Black holes admitting a Freudenthal dual

The quantised charges x of four dimensional stringy black holes may be assigned to elements of an integral Freudenthal triple system whose automorphism group is the corresponding U-duality and whose U-invariant quartic norm Delta(x) determines the lowest order entropy. Here we introduce a Freudenthal duality x -> \tilde{x}, for which \tilde{\tilde{x}}=-x. Although distinct from U-duality it nevertheless leaves Delta(x) invariant. However, the requirement that \tilde{x} be integer restricts us to the subset of black holes for which Delta(x) is necessarily a perfect square. The issue of higher-order corrections remains open as some, but not all, of the discrete U-duality invariants are Freudenthal invariant. Similarly, the quantised charges A of five dimensional black holes and strings may be assigned to elements of an integral Jordan algebra, whose cubic norm N(A) determines the lowest order entropy. We introduce an analogous Jordan dual A*, with N(A) necessarily a perfect cube, for which A**=A and which leaves N(A) invariant. The two dualities are related by a 4D/5D lift.Comment: 32 pages revtex, 10 tables; minor corrections, references adde

Observations on Integral and Continuous U-duality Orbits in N=8 Supergravity

One would often like to know when two a priori distinct extremal black p-brane solutions are in fact U-duality related. In the classical supergravity limit the answer for a large class of theories has been known for some time. However, in the full quantum theory the U-duality group is broken to a discrete subgroup and the question of U-duality orbits in this case is a nuanced matter. In the present work we address this issue in the context of N=8 supergravity in four, five and six dimensions. The purpose of this note is to present and clarify what is currently known about these discrete orbits while at the same time filling in some of the details not yet appearing in the literature. To this end we exploit the mathematical framework of integral Jordan algebras and Freudenthal triple systems. The charge vector of the dyonic black string in D=6 is SO(5,5;Z) related to a two-charge reduced canonical form uniquely specified by a set of two arithmetic U-duality invariants. Similarly, the black hole (string) charge vectors in D=5 are E_{6(6)}(Z) equivalent to a three-charge canonical form, again uniquely fixed by a set of three arithmetic U-duality invariants. The situation in four dimensions is less clear: while black holes preserving more than 1/8 of the supersymmetries may be fully classified by known arithmetic E_{7(7)}(Z) invariants, 1/8-BPS and non-BPS black holes yield increasingly subtle orbit structures, which remain to be properly understood. However, for the very special subclass of projective black holes a complete classification is known. All projective black holes are E_{7(7)}(Z) related to a four or five charge canonical form determined uniquely by the set of known arithmetic U-duality invariants. Moreover, E_{7(7)}(Z) acts transitively on the charge vectors of black holes with a given leading-order entropy.Comment: 43 pages, 8 tables; minor corrections, references added; version to appear in Class. Quantum Gra

On the precipitation hardening of selective laser melted AlSi10Mg

Precipitation hardening of selective laser melted AlSi10Mg was investigated in terms of solution heat treatment and aging duration. The influence on the microstructure and hardness was established, as was the effect on the size and density of Si particles. Although the hardness changes according to the treatment duration, the maximum hardening effect falls short of the hardness of the as-built parts with their characteristic fine microstructure. This is due to the difference in strengthening mechanisms

Evaluation of High Resolution Thermal Imaging to Determine the Effect of Vertebral Fractures on Associated Skin Surface Temperature in Children with Osteogenesis Imperfecta

Vertebral fractures are common in children with osteogenesis imperfecta (OI). Current imaging methods for fracture detection (X-ray and DXA) use ionising radiation. This pilot study explored whether the alteration in blood flow in vertebral fractures results in skin temperature changes that may be detected using high resolution thermal imaging (HRTI) and thus assist diagnosis and monitoring of fractures in OI patients. Eleven participants aged 5-18 years with OI and known vertebral fractures were enrolled. Small metal discs were placed on the skin surface alongside the vertebrae before participants had DXA and X-ray scans and thermal imaging of their backs. Visibility of the discs on the DXA and X-ray scans and thermal images allowed the temperatures of the skin surface above vertebrae without (healthy) and with fractures to be compared to their respective adjacent skin surface regions (Region of Reference, ROR) by calculating the temperature percentage change (TPC). The TPC between the skin temperature over the fractured thoracic vertebrae (n=11) and the ROR was significant (1.44%, p=0.002, 95% confidence). TPC between the skin temperature over healthy thoracic vertebrae and ROR was not (0.97%, p=0.15, 95% confidence). HRTI may provide a novel tool for assisting in detection of vertebral fractures in OI. Keywords: Computerised medical diagnosis, thermal imaging, vertebral fracture detection, osteogenesis imperfecta

Morphology of the first instar larva of obligatory traumatic myiasis agents (Diptera: Calliphoridae, Sarcophagidae)

There are only three fly species that are obligate agents of traumatic myiasis of humans and livestock: a single species of flesh fly, Wohlfahrtia magnifica (Sarcophagidae), and two species of blow flies, Chrysomya bezziana and Cochliomyia hominivorax (Calliphoridae). The morphology of their first instar larvae is thoroughly and consistently documented here with light microscopy photographs and scanning electron microscopy micrographs. The following morphological structures are documented: pseudocephalon, antennal complex, maxillary palpus, oral ridges, thoracic and abdominal spinulation, spiracular field, posterior spiracles and cephaloskeleton. New diagnostic features drawn from the cephaloskeleton and the spinulation of abdominal segments, including the anal pad, are discovered and extensively described. Earlier descriptions in the literature are revisited, and major discrepancies between these and the results of the current study are discussed. The present results allow clarification, correction and, especially, complementation of information provided by earlier authors. The relatively distant taxonomic position of all three species is evidence that obligatory myiasis has arisen independently, and the extensively similar morphology in the first instar larvae of Chrysomya bezziana, Cochliomyia hominivorax and W. magnifica in comparison to necrophagous species, especially the enhancement of the anterior part of the cephaloskeleton and the segmental spinulation, is therefore best interpreted as homoplasic adaptations to a life strategy as obligate vertebrate parasites. An identification key for first instar larvae of all obligatory traumatic myiasis agents of mammals is provided.Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited

Osteopenia, decreased bone formation and impaired osteoblast development in Sox4 heterozygous mice

The transcription factor Sox4 is vital for fetal development, as Sox4–/– homozygotes die in utero. Sox4 mRNA is expressed in the early embryonic growth plate and is regulated by parathyroid hormone, but its function in bone modeling/remodeling is unknown. We report that Sox4+/– mice exhibit significantly lower bone mass (by dual-energy X-ray absorptiometry) from an early age, and fail to obtain the peak bone mass of wild-type (WT) animals. Microcomputed tomography (μCT), histomorphometry and biomechanical testing of Sox4+/– bones show reduced trabecular and cortical thickness, growth plate width, ultimate force and stiffness compared with WT. Bone formation rate (BFR) in 3-month-old Sox4+/– mice is 64% lower than in WT. Primary calvarial osteoblasts from Sox4+/– mice demonstrate markedly inhibited proliferation, differentiation and mineralization. In these cultures, osterix (Osx) and osteocalcin (OCN) mRNA expression was reduced, whereas Runx2 mRNA was unaffected. No functional defects were found in osteoclasts. Silencing of Sox4 by siRNA in WT osteoblasts replicated the defects observed in Sox4+/– cells. We demonstrate inhibited formation and altered microarchitecture of bone in Sox4+/– mice versus WT, without apparent defects in bone resorption. Our results implicate the transcription factor Sox4 in regulation of bone formation, by acting upstream of Osx and independent of Runx2