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We prove the following results: (1) Every group is a maximal subgroup of some free idempotent generated semigroup. (2) Every finitely presented group is a maximal subgroup of some free idempotent generated semigroup arising from a finite semigroup. (3) Every group is a maximal subgroup of some free regular idempotent generated semi-group. (4) Every finite(More)
The foreskin is the main site of heterosexual human immunodeficiency virus (HIV) acquisition in uncircumcised men, but functional data regarding T-cell subsets present at this site are lacking. Foreskin tissue and blood were obtained from Ugandan men undergoing elective adult circumcision. Tissue was treated by mechanical and enzymatic digestion followed by(More)
Dr Fabio Boschetti describes himself as an applied mathematician. For many years his work focused on geoscientific applications. More recently he started to be interested in Complex System Science and to apply his past experience to ecological modelling with a view to improve our understanding of how ecosystems and their interaction with human activities(More)
The relationship between posets that are cycle-free and graphs that have more than one end is considered. We show that any locally finite bipartite graph corresponding to a cycle-free partial order has more than one end, by showing a correspondence between the ends of the graph and those of the Hasse graph of its Dedekind–MacNeille completion. If, in(More)
Shifting the emphasis from a model to a modelling task, which involves both a computer model and a modeller, we ask what makes a problem complex. We propose that a modelling task can be seen as a set of questions-and-answers, nested at multiple levels. The role of the modeller then lies in posing the questions and choosing the best procedure to answer them,(More)
A formula for the rank of an arbitrary finite completely 0-simple semigroup, represented as a Rees matrix semigroup M 0 Ruškuc concerning the rank of connected finite completely 0-simple semigroups. The rank is expressed in terms of |I| , |Λ| , the number of connected components k of P and a number rmin which we define. We go on to show that the number rmin(More)
Given a finitely generated semigroup S and subsemigroup T of S we define the notion of the boundary of T in S which, intuitively, describes the position of T inside the left and right Cayley graphs of S. We prove that if S is finitely generated and T has a finite boundary in S then T is finitely generated. We also prove that if S is finitely presented and T(More)