A widely applicable, general methodology for estimation of traosfer function parameters from frequency response data is presented The procedure is bawd on tbe solution of a linear least squares pioblem by the singular value decomposition (SVD). The condition of the problem is discussed and approaclw refened to as shifting and scaling are introduced to reduce the condition number. To extend the application to practical caws with measurement emrs and/or a large number of poles, a partitioned estimation method with Gauss-Seidel iteratiws is develcped. M y , an iterative improvement process w i t h c " i n t s on the poles is applied to increase the accurscy and to avoid the possibility of obtaining unstable poles. The application of the suggested method of estimation to the ~presentation of transformers is pmented with practical examples. Elither transfer fuodion or state equation representation can be obtained for mawformers described by their terminal frequency responses.

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A direct method based on tlie linear least squares approach is applied for obtaining reduced order approximations of the propagation and characteristic admittance transfer functions of transmission lines for use in calculation of transients. The practical level of the acceptable error is discussed in terms of the precision of the frequency domain input data. The proposed approach provides satisfactory accuracy with a small number of ical and/or complex poles. The low order approximation could improve the efficiency of the E M " by reducing the computation time.

A general methodology is presented for the state equation appmximation of a multiple input-output linear system from transfer matrix data A complex transformation matrix, obtained by eigenandysis at a fixed frequency. is used for diagonalization of the trapsfer matrix over the whole frequency range. A scalar estimation r e d u r e is applied for identification of the modal transfer functions. e state equations in the original coordinates are obtained by inverse transformation. An iterative Gauss-Newton refinement process is used to reduce the overall QIor of the approximation.The developed methodology is applied to the phase domain modeling of untransped transmission lines. The approach makes it possible to paform EMTP calculations directly in the phase domain. This results in conceptual simplification and savings in computation time since modal transformations are not needed in the sequences of the transient analysis. The presented procedure is compared with the conventional modal approach in terms of accuracy and computation time.dence is not too significant, the non-diagonal elements of the transformed H p and Yc mairices may be neglected, so that the modes can be assumed decoupled. 93 WM 240-2 PWRS A paper recommended and approved by the IEEE Power System Engineering Committee of the IEEE Power Engineering Society for presentation at the IEEE/PES A Marched L Muti md J Oumn a a "A High Fzcquq~cy Tkifonner ' Model f a the EM"*. Ed P&B2 Summer Mceung. Pacer No. 9'2 SM 359-0-FWRD. A S Marched J.H. ODeV en, and L Muti "Multi-Port Fnzqucncy J&dcnt Nitwork %nu for the EM"*, IEEWES Summa Meeting. Paper No. %%461-4-PWRD. T W t h Linear Sytem, chrpa 6, Plentice-HIU, Inc., Englewood Ciiffs. NI. 1980. L Marti "Simuluioo of T d m u in Underground Cable1 With F' uenj-Lkpndmt Modal Tnnlfomution Murices'' IEEE T~I . h c a -d Nmne&d ! h~d t h c Effcaa 0fFreq~ency Dcpmdarceof Modal Canptum" Trmr. on P o w Apprntur ud Syuans. Vol. PAS-9 LID ~1008.1w3. J.M. Onega and W.C Rhcinbo Iteratiw Sduion of N o d w Eqvorwns in Several Variablu !&per 76, Acrdanic R u r , New York. Landon. 1970. EmU. T~r u r n i r~b~ Line R erence Book 345 kV and Above, Elearic Power R-rch Institute. P A Alto, CA, USA, 1975. APPENDICES Appendix A. State Equation Formulation With Real Parameters Assume that the state equations have been obtained with complex parameters as x(t) = h ( t ) + Bu(t) Y ( 0 = Cx

Object. Thyroid cancer (TC) is a rare type of cancer which occurs as a result of environmental and genetic factors. Although different types of genetic and epigenetic changes are associated with TC, the molecular mechanism still remains unclear. SRY-box transcription factor 15 (SOX15) is an important transcription factor, and its expression is altered in many cancer types by epigenetic modifications. Recently, miR-147b overexpression has been associated with SOX15 silencing in TC. Methods. In this study, qRT-PCR was used to investigate the expression levels of the SOX15 gene and of miR-182, miR-183, miR-375, and miR-96 in thyroid tumors and adjacent noncancerous tissues. We also investigated the methylation status of the SOX15 promoter by methylation-specific PCR in tumors and adjacent noncancerous tissues. Results. We observed a statistically significant downregulation of SOX15 expression in tumors compared to noncancerous tissue samples. The methylation levels of tumors and matched noncancerous tissues were similar, but miR-182, miR-183, and miR-375 expression levels were elevated in tumor tissues compared to noncancerous tissue samples. Conclusions. Our results indicate that SOX15 gene expression is associated with the pathogenesis of papillary thyroid carcinoma (PTC), and the epigenetic control of the SOX15 gene is regulated by miRNAs rather than by promoter methylation.

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Switching operations cause high frequency oscillations in power supply networks. During thes oscillations, transformer windings are subject to voltage stresses. For the analysis of such transient phenomena, lumped networks consisting of R, L, C parameters calculated from the geometric dimensions of transformer windings have been used.In this paper, a new method is described for modelling of transformer windings by their terminal impedance characteristics. It is shown that, by the use of the given models the transient oscillations occuring on the transformer Windings can be examined through the state equations. Examples are given for a reduced scale model transformer and an industrial supply system.