Decompositions of complete tripartite graphs into triangles with an edge attached

Let K(r, s, t) denote the complete tripartite graph with partite sets of size r, s and t, where r less than or equal to s less than or equal to t. Let D be the graph consisting of a triangle with an edge attached. We show that K(r, s, t) may be decomposed into copies of D if and only if 4 divides rs + st + rt and t less than or equal to 3rs/(r + s).

Living on the edge: parasite taxonomy in Australia

The way in which the huge Australian parasite fauna is described (discovery and naming) is the subject of this address. The approach to the task has never been well-organised so that a few groups of parasites are now relatively well-known because of the efforts of small groups of workers who have made sustained efforts in these groups, but equally some host-parasite systems have been almost completely ignored in that no worker has ever given them sustained attention. A high proportion of Australian parasites have been described by international workers; The sustaining of interest in a group of parasites over a long period is the key to real progress being made. The nature of the organisation of Australian science presently means that few positions are available for parasite taxonomists and funding for taxonomic research is scarce. Thus, parasite taxonomy (like the taxonomy of many groups of Australian plants and animals) can only be considered to be in crisis. (C) 2003 Australian Society for Parasitology Inc. Published by Elsevier Ltd. All rights reserved.

Cutting edge: Species-specific TLR9-mediated recognition of CpG and non-CpG phosphorothioate-modified ohgonucleotides

Different DNA motifs are required for optimal stimulation Of mouse and human immune cells by CpG oligode-oxynucleotides (ODN). These species differences presumably reflect sequence differences in TLR9, the CPG DNA receptor. In this study, we show that this sequence specificity is restricted to phosphorothioate (PS)-modified ODN and is not observed when a natural phosphodiester backbone is used. Thus, human and mouse cells have not evolved to recognize different CpG motifs in natural DNA. Nonoptimal PS-ODN (i.e., mouse CpG motif on human cells and vice versa) gave delayed and less sustained phosphorylation of p38 AWK than optimal motifs. When the CpG dinucleotide was inverted to GC In each ODN some residual activity of the PS-ODN was retained in a species-specific, TLR-9-dependent manner. Thus, TLR9 may he responsible for mediating many published CpG-independent responses to PS-ODN.

Local edge detectors: A substrate for fine spatial vision at low temporal frequencies in rabbit retina

Visual acuity is limited by the size and density of the smallest retinal ganglion cells, which correspond to the midget ganglion cells in primate retina and the beta- ganglion cells in cat retina, both of which have concentric receptive fields that respond at either light- On or light- Off. In contrast, the smallest ganglion cells in the rabbit retina are the local edge detectors ( LEDs), which respond to spot illumination at both light- On and light- Off. However, the LEDs do not predominate in the rabbit retina and the question arises, what role do they play in fine spatial vision? We studied the morphology and physiology of LEDs in the isolated rabbit retina and examined how their response properties are shaped by the excitatory and inhibitory inputs. Although the LEDs comprise only similar to 15% of the ganglion cells, neighboring LEDs are separated by 30 - 40 mu m on the visual streak, which is sufficient to account for the grating acuity of the rabbit. The spatial and temporal receptive- field properties of LEDs are generated by distinct inhibitory mechanisms. The strong inhibitory surround acts presynaptically to suppress both the excitation and the inhibition elicited by center stimulation. The temporal properties, characterized by sluggish onset, sustained firing, and low bandwidth, are mediated by the temporal properties of the bipolar cells and by postsynaptic interactions between the excitatory and inhibitory inputs. We propose that the LEDs signal fine spatial detail during visual fixation, when high temporal frequencies are minimal.