Initial algebra for a system of right-linear functors

In 2003 we showed that right-linear systems of equations over regular expressions, when interpreted in a category of trees, have a solution when ever they enjoy a specific property that we called hierarchicity and that is instrumental to avoid critical mutual recursive definitions. In this note, we prove that a right-linear system of polynomial endofunctors on a cocartesian monoidal closed category which enjoys parameterized left list arithmeticity, has an initial algebra, provided it satisfies a property similar to hierarchicity

A doctrinal approach to modal/temporal Heyting logic and non-determinism in processes

The study of algebraic modelling of labelled non-deterministic concurrent processes leads us to consider a category LB , obtained from a complete meet-semilattice B and from B-valued equivalence relations. We prove that, if B has enough properties, then LB presents a two-fold internal logical structure, induced by two doctrines definable on it: one related to its families of subobjects and one to its families of regular subobjects. The first doctrine is Heyting and makes LB a Heyting category, the second one is Boolean. We will see that the difference between these two logical structures, namely the different behaviour of the negation operator, can be interpreted in terms of a distinction between non-deterministic and deterministic behaviours of agents able to perform computations in the context of the same process. Moreover, the sorted first-order logic naturally associated with LB can be extended to a modal/temporal logic, again using the doctrinal setting. Relations are also drawn to other computational model

Accepting networks of evolutionary picture processors

We extend the study of networks of evolutionary processors accepting words to a similar model, processing rectangular pictures. To this aim, we introduce accepting networks of evolutionary picture processors and investigate their computational power. We show that these networks can accept the complement of any local picture language as well as picture languages that are not recognizable. Some open problems regarding decidability issues and closure properties are finally discussed

Accepting networks of evolutionary picture processors

We extend the study of networks of evolutionary processors accepting words to a similar model, processing rectangular pictures. To this aim, we introduce accepting networks of evolutionary picture processors and investigate their computational power. We show that these networks can accept the complement of any local picture language as well as picture languages that are not recognizable. Some open problems regarding decidability issues and closure properties are finally discussed

Initial algebra for a system of right-linear functors

In 2003 we showed that right-linear systems of equations over regular expressions, when interpreted in a category of trees, have a solution whenever they enjoy a specific property that we called hierarchicity and that is instrumental to avoid critical mutual recursive definitions. In this note, we prove that a right-linear system of polynomial endofunctors on a cocartesian monoidal closed category which enjoys parameterized left list arithmeticity, has an initial algebra, provided it satisfies a property similar to hierarchicity

Expanding the Cyanobacterial Nitrogen Regulatory Network: The GntR-Like Regulator PlmA Interacts with the PII-PipX Complex

Cyanobacteria, phototrophic organisms that perform oxygenic photosynthesis, perceive nitrogen status by sensing 2-oxoglutarate levels. PII, a widespread signaling protein, senses and transduces nitrogen and energy status to target proteins, regulating metabolism and gene expression. In cyanobacteria, under conditions of low 2-oxoglutarate, PII forms complexes with the enzyme N-acetyl glutamate kinase, increasing arginine biosynthesis, and with PII-interacting protein X (PipX), making PipX unavailable for binding and co-activation of the nitrogen regulator NtcA. Both the PII-PipX complex structure and in vivo functional data suggested that this complex, as such, could have regulatory functions in addition to PipX sequestration. To investigate this possibility we performed yeast three-hybrid screening of genomic libraries from Synechococcus elongatus PCC7942, searching for proteins interacting simultaneously with PII and PipX. The only prey clone found in the search expressed PlmA, a member of the GntR family of transcriptional regulators proven here by gel filtration to be homodimeric. Interactions analyses further confirmed the simultaneous requirement of PII and PipX, and showed that the PlmA contacts involve PipX elements exposed in the PII-PipX complex, specifically the C-terminal helices and one residue of the tudor-like body. In contrast, PII appears not to interact directly with PlmA, possibly being needed indirectly, to induce an extended conformation of the C-terminal helices of PipX and for modulating the surface polarity at the PII-PipX boundary, two elements that appear crucial for PlmA binding. Attempts to inactive plmA confirmed that this gene is essential in S. elongatus. Western blot assays revealed that S. elongatus PlmA, irrespective of the nitrogen regime, is a relatively abundant transcriptional regulator, suggesting the existence of a large PlmA regulon. In silico studies showed that PlmA is universally and exclusively found in cyanobacteria. Based on interaction data, on the relative amounts of the proteins involved in PII-PipX-PlmA complexes, determined in western assays, and on the restrictions imposed by the symmetries of trimeric PII and dimeric PlmA molecules, a structural and regulatory model for PlmA function is discussed in the context of the cyanobacterial nitrogen interaction network.This work was supported by grants BFU2015-66360-P to AC and BFU2014-58229-P to VR from the Spanish Ministry of Economy and Competitivity. AO was the recipient of Grisolia Fellowship from Consellería d'Educació of the Valencian Government and AF-N and LT held FPI fellowships/contracts from Ministry of Economy and Competitivity. JE and VR were supported by grants GV/2014/073 and PrometeoII/2014/029, respectively, from the Consellería d'Educació of the Valencian Government

Expandin Cyanobacterial Nitrogen Regulatory Network: The GntR-Like Regulator PlmA Interacts with the PII-PipX Complex

17 páginas, 8 figuras, 3 tablas. Tiene material suplementario en: http://journal.frontiersin.org/article/10.3389/fmicb.2016.01677/full#supplementary-materialCyanobacteria, phototrophic organisms that perform oxygenic photosynthesis, perceive nitrogen status by sensing 2-oxoglutarate levels. PII, a widespread signaling protein, senses and transduces nitrogen and energy status to target proteins, regulating metabolism and gene expression. In cyanobacteria, under conditions of low 2-oxoglutarate, PII forms complexes with the enzyme N-acetyl glutamate kinase, increasing arginine biosynthesis, and with PII-interacting protein X (PipX), making PipX unavailable for binding and co-activation of the nitrogen regulator NtcA. Both the PII-PipX complex structure and in vivo functional data suggested that this complex, as such, could have regulatory functions in addition to PipX sequestration. To investigate this possibility we performed yeast three-hybrid screening of genomic libraries from Synechococcus elongatus PCC7942, searching for proteins interacting simultaneously with PII and PipX. The only prey clone found in the search expressed PlmA, a member of the GntR family of transcriptional regulators proven here by gel filtration to be homodimeric. Interactions analyses further confirmed the simultaneous requirement of PII and PipX, and showed that the PlmA contacts involve PipX elements exposed in the PII-PipX complex, specifically the C-terminal helices and one residue of the tudor-like body. In contrast, PII appears not to interact directly with PlmA, possibly being needed indirectly, to induce an extended conformation of the C-terminal helices of PipX and for modulating the surface polarity at the PII-PipX boundary, two elements that appear crucial for PlmA binding. Attempts to inactive plmA confirmed that this gene is essential in S. elongatus. Western blot assays revealed that S. elongatus PlmA, irrespective of the nitrogen regime, is a relatively abundant transcriptional regulator, suggesting the existence of a large PlmA regulon. In silico studies showed that PlmA is universally and exclusively found in cyanobacteria. Based on interaction data, on the relative amounts of the proteins involved in PII-PipX-PlmA complexes, determined in western assays, and on the restrictions imposed by the symmetries of trimeric PII and dimeric PlmA molecules, a structural and regulatory model for PlmA function is discussed in the context of the cyanobacterial nitrogen interaction network.This work was supported by grants BFU2015-66360-P to AC and BFU2014-58229-P to VR from the Spanish Ministry of Economy and Competitivity. AO was the recipient of Grisolia Fellowship from Consellería d'Educació of the Valencian Government and AF-N and LT held FPI fellowships/contracts from Ministry of Economy and Competitivity. JE and VR were supported by grants GV/2014/073 and PrometeoII/2014/029, respectively, from the Consellería d'Educació of the Valencian GovernmentPeer reviewe

Tree morphisms and bisimulations

A category of (action labelled) trees is defined that can be used to model unfolding of labelled transition systems and to study behavioural relations over them. In this paper we study five different equivalences based on bisimulation for our model. One, that we called resource bisimulation, amounts essentially to three isomorphism. Another, its weak counterpart, permits abstracting from silent actions while preserving the tree structure. The other three are the well known strong, branching and weak bisimulation equivalence. For all bisimulations, but weak, canonical representatives are constructed and it is shown that they can be obtained via enriched functors over our categories of trees, with and without silent actions. Weak equivalence is more problematic; a canonical minimal representative for it cannot be denned by quotienting our trees. The common framework helps in understanding the relationships between the various equivalences and the results provide support to the claim that branching bisimulation is the natural generalization of strong bisimulation to systems with silent moves and that resource and weak resource have an interest of their own