Explore the vast range of titles available.

Convergent rewriting systems on algebraic structures give methods to solve decision problems, to prove coherence results, and to compute homological invariants. These methods are based on higher-dimensional extensions of the critical branching lemma that proves local confluence from confluence of the critical branchings. The analysis of local confluence of rewriting systems on algebraic structures, such as groups or linear algebras, is complicated because of the underlying algebraic axioms. This article introduces the structure of algebraic polygraph modulo that formalizes the interaction between the rules of an algebraic rewriting system and the inherent algebraic axioms, and we show a critical branching lemma for algebraic polygraphs. We deduce a critical branching lemma for rewriting systems on algebraic models whose axioms are specified by convergent modulo rewriting systems. We illustrate our constructions for string, linear, and group rewriting systems.

Les Liaisons dangereuses (1782) by Choderlos de Laclos is one of the best-known and most imitated novels in French literature. Despite the great number of adaptations and rewritings that have appeared since the second half of the 20th century, these continue to be made, assimilating the world of the libertines into that of teenagers. This study looks at the novel transposition from a film script, published in 2022 by Rachel Suissa and Wendy Thévin, under the same title Les Liaisons dangereuses. The paper analyses the way in which Laclos’s novel is adapted to the age of social networks and shows how the strategies of modernisation oscillate between “vagueness” and “precision”, considering the narrative technique, the libertine theme and the intertextual relationship between the rewriting and the original novel.

The article analyses Margaret Atwood’s reinterpretation of the Ithacan queen, Penelope, the wife of Odysseus, taking into consideration the silence-voice interplay between the original female character and her postmodernist re-representation, Penelope 2.0, the protagonist of . In the Canadian writer’s novel, Penelope’s voice gets empowered through narrative means. Her voice reaches its peak or highest degree of expression in Atwood’s , namely due to its main character and narrator, Penelope 2.0. Considering that a female first-person narrator elaborates the novel’s narrative, the article demonstrates how Penelope 2.0 expresses her feelings and thoughts regarding a series of events which occurred in the original text of The Odyssey, events which she elucidates by offering direct, well-developed insight, without any constraints.

Higher-dimensional rewriting systems are tools to analyse the structure of formally reducing terms to normal forms, as well as comparing the different reduction paths that lead to those normal forms. This higher structure can be captured by finding a homotopy basis for the rewriting system. We show that the basic notions of confluence and wellfoundedness are sufficient to recursively build such a homotopy basis, with a construction reminiscent of an argument by Craig C. Squier. We then go on to translate this construction to the setting of homotopy type theory, where managing equalities between paths is important in order to construct functions which are coherent with respect to higher dimensions. Eventually, we apply the result to approximate a series of open questions in homotopy type theory, such as the characterisation of the homotopy groups of the free group on a set and the pushout of 1-types. This paper expands on our previous conference contribution Coherence via Wellfoundedness by laying out the construction in the language of higher-dimensional rewriting.

Understanding how to program biological functions into artificial DNA sequences remains a key challenge in synthetic genomics. Here, we report the chemical synthesis and testing of Caulobacter ethensis-2.0 (C. eth-2.0), a rewritten bacterial genome composed of the most fundamental functions of a bacterial cell. We rebuilt the essential genome of Caulobacter crescentus through the process of chemical synthesis rewriting and studied the genetic information content at the level of its essential genes. Within the 785,701-bp genome, we used sequence rewriting to reduce the number of encoded genetic features from 6,290 to 799. Overall, we introduced 133,313 base substitutions, resulting in the rewriting of 123,562 codons. We tested the biological functionality of the genome design in C. crescentus by transposon mutagenesis. Our analysis revealed that 432 essential genes of C. eth-2.0, corresponding to 81.5% of the design, are equal in functionality to natural genes. These findings suggest that neither changing mRNA structure nor changing the codon context have significant influence on biological functionality of synthetic genomes. Discovery of 98 genes that lost their function identified essential genes with incorrect annotation, including a limited set of 27 genes where we uncovered noncoding control features embedded within protein-coding sequences. In sum, our results highlight the promise of chemical synthesis rewriting to decode fundamental genome functions and its utility toward the design of improved organisms for industrial purposes and health benefits.

Biological systems are frequently viewed as performing computations that are implemented by chemical transformations underlying the turn-over of their molecular components. In chemical reaction networks, computation may refer to at least two fundamentally different aspects: concentrations of molecules, and molecular structures. The latter can be captured by modeling chemical reactions as a rewriting system acting on structural formulae, i.e. labeled graphs. We investigate the computational power of double-pushout (DPO) graph rewriting restricted to chemical graphs and show that chemical graph rewriting is sufficient to emulate Turing machines and two-tag systems on polymeric graphs that act as tapes. Moreover, we raise the question whether chemistry, modeled as DPO graph rewriting together with some additional form of chemical programs, may be computationally universal in the strong sense, i.e. capable of computing any computable function on chemical graphs.

This paper introduces a novel hybrid model of natural computing, termed the hyper-edge replacement graph rewriting PR system, by synergistically combining the principles of reaction systems with the hyper-edge replacement graph rewriting P system. Inspired by biological cells, this model leverages hierarchical membrane structures to encapsulate regions operating as reaction systems, facilitating complex biochemical interaction modeling. By integrating facilitation and inhibition mechanisms with graph generation capabilities, this framework expands the capabilities of both paradigms, offering a powerful tool for simulating and analyzing complex graph-based structures. The properties and dynamics of this innovative model are explored, demonstrating its potential for advancing natural computing research. A comparative analysis with existing model further demonstrate its efficacy and broader applicability.

Symmetric monoidal theories (SMTs) generalise algebraic theories in a way that make them suitable to express resource-sensitive systems, in which variables cannot be copied or discarded at will. In SMTs, traditional tree-like terms are replaced by string diagrams, topological entities that can be intuitively thought of as diagrams of wires and boxes. Recently, string diagrams have become increasingly popular as a graphical syntax to reason about computational models across diverse fields, including programming language semantics, circuit theory, quantum mechanics, linguistics, and control theory. In applications, it is often convenient to implement the equations appearing in SMTs as rewriting rules. This poses the challenge of extending the traditional theory of term rewriting, which has been developed for algebraic theories, to string diagrams. In this paper, we develop a mathematical theory of string diagram rewriting for SMTs. Our approach exploits the correspondence between string diagram rewriting and double pushout (DPO) rewriting of certain graphs, introduced in the first paper of this series. Such a correspondence is only sound when the SMT includes a Frobenius algebra structure. In the present work, we show how an analogous correspondence may be established for arbitrary SMTs, once an appropriate notion of DPO rewriting (which we call convex) is identified. As proof of concept, we use our approach to show termination of two SMTs of interest: Frobenius semi-algebras and bialgebras.

In Harrouda of Tahar Ben Jelloun, the rewriting of oneself in the other is intended as a form of self-apprehension. By placing himself between two codes, different from each other by their respective referents, Ben Jelloun digs a distance from the collective ego and tries to appropriate an equivalent self that is not grounded in the community culture. Aware that the test of otherness accomplished in the signs and referents specific to the mortgaged language can dig another gap in the being, Ben Jelloun in no way slows down the effort to remain himself by negotiating the acquisition of a new identity outside the roots where his people have forged their being. En Harrouda de Tahar Ben Jelloun, la reescritura de uno mismo en el otro pretende ser un modo de autoaprehensión. Al situarse entre dos códigos, diferentes entre sí por sus respectivos referentes, Ben Jelloun se distancia del ego colectivo y trata de apropiarse de un yo equivalente que no está arraigado en la cultura comunitaria. Consciente de que la prueba de alteridad realizada en los signos y referentes propios de la lengua hipotecada puede cavar otro hueco en el ser, Ben Jelloun no frena en modo alguno el esfuerzo por seguir siendo él mismo negociando la adquisición de una nueva identidad fuera de las raíces donde vive su pueblo. han forjado su ser. Dans Harrouda de Tahar Ben Jelloun, la réécriture de soi dans l’autre se veut un mode d’appréhension de soi. En se plaçant entre deux codes, différents l’un de l’autre par leurs référents respectifs, Ben Jelloun creuse une distance par rapport à l’ego collectif et tente de s’approprier un équivalent de soi non fondé dans la culture communautaire. Conscient que l’épreuve de l’altérité accomplie dans les signes et les référents propres à la langue hypothéquée peut creuser une autre béance dans l’être, Ben Jelloun ne ralentit en aucun cas l’effort de rester lui-même en négociant l’acquisition d’une nouvelle identité en dehors des racines où les siens ont forgé son être.