The paper describes three models of the real field based on subsets of the integer sequences. The three models are compared to the Harthong–Reeb line. Two of the new models, contrary to the Harthong–Reeb line, provide accurate integer “views” on real numbers at a sequence of growing scales $B^n$($B\ge2$).

The family ${\mathcal{R}} X^*$ of regular subsets of the free monoid $X^*$ generated by a finite set X is the standard example of a ${}^*$-continuous Kleene algebra. Likewise, the family ${\mathcal{C}} X^*$ of context-free subsets of $X^*$ is the standard example of a $\mu$-continuous Chomsky algebra, i.e. an idempotent semiring that is closed under a well-behaved least fixed-point operator $\mu$. For arbitrary monoids M, ${\mathcal{C}} M$ is the closure of ${\mathcal{R}}M$ as a $\mu$-continuous Chomsky algebra, more briefly, the fixed-point closure of ${\mathcal{R}} M$. We provide an algebraic representation of ${\mathcal{C}} M$ in a suitable product of ${\mathcal{R}} M$ with $C_2'$, a quotient of the regular sets over an alphabet $\Delta_2$ of two pairs of bracket symbols. Namely, ${\mathcal{C}}M$ is isomorphic to the centralizer of $C_2'$ in the product of ${\mathcal{R}} M$ with $C_2'$, i.e. the set of those elements that commute with all elements of $C_2'$. This generalizes a well-known result of Chomsky and Schützenberger (1963, Computer Programming and Formal Systems, 118–161) and admits us to denote all context-free languages over finite sets $X\subseteq M$ by regular expressions over $X\cup\Delta_2$ interpreted in the product of ${\mathcal{R}} M$ and $C_2'$. More generally, for any ${}^*$-continuous Kleene algebra K the fixed-point closure of K can be represented algebraically as the centralizer of $C_2'$ in the product of K with $C_2'$.

Financial inclusion depends on providing adjusted services for citizens with disclosed vulnerabilities. At the same time, the financial industry needs to adhere to a strict regulatory framework, which is often in conflict with the desire for inclusive, adaptive, and privacy-preserving services. In this article we study how this tension impacts the deployment of privacy-sensitive technologies aimed at financial inclusion. We conduct a qualitative study with banking experts to understand their perspectives on service development for financial inclusion. We build and demonstrate a prototype solution based on open source decentralized identifiers and verifiable credentials software and report on feedback from the banking experts on this system. The technology is promising thanks to its selective disclosure of vulnerabilities to the full control of the individual. This supports GDPR requirements, but at the same time, there is a clear tension between introducing these technologies and fulfilling other regulatory requirements, particularly with respect to “Know Your Customer.” We consider the policy implications stemming from these tensions and provide guidelines for the further design of related technologies.

A method is presented for configuration selection to obtain the best tip-over stability of a modular reconfigurable mobile manipulator (MRMM) under various application situations. The said MRMM consists of a modular reconfigurable robot (MRR) mounted on a mobile platform. The MRR in different configurations creates different wrenches onto the mobile platform, leading to different tip-over moments of the MRMM, even though the joint speeds or tip speeds remain the same. The underlying problem pertains to selecting one configuration of MRR for reconfiguration that would obtain the best tip-over stability under a given application. First, all the permissible configurations are identified through an enumeration method. Then, the feasible configurations are determined based on application-oriented workspace classifications. At last, two workspace indices, vertical reach and horizontal reach, are used to select an optimal configuration. The tip-over stability analysis and evaluation of MRMM are carried out for verification for three cases including vertical, horizontal, and general 3D space applications. The results demonstrate the effectiveness of the proposed method.

By using algebraic structures in a presheaf category over finite sets, following Fiore, Plotkin and Turi, we develop sound and complete models of second-order rewriting systems called second-order computation systems (CSs). Restricting the algebraic structures to those equipped with well-founded relations, we obtain a complete characterisation of terminating CSs. We also extend the characterisation to rewriting on meta-terms using the notion of $\Sigma$-monoid.