neuron-request@HPLMS2.HPL.HP.COM ("Neuron-Digest Moderator Peter Marvit") (02/28/91)
Neuron Digest Wednesday, 27 Feb 1991 Volume 7 : Issue 11 Today's Topics: Kohone's Network Intro and Help Alopex algorithm and ANNs New M.A. Course in the U.K. Student Conference Sponsorships Limited precision implementations (updated posting) Special message to SF Bay Area Neural Net Researchers Looking for Phoneme Data Postdoc & Research Assistant openings in the COGNITIVE & NEURAL BASES OF LEARNI summer position neural net position available Question regarding Back-propagation Rule........ RE: Transputers for neural networks? Send submissions, questions, address maintenance and requests for old issues to "neuron-request@hplabs.hp.com" or "{any backbone,uunet}!hplabs!neuron-request" Use "ftp" to get old issues from hplpm.hpl.hp.com (15.255.176.205). ------------------------------------------------------------ Subject: Kohone's Network From: harish@enme.ucalgary.ca (Anandarao Harish) Date: Tue, 05 Feb 91 15:11:32 -0700 I was wondering whether any of you had some information for me on Kohonen's network. I am a mechanical engr. student working in the area of Computer aided Manufacturing (specifically in the area of machine cell design) and was thinking of using kohonen's network for the problem of machine cell grouping. I would really appreciate if you could inform me of a simulation package available (like the backpropagation algorithm by Donald R. Tveter) you know of, that is available on public domain. Thanking you harish Harish A. Rao Dept. of Mechanical Engr. The University of Calgary Calgary, Canada ------------------------------ Subject: Intro and Help From: JHDCI@canal.crc.uno.edu Date: Tue, 12 Feb 91 21:38:00 -0600 I am a doctoral student in education at the University of New Orleans and am planning on writing my dissertation on some form of simulation as it applies to education...e.g., class room simulation, curriculum sim., trend sim., etc. ad nauseum. I have been avidly reading everything I can get my hands on concerning neural nets, complexity, genetic algorithms, cellular automata, emergence, and anything else that appears nonlinear. There appears to be more than enough literature. I have been especially impressed with "Genetic Algorithms..." by David Goldberg although I am having a little trouble in reading the PASCAL code (I, unfortunately write in QuickBasic). Chris Langton's writings have also influenced my thinking and given me a mad desire to create an "Artificial School." My desires are for a reasonably simple computer simulation program (public domain if possible) that can be run on a PC. I would also like to do more reading on GA's and artificial life. I have already copied the digests from ALife, Neuron, and Simulator and am plowing through them as fast as possible. It would also be nice to see some more genetic algorithm code (even in PASCAL, I can read it at about the same speed I read Urdu). Any info that any of you could send me, FTP addresses, product names, people to contact would be greatly appreciated. Thank you all for your help. Jack DeGolyer [JHDCI@UNO.EDU] University of New Orleans ------------------------------ Subject: Alopex algorithm and ANNs From: venu%sea.oe.fau.EDU@CUNYVM.CUNY.EDU Date: Wed, 13 Feb 91 22:40:25 -0500 Hi I am trying to gather information about the works going on on Alopex algorithm, applied to ANNs. I know about some of the works going on at Syracuse Univ (under Prof. Harth, who developed it) and at some other places. We are working on the digital hardware implementation of the algorithm as well as on some modifications and applications. I would appreciate if the fellow researchers respond to this request. Thanks, K P Venugopal venu@sea4.oe.fau.edu Dept. of Elec. Engineering Ph. 407-367-2731 Florida Atlantic University Boca Raton, FL 33431. ------------------------------ Subject: New M.A. Course in the U.K. From: Andy Clark <andycl@syma.sussex.ac.uk> Date: Mon, 18 Feb 91 20:25:47 +0000 Dear People, Here is a short ad concerning a new course which may be of interest to you or your students. NOTICE OF NEW M.A.COURSE BEGINNING OCT. 1991 UNIVERSITY OF SUSSEX, BRIGHTON, ENGLAND SCHOOL OF COGNITIVE AND COMPUTING SCIENCES M.A. in the PHILOSOPHY OF COGNITIVE SCIENCE This is a one year taught course which examines issues relating to computational models of mind. A specific focus concerns the significance of connectionist models and the role of rules and symbolic representation in cognitive science. Students would combine work towards a 20,000 word philosophy dissertation with subsidiary courses introducing aspects of A.I. and the other Cognitive Sciences. For information about this new course contact Dr Andy Clark, School of Cognitive and Computing Sciences, University of Sussex,Brighton, BN1 9QH, U.K. E-mail: andycl@uk.ac.sussex.syma ------------------------------ Subject: Student Conference Sponsorships From: issnnet@park.bu.edu (Student Society Account) Date: Fri, 22 Feb 91 12:54:24 -0500 ---- THIS NOTE CONTAINS MATERIAL OF INTEREST TO ALL STUDENTS ---- (and some non-students) This message is a brief update of the International Student Society for Neural Networks (ISSNNet), and also an ANNOUNCEMENT OF AVAILABLE STUDENT SPONSORSHIP AT UPCOMING NNets CONFERENCES. ---------------------------------------------------------------------- NOTE TO ISSNNet MEMBERS: If you have joined the society but did not receive our second newsletter, or have not heard from us in the recent past, please send e-mail to <issnnet@park.bu.edu>. ---------------------------------------------------------------------- 1) We had a problem with our Post Office Box (in the USA), which was inadvertently shut down for about one month between Christmas and the end of January. If you sent us surface mail which was returned to you, please send it again. Our apologies for the inconvenience. 2) We are about to distribute the third newsletter. This is a special issue that includes our bylaws, a description of the various officer positions, and a call for nominations for upcoming elections. In addition, a complete membership list will be included. ISSNNet MEMBERS: If you have not sent us a note about your interests in NNets, you must do so by about the end of next week to insure it appears in the membership list. Also, all governors should send us a list of their members if they have not done so already. 3) STUDENT SPONSORSHIPS AVAILABLE: We have been in contact with the IEEE Neural Networks Council. We donated $500 (about half of our savings to this point) to pay the registration for students who are presenting articles (posters or oral presentations) at the Helsinki (ICANN), Seattle (IJCNN), or Singapore (IJCNN) conferences. The IEEE Neural Networks Council has augmented our donation with an additional $5,000 to be distributed between the two IJCNN conferences, and we are currently in contact with the International Neural Networks Society (INNS) regarding a similar donation. We are hoping to pay for registration and proceedings for an approximately equal number of students at each of the three conferences. Depending on other donations and on how many people are eligible, only a limited number of sponsorships may be available. The details of eligibility will be officially published in our next newsletter and on other mailing lists, but generally you will need to be the person presenting the paper (if co-authored), and you must receive only partial or no support from your department. Forms will be included with the IJCNN paper acceptance notifications. It is not necessary to be a member of any of these societies, although we hope this will encourage future student support and increased society membership. IF YOU HAVE SUBMITTED A PAPER TO ONE OF THE IJCNN CONFERENCES, YOU WILL RECEIVE DETAILS WITH YOUR NOTIFICATION FROM IJCNN. Details on the ICANN conference will be made available in the near future. For other questions send us some e-mail <issnnet@park.bu.edu>. ISSNNet, Inc. PO Box 557, New Town Branch Boston, MA 02258 Sponsors will be officially recognized in our future newsletters, and will be mentioned by the sponsored student during the presentations and posters. 6) We are considering the possibility of including abstracts from papers written by ISSNNet members in future newsletters. Depending on how many ISSNNet papers are accepted at the three conferences, we may be able to publish the abstracts in the fourth newsletter, which should come out before the ICANN conference. This would give the presenters some additional publicity, and would give ISSNNet members a sneak preview of what other people are doing. MORE DETAIL ON THESE TOPICS WILL BE INCLUDED IN OUR NEXT NEWSLETTER, WHICH WE EXPECT TO PUBLISH AROUND THE END OF THIS MONTH. For more details on ISSNNet, or to receive a sample newsletter, send e-mail to <issnnet@park.bu.edu>. You need not be a student to become a member! ------------------------------ Subject: Limited precision implementations (updated posting) From: MURRE%rulfsw.LeidenUniv.nl@BITNET.CC.CMU.EDU Date: Mon, 25 Feb 91 16:57:00 +0700 Connectionist researchers, Here is an updated posting on limited precision implementations of neural networks. It is my impression that research in this area is still fragmentary. This is surprising, because the literature on analog and digital implementations is growing very fast. There is a wide range of possibly applicable rules of thumb. Claims about sufficient precision differ from single bits to 20 bits or more for certain models. Hard problems may need higher precision. There may be a trade-off between few weights (nodes) with high precision weights (activations) versus many weights (nodes) with low precision weights (act.). The precise relation between precision in weights and activations remains unclear, as does the relation between the effect of precision on learning and recall. Thanks for all comments so far. Jaap Jacob M.J. Murre Unit of Experimental and Theoretical Psychology Leiden University P.O. Box 9555 2300 RB Leiden The Netherlands General comments by researchers By Soheil Shams: As far as the required precision for neural computation is concerned, the precision is directly proportional to the difficulty of the problem you are trying to solve. For example in training a back-propagation network to discriminate between two very similar classes of inputs, you will need to have high precision values and arithmetic to effectively find the narrow region in the space that the separating hyperplane has to be drawn at. I believe that the lack of analytical information in this area is due to this relationship between the specific application and the required precision . At the NIPS90 workshop on massively parallel implementations, some people indicated they have determined, EMPERICALLY, that for most problems, 16-bit precision is required for learning and 8-bit for recall of back-propagation. By Roni Rosenfeld: Santosh Venkatesh (of Penn State, I believe, or is it U. Penn?) did some work a few years ago on how many bits are needed per weight. The surprising result was that 1 bit/weight did most of the work, with additional bits contributing surprisingly little. By Thomas Baker: ... We have found that for backprop learning, between twelve and sixteen bits are needed. I have seen several other papers with these same results. After learning, we have been able to reduce the weights to four to eight bits with no loss in network performance. I have also seen others with similar results. One method that optical and analog engineers use is to calculate the error by running the feed forward calculations with limited precision, and learning the weights with a higher precision. The weights are quantized and updated during training. I am currently collecting a bibliography on limited precision papers. ... I will try to keep in touch with others that are doing research in this area. References Brause, R. (1988). Pattern recognition and fault tolerance in non-linear neural networks. Biological Cybernetics, 58, 129-139. Hollis, P.W., J.S. Harper, J.J. Paulos (1990). The effects of precision constraints in a backpropagation learning network. Neural Computation, 2, 363-373. Holt, J.L., & J-N. Hwang (in prep.). Finite precision error analysis of neural network hardware implementations. Univ. of Washington, FT-10, WA 98195. (Comments by the authors: We are in the process of finishing up a paper which gives a theoretical (systematic) derivation of the finite precision neural network computation. The idea is a nonlinear extension of "general compound operators" widely used for error analysis of linear computation. We derive several mathematical formula for both retrieving and learning of neural networks. The finite precision error in the retrieving phase can be written as a function of several parameters, e.g., number of bits of weights, number of bits for multiplication and accumlation, size of nonlinear table-look-up, truncation/rounding or jamming approaches, and etc. Then we are able to extend this retrieving phase error analysis to iterative learning to predict the necessary number of bits. This can be shown using a ratio between the finite precision error and the (floating point) back-propagated error. Simulations have been conducted and matched the theoretical prediction quite well.) Hong, J. (1987). On connectionist models. Tech. Rep., Dept. Comp. Sci., Univ. of Chicago, May 1987. (Demonstrates that a network of perceptrons needs only finite-precision weights.) Jou, J., & J.A. Abraham (1986). Fault-tolerant matrix arithmetic and signal processing on highly concurrent computing structures. Proceedings of the IEEE, 74, 732-741. Kampf, F., P. Koch, K. Roy, M. Sullivan, Z. Delalic, & S. DasGupta (1989). Digital implementation of a neural network. Tech. Rep. Temple Univ., Philadelphia PA, Elec. Eng. Div. Moore, W.R. (1988). Conventional fault-tolerance and neural computers. In: R. Eckmiller, & C. Von der Malsburg (Eds.). Neural Computers. NATO ASI Series, F41, (Berling: Springer-Verlag), 29-37. Nadal, J.P. (1990). On the storage capacity with sign-constrained synaptic couplings. Network, 1, 463-466. Nijhuis, J., & L. Spaanenburg (1989). Fault tolerance of neural associative memories. IEE Proceedings, 136, 389-394. Rao, A., M.R. Walker, L.T. Clark, & L.A. Akers (1989). Integrated circuit emulation of ART networks. Proc. First IEEE Conf. Artificial Neural Networks, 37-41, Institution of Electrical Engineers, London. Rao, A., M.R. Walker, L.T. Clark, L.A. Akers, & R.O. Grondin (1990). VLSI implementation of neural classifiers. Neural Computation, 2, 35-43. (The paper by Rao et al. give an equation for the number of bits of resolution required for the bottom-up weights in ART 1: t = (3 log N) / log(2), where N is the size of the F1 layer in nodes.) ------------------------------ Subject: Special message to SF Bay Area Neural Net Researchers From: "Andras Pellionisz" <pellioni@pioneer.arc.nasa.gov> Date: Mon, 25 Feb 91 09:51:01 -0800 "Special message too Neural Net researchers in the San Francisco Region: San Francisco Bay Area Special Interest Group of the International Neural Network Society (SF-SIGINNS) has been established. If interested in free enrollment, please contact Dr. Pellionisz with your name, mailing and/or E-mail address. Andras J. Pellionisz can be reached: NASA Ames Research Center Neurocomputer Laboratory, Bldg.261-3 Moffett Fields, CA 94035-1000 Voice/messages: (415) 604-4821 Fax: (415) 604-0046 E-mail: pellioni@pioneer.arc.nasa.gov Please join in! A. Pellionisz" ------------------------------ Subject: Looking for Phoneme Data From: gunhan@otis.hssc.scarolina.edu (The Young Turk) Date: Mon, 25 Feb 91 13:40:54 -0500 I am looking for speech data that I can use as input into a phoneme recognition neural network. I am working on alternative neural network models that have improved learning rates in terms of time and I need to test these algorithms with speech data used with traditional implementations of neural network based speech recognition packages. Any information on where and how to get this speech input data would be greatly appreciated. Thanks. Gunhan H. Tatman Computer Engineering Dept. The University of South Carolina Columbia, SC 29201 e-mail: gunhan@otis.hssc.scarolina.edu (gunhan@129.252.1.2) ------------------------------ Subject: Postdoc & Research Assistant openings in the COGNITIVE & NEURAL BASES OF LEARNING (Rutgers, NJ) From: gluck%psych@Forsythe.Stanford.EDU (Mark Gluck) Date: Mon, 25 Feb 91 11:03:40 -0800 Postdoctoral & Research/Programming Positions in: THE COGNITIVE & NEURAL BASES OF LEARNING ---------------------------------------------------------------------------- Rutgers University Center for Molecular & Behavioral Neuroscience 195 University Avenue Newark, NJ 07102 Postdoctoral Positions in: -------------------------- 1. EMPIRICAL STUDIES OF HUMAN LEARNING: Including: designing and conducting studies of human learning and decision making, especially categorization learning. These are primarily motivated by a desire to evaluate and refine adaptive network models of learning and memory (see, e.g., the experimental studies described in Gluck & Bower, 1988a; Pavel, Gluck, & Henkle, 1988). This work requires a familiarity with psychological methods of experimental design and data analysis. 2. COMPUTATIONAL MODELS OF ANIMAL & HUMAN LEARNING: Including: developing and extending current network models of learning to more accurately reflect a wider range of animal and human learning behaviors. This work requires strong programming skills, familiarity with adaptive network theories and methods, and some degree of mathematical and analytic training. 3. COMPUTATIONAL MODELS OF THE NEUROBIOLOGY OF LEARNING & MEMORY: Including: (1) Models and theories of the neural bases of classical and operant conditioning; (2) Neural mechansims for human associative learning; (3) Theoretical studies which seek to form links, behavioral or biological, between animal and human learning (see, e.g., Gluck, Reifsnider, & Thompson (1989), in Gluck & Rumelhart (Eds.) Neuroscience & Connectionist Theory). and Connectionist Theory). Full or Part-Time Research & Programming Positions: --------------------------------------------------- These positions are ideal for someone who has just graduated with an undergraduate degree and would like a year or two of "hands on" experience in research before applying to graduate school in one of the cognitive sciences (e.g., neuroscience, psychology, computer science). We are looking for two types of people: 1) a RESEARCH PROGRAMMER with strong computational skills (especially with C/Unix and SUN systems) and experience with PDP models and theory, and (2) an EXPERIMENTAL RESEARCH ASSISTANT to assist in running and designing human learning experiments. Some research experience required (familiarity with Apple MACs a plus). Application Procedure: ---------------------- For more information on learning research at the CMBN/Rutgers or to apply for these positions, please send a cover letter with a statement of your research interests, a CV, copies of relevant preprints, and the the names & phone numbers of references to: Dr. Mark A. Gluck Phone: (415) 725-2434 Dept. of Psychology <-[Current address to 4/91] FAX: (415) 725-5699 Jordan Hall; Bldg. 420 Stanford University email: gluck@psych.stanford.edu Stanford, CA 94305-2130 ------------------------------ Subject: summer position From: giles@fuzzy.nec.com (Lee Giles) Date: Mon, 25 Feb 91 14:08:40 -0500 NEC Research Institute in Princeton, N.J. has available a 3 month summer research and programming position. The research emphasis will be on exploring the computational capabilities of recurrent neural networks. The successful candidate will have a background in neural networks and strong programming skills in the C/Unix environment. Computer science background preferred. Interested applicants should send their resumes by mail, fax, or email to the address below. The application deadline is March 25, 1991. Applicants must show documentation of eligibility for employment. Because this is a summer position, the only expenses to be paid will be salary. NEC is an equal opportunity employer. C. Lee Giles NEC Research Institute 4 Independence Way Princeton, NJ 08540 USA Internet: giles@research.nj.nec.com UUCP: princeton!nec!giles PHONE: (609) 951-2642 FAX: (609) 951-2482 ------------------------------ Subject: neural net position available From: Andras Pellionisz -- SL <pellioni@pioneer.arc.nasa.gov> Date: Mon, 25 Feb 91 11:44:46 -0800 Neural Network Research Position Available Effective March 1,1990 Place: Nuclear Science Division Lawrence Berkeley Laboratory Area: Neural Network Computing with Application to Complex Pattern Recognition Problems in High Energy and Nuclear Physics Description: Experiments in high energy and nuclear physics are confronted with increasingly difficult pattern recognition problems, for example tracking charged particles and identifying jets in very high multiplicity and noisy environments. In 1990, a generic R&D program was initiated at LBL to develop new computational strategies to address such problems. The emphasis is on developing and testing artificial neural network algorithms for applications to experimental physics. Last year we developed a new Elastic Network type tracking algorithm that is able to track at densities an order of magnitude higher than conventional Road Finding algorithms and even Hopfield Network type algorithms. This year we plan on a number of followup studies and extensions of that work as well as begin research on jet finding algorithms. Jets are formed through the fragmentation of high energy quarks and gluons in rare processes in high energy collisions of hadrons or nuclei. The problem of identifying such jets via calorimetric or tracking detectors is greatly complicated by the very high multiplicity of fragments produced via other processes. The research will involve developing new preprocessing strategies and network architectures to be trained by simulated Monte Carlo data. Required Qualifications: General understanding of basic neural computing algorithms such as multilayer feed forward and recurrent nets and a variety of training algorithms. Experience and proficiency in programing in Fortran and C on a variety of systems VAX/VMS and/or Sparc/UNIX. Physics background preferred. For more information and applications please contact: Miklos Gyulassy Mailstop 70A-3307 Lawrence Berkeley Laboratory Berkeley, CA 94720 E-mail: GYULASSY@LBL.Bitnet Telephone: (415) 486-5239 ------------------------------ Subject: Question regarding Back-propagation Rule........ From: ELEE6NY@jetson.uh.edu Date: Mon, 25 Feb 91 19:00:00 -0600 Dear Sir, I am graduate student at University of Houston and I am working on Neural Network applications. I am working on some recurrent networks. I am using Rochester Connectionist Simulator (RCS) for net. The version of simulator i have has not got Recurrent backpropagation algorithm. so,i am finding problem in using backpropagation rule for this kind of recurrent net. I would appreaciate if i would get modified backpropagation algorithm that includes the recurrent net. I would also like to get any suggestions from you. I will look forward for your quick reply. Thanks in advance. pratish ------------------------------ Subject: RE: Transputers for neural networks? From: rolf@pallas.neuroinformatik.ruhr-uni-bochum.de (ROLF WUERTZ) Date: Wed, 27 Feb 91 17:16:09 +0100 Dear Tom, let me answer your questions briefly and use the opportunity to advertise our work a little bit. We have set up a system that is capable of recognizing human faces from video camera images. It can handle a fair range of realistic conditions. For more details I refer to our publications, which I will be glad to supply copies of. The system as it currently stands is implemented on a system of 23 T800 transputers, one of which is a special interface to a video camera and a graphics display. The configuration is hardwired as a tree. The application is completely written in occam under the multitool environment (a slightly modified TDS by PARSYTEC/Aachen). We have developped three pieces of generally useful software: 1) an efficient farming system that will support any tree of transputers. 2) An implementation of remote procedure calls for the use of host devices (keyboard, screen, clock, files, etc. on a remote transputer). 3) A set of assembler routines to speed up pieces of code that are crucial for the scalability of the tree size. The goal of the system is not so much practical or commercial use but the illustration of a new neural network paradigm called the "Dynamic Link Architecture" (DLA) developped by Christoph von der Malsburg. This concept proposes correlation-based learning on a very short time scale as a solution to conceptual problems of neural networks such as binding or higher order objects. Our simulations, therefore, fall in the category "something more dynamic". Again, I will provide further details on request. Parallelism is handled in the simplest way possible. In the recognition algorithm, incoming data is matched to a stored object by a random process which models the above mentioned dynamics. All network dynamics happen on a single transputer, but in parallel for the persons stored in the database. So each tranputer matches the incoming image to one stored person at a time. Implementation details are discussed in \cite{bonas,kosko} We do like the performance. The latest figures are around 30 secs for recognizing a person out of a database of 86 with acceptable reliability. For details on computation time, see \cite{icnc90,kosko}. For a detailed analysis of the reliability of the recognition see \cite{transcomp}. No fine grained parallel system maps nicely onto a coarse grained MIMD structure, so we use the transputers because they're fast or, rather, because of their price/performance ratio. However, we appreciate the didactical outcomes about parallelism in general. No sales, no price, no clients. The following are the relevant publications in BIBTEX format. \cite{icnc90} is very brief, but currently available in print. The availability of the others is expected within 1991. @incollection{kosko, author="J. Buhmann and J. Lange and C. {v.\,d.\,}Malsburg and J. C. Vorbr{\"u}ggen and R. P. W{\"u}rtz", editor="B. Kosko", booktitle="Neural Networks: A Dynamical Systems Approach to Machine Intelligence", title="Object Recognition in the Dynamic Link Architecture --- Parallel Implementation on a Transputer Network", year="1990", note="In print", publisher="Prentice Hall, New York"} @incollection{icnc90, author="R. P. W{\"u}rtz and J.C. Vorbr{\"uggen} and C. {v.\,d.\,}Malsburg", editor="R. Eckmiller and G. Hartmann and G. Hauske", booktitle="Parallel Processing in Neural Systems and Computers", title="A Transputer System for the Recognition of Human Faces by Labeled Graph Matching", pages="37--41", year="1990", publisher="North Holland, Amsterdam"} @inproceedings{bonas, author={Rolf P. W{\"u}rtz and Jan C. Vorbr{\"u}ggen and Christoph von der Malsburg and J{\"o}rg Lange}, title={A Transputer-based Neural Object Recognition System}, year=1990, booktitle={From Pixels to Features II -- Parallelism in Image Processing}, publisher={Elsevier}, editor={H. Burkhardt and J.C. Simon} } @unpublished{transcomp, author={Martin Lades and Jan C. Vorbr{\"u}ggen and Joachim Buhmann and Wolfgang Konen and Christoph v.d. Malsburg and Rolf P. W{\"u}rtz}, title={Distortion Invariant Object Recognition in the Dynamic Link Architecture}, year=1991, note={Submitted to IEEE Transactions on Computers}} ***************************************************************************** * * * Rolf P. W"urtz rolf@bun.neuroinformatik.ruhr-uni-bochum.de * * * * Ruhr-Universit"at Bochum phone: +49 234 700-7996 or * * Institut f"ur Neuroinformatik -7997 (dept. secr.) * * ND03-33 fax: +49 234 700-7995 * * Postfach 102148 * * D-4630 Bochum 1 * * Germany * * * ***************************************************************************** ------------------------------ End of Neuron Digest [Volume 7 Issue 11] ****************************************