TY - JOUR A1 - Dimitrova, Ilinka A1 - Koppitz, Jörg T1 - On relative ranks of the semigroup of orientation-preserving transformations on infinite chain with restricted range JF - Communications in algebra N2 - 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. KW - Order-preserving transformations KW - orientation-preserving KW - transformations KW - relative rank KW - restricted range KW - transformation KW - semigroups on infinite chain Y1 - 2022 U6 - https://doi.org/10.1080/00927872.2021.2000998 SN - 0092-7872 SN - 1532-4125 VL - 50 IS - 5 SP - 2157 EP - 2168 PB - Taylor & Francis Group CY - Philadelphia ER - TY - JOUR A1 - Poltz, Nadine A1 - Quandte, Sabine A1 - Kohn, Juliane A1 - Kucian, Karin A1 - Wyschkon, Anne A1 - von Aster, Michael A1 - Esser, Günter T1 - Does It Count? Pre-School Children’s Spontaneous Focusing on Numerosity and Their Development of Arithmetical Skills at School JF - Brain Sciences N2 - 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. KW - SFON KW - school mathematics KW - mathematical precursor KW - counting KW - number knowledge KW - magnitude estimation KW - transformation KW - pre-school KW - longitudinal KW - development Y1 - 2022 U6 - https://doi.org/10.3390/brainsci12030313 SN - 2076-3425 VL - 12 SP - 1 EP - 18 PB - MDPI CY - Basel, Schweiz ET - 3 ER - TY - JOUR A1 - Schneider, Sven A1 - Maximova, Maria A1 - Sakizloglou, Lucas A1 - Giese, Holger T1 - Formal testing of timed graph transformation systems using metric temporal graph logic JF - International journal on software tools for technology transfer N2 - 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. KW - formal testing KW - typed attributed symbolic graphs KW - timed graph KW - transformation KW - graph conditions KW - metric temporal graph logic Y1 - 2021 U6 - https://doi.org/10.1007/s10009-020-00585-w SN - 1433-2779 SN - 1433-2787 VL - 23 IS - 3 SP - 411 EP - 488 PB - Springer CY - Heidelberg ER -