Frameworks, Symmetry and Rigidity

Symmetry equations are obtained for the rigidity matrix of a bar-joint framework in R^d. These form the basis for a short proof of the Fowler-Guest symmetry group generalisation of the Calladine-Maxwell counting rules. Similar symmetry equations are obtained for the Jacobian of diverse framework systems, including constrained point-line systems that appear in CAD, body-pin frameworks, hybrid systems of distance constrained objects and infinite bar-joint frameworks. This leads to generalised forms of the Fowler-Guest character formula together with counting rules in terms of counts of symmetry-fixed elements. Necessary conditions for isostaticity are obtained for asymmetric frameworks, both when symmetries are present in subframeworks and when symmetries occur in partition-derived frameworks.Comment: 5 Figures. Replaces Dec. 2008 version. To appear in IJCG

Rigidity of Frameworks Supported on Surfaces

A theorem of Laman gives a combinatorial characterisation of the graphs that admit a realisation as a minimally rigid generic bar-joint framework in \bR^2. A more general theory is developed for frameworks in \bR^3 whose vertices are constrained to move on a two-dimensional smooth submanifold \M. Furthermore, when \M is a union of concentric spheres, or a union of parallel planes or a union of concentric cylinders, necessary and sufficient combinatorial conditions are obtained for the minimal rigidity of generic frameworks.Comment: Final version, 28 pages, with new figure

Strain-Modified RKKY Interaction in Carbon Nanotubes

For low-dimensional metallic structures, such as nanotubes, the exchange coupling between localized magnetic dopants is predicted to decay slowly with separation. The long-range character of this interaction plays a significant role in determining the magnetic order of the system. It has previously been shown that the interaction range depends on the conformation of the magnetic dopants in both graphene and nanotubes. Here we examine the RKKY interaction in carbon nanotubes in the presence of uniaxial strain for a range of different impurity configurations. We show that strain is capable of amplifying or attenuating the RKKY interaction, significantly increasing certain interaction ranges, and acting as a switch: effectively turning on or off the interaction. We argue that uniaxial strain can be employed to significantly manipulate magnetic interactions in carbon nanotubes, allowing an interplay between mechanical and magnetic properties in future spintronic devices. We also examine the dimensional relationship between graphene and nanotubes with regards to the decay rate of the RKKY interaction.Comment: 7 pages, 6 figures, submitte

Warm Dark Haloes Accretion Histories and their Gravitational Signatures

We study clusters in Warm Dark Matter (WDM) models of a thermally produced dark matter particle $0.5$ keV in mass. We show that, despite clusters in WDM cosmologies having similar density profiles as their Cold Dark Matter (CDM) counterparts, the internal properties, such as the amount of substructure, shows marked differences. This result is surprising as clusters are at mass scales that are {\em a thousand times greater} than that at which structure formation is suppressed. WDM clusters gain significantly more mass via smooth accretion and contain fewer substructures than their CDM brethren. The higher smooth mass accretion results in subhaloes which are physically more extended and less dense. These fine-scale differences can be probed by strong gravitational lensing. We find, unexpectedly, that WDM clusters have {\em higher} lensing efficiencies than those in CDM cosmologies, contrary to the naive expectation that WDM clusters should be less efficient due to the fewer substructures they contain. Despite being less dense, the larger WDM subhaloes are more likely to have larger lensing cross-sections than CDM ones. Additionally, WDM subhaloes typically reside at larger distances, which radially stretches the critical lines associated with strong gravitational lensing, resulting in excess in the number of clusters with large radial cross-sections at the $\sim2\sigma$ level. Though lensing profile for an individual cluster vary significantly with the line-of-sight, the radial arc distribution based on a sample of $\gtrsim100$ clusters may prove to be the crucial test for the presence of WDM.Comment: 13 pages, 14 figures, submitted to MNRA

On the 2-categories of weak distributive laws

A weak mixed distributive law (also called weak entwining structure) in a 2-category consists of a monad and a comonad, together with a 2-cell relating them in a way which generalizes a mixed distributive law due to Beck. We show that a weak mixed distributive law can be described as a compatible pair of a monad and a comonad, in 2-categories extending, respectively, the 2-category of comonads and the 2-category of monads. Based on this observation, we define a 2-category whose 0-cells are weak mixed distributive laws. In a 2-category K which admits Eilenberg-Moore constructions both for monads and comonads, and in which idempotent 2-cells split, we construct a fully faithful 2-functor from this 2-category of weak mixed distributive laws to K^{2 x 2}.Comment: 15 pages LaTeX source, final version to appear in Comm. Algebr

Seasonal Occurrence of the Sod Webworm Moths (Lepidoptera: Crambidae) of Ohio

While nearly 100 species of sod webworms are known to occur in North America, the species complex and seasonal occurrence of these moths has been documented in relatively few states. For Ohio, there is little published record of the sod webworm species complex, and the seasonal occurrence of only a few economically important species has been documented. Using black light traps, sod web worm adult flight activity was monitored over the course of three to five years at four different locations throughout Ohio. In this paper we report the seasonal occurrence of sod web worms species captured at these locations. These data provide a historical benchmark of sod web­worm species diversity, local abundance, and seasonal occurrence in Ohio

Neuronal response in Alzheimer's and Parkinson's disease: the effect of toxic proteins on intracellular pathways

Accumulation of protein aggregates is the leading cause of cellular dysfunction in neurodegenerative disorders. Alzheimer's disease (AD), Parkinson's disease (PD), Huntington's disease, Prion disease and motor disorders such as amyotrophic lateral sclerosis, present with a similar pattern of progressive neuronal death, nervous system deterioration and cognitive impairment. The common characteristic is an unusual misfolding of proteins which is believed to cause protein deposition and trigger degenerative signals in the neurons. A similar clinical presentation seen in many neurodegenerative disorders suggests the possibility of shared neuronal responses in different disorders. Despite the difference in core elements of deposits in each neurodegenerative disorder, the cascade of neuronal reactions such as activation of glycogen synthase kinase-3 beta, mitogen-activated protein kinases, cell cycle re-entry and oxidative stress leading to a progressive neurodegeneration are surprisingly similar. This review focuses on protein toxicity in two neurodegenerative diseases, AD and PD. We reviewed the activated mechanisms of neurotoxicity in response to misfolded beta-amyloid and α-synuclein, two major toxic proteins in AD and PD, leading to neuronal apoptosis. The interaction between the proteins in producing an overlapping pathological pattern will be also discussed.Shohreh Majd, John H. Power and Hugh J.M. Grantha