Split-2 Bisimilarity has a Finite Axiomatization over CCS with<br> Hennessy&#39;s Merge

This note shows that split-2 bisimulation equivalence (also known as timed equivalence) affords a finite equational axiomatization over the process algebra obtained by adding an auxiliary operation proposed by Hennessy in 1981 to the recursion, relabelling and restriction free fragment of Milner's Calculus of Communicating Systems. Thus the addition of a single binary operation, viz. Hennessy's merge, is sufficient for the finite equational axiomatization of parallel composition modulo this non-interleaving equivalence. This result is in sharp contrast to a theorem previously obtained by the same authors to the effect that the same language is not finitely based modulo bisimulation equivalence

An Equational Axiomatization for Multi-Exit Iteration

This paper presents an equational axiomatization of bisimulation equivalence over the language of Basic Process Algebra (BPA) with multi-exit iteration. Multi-exit iteration is a generalization of the standard binary Kleene star operation that allows for the specification of agents that, up to bisimulation equivalence, are solutionsof systems of recursion equations of the formX1 = P1 X2 + Q1...Xn = Pn X1 + Qnwhere n is a positive integer, and the Pi and the Qi are process terms. The additionof multi-exit iteration to BPA yields a more expressive language than that obtained by augmenting BPA with the standard binary Kleene star (BPA). As aconsequence, the proof of completeness of the proposed equational axiomatizationfor this language, although standard in its general structure, is much more involvedthan that for BPA. An expressiveness hierarchy for the family of k-exit iteration operators proposed by Bergstra, Bethke and Ponse is also offered.

A Note on an Expressiveness Hierarchy for Multi-exit Iteration

Multi-exit iteration is a generalization of the standard binary Kleene star operation that allows for the specification of agents that, up to bisimulation equivalence, are solutions of systems of recursion equations of the formX_1 = P_1 X_2 + Q_1 X_n = P_n X_1 + Q_n where n is a positive integer, and the P_i and the Q_i are process terms. The addition of multi-exit iteration to Basic Process Algebra (BPA) yields a more expressive language than that obtained by augmenting BPA with the standard binary Kleene star. This note offers an expressiveness hierarchy, modulo bisimulation equivalence, for the family of multi-exit iteration operators proposed by Bergstra, Bethke and Ponse

A Cook’s Tour of Equational Axiomatizations for Prefix Iteration

Prefix iteration is a variation on the original binary version of theKleene star operation P*Q, obtained by restricting the first argument to be an atomic action, and yields simple iterative behaviours that can be equationally characterized by means of finite collections of axioms. In this paper, we present axiomatic characterizations for a significant fragment of the notions of equivalence and preorder in van Glabbeek's linear-time/branching-time spectrum over Milner's basic CCS extended with prefix iteration. More precisely, we consider ready simulation, simulation, readiness, trace and language semantics, and provide complete (in)equational axiomatizations for each of these notions over BCCS with prefix iteration. All of the axiom systems we present are finite, if so is the set of atomic actions under consideration

A Finite Equational Base for CCS with Left Merge and Communication Merge

Using the left merge and communication merge from ACP, we present an equational base for the fragment of CCS without restriction and relabelling. Our equational base is finite if the set of actions is finite

Bisimilarity is not Finitely Based over BPA with Interrupt

This paper shows that bisimulation equivalence does not afford a finite equational axiomatization over the language obtained by enriching Bergstra and Klop's Basic Process Algebra with the interrupt operator. Moreover, it is shown that the collection of closed equations over this language is also not finitely based

Axiomatizing Prefix Iteration with Silent Steps

Prefix iteration is a variation on the original binary version of the Kleene star operation P*Q, obtained by restricting the first argument to be an atomic action. The interaction of prefix iteration with silent steps is studied in the setting of Milner's basic CCS. Complete equational axiomatizations are given for four notions of behavioural congruence over basic CCS with prefix iteration, viz. branching congruence, eta-congruence, delay congruence and weak congruence. The completeness proofs for eta-, delay, and weak congruence are obtained by reduction to the completeness theorem for branching congruence. It is also argued that the use of the completeness result for branching congruence in obtaining the completeness result for weak congruence leads to a considerable simplification with respect to the only direct proof presented in the literature. The preliminaries and the completeness proofs focus on open terms, i.e. terms that may contain process variables. As a by-product, the omega-completeness of the axiomatizations is obtained as well as their completeness for closed terms. AMS Subject Classification (1991): 68Q10, 68Q40, 68Q55.CR Subject Classification (1991): D.3.1, F.1.2, F.3.2.Keywords and Phrases: Concurrency, process algebra, basic CCS, prefix iteration, branching bisimulation, eta-bisimulation, delay bisimulation, weak bisimulation, equational logic, complete axiomatizations

Nested Semantics over Finite Trees are Equationally Hard

This paper studies nested simulation and nested trace semantics over the language BCCSP, a basic formalism to express finite process behaviour. It is shown that none of these semantics affords finite (in)equational axiomatizations over BCCSP. In particular, for each of the nested semantics studied in this paper, the collection of sound, closed (in)equations over a singleton action set is not finitely based

Balancing Enzyme Encapsulation Efficiency and Stability in Complex Coacervate Core Micelles

Encapsulation of charged proteins into complex coacervate core micelles (C3Ms) can be accomplished by mixing them with oppositely charged diblock copolymers. However, these micelles tend to disintegrate at high ionic strength. Previous research showed that the addition of a homopolymer with the same charge sign as the protein improved the stability of protein-containing C3Ms. In this research, we used fluorescence correlation spectroscopy (FCS) and dynamic light scattering (DLS) to study how the addition of the homopolymer affects the encapsulation efficiency and salt stability of the micelles. We studied the encapsulation of laccase spore coat protein A (CotA), a multicopper oxidase, using a strong cationic-neutral diblock copolymer, poly(N-methyl-2-vinyl-pyridinium iodide)-block-poly(ethylene oxide) (PM2VP128-b-PEO477), and a negatively charged homopolymer, poly(4-styrenesulfonate) (PSS215). DLS indeed showed an improved stability of this three-component C3M system against the addition of salt compared to a two-component system. Remarkably, FCS showed that the release of CotA from a three-component C3M system occurred at a lower salt concentration and over a narrower concentration range than the dissociation of C3Ms. In conclusion, although the addition of the homopolymer to the system leads to micelles with a higher salt stability, CotA is excluded from the C3Ms already at lower ionic strengths because the homopolymer acts as a competitor of the enzyme for encapsulation

Population Pharmacokinetic Modelling of Intravenous Immunoglobulin Treatment in Patients with Guillain–Barré Syndrome

BACKGROUND AND OBJECTIVE: Intravenous immunoglobulin (IVIg) at a standard dosage is the treatment of choice for Guillain–Barré syndrome. The pharmacokinetics, however, is highly variable between patients, and a rapid clearance of IVIg is associated with poor recovery. We aimed to develop a model to predict the pharmacokinetics of a standard 5-day IVIg course (0.4 g/kg/day) in patients with Guillain–Barré syndrome. METHODS: Non-linear mixed-effects modelling software (NONMEM(®)) was used to construct a pharmacokinetic model based on a model-building cohort of 177 patients with Guillain–Barré syndrome, with a total of 589 sequential serum samples tested for total immunoglobulin G (IgG) levels, and evaluated on an independent validation cohort that consisted of 177 patients with Guillain–Barré syndrome with 689 sequential serum samples. RESULTS: The final two-compartment model accurately described the daily increment in serum IgG levels during a standard IVIg course; the initial rapid fall and then a gradual decline to steady-state levels thereafter. The covariates that increased IgG clearance were a more severe disease (as indicated by the Guillain–Barré syndrome disability score) and concomitant methylprednisolone treatment. When the current dosing regimen was simulated, the percentage of patients who reached a target ∆IgG > 7.3 g/L at 2 weeks decreased from 74% in mildly affected patients to only 33% in the most severely affected and mechanically ventilated patients (Guillain–Barré syndrome disability score of 5). CONCLUSIONS: This is the first population-pharmacokinetic model for standard IVIg treatment in Guillain–Barré syndrome. The model provides a new tool to predict the pharmacokinetics of alternative regimens of IVIg in Guillain–Barré syndrome to design future trials and personalise treatment. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s40262-022-01136-z