TY - THES A1 - Lieb, Julia T1 - Counting Polynomial Matrices over Finite Fields : Matrices with Certain Primeness Properties and Applications to Linear Systems and Coding Theory BT - Matrices with Certain Primeness Properties and Applications to Linear Systems and Coding Theory N2 - 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. N2 - Diese Dissertation beschäftigt sich mit drei Teilgebieten der Mathematik, nämlich Polynommatrizen über endlichen Körpern, linearen Systemen und Faltungscodes. Teilerfremdheitseigenschaften für Polynommatrizen stellen Kriterien für die Erreichbarkeit und Beoabachtbarkeit eines vernetzten linearen Systems zur Verfügung. Da zeit-diskrete lineare dynamische Systems und Faltungscodes im Prinzip diesselben Objekte darstellen, können diese Resultate in Kriterien dafür, dass ein Faltungscode nicht-katastrophal ist, übersetzt werden. Wir berechnen die Wahrscheinlichkeit, dass Polynommatrizen von spezieller Struktur rechtsprim sind. Im Besonderen, werden Formeln für die Anzahl paarweise teilerfremder Polynome sowie für die Anzahl wechselweise links-teilerfremder Polynommatrizen berechnet. Dies führt zu der Wahrscheinlichkeit, dass eine Parallelschaltung linearer Systeme erreichbar ist und dass eine Parallelschaltung von Faltungscodes nicht-katastrophal ist. Zudem werden andere Netzwerke linearen Systeme und von Faltungscodes, wie z.B. Reihenschaltung betrachtet. Des weiteren werden die Wahrscheinlichkeiten, dass ein Faltungscode MDP und dass ein Blockcode MDS ist, approximiert. Schließlich, betrachten wir die Wahrscheinlichkeit, eine Lösung für ein lineares Netzwerk-Kodierungsproblem zu finden. KW - Lineares System KW - Faltungscode KW - Polynomial matrices KW - linear system KW - convolutional code KW - Matrizenpolynom KW - Matrixpolynom Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-151303 SN - 978-3-95826-064-1 (print) SN - 978-3-95826-065-8 (online) N1 - Parallel erschienen als Druckausgabe in Würzburg University Press, 978-3-95826-064-1, 24,90 EUR. PB - Würzburg University Press CY - Würzburg ET - 1. Auflage ER - TY - JOUR A1 - Tanoey, Justine A1 - Baechle, Christina A1 - Brenner, Hermann A1 - Deckert, Andreas A1 - Fricke, Julia A1 - Günther, Kathrin A1 - Karch, André A1 - Keil, Thomas A1 - Kluttig, Alexander A1 - Leitzmann, Michael A1 - Mikolajczyk, Rafael A1 - Obi, Nadia A1 - Pischon, Tobias A1 - Schikowski, Tamara A1 - Schipf, Sabine M. A1 - Schulze, Matthias B. A1 - Sedlmeier, Anja A1 - Moreno Velásquez, Ilais A1 - Weber, Katharina S. A1 - Völzke, Henry A1 - Ahrens, Wolfgang A1 - Gastell, Sylvia A1 - Holleczek, Bernd A1 - Jöckel, Karl-Heinz A1 - Katzke, Verena A1 - Lieb, Wolfgang A1 - Michels, Karin B. A1 - Schmidt, Börge A1 - Teismann, Henning A1 - Becher, Heiko T1 - Birth order, Caesarean section, or daycare attendance in relation to child- and adult-onset type 1 diabetes: results from the German National Cohort JF - International Journal of Environmental Research and Public Health N2 - (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. KW - perinatal KW - adult-onset KW - late-onset KW - autoimmune KW - delivery mode KW - sex KW - offspring KW - NAKO Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-286216 SN - 1660-4601 VL - 19 IS - 17 ER -