Self-Automaton Semigroups

After reviewing automaton semigroups, we introduce Cayley Automata and the corresponding Cayley Automaton semigroups. We investigate which semigroups are isomorphic to their Cayley Automaton semigroup and give some results for special classes of semigroups. We answer a question posed by Cain relating to the dual construction.Comment: 18 page

Local perceptions of climate change impacts and migration patterns in Malé, Maldives

For the last few decades, Maldives has been seen as being at the forefront of addressing climate change impacts. The low elevation of the islands makes them vulnerable to slow-onset hazards, such as coastal erosion, sea-level rise, salinity intrusion, and change in monsoon patterns and hence rainfall. Consequently, migration has long been discussed as an adaptation strategy for the population. This study covers outcomes from our field research conducted among islanders in Malé, the capital of Maldives, in 2013. It contributes empirical evidence toward understanding complex relations among environmental challenges, climate change, and migration. We set up two main research questions. The first question explored islanders' perceptions of impacts of climatic variability in recent years and possible impacts of future climate change. The second question probed whether out-migration from the islands might be considered to be an adaptation strategy and whether the islanders were willing to move outside Maldives due to projected climate change impacts. We conducted our field research in the capital Malé and nearby residential islands, using quantitative questionnaires with local respondents (N=347). Our results suggest that, besides a set of actually experienced environmental and climate challenges, slow-onset climate change impacts such as sea-level rise are perceived as being one of the key factors affecting Maldivian society and livelihoods. More than 50% of respondents perceive future sea-level rise to be a serious challenge at the national level and they accept that migration from islands to other countries might be a potential option. Conversely, from the individual perspective, sea-level rise is not perceived by the local population as being one of their own important challenges. The reason is that many other factors - cultural, religious, economic and social - play an important role in decisionmaking about migrating or not

Cayley automaton semigroups

Let S be a semigroup, C(S) the automaton constructed from the right Cayley graph of S with respect to all of S as the generating set and ∑(C(S)) the automaton semigroup constructed from C(S). Such semigroups are termed Cayley automaton semigroups. For a given semigroup S we aim to establish connections between S and ∑(C(S)). For a finite monogenic semigroup S with a non-trivial cyclic subgroup C[sub]n we show that ∑(C(S)) is a small extension of a free semigroup of rank n, and that in the case of a trivial subgroup ∑(C(S)) is finite. The notion of invariance is considered and we examine those semigroups S satisfying S ≅ ∑(C(S)). We classify which bands satisfy this, showing that they are those bands with faithful left-regular representations, but exhibit examples outwith this classification. In doing so we answer an open problem of Cain. Following this, we consider iterations of the construction and show that for any n there exists a semigroup where we can iterate the construction n times before reaching a semigroup satisfying S ≅ ∑(C(S)). We also give an example of a semigroup where repeated iteration never produces a semigroup satisfying S ≅ ∑(C(S)). Cayley automaton semigroups of infinite semigroups are also considered and we generalise and extend a result of Silva and Steinberg to cancellative semigroups. We also construct the Cayley automaton semigroup of the bicyclic monoid, showing in particular that it is not finitely generated