Maximal subsemigroups of the semigroup of all mappings on an infinite set

In this paper we classify the maximal subsemigroups of the \emph{full transformation semigroup} $\Omega^\Omega$, which consists of all mappings on the infinite set $\Omega$, containing certain subgroups of the symmetric group \sym(\Omega) on $\Omega$. In 1965 Gavrilov showed that there are five maximal subsemigroups of $\Omega^\Omega$ containing \sym(\Omega) when $\Omega$ is countable and in 2005 Pinsker extended Gavrilov's result to sets of arbitrary cardinality. We classify the maximal subsemigroups of $\Omega^\Omega$ on a set $\Omega$ of arbitrary infinite cardinality containing one of the following subgroups of \sym(\Omega): the pointwise stabiliser of a non-empty finite subset of $\Omega$, the stabiliser of an ultrafilter on $\Omega$, or the stabiliser of a partition of $\Omega$ into finitely many subsets of equal cardinality. If $G$ is any of these subgroups, then we deduce a characterisation of the mappings $f,g\in \Omega^\Omega$ such that the semigroup generated by $G\cup \{f,g\}$ equals $\Omega^\Omega$.Comment: Revised according to comments by the referee, 29 pages, 11 figures, to appear in Trans. American Mathematical Societ

Dorsal root ganglion neurons maintained in a 3D culture model exhibit similar electrophysiological properties to fresh explants

Tissue engineered culture models provide a powerful tool for neuroscience research1. They overcome limitations associated with monolayer cultures of neurons and glia by maintaining cells in a more realistic 3D spatial arrangement, and permit continuous monitoring and control of variables that cannot be achieved in animal models. Here we report the development of a system for recording electrophysiological behaviour in neurons in 3D culture

Modelling the injured spinal cord using 3-dimensional cell cultures; strategies for improving tissue engineered repair

Abstract not available

Uptake and binding of some neurotransmitter substances and their analogues in the developing cerebellum of normal rodents and neurologically mutant mice.

Cells dissociated from the postnatally developing rat cerebellum retain their high affinity carrier-mediated transport system for (3H) GABA (Kt = 1 .9 uM, V = 1.8 pmol per 106 cells per min.) and (3H) glutamate (Kt = 10 uM, V = 7.9 pmol per 106 cells per min.). Using a unit gravity sedimentation technique it was demonstrated that (3H) GABA was taken up principally into fractions which were enriched in such neuronal types as Purkinje, stellate and basket cells. (3H) 3-alanine (which is known to be taken up specifically by the glial GABA transport system) and (3H) glutamate were concentrated by cells of the same size range. (3H) glutamate uptake was minimal in fractions enriched in precursors of granule cells. These results are discussed in relation to reports of high affinity (3H) glutamate uptake by glia. The role of glutamate transport in glutamatergic cells is also considered. In addition the development of GABA, 3-adrenergic and muscarinic acetylcholine receptors in the cerebella of weaver (wv), reeler, (rl) staggerer (sg) and jimpy (jp), neurological mutant mice and their normal counterparts was examined using the radioligands, (3H) muscimol, (3H) dihydroalprenolol ((3H) DHA) and (3H) quinuclidinylbenzilate ( (3H) QNB) . The maximum increase in ligand binding occurred during the period 15-20 days for (3H) muscimol, 10-15 days for (3H) DHA, 5-15 days for (3H) QNB. Binding of all ligands was significantly reduced with respect to controls in the cerebellar mutants, wv, rl and sg. (3H) Muscimol binding was the most affected (4-19 per cent control at 20 days) and (3H) QNB binding was least affected (36-50 percent control at 20 days). The corresponding figures for (3H) DHA were 14-22 percent. Binding of these ligands to jp tissue was not significantly different from control except for (3H) QNB binding which was 80 percent of control at 20 days. Binding of all ligands was saturable and of high affinity (muscimol Kd = 12.8 nM; DHA Kd = 0.26 nM; QNB Kd = 0.14 nM) and the affinity constants for binding did not change significantly during development. These data are discussed in relation to (i) the known pharmacology and development of cerebellar neurons and (ii) the effects of the mutations on the development of cerebellar neurons

Education, Exploration and the Elephant in the Room: A Narrative Inquiry of Sexuality and Sex Education among Adolescents with Physical Disabilities

Guided by a constructivist paradigm, this qualitative research study used a multidimensional form of narrative inquiry in order to understand the experiences of learning about sexuality among adolescents with physical disabilities, and in turn, how these experiences influence the way they view themselves as sexual beings. For the purposes of this research, in-depth narrative interviews were conducted with adolescents who have physical disabilities and parents of youth with physical disabilities, as well as a focus group with health professionals. The findings from this study demonstrate that these adolescents often face challenges in accessing disability- specific sex information due to a lack of appropriate resources, discomfort with the topic among educators, health professionals and parents, as well as the pervasive social myth that views people with disabilities as asexual. The data from this study contributes to the literature about sexuality among adolescents with physical disabilities by drawing attention to this important but often overlooked issue, as well as offering recommendations for future resource development that could help empower these youth with the knowledge and skills needed to engage in safe, healthy and fulfilling relationships

Superlattice barrier varactors

SBV (Single Barrier Varactor) diodes have been proposed as alternatives to Schottky barrier diodes for harmonic multiplier applications. However, these show a higher current than expected. The excess current is due to X valley transport in the barrier. We present experimental results showing that the use of a superlattice barrier and doping spikes in the GaAs depletion regions on either side of the barrier can reduce the excess current and improve the control of the capacitance vs. voltage characteristic. The experimental results consist of data taken from two types of device structures. The first test structure was used to study the performance of AlAs/GaAs superlattice barriers. The wafer was fabricated into 90 micron diameter mesa diodes and the resulting current vs. voltage characteristics were measured. A 10 period superlattice structure with a total thickness of approximately 400 A worked well as an electron barrier. The structure had a current density of about one A/sq cm at one volt at room temperature. The capacitance variation of these structures was small because of the design of the GaAs cladding layers. The second test structure was used to study cladding layer designs. These wafers were InGaAs and InAlAs layers lattice matched to an InP substrate. The layers have n(+) doping spikes near the barrier to increase the zero bias capacitance and control the shape of the capacitance vs. voltage characteristic. These structures have a capacitance ratio of 5:1 and an abrupt change from maximum to minimum capacitance. The measurements were made at 80 K. Based on the information obtained from these two structures, we have designed a structure that combines the low current density barrier with the improved cladding layers. The capacitance and current-voltage characteristics from this structure are presented

Braids and factorizable inverse monoids

What is the untangling effect on a braid if one is allowed to snip a string, or if two specified strings are allowed to pass through each other, or even allowed to merge and part as newly reconstituted strings? To calculate the effects, one works in an appropriate factorizable inverse monoid, some aspects of a general theory of which are discussed in this paper. The coset monoid of a group arises, and turns out to have a universal property within a certain class of factorizable inverse monoids. This theory is dual to the classical construction of fundamental inverse semigroups from semilattices. In our braid examples, we will focus mainly on the ``merge and part'' alternative, and introduce a monoid which is a natural preimage of the largest factorizable inverse submonoid of the dual symmetric inverse monoid on a finite set, and prove that it embeds in the coset monoid of the braid group

Presentations of factorizable inverse monoids

It is well-known that an inverse monoid is factorizable if and only if it is a homomorphic image of a semidirect product of a semilattice (with identity) by a group. We use this structure to describe a presentation of an arbitrary factorizable inverse monoid in terms of presentations of its group of units and semilattice of idempotents, together with some other data. We apply this theory to quickly deduce a well known presentation of the symmetric inverse monoid on a nite set