@phdthesis{Lieb2017,
  author    = {Lieb, Julia},
  title     = {Counting Polynomial Matrices over Finite Fields : Matrices with Certain Primeness Properties and Applications to Linear Systems and Coding Theory},
  edition   = {1. Auflage},
  publisher = {W{\"u}rzburg University Press},
  address   = {W{\"u}rzburg},
  isbn      = {978-3-95826-064-1 (print)},
  doi       = {10.25972/WUP-978-3-95826-065-8},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-151303},
  school      = {W{\"u}rzburg University Press},
  pages     = {164},
  year      = {2017},
  abstract  = {This dissertation is dealing with three mathematical areas, namely polynomial matrices over finite fields, linear systems and coding theory. Coprimeness properties of polynomial matrices provide criteria for the reachability and observability of interconnected linear systems. Since time-discrete linear systems over finite fields and convolutional codes are basically the same objects, these results could be transfered to criteria for non-catastrophicity of convolutional codes. We calculate the probability that specially structured polynomial matrices are right prime. In particular, formulas for the number of pairwise coprime polynomials and for the number of mutually left coprime polynomial matrices are calculated. This leads to the probability that a parallel connected linear system is reachable and that a parallel connected convolutional codes is non-catastrophic. Moreover, the corresponding probabilities are calculated for other networks of linear systems and convolutional codes, such as series connection. Furthermore, the probabilities that a convolutional codes is MDP and that a clock code is MDS are approximated. Finally, we consider the probability of finding a solution for a linear network coding problem.},
  subject      = {Lineares System},
  language  = {en}
}
@article{TanoeyBaechleBrenneretal.2022,
  author    = {Tanoey, Justine and Baechle, Christina and Brenner, Hermann and Deckert, Andreas and Fricke, Julia and G{\"u}nther, Kathrin and Karch, Andr{\´e} and Keil, Thomas and Kluttig, Alexander and Leitzmann, Michael and Mikolajczyk, Rafael and Obi, Nadia and Pischon, Tobias and Schikowski, Tamara and Schipf, Sabine M. and Schulze, Matthias B. and Sedlmeier, Anja and Moreno Vel{\´a}squez, Ilais and Weber, Katharina S. and V{\"o}lzke, Henry and Ahrens, Wolfgang and Gastell, Sylvia and Holleczek, Bernd and J{\"o}ckel, Karl-Heinz and Katzke, Verena and Lieb, Wolfgang and Michels, Karin B. and Schmidt, B{\"o}rge and Teismann, Henning and Becher, Heiko},
  title     = {Birth order, Caesarean section, or daycare attendance in relation to child- and adult-onset type 1 diabetes: results from the German National Cohort},
  series = {International Journal of Environmental Research and Public Health},
  volume    = {19},
  journal   = {International Journal of Environmental Research and Public Health},
  number    = {17},
  issn      = {1660-4601},
  doi       = {10.3390/ijerph191710880},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-286216},
  year      = {2022},
  abstract  = {(1) Background: Global incidence of type 1 diabetes (T1D) is rising and nearly half occurred in adults. However, it is unclear if certain early-life childhood T1D risk factors were also associated with adult-onset T1D. This study aimed to assess associations between birth order, delivery mode or daycare attendance and type 1 diabetes (T1D) risk in a population-based cohort and whether these were similar for childhood- and adult-onset T1D (cut-off age 15); (2) Methods: Data were obtained from the German National Cohort (NAKO Gesundheitsstudie) baseline assessment. Self-reported diabetes was classified as T1D if: diagnosis age ≤ 40 years and has been receiving insulin treatment since less than one year after diagnosis. Cox regression was applied for T1D risk analysis; (3) Results: Analyses included 101,411 participants (100 childhood- and 271 adult-onset T1D cases). Compared to "only-children", HRs for second- or later-born individuals were 0.70 (95\% CI = 0.50-0.96) and 0.65 (95\% CI = 0.45-0.94), respectively, regardless of parental diabetes, migration background, birth year and perinatal factors. In further analyses, higher birth order reduced T1D risk in children and adults born in recent decades. Caesarean section and daycare attendance showed no clear associations with T1D risk; (4) Conclusions: Birth order should be considered in both children and adults' T1D risk assessment for early detection.},
  language  = {en}
}