Journal of Information and Data Management

ISSN 2166 - 6261 (Print)

ISSN 2166 - 6288 (Online)

Website: http://www.researchpub.org/journal/jidm/jidm.html


Volterra Kernel Identification by Wavelet Networks and its Applications to Nonlinear Nonstationary Time Series
Author(s) Minu.K.K. and Jessy John.C.

Volterra series representation is the earliest method for the description of a nonlinear system. Volterra kernels completely characterize the Volterra series. Volterra series has been extended to incorporate the non stationarity. Even though Volterra series modeling was suggested much earlier, no canonical method for the identification of the Volterra kernel was available due to the exponential growth of parameters in the kernel with the order of expansion. Developments in the theories of Artificial Neural Networks and Wavelets gave rise to the concept of Wavelet Networks which are found to be effective in modeling the nonlinear nonstationary structures. In this paper a method for identifying the Volterra kernels is developed by applying Wavelet Network. Thereby the Volterra series is applied for the analysis of nonlinear nonstationary time series providing a powerful method in the analysis of nonlinear nonstationary time series, which appear quite often in various fields of study.

[ 1 ] V. Volterra, 揟heory of functionals and of integral and integro differential equations? Dover,1959.
[ 2 ] Y.W.Lee and M. Schetzen, 揗easurement of the Wiener kernels of a non linear system by cross correlation? Int. J.Control, 2:pp.237- 254,1965
[ 3 ] Tony J Dodd and Robert F.Harrison, 揂 new solution to Volterra series estimation? 15th Triennial IFAC World Congress, 2002
[ 4 ] Maria Iatron, T.W.Berger and Vasillis.Z.Marmarelis, 揗odeling of nonlinear nonstationary random system with a novel class of ANN? IEEE Transactions on Neural Networks, Volume 10,Number2,pp.327-339, 1999.
[ 5 ] K.J. Friston A. Mechelli, R.Turner, and C.J. Price, Non linear response in MRI: the balloon model, Volterra kernel and other hemodynamics Neuro Image, Volume 12, pp.466-477, 2000
[ 6 ] Norden.E.Huang, etal, The empirical mode decomposition and the Hilbert spectrum for nonlinear and non stationary time series analysis, Proc.R.Soc,London, Volume 454,pp.903-995,1998
[ 7 ] M.J. Niedzwiecki, Identification of Time- varying Process, Wiley and Sons,Ltd.2000
[ 8 ] T.Subba Rao, 揟he fitting of nonstationary time series with time dependant parameters? J.R. Statist.Vol-32,B12,pp.312-322, 1970
[ 9 ] S. G. Mallat,揗ultiresolution approximation and wavelets orthonormal basis for L2(IR)? Trans.Amer.Math.Soc. vol.315,pp.69-87, 1989
[ 10 ] K. Hornik,M.Tichombeand H. White, 揗ultilayer feed forward networks are universal approximators? Neural Networks, Volume 2, pp.359-366,1989
[ 11 ] Q.Zhang, and A.Benveniste, 揥avelet networks? IEEE Transactions on Neural Networks, Vol 3,Number 6, pp.889-898,1992
[12] Y.C. Pati and P.S. Krishnaprasad., 揂nalysis and synthesis of feed forward neural networks using discrete affine wavelet transformations? Technical research Report, University of Maryland,Collegepark,pp1-9,1990
[13] S. Sitharam Iyengar, E.C.Cho and Vir.V.Phoha, Foundations of Wavelet Networks and Applications, chapman and Hall\CRC, 2002
[14] M.B.Priestly., Nonlinear Non stationary Time Series Analysis, Academic Press, 1985
[15] S.Boyd and L. Chua, 揊ading memory and the problem of approximating non linear operators with Volterra series? IEEE Transaction on Circuits and Systems, Volume 32,Issue 11,pp.1150-1161, 1985
[16] I. Daubechies, Ten Lectures on Wavelets, SIAM,NEWYORK, 1992
[17] T. Poggio and F. Girosi, 揘etworks for approximation and learning? Proceedings of the IEEE Volume 78, pp. 1481-1497, 1990.
[18] Y.W.Lee and M. Schetzen, 揗easurement of the Wiener kernels of a non linear system by cross correlation? Int. J.Control, volume 2:pp.237-254,1965
[19] Georgina Stegmayer, 揤olterra series and neural networks to model an electronic device nonlinear behaviour? Proceedings of IEEE International Conference on Neural Networks, Volume 4,pp.2907-2910,2004
[20] M. Holschneider., Wavelets: An Analysis Tool, Clarendon Press, 1998
[21] W.Rudin, Functional Analysis, Mc-GrawHill, 1974

Variability of Electrojet Strength along the Magnetic Equator Using MAGDAS/CPMN Data
Author(s) Abbas M., Joshua B. D. Bonde, Adimula I. A., A. B. Rabiu and O.R. Bello

One year data of hourly values of H component of the earth magnetic field were used to study the magnetic strength of some selected stations along the 96O Magnetic Meridian (MM). The results revealed that the amplitude of dH has diurnal variation which peaks during the day at about local noon. This diurnal variation in H component is attributed to the enhancement dynamo action at this region. The diurnal variation along the 960 MM reveals a clear nocturnal minimum variation which could be attributed to distant current of non-ionospheric origin. The observed minimum variation could be as a result of a partial ring current. The electrojet strength at Addis Ababa with respect to Khartoum are 44.05 nT,60 nT and 12.88 nT for January, February and August around local noon, which is stronger than the electrojet strength observed with respect to Nairobi, 40.86 nT,42.41 nT and 19.12 nT .However, the pre-noon and post-noon minimum variation may be attributed to distant magnetospheric current.

[1] Stewart, B. Hypothetical views regarding the connection between state of the sun and terrestrial magnetism in 揈ncyclopedia Brittanica? 9th edition, vol. 16, 181-184.
[2] Chapman, S., The solar and lunar diurnal variations of terrestrial magnetism, Philos. Trans. Roy. Soc., London, A 218, 1-118.
[3] Chapman S., (1951). The equatorial electrojet as detected from the abnormal electric current distribution above Huancayo and elsewhere, Arch. Meteorl. Geophys. Bioclimatol, A 4, 368-392.
[4] Chapman, S., J. C Gupta, and S. R. C. Malin (1971). The sunspot cycle influence on the solar and lunar daily geomagnetic variations, Proc. Roy.Soc. A324, 1-15.
[5] Doumouya, V., Cohen, Y., Arora, B. R., and Yumoto, K.., (2003), J. Atoms. Terr. Phys., 65,1265.
[6] Chandra, H., H. S. S. Sinha, and R. G. Rastogi, (2000). Equatorial electrojet studies from rocket and ground measurements, Earth Planet Space, 52, 111?120.
[7] Yacob, A. (1977). Internal induction by the equatorial electrojet in India examined with surface and satellite geomagnetic observations, J. Atmos. Terr. Phys., 39, 601?06.
[8] Alex, S., and S. Mukherjee (2001), Local time dependence of the equatorial counter electrojet effect in a narrow longitudinal belt, Earth Planets Space, 53, 1151?161.
[9] Anderson, D., A. Anghel, K. Yumoto, M. Ishitsuka, and E. Kudeki (2002), Estimating daytime vertical E x B drift velocities in the equatorial F-region using ground-based magnetometer observations, Geophys. Res. Lett., 29(12), 1596, doi:10.1029/2001GL014562.
[10] Rabiu, A. B., Nagarajan, N., Okeke, F. N., Anyibi. E. A., (2007). A study of day-to-day variability in geomagnetic field variations at the electrojet zone of Addis Ababa, East Africa, AJST. Vol.8 pp 54-63.
[11] Onwumechili, C. A., (1967), In: Eds. Matsushita S. and Campbell, W. H. Physics of Geomagnetic Phenomena. 1: 425-507. Academic press, New York.
[12] Onwumechili, C. A., The Equatorial Electrojet, Gordon and Breach Science Publishers, Netherlands.
[13] Forbes, J. M., (1981), Rev. Geoph. Space Phys., 19, 469.
[14] Onwumechili, C.A. and Ezema, P.O., (1977). On course of the geomagnetic daily variation in low latitudes. Atoms. Terr: Phys., 39.
[15] Onwumechili, C.A., (1960). Fluctuations in the geomagnetic field near the magnetic equator.J. Amos. Terr. Phys., 17,286-294.
[16] Matsushita, S., (1969). Dynamo Currents, Winds, and Electric Fields, Radio Sci., 4, 771.
[17] Okeke, F. N., C. A. Onwumechili, and A. B. Rabiu (1998), Day to day varaibility of geomagnetic hourly amplitudes in low latitude, Geophys. J. Int., 134, 484?500.
[18] Hasegawa, M., (1960). On the position of the focus of the geomagnetic sq current system, J. Geophys. Res. 65. 1437-1447.
[19] Bhargava, B. N and Yacob, A.,( 1971). Solar wind associated component in the low-latitude magnetic daily variation, Journ. Geomagnetic geo elect. 23, p. 249-253.
[20] Rajaram, M., (1983). Determination of the latitude of sq focus and its relation to the electrojet variations, J .atmos. Terr. phys., 45, 573-578.

Analysis of a New Random Key Pre-distribution Scheme for WSN Based on Random Graph Theory and Kryptograph
Author(s) Seema Verma and Prachi

Wireless Sensor Networks (WSNs) vast myriad of futuristic applications makes it matter of incessant research interest. Key management is crucial for WSN due to their high security requirements and resource constrained nature. Randomized key pre-distribution seems to be best suited solution for WSN due to scarceness of resources. However, most of the earlier proposed schemes are based on random graph theory model which is not that suitable for WSN. In this paper we present and implement a new randomized key pre-distribution scheme on TinyOS. Later on, we perform a rigorous mathematical analysis of our scheme under random graph theory on which most of the earlier proposed schemes are based and recently introduced kryptograph model. Our results prove that kryptograph model is more vital for secure WSNs.

[1] Kamini Prajapati and Jabulani Nyathi, 揂n Efficient Key Update Scheme for Wireless Sensor Networks? In Proceedings of the 2006 International Conference on Wireless Networks, June 26-29, 2006.
[2] W. Diffie and M. Hellman, 揘ew directions in cryptography? IEEE Transactions on Information Theory, 22(6):644?54, November 1976.
[3] Eschenauer Land Gligor V D (2002-11). 揂 key management scheme for distributed sensor networks? In Proceedings of the 9th ACM conference on Computer and communications security
[4] Chan H, Perrig A, and Song D (2003). 揜andom key predistribution schemes for sensor networks. In IEEE Symposium on Security and Privacy.
[5] T. Shan, C. Liu, Enhancing the key pre-distribution scheme on wireless sensor networks, in: IEEE Asia-Pacific Conference on Services Computing, IEEE Computer Society, Los Alamitos, CA, USA, 2008, pp. 1127?131.
[6] C.-F. Law, K.-S. Hung, Y.-K. Kwok, A novel key redistribution scheme for wireless sensor networks, in: IEEE International Conference on Communications (ICC?7), IEEE Computer Society, Washington, DC, USA, 2007, pp. 3437?442.C. J. Kaufman, Rocky Mountain Research Lab., Boulder, CO, private communication, May 1995.
[7] S. Zhu, S. Xu, S. Setia, S. Jajodia, Establishing pairwise keys for secure communication in ad hoc networks: a probabilistic approach, in: Proceedings of the 11th IEEE International Conference on Network Protocols (ICNP?3), IEEE Computer Society, Washington, DC, USA, 2003, pp. 326?35.
[8] Philip Levis, Nelson Lee, Matt Welsh, and David Culler, 揟OSSIM: Accurate and Scalable Simulation of Entire TinyOS Applications? In Proceedings of the first ACM Conference on Embedded Networked Sensor Systems (SenSys) 2003, Nov. 2003
[9] J. Spencer, 揟he Strange Logic of Random Graphs, Algorithms and Combinatorics 22? Springer-Verlag 2000, ISBN 3-540-41654-4.
[10] R. D. Pietro, L. V. Mancini, A. Mei, And A. Panconesi, J. Radhakrishnan, Redoubtable Sensor Networks, ACM Transactions on Information and Systems Security, Vol. 11, No. 3, Article 13, Pub. date: March 2008.

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