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One of Robert Rosen's main contributions to the scientific community is summarized in his book Life itself. There Rosen presents a theoretical framework to define living systems; given this definition, he goes on to show that living systems are not realizable in computational universes. Despite being well known and often cited, Rosen's central proof has so far not been evaluated by the scientific community. In this article we review the essence of Rosen's ideas leading up to his rejection of the possibility of real artificial life in silico. We also evaluate his arguments and point out that some of Rosen's central notions are ill defined. The conclusion of this article is that Rosen's central proof is wrong.

Despite the increasing presence of computational thinking (CT) in the mathematics context, the connection between CT and mathematics in a practical classroom context is an important area for further research. This study intends to investigate the impact of CT activities in the topic of number patterns on the learning performance of secondary students in Singapore. The Rasch model analysis was employed to assess differences of ability between students from the experimental group and control group. 106 Secondary One students (age 13 years old) from a secondary school in Singapore took part in this study. A quasi-experimental non-equivalent groups design was utilized where 70 students were assigned into the experimental group, and 36 students were assigned into the control group. The experimental group was given intervention with CT-infused activities both on- and off-computer, while the control group received no such intervention. Both groups were administered the pretest before the intervention and the posttest after the intervention. The data gathered were analyzed using the partial credit version of the Rasch model. Analysis of pretest and posttest results revealed that the performance of the experimental group was similar to the control group. The findings did not support the hypothesis that integrating CT in lessons can result in improved mathematics learning. However, the drastic improvement was observed in individual students from the experimental group, while there is no obvious or extreme improvement for the students from the control group. This study provides some new empirical evidence and practical contributions to the infusion of CT practices in the mathematics classroom.

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In this paper, we tailor-make new approximation operators inspired by rough set theory and specially suited for domain theory. Our approximation operators offer a fresh perspective to existing concepts and results in domain theory, but also reveal ways to establishing novel domain-theoretic results. For instance, (1) the well-known interpolation property of the way-below relation on a continuous poset is equivalent to the idempotence of a certain set-operator; (2) the continuity of a poset can be characterized by the coincidence of the Scott closure operator and the upper approximation operator induced by the way below relation; (3) meet-continuity can be established from a certain property of the topological closure operator. Additionally, we show how, to each approximating relation, an associated order-compatible topology can be defined in such a way that for the case of a continuous poset the topology associated to the way-below relation is exactly the Scott topology. A preliminary investigation is carried out on this new topology.

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In a recent article in Artificial Life, Chu and Ho suggested that Rosen's central result about the simulability of living systems might be flawed. This argument was later declared ''null and void'' by Louie. In this article the validity of Louie's objections are examined.

The class of well-filtered spaces is one of the important class of topological spaces in domain theory. Recently, the existence of well-filterification of T0-spaces has been established. In this paper, we introduce the definition of wf-rank and prove that for any ordinal ?, there exists a T0-space whose wf-rank equals ?.