a minimum amount of graphite, i.e., the tiles hit by the strike points. To support the design and preparation of ITER, JET will install a completely new wall, consisting of Be in the main chamber and W in the divertor [2]. The implementation of a fully metallic wall will assess the compatibility between the scenarios being developed and the properties of ITER-relevant materials, which is one of the crucial steps on the development of a viable fusion reactor. On the other hand, the use of JET with a full metal wall will pose significant safety and operational issues. Particular attention will have to be devoted to the integrity of the first wall, considering that Be is certainly a much less forgiving material than the present ones. In this framework, significant developments of JET imaging diagnostics are under way, considering that video cameras are considered the best solution for surveillance. Detection in both the visible and the infrared (IR) wavelength will be used. From the point of view of monitoring the status of the first wall, IR thermography will play a central role (Section II). Given the high input power to be injected in JET plasmas, now up to 25 MW of additional power that will be upgraded to 45 MW for future operation, preserving the integrity of the first wall real-time image processing will be indispensable. The time scales for successful detection of problems and timely recovery actions are estimated to be on the order of 100 ms. In order to analyze images at that speed, the technology of cellular nonlinear networks (CNNs) is being investigated (see Section III). The main advantage of this paradigm and the technology used to implement it resides in the fact that the image pixels can be processed in parallel. This, together with a series of already available algorithms, allows for the development of quite sophisticated but at the same time

0093-3813/$25.00 © 2008 IEEE

Authorized licensed use limited to: UNIVERSITA DI CATANIA. Downloaded on March 2, 2009 at 06:59 from IEEE Xplore. Restrictions apply.

VAGLIASINDI et al.: APPLICATION OF NETWORK METHODS TO IDENTIFICATION OF HOT SPOTS IN JET

Fig. 1.

147

Structure of JET IR wide-angle camera system.

relative fast image-processing schemes. Using the chip platform ACE16K, the CNN technique is applied to the images of JET IR wide-angle camera for the real-time identification of hot spots (see Section IV). Quick detection of regions where the temperature exceeds the safety level, the hot spots, is considered an essential element in the safety strategy for JET operation with the Be wall in order to prevent melting and other accidents. Two different approaches have been investigated. The first one consists of a static method, whereby for each individual image, the areas exceeding predefined dimensions and photon emission are identified. A second alternative proceeds in a dynamic way by analyzing the difference between subsequent frames and following the time evolution of the hot spots. This can prove to be useful in implementing a differential safety strategy by issuing alarms before hot spots hit particular dangerous parts of the vessel, such as the radio frequency antennas. Moreover, such an incremental analysis of IR images has the potential of allowing detection, in real time, of macroscopic dust present in the plasma and its movements during the discharge. II. JET IR W IDE -A NGLE C AMERA Given the importance of the plasma–wall interactions in the present and future JET program, a new dedicated endoscope providing a wide-angle view (field of view of 70◦ ) in the IR range (3.5–5 μm) has just been installed. It allows one to, for the first time, study the power loads and IR thermography in the JET main chamber (until 2004/2005, shutdown IR views were limited to the divertor). The endoscope consists of a metallic tube containing the front head mirrors, a Cassegrain telescope, and a relay group of lenses, which finally transfers the collected image to the input optics of the camera, located outside the endoscope [3]. An overview of the system is shown in Fig. 1. It is worth mentioning that in order to increase the reactor relevance of the diagnostic, reflective optical components were chosen for the front end, considering that lenses are believed to be unable to sustain the high neutron radiation in ITER. The diagnostic has a global transmission higher than 60%, and it is designed to cover the entire temperature range from the JET operating temperature of 200 ◦ C up to a maximum temperature of 2000 ◦ C. The system has an overall spatial resolution of 2 cm at 3 m, determined experimentally on the bench using the modulation transfer function technique.

Fig. 2. Frame from the KL7 IR camera (#66736).

At full image size, a frame rate of 100 Hz can be achieved, and it can be increased up to 10 kHz by reducing the image size to 128 × 8 pixels. The camera provides also an analog video output, which is meant to be the input to the CNNs (see Section V) in the final version of a new project, aimed at testing this technology during subsequent JET campaigns. A typical image acquired during a JET discharge is shown in Fig. 2. III. CNNs: P ARADIGM AND I MPLEMENTATION The abstract concept of CNNs was originally introduced by Chua and Yang [4] in 1988 and can be concisely described as a 1-, 2-, or 3-D infinite array of nonlinear dynamic units called cells, located at the nodes of the array. The cells interact locally via weighted connections and within a finite radius r, which can be defined depending on the application and which is called the neighborhood of the cell. Various mathematical models have been developed to determine the value of the core cell on the basis of its input and the neighborhood. The one adopted in the implementation described in this paper is the full signal range model [5]. For various models, libraries of functions implementing basic operations on the cells are available. These basic functions are called templates and allow one to use basic steps such as thresholding or interpolation. The simplest templates are linear, time, and space invariant. The paradigm of the CNNs has been applied to a wide series of applications, ranging from image processing to differential equation solutions, as well as modeling of complex biological systems. The local connectivity and the repetition of identical cells render the CNNs particularly suited to VSLI implementation. Moreover, the inherent potential of the CNNs to process various cells in parallel is a competitive advantage which makes them particularly useful in real-time applications. Indeed, their analog local core permits parallel processing because the exchange of information between the cells can take place in a very short

Authorized licensed use limited to: UNIVERSITA DI CATANIA. Downloaded on March 2, 2009 at 06:59 from IEEE Xplore. Restrictions apply.

148

IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 37, NO. 1, JANUARY 2009

time. On the other hand, the analog nature of the original architecture results in a lack of programmability, which can be a significant drawback. To overcome this difficulty, Chua and Roska [6] introduced the CNN—universal machine (CNNUM), which tries to combine the advantages of both analog and digital domains. The CNN-UM architecture, which provides the capability to program sequential operations and to store the intermediate results, consists of the following: 1) an array of locally connected nonlinear analog processors; 2) a set of local memories to store, pixel by pixel, the intermediate computational results; 3) a programming memory. It can be demonstrated that this computational paradigm is as universal as a Turing machine [7]. Moreover, once implemented as a mixed-signal VLSI chip, this architecture is capable of performing real-time processing at a rate of billions of operations per second. The hardware implementation used in the applications described in this paper is the ACE16K [8], the third generation of CNN chips, developed following the concept of singleinstruction multiple-data architectures. It consists of an array of 128 × 128 identical analog cells. Each cell is called a processing unit and comprises the following functional blocks: 1) photoreceptors—to perform acquisition of images directly through the focal plane in different lighting conditions; 2) analog processing unit—which permits the execution of analog instructions, such as convolutions on grayscale images; 3) logic processing units—for the storage of up to eight grayscale images and two binary ones. The images can be acquired directly by the device or can be provided by means of a 32-b bidirectional data bus (this second alternative is the feature used in the applications described in this paper). The chip guarantees the following performance: 1) 330 gigaoperations per second of peak computing figures; 2) imagewise Boolean combination in less than 200 ns; 3) accomplishes linear convolution of 33 × 33 neighborhood in less than 3 μs. IV. A PPLICATION OF CNNs TO JET IR W IDE -A NGLE C AMERA I MAGES Considering that, as already mentioned, preserving the integrity of the plasma facing components will be one of the main issues presented by the operation of JET with a Be wall, the CNN technology was applied to the real-time identification of hot spots, considering, naturally, the points more prone to significant damage. A systematic analysis of JET cameras’ data showed that there are three main sources of high emission in the IR region of the spectrum in JET (Fig. 3). Some parts of the vacuum vessel, such as the limiters or target plates in the divertor, can reach high temperatures (1500 ◦ C) because they are the regions where most of the plasma–wall interactions take place in normal conditions. These locations will have to be monitored continuously once the new JET wall is installed in

Fig. 3. Example of the three main types of hot spots, as seen with the JET wide-angle IR camera (#66503). The smallest circular bright spots are particles entering the plasma. The big crescent-shaped bright regions are on the limiters, locations designed to withstand high powers. Some smaller bright spots on top are due to plasma–wall interactions changing fast with time.

order to understand the behavior of the materials and to guarantee safety while the device is in operation. On the other hand, these regions are designed to withstand high-energy fluxes [9], and therefore, specific thresholds will have to be used for them. Moreover, their position and shape are fixed, even if the image could be shaken during big ELMs or disruptions, and therefore, their monitoring is relatively straightforward. A different source of high IR emission appears when other parts of the first wall, not meant to absorb a lot of energy, are subject to strong heating in case of particular events, such as disruptions, ELMs, or errors in the setup of the magnetic configuration. The shape of these hot spots can be very different and their location inside the viewing cone of the camera quite unpredictable. Moreover, their position can change during the discharge. In particular, during fast events, with a typical time scale of 1 ms or less, such as ELMs and disruptions, a third source of IR emission can be due to particles ejected from the first wall, which enter into the plasma. If these particles are big enough that they are not immediately vaporized, when they are struck by the plasma, they can reach high temperatures and be clearly detected in the IR images. They have normally relatively small dimensions and a fast changing position inside the field of view. The different natures of these IR emissions suggested the development of two different types of algorithms for the identification of the hot spots. The first one, for the so-called static detection (see Section IV-A), performs the analysis of a single frame at the time. It is more suited to the monitoring of the fixed parts of the machines, such as the plasma facing components (limiters and divertor). A second approach, called dynamic detection (see Section IV-B), is based on the difference between subsequent frames. These algorithms are more complicated; however, they

Authorized licensed use limited to: UNIVERSITA DI CATANIA. Downloaded on March 2, 2009 at 06:59 from IEEE Xplore. Restrictions apply.

VAGLIASINDI et al.: APPLICATION OF NETWORK METHODS TO IDENTIFICATION OF HOT SPOTS IN JET

Fig. 4.

149

Flowchart of the algorithm for the static identification of the hot spots.

allow for the monitoring of the growth of the hot spots and their movements inside the field of view. A. Static Detection of Hot Spots This algorithm, as already mentioned before, is intended for monitoring those kinds of hot spots which appear in fixed positions as a consequence of the high temperature reached by particular regions of the vacuum vessel. Fig. 4 shows a flow diagram of this algorithm. After an INITIALIZATION phase, during which all the constants and variables required by the algorithm (such as threshold or templates values) are initialized, a frame is extracted from the video sequence, and an INVERSION operation is performed on it. This step is required as the CNNs operate with a gray scale inverted with respect to the usual image-processing software. Subsequently, a THRESHOLD operation is performed with a predefined threshold to select, from the image, those pixels which have a higher luminosity that, in an IR image, represents also a higher temperature. The “thresholded” image is then filtered in order to eliminate isolated high-luminosity pixels which are likely to be noise

Fig. 5. spots.

Flowchart of the algorithm for the dynamic identification of the hot

TABLE I UNITS FOR MAGNETIC PROPERTIES

caused by the CNN analog processing or camera noise likely to be induced by neutrons. Subsequently, the filtered image is “ANDed,” with some masks depicting the various regions of the vacuum vessel. In the specific application described here, the regions taken into account are the limiters and the RF antennas in the field of view of the camera; however, other parts could be included just by modifying the masks. Then, the result of the AND, which represents the pixels above the predefined threshold in the specific region, is subjected to a

Authorized licensed use limited to: UNIVERSITA DI CATANIA. Downloaded on March 2, 2009 at 06:59 from IEEE Xplore. Restrictions apply.

150

IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 37, NO. 1, JANUARY 2009

Fig. 6. Outputs of the image-processing flow of the dynamic algorithm (#66503). (a) Frame N . (b) N + 1. (c) Output of the filtering step on frame N . (d) Output of the filtering on frame N + 1. (e) Difference between (c) and (d).

pixel counting, and the result is compared with a numeric threshold K. This value represents the minimal area, expressed in number of pixels, of the region whose emission is above the specified threshold (the value defined by the parameter THRESHOLD). If this area is above the threshold, a warning message is provided; otherwise, the processing goes on with the next frame in the video sequence. Obviously, both the threshold for the binarization and the area dimension can be customized for each region of the first wall. This way, it is possible to specify both the IR emission considered dangerous and the dimension of the area, above that emission level, which represent a threat for the specified region. Hence, if a part of the machine can cope with higher temperatures, it is possible to rise the threshold for the binarization and fix a bigger warning area. On the other hand, if a region is more sensible to overheating, the threshold can be fixed at a lower value, and a warning can be provided for smaller hot areas in that zone.

particular, to focus on the dynamic changes of the images, the difference between a frame and the previous one is the basis of the analysis technique. In more detail, the first steps, apart from the starting initialization phase, comprise the INVERSION and THRESHOLD operations which are the same as the algorithm described in the previous section. Subsequently, the image is filtered in order to eliminate the spurious pixels. Then, the two frames (N and N + 1) are subtracted from each other, performing a XOR logical function, in order to select only the pixels which differ between the two images, followed by an AND, whose role is to select the new hot pixels which appear only in the new frame. This way, only displacements or increases in the size of the hot spots are detected, assuming that these are the only dynamic changes which are really interesting, for safety purposes. Finally, the pixel counting is performed. This way, the output of this step represents only the area of the hot spots’ dynamic parts due to growth or to movement. C. Experimental Results

B. Dynamic Detection of Hot Spots In this case, the objective of the processing is to monitor the dynamic evolution of the hot regions during the experiments. The devised algorithm is shown in Fig. 5. The steps are similar to the ones described in the previous section, except for some additional ones required by the different emphases on the time evolution of the images. In

Both algorithms were tested using frames acquired by the KL7 camera. The algorithms were executed on the Aladdin Professional platform [10], the hardware platform that hosts the chip. The ACE16K is able to process an image of 128 × 128 pixels; however, it is possible to process wider images by performing a tiling, i.e., the decomposition of the starting

Authorized licensed use limited to: UNIVERSITA DI CATANIA. Downloaded on March 2, 2009 at 06:59 from IEEE Xplore. Restrictions apply.

VAGLIASINDI et al.: APPLICATION OF NETWORK METHODS TO IDENTIFICATION OF HOT SPOTS IN JET

image in portions of 128 × 128, which are processed by the chip and then joined together to rebuild the whole frame. As the images available from the videos taken into account for this work are 408 × 504 pixel wide, a total of 16 (4 × 4) tiling steps would be required to process the whole frame. As parts of the image are not relevant to the end of detecting hot spots (because they include regions of the vessel not in contact with the plasma), the frame was cropped before it was processed in order to reduce the total number of tiling steps. The processed image is reduced to 384 × 384, eliminating also the portion of the frame which shows the divertor, as there is already another IR camera (KL3) that monitors this part of the machine with greater spatial accuracy. The execution times for both algorithms are reported in Table I. The execution time is about 60 ms in order to process the whole 384 × 384 frame. The time required to process only a 128 × 128 subframe is on the order of 10 ms. This higher time resolution could be very helpful for machine protection. For instance, particularly delicate parts of the machine, such as the RF antennas (which occupy a region of the image not wider than two 128 × 128 images) could be monitored with a high time resolution. To illustrate graphically the various process of the image processing, Fig. 6 shows the output of the various step of the dynamic algorithm shown in Fig. 5. Fig. 6(a) shows the input frame N , while Fig. 6(b) shows the input frame N + 1. Fig. 6(c) and (d) shows the outputs of the thresholding and filtering for frames N and N + 1, respectively. The two pictures are subtracted from each other, producing the output shown in Fig. 6(e). V. F UTURE P ROSPECTS The approach reported in this paper is the first application of CNN-based algorithms and hardware for real-time identification of hot spots. The adoption of the ACE16K chip allows for the full processing of the frame in about 60 ms. The time resolution can be significantly increased to 10 ms if, instead of the full frame, only a specific 128 × 128 portion of the image is processed. To further assess the capability of the CNN approach, a device hosting the ACE16K is installed at JET during the 2007 shutdown for operation during the entire JET campaigns. This allows for proving the potential of the technology in the real environment of a reactor-grade tokamak experiment. In the context of this project, the ACE16K is connected directly to the video output of the wide-angle camera. This is expected to result in an improvement of the performance in terms of speed, considering that the uploading of the frames from the camera should be faster than in the present tests on the bench. R EFERENCES [1] G. Janeschitz and ITER JCT and ITER HTs, “Plasma–wall interaction issues in ITER,” J. Nucl. Mater., vol. 290–293, pp. 1–11, Mar. 2001. [2] J. Paméla et al., “The JET programme in support of ITER,” Fusion Eng. Design, vol. 82, no. 5, pp. 590–602, Oct. 2007. [3] E. Gauthier et al., “Iter-like wide-angle infrared thermography and visible observation diagnostic using reflective optics,” Fusion Eng. Des., vol. 82, no. 5–14, pp. 1335–1340, Oct. 2007. [4] L. O. Chua and L. Yang, “Cellular neural networks: Theory,” IEEE Trans. Circuits Syst., vol. 35, no. 10, pp. 1257–1272, Oct. 1988.

151

[5] S. Espejo, A. Rodriguez-Vazquez, R. Dominguez-Castro, and R. Carmona, “Convergence and stability of the FSR CNN model,” in Proc. 3rd Int. Workshop CNNA, Rome, Italy, Dec. 18–21, 1994, pp. 411–416. [6] T. Roska and L. O. Chua, “The CNN universal machine: An analogic array computer,” IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process., vol. 40, no. 3, pp. 163–173, Mar. 1993. [7] K. R. Crounse and L. O. Chua, “The CNN universal machine is as universal as a Turing machine,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 43, no. 4, pp. 353–355, Apr. 1996. [8] A. Rodríguez-Vázquez et al., “ACE16K: The third generation of mixedsignal SIMD-CNN ACE chips toward VSoCs,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 51, no. 5, pp. 851–863, May 2004. [9] P. Andrew et al., “Transient heat loads on the JET main chamber wall,” in Proc. 34th EPS Conf. Control Fusion Plasma Phys., Warsaw, Poland, Jul. 2–6, 2007. [10] A. Zaràndy, T. Roska, P. Szolgay, S. Zöld, P. Földesy, and I. Petràs, “CNN chip prototyping and development systems,” in Proc. ECCTDDAD, Stresa, Italy, 1999, pp. 69–81.

Guido Vagliasindi (S’04) was born in Catania, Italy, in 1979. He received the M.S. degree in electrical engineering and the Ph.D. degree in electronic and automation engineering from the Università degli Studi di Catania, Catania, in 2003 and 2007, respectively. He currently holds a postdoctoral position with the Dipartimento di Ingegneria Elettrica Elettronica e dei Sistemi, Università degli Studi di Catania. His main scientific interests are focused on cellular nonlinear networks and image and signal processing applied to nuclear fusion experiments.

Andrea Murari was born in Verona, Italy, on August 19, 1963. He received the B.A. degree in applied electronics, the M.S. degree in plasma engineering, and the Ph.D. degree in nuclear power plants from the University of Padova, Padua, Italy, in 1989, 1991, and 1993, respectively. He has mainly worked in the field of measurements for nuclear fusion experiments. He has installed various diagnostic systems on several European experiments, and between 1998 and 2002, he was responsible for the support to all the diagnostics of the RFX experiment. Since 2002, he has been the Task Force Leader for Diagnostics (TFD) at the Joint European Torus (JET). Since 2003, he has been a member of the Euroforum working group on measurements. Since January 2008, he has been a Co-Chair of the European Fusion Development Agreement (EFDA) Topical Group on Diagnostics and the Coordinator of the European Delegation to the International Tokamak Programme Agreement (ITPA) Topical Group on Diagnostics. In 2008, he has also been nominated as the Group Leader of Diagnostics Control and Data Acquisition in JET. He is currently with Consorzio RFX, Associazione EURATOM ENEA per la Fusione, Padua.

Paolo Arena (S’93–M’97–SM’01) received the Master degree in electronic engineering and the Ph.D. degree in electrical engineering from the University of Catania, Catania, Italy, in 1990 and 1994, respectively. He is currently an Associate Professor of System Theory with the Dipartimento di Ingegneria Elettrica Elettronica e dei Sistemi, Università degli Studi di Catania, Catania. He published more than 130 technical papers, six books, and several international patents. His research interests include adaptive and learning systems, nonlinear systems, neural networks, cellular neural networks, collective behavior in living and artificial neural structures, and cognitive systems. Dr. Arena served as an Associate Editor of the IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—PART I.

Authorized licensed use limited to: UNIVERSITA DI CATANIA. Downloaded on March 2, 2009 at 06:59 from IEEE Xplore. Restrictions apply.

152

IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 37, NO. 1, JANUARY 2009

Luigi Fortuna (M’90–SM’99–F’00) received the M.S. degree in electrical engineering from the Università degli Studi di Catania, Catania, Italy, in 1977. Until 1987, he was a Researcher in electronics with the Dipartimento di Ingegneria Elettrica Elettronica e dei Sistemi, Università degli Studi di Catania, where he later became an Associate Professor of automatic control. He has been a Full Professor of system theory since 1994 and is currently the Dean of the School of Engineering. He has coordinated research projects that are supported by public institutions and a consortium of private companies. He is the coauthor of six books, among which is Cellular Neural Networks (Springer, 1999). He is the holder of several U.S. patents. His research interests include nonlinear science and complexity, chaos, and cellular neural networks, with applications in bioengineering.

Gilles Arnoux, photograph and biography not available at the time of publication.

Eric Gauthier, photograph and biography not available at the time of publication.

Authorized licensed use limited to: UNIVERSITA DI CATANIA. Downloaded on March 2, 2009 at 06:59 from IEEE Xplore. Restrictions apply.