Rational Function Interpolation of Electromagnetic Transfer Functions of High-Speed Interconnect Systems from Discrete Time-Domain and Frequency-Domain Data

We present new methodologies to generate rational function approximations of broadband electromagnetic responses of linear and passive networks of high-speed interconnects, and to construct SPICE-compatible, equivalent circuit representations of the generated rational functions. These new methodologies are driven by the desire to improve the computational efficiency of the rational function fitting process, and to ensure enhanced accuracy of the generated rational function interpolation and its equivalent circuit representation. Toward this goal, we propose two new methodologies for rational function approximation of high-speed interconnect network responses. The first one relies on the use of both time-domain and frequency-domain data, obtained either through measurement or numerical simulation, to generate a rational function representation that extrapolates the input, early-time transient response data to late-time response while at the same time providing a means to both interpolate and extrapolate the used frequency-domain data. The aforementioned hybrid methodology can be considered as a generalization of the frequency-domain rational function fitting utilizing frequency-domain response data only, and the time-domain rational function fitting utilizing transient response data only. In this context, a guideline is proposed for estimating the order of the rational function approximation from transient data. The availability of such an estimate expedites the time-domain rational function fitting process. The second approach relies on the extraction of the delay associated with causal electromagnetic responses of interconnect systems to provide for a more stable rational function process utilizing a lower-order rational function interpolation. A distinctive feature of the proposed methodology is its utilization of scattering parameters. For both methodologies, the approach of fitting the electromagnetic network matrix one element at a time is applied. It is shown that, with regard to the computational cost of the rational function fitting process, such an element-by-element rational function fitting is more advantageous than full matrix fitting for systems with a large number of ports. Despite the disadvantage that different sets of poles are used in the rational function of different elements in the network matrix, such an approach provides for improved accuracy in the fitting of network matrices of systems characterized by both strongly coupled and weakly coupled ports. Finally, in order to provide a means for enforcing passivity in the adopted element-by-element rational function fitting approach, the methodology for passivity enforcement via quadratic programming is modified appropriately for this purpose and demonstrated in the context of element-by-element rational function fitting of the admittance matrix of an electromagnetic multiport.

Effects of supplemental osteopontin on intestinal development and serum antibody responses to rotavirus vaccination in piglets

Milk contains numerous bioactive substances including immunoglobulins, cytokines, growth factors and components that exert antibiotic and prebiotic activity (Field, 2005). Little is known about the biological effects of individual milk bioactives, despite the fact that natural milk improves intestinal development and immune system functions in neonates (Donovan et al., 1994; Field, 2005) relative to milk formula. Characterization of the biological effects of such components is important for optimal production of infant milk formulas to be used when mother’s milk is not available. Milk components with preliminary evidence of positive effects on the intestinal growth and mucosal immunity include osteopontin (OPN). Osteopontin is a phosphorylated acidic glycoprotein expressed by a number of different immune and non-immune cells and tissues (Sodek et al., 2000). It is also present in body fluids including blood, bile and milk (Sodek et al., 2000). Osteopontin is a multifunctional protein that is implicated in a wide number of biological processes including cell survival, bone remodeling, and immune modulatory functions (Sodek et al., 2000). Furthermore, Schack and colleagues (2009) demonstrated that the concentration of OPN in human milk is considerably higher than in bovine milk and infant formulas. Taken together, it is likely that OPN plays a role in the early development of gastrointestinal tract and mucosal immune responses in infants. Since the neonatal pig shares anatomical, physiological, immunological, and metabolic similarities with the human infants (Moughan, et al., 1992), they were selected as the animal model in our studies. Our first aim was to investigate the effects of OPN on piglet intestinal development. Newborn, colostrum-deprived piglets (n=27) were randomized to receive three treatments: formula with bovine OPN (OPN; 140 mg/L); formula alone (FF); or sow reared (SR) for 21 days. Body weight, intestinal weight and length, mucosal protein and DNA content, disaccharidase activity, villus morphology, and crypt cell proliferation were measured. Statistical significance was assigned at P<0.05. No significant effects of OPN were observed for body weight, intestinal weight and length. Mucosal protein content of SR piglets was lower than FF and OPN piglets in the duodenum, but higher than FF and OPN piglets in the ileum. No significant effects of diet in mucosal DNA content were detected for the three regions of the small intestine. Lactase and sucrase activities of SR piglets were higher than the two formula-fed groups in the duodenum, lower in the ileum. No significant effects of diet on lactase and sucrase activities were noted between two formula-fed groups in the duodenum and ileum. Jejunal lactase activity of FF piglets was higher than SR piglets, whereas no significant effect of diet was observed in jejunal sucrase activity among the three groups. Duodenal and ileal villus height and villus area of SR piglets were lower than two formula-fed groups, while OPN piglets did not differ from FF piglets. There was a significant effect of diet (P<0.0001) on jejunal crypt cell proliferation, with proliferation in OPN piglets being intermediate between that of FF and SR. In summary, supplemental OPN increased jejunal crypt cell proliferation, independent of evident morphological growth, and had a minor impact on disaccharidase activity in the small intestine of neonatal piglets. Rotavirus (RV) is the most common viral cause of severe gastroenteritis in infants and young children worldwide (Parashar et al., 2006). Maeno et al. (2009) reported that OPN knockout (OPN-KO) suckling mice were more susceptible to RV infection compared to wild-type (WT) suckling mice. To detect the role of OPN in intestinal immune responses of neonates, the goal of the second study was to evaluate whether supplemental OPN influenced the serum antibody responses to RV vaccination in neonatal piglets. Newborn, colostrum-deprived piglets were randomized into two dietary groups: formula with bovine OPN (OPN; 140 mg/L) and formula alone (FF) for 35 days. On d7, piglets in each dietary group were further randomized to receive rotavirus (RV) vaccination (Rotarix®) (FF+RV and OPN+RV) or remained non-vaccinated (FF+NV and OPN+NV). Booster vaccination was provided on d14. Blood samples were collected on d7, 14, 21, 28 and 35. RV-specific serum immunoglobulin (Ig) G, IgA, IgM and total serum IgG, IgA, IgM were measured by ELISA. Statistical significance was assigned at P<0.05, with trends reported as P<0.10. Body weight gain was unaffected by diet and/or vaccination. No significant effect of oral OPN supplementation was observed for RV-specific antibody responses and total Igs levels. After the combination of dietary groups, RV piglets had significantly higher RV-specific IgM concentrations compared to NV piglets. Although there were higher means of RV-specific IgG and RV-specific IgA concentrations in RV group than their counterparts in NV group, the difference did not reach statistical significance. RV-specific IgM reached a peak at d7 post booster vaccination (PBV), whereas the RV-specific IgG and IgA peaked later at PBV 14 or 21. Total Igs were unaffected by RV vaccination but were significantly increased over time, following similar pattern as RV-specific Igs. In summary, neonatal piglets generated weak antibody responses to RV vaccination. Supplemental OPN did not enhance RV-specific serum antibody responses and total serum Igs levels in neonatal piglets with or without RV vaccination. In conclusion, we observed normal developmental changes in the small intestine and serum Igs levels in neonatal piglets over time. Oral OPN supplementation showed minimal impacts on intestinal development and no effect on serum Igs levels. The role of supplemental OPN on the growth and development of infants is still inconclusive. Future studies should measure other physiological and immunological parameters by using different models of vaccination or infection.