Cascade synthesis of finite-state machines

One can construct any finite-state machine as a cascade interconnection of machines whose inputs either permute the states or reset them all to one state. Each permutation group needed in the construction is a homomorphic image of a group generated by the action of a set of input sequences on a state subset of the original machine. Proofs of these facts will be given and their application to the Krohn-Rhodes theory described

SgpDec : Cascade (de)compositions of finite transformation semigroups and permutation groups

We describe how the SgpDec computer algebra package can be used for composing and decomposing permutation groups and transformation semigroups hierarchically by directly constructing substructures of wreath products, the so called cascade products.Final Accepted Versio

Algebraic analysis of the computation in the Belousov-Zhabotinksy reaction

We analyse two very simple Petri nets inspired by the Oregonator model of the Belousov-Zhabotinsky reaction using our stochastic Petri net simulator. We then perform the Krohn-Rhodes holonomy decomposition of the automata derived from the Petri nets. The simplest case shows that the automaton can be expressed as a cascade of permutation-reset cyclic groups, with only 2 out of the 12 levels having only trivial permutations. The second case leads to a 35-level decomposition with 5 different simple non-abelian groups (SNAGs), the largest of which is A 9. Although the precise computational significance of these algebraic structures is not clear, the results suggest a correspondence between simple oscillations and cyclic groups, and the presence of SNAGs indicates that even extremely simple chemical systems may contain functionally complete algebras

International consensus on (ICON) pediatric asthma

Asthma is the most common chronic lower respiratory disease in childhood throughout the world. Several guidelines and/or consensus documents are available to support medical decisions on pediatric asthma. Although there is no doubt that the use of common systematic approaches for management can considerably improve outcomes, dissemination and implementation of these are still major challenges. Consequently, the International Collaboration in Asthma, Allergy and Immunology (iCAALL), recently formed by the EAACI, AAAAI, ACAAI, and WAO, has decided to propose an International Consensus on (ICON) Pediatric Asthma. The purpose of this document is to highlight the key messages that are common to many of the existing guidelines, while critically reviewing and commenting on any differences, thus providing a concise reference. The principles of pediatric asthma management are generally accepted. Overall, the treatment goal is disease control. To achieve this, patients and their parents should be educated to optimally manage the disease, in collaboration with healthcare professionals. Identification and avoidance of triggers is also of significant importance. Assessment and monitoring should be performed regularly to re-evaluate and fine-tune treatment. Pharmacotherapy is the cornerstone of treatment. The optimal use of medication can, in most cases, help patients control symptoms and reduce the risk for future morbidity. The management of exacerbations is a major consideration, independent of chronic treatment. There is a trend toward considering phenotype-specific treatment choices; however, this goal has not yet been achieved. © 2012 John Wiley & Sons A/S