@article{DimitrovaKoppitz2022,
  author    = {Dimitrova, Ilinka and Koppitz, J{\"o}rg},
  title     = {On relative ranks of the semigroup of orientation-preserving transformations on infinite chain with restricted range},
  series = {Communications in algebra},
  volume    = {50},
  journal   = {Communications in algebra},
  number    = {5},
  publisher = {Taylor \& Francis Group},
  address   = {Philadelphia},
  issn      = {0092-7872},
  doi       = {10.1080/00927872.2021.2000998},
  pages     = {2157 -- 2168},
  year      = {2022},
  abstract  = {Let X be an infinite linearly ordered set and let Y be a nonempty subset of X. We calculate the relative rank of the semigroup OP(X,Y) of all orientation-preserving transformations on X with restricted range Y modulo the semigroup O(X,Y) of all order-preserving transformations on X with restricted range Y. For Y = X, we characterize the relative generating sets of minimal size.},
  language  = {en}
}
@article{PoltzQuandteKohnetal.2022,
  author    = {Poltz, Nadine and Quandte, Sabine and Kohn, Juliane and Kucian, Karin and Wyschkon, Anne and von Aster, Michael and Esser, G{\"u}nter},
  title     = {Does It Count? Pre-School Children's Spontaneous Focusing on Numerosity and Their Development of Arithmetical Skills at School},
  series = {Brain Sciences},
  volume    = {12},
  journal   = {Brain Sciences},
  edition   = {3},
  publisher = {MDPI},
  address   = {Basel, Schweiz},
  issn      = {2076-3425},
  doi       = {10.3390/brainsci12030313},
  pages     = {1 -- 18},
  year      = {2022},
  abstract  = {Background: Children's spontaneous focusing on numerosity (SFON) is related to numerical skills. This study aimed to examine (1) the developmental trajectory of SFON and (2) the interrelations between SFON and early numerical skills at pre-school as well as their influence on arithmetical skills at school. Method: Overall, 1868 German pre-school children were repeatedly assessed until second grade. Nonverbal intelligence, visual attention, visuospatial working memory, SFON and numerical skills were assessed at age five (M = 63 months, Time 1) and age six (M = 72 months, Time 2), and arithmetic was assessed at second grade (M = 95 months, Time 3). Results: SFON increased significantly during pre-school. Path analyses revealed interrelations between SFON and several numerical skills, except number knowledge. Magnitude estimation and basic calculation skills (Time 1 and Time 2), and to a small degree number knowledge (Time 2), contributed directly to arithmetic in second grade. The connection between SFON and arithmetic was fully mediated by magnitude estimation and calculation skills at pre-school. Conclusion: Our results indicate that SFON first and foremost influences deeper understanding of numerical concepts at pre-school and—in contrast to previous findings -affects only indirectly children's arithmetical development at school.},
  language  = {en}
}
@article{SchneiderMaximovaSakizloglouetal.2021,
  author    = {Schneider, Sven and Maximova, Maria and Sakizloglou, Lucas and Giese, Holger},
  title     = {Formal testing of timed graph transformation systems using metric temporal graph logic},
  series = {International journal on software tools for technology transfer},
  volume    = {23},
  journal   = {International journal on software tools for technology transfer},
  number    = {3},
  publisher = {Springer},
  address   = {Heidelberg},
  issn      = {1433-2779},
  doi       = {10.1007/s10009-020-00585-w},
  pages     = {411 -- 488},
  year      = {2021},
  abstract  = {Embedded real-time systems generate state sequences where time elapses between state changes. Ensuring that such systems adhere to a provided specification of admissible or desired behavior is essential. Formal model-based testing is often a suitable cost-effective approach. We introduce an extended version of the formalism of symbolic graphs, which encompasses types as well as attributes, for representing states of dynamic systems. Relying on this extension of symbolic graphs, we present a novel formalism of timed graph transformation systems (TGTSs) that supports the model-based development of dynamic real-time systems at an abstract level where possible state changes and delays are specified by graph transformation rules. We then introduce an extended form of the metric temporal graph logic (MTGL) with increased expressiveness to improve the applicability of MTGL for the specification of timed graph sequences generated by a TGTS. Based on the metric temporal operators of MTGL and its built-in graph binding mechanics, we express properties on the structure and attributes of graphs as well as on the occurrence of graphs over time that are related by their inner structure. We provide formal support for checking whether a single generated timed graph sequence adheres to a provided MTGL specification. Relying on this logical foundation, we develop a testing framework for TGTSs that are specified using MTGL. Lastly, we apply this testing framework to a running example by using our prototypical implementation in the tool AutoGraph.},
  language  = {en}
}