Differential equations for the cuspoid canonical integrals

Differential equations satisfied by the cuspoid canonical integrals I_n(a) are obtained for arbitrary values of n≥2, where n−1 is the codimension of the singularity and a=(ɑ_1,ɑ_2,...,ɑ_(n−1)). A set of linear coupled ordinary differential equations is derived for each step in the sequence I_n(0,0,...,0,0) →I_n(0,0,...,0,ɑ_(n−1)) →I_n(0,0,...,ɑ_(n−2),ɑ_(n−1)) →...→I_n(0,ɑ_2,...,ɑ_(n−2),ɑ_(n−1)) →I_n(ɑ_1,ɑ_2,...,ɑ_n−2,ɑ_(n−1)). The initial conditions for a given step are obtained from the solutions of the previous step. As examples of the formalism, the differential equations for n=2 (fold), n=3 (cusp), n=4 (swallowtail), and n=5 (butterfly) are given explicitly. In addition, iterative and algebraic methods are described for determining the parameters a that are required in the uniform asymptotic cuspoid approximation for oscillating integrals with many coalescing saddle points. The results in this paper unify and generalize previous researches on the properties of the cuspoid canonical integrals and their partial derivatives

Cloud fluid models of gas dynamics and star formation in galaxies

The large dynamic range of star formation in galaxies, and the apparently complex environmental influences involved in triggering or suppressing star formation, challenges the understanding. The key to this understanding may be the detailed study of simple physical models for the dominant nonlinear interactions in interstellar cloud systems. One such model is described, a generalized Oort model cloud fluid, and two simple applications of it are explored. The first of these is the relaxation of an isolated volume of cloud fluid following a disturbance. Though very idealized, this closed box study suggests a physical mechanism for starbursts, which is based on the approximate commensurability of massive cloud lifetimes and cloud collisional growth times. The second application is to the modeling of colliding ring galaxies. In this case, the driving processes operating on a dynamical timescale interact with the local cloud processes operating on the above timescale. The results is a variety of interesting nonequilibrium behaviors, including spatial variations of star formation that do not depend monotonically on gas density

Resolving the Surfaces of Extrasolar Planets With Secondary Eclipse Light Curves

We present a method that employs the secondary eclipse light curves of transiting extrasolar planets to probe the spatial variation of their thermal emission. This technique permits an observer to resolve the surface of the planet without the need to spatially resolve its central star. We evaluate the feasibility of this technique for the HD 209458 system [..]. We consider two representations of the planetary thermal emission; a simple model parameterized by a sinusoidal dependence on longitude and latitude, as well as the results of a three-dimensional dynamical simulation of the planetary atmosphere previously published by Cooper & Showman. We find that observations of the secondary eclipse light curve are most sensitive to a longitudinal offset in the geometric and photometric centroids of the hemisphere of the planet visible near opposition. To quantify this signal, we define a new parameter, the ``uniform time offset,'' which measures the time lag between the observed secondary eclipse and that predicted by a planet with a uniform surface flux distribution. We compare the predicted amplitude of this parameter for HD 209458 with the precision with which it could be measured with IRAC. We find that IRAC observations at 3.6um a single secondary eclipse should permit sufficient precision to confirm or reject the Cooper & Showman model of the surface flux distribution for this planet. We quantify the signal-to-noise ratio for this offset in the remaining IRAC bands (4.5um, 5.8um, and 8.0um), and find that a modest improvement in photometric precision (as might be realized through observations of several eclipse events) should permit a similarly robust detection.Comment: AASTeX 5.2, 24 pages, 5 figures, accepted for publication in ApJ; v2: clarifications, updated to version accepted by ApJ; v3: try to reduce spacin

Fixation principles in metaphyseal bone—a patent based review

Osteoporotic changes start in cancellous bone due to the underlying pathophysiology. Consequently, the metaphyses are at a higher risk of "osteoporotic” fracture than the diaphysis. Furthermore, implant purchase to fix these fractures is also affected by the poor bone quality. In general, researchers and developers have worked on three different approaches to address the problem of fractures to osteoporotic bone: adapted anchoring techniques, improved load distribution as well as transfer with angular stable screws, and augmentation techniques using bone substitutes. A patent-based review was performed to evaluate which ideas were utilized to improve fixation in osteoporotic, metaphyseal bone, especially in the proximal femur, and to analyze whether the concept had entered clinical use. Anchoring devices that are either extramedullary or intramedullary have a long clinical history. However, demanding surgical techniques and complications, especially in poor quality bone, are justification that such implants and their corresponding surgical techniques need to be improved upon. Expanding elements have been evaluated in the laboratory. The results are promising and the potential of this approach has yet to be fully exploited in the clinics. Internal fixators with angular stable screws open the door for many new anchorage ideas and have great potential for further optimization of load distribution and transfer. Augmentation techniques may improve anchorage in osteoporotic bone. However, the properties of bone substitute materials will need to be modified and improved upon in order to meet the demanding requirements. If we summarise the development process and the clinical use of implants to date, we have to clearly state that more factors than simply biomechanical advantage will determine the clinical success of a new fixation principle or a new implant. Instead, fracture treatment of patients with osteoporosis really needs an interdisciplinary approach

Visualising muscle anatomy using three-dimensional computer models - an example using the head and neck muscles of Sphenodon

We demonstrate how the computer-based technique of multi-body dynamics analysis (MDA) can be used to create schematic, but informative three-dimensional (3D) representations of complex muscle anatomy. As an example we provide an overview of the head and neck muscles present in Sphenodon (Diapsida: Lepidosauria: Rhynchocephalia). First a computer model based on micro-computed tomography datasets provides a detailed and anatomically correct three-dimensional (3D) framework to work from. Secondly, muscles are represented by groups of cylinders that can be colour coded as desired. This allows muscle positions, attachment areas, and 3D orientation to be visualised clearly. This method has advantages over imaging techniques such as two-dimensional drawings and permits the form and function of the muscles to be understood in a way that is not always possible with more classical visualisation techniques. Copyright: Palaeontological Association December 2009

The head and neck muscles associated with feeding in sphenodon (Reptilia: Lepidosauria: Rhynchocephalia)

Feeding in Sphenodon, the tuatara of New Zealand, is of interest for several rea-sons. First, the modern animal is threatened by extinction, and some populations are in competition for food with Pacific rats. Second, Sphenodon demonstrates a feeding apparatus that is unique to living amniotes: an enlarged palatine tooth row, acrodont dentition, enlarged incisor-like teeth on the premaxilla, a posterior extension of the dentary and an elongate articular surtace that permits prooral shearing. Third, Spheno-don has a skull with two complete lateral temporal bars and is therefore structurally analogous to the configuration hypothesised for the ancestral diapsid reptile. Further-more, the fossil relatives of Sphenodon demonstrate considerable variation in terms of feeding apparatus and skull shape. Lastly, as Sphenodon is the only extant rhyn-chocephalian it represents a potentially useful reference taxon for both muscle recon-struction in extinct reptile taxa and determination of muscle homology in extant taxa. Here we provide an up-to-date consensus view of osteology and musculature in Sphenodon that is relevant to feeding. Discrepancies within previous descriptions are evaluated and synthesised with new observations. This paper displays the complex muscle arrangement using a range of different imaging techniques and a variety of different angles. This includes photographs, illustrations, schematic diagrams, and microcomputed tomography (micro-CT) slice images. © Palaeontological Association August 2009

Large-scale Star Formation Triggering in the Low-mass Arp 82 System: A Nearby Example of Galaxy Downsizing Based on UV/Optical/Mid-IR Imaging

As part of our Spitzer Spirals, Bridges, and Tails project to help understand the effects of galaxy interactions on star formation, we analyze GALEX ultraviolet, SARA optical, and Spitzer infrared images of the interacting galaxy pair Arp 82 (NGC 2535/6) and compare to a numerical simulation of the interaction. We investigate the multiwavelength properties of several individual star forming complexes (clumps). Using optical and UV colors, EW(Halpha), and population synthesis models we constrain the ages of the clumps and find that the median clump age is about 12 Myr. The clumps have masses ranging from a few times 10^6 to 10^9 solar masses. In general, the clumps in the tidal features have similar ages to those in the spiral region, but are less massive. The 8 micron and 24 micron luminosities are used to estimate the far-infrared luminosities and the star formation rates of the clumps. The total clump star formation rate is 2.0+/-0.8 solar masses per year, while the entire Arp 82 system is forming stars at a rate of 4.9+/-2.0 solar masses per year. We find, for the first time, stars in the HI arc to the southeast of the NGC 2535 disk. Population synthesis models indicate that all of the observed populations have young to intermediate ages. We conclude that although the gas disks and some old stars may have formed early-on, the progenitors are late-type or low surface brightness and the evolution of these galaxies was halted until the recent encounter.Comment: Accepted for publication in the AJ, 22 Figures, 5 Table

Obtaining patient torso geometry for the design of scoliosis braces. A study of the accuracy and repeatability of handheld 3D scanners

Objective: Obtaining patient geometry is crucial in scoliosis brace design for patients with adolescent idiopathic scoliosis. Advances in 3D scanning technologies provide the opportunity to obtain patient geometries quickly with fewer resources during the design process compared with the plaster-cast method. This study assesses the accuracy and repeatability of such technologies for this application. Methods: The accuracy and repeatability of three different handheld scanners and phone-photogrammetry was assessed using different mesh generation software. Twenty-four scans of a single subject's torso were analyzed for accuracy and repeatability based on anatomical landmark distances and surface deviation maps. Results: Mark II and Structure ST01 scanners showed maximum mean surface deviations of 1.74 ± 3.63 mm and 1.64 ± 3.06 mm, respectively. Deviations were lower for the Peel 1 scanner (maximum of −0.35 ± 2.8 mm) but higher with the use of phone-photogrammetry (maximum of −5.1 ± 4.8 mm). The mean absolute errors of anatomical landmark distance measurements from torso meshes obtained with the Peel 1, Mark II, and ST01 scanners were all within 9.3 mm (3.6%), whereas phone-photogrammetry errors were as high as 18 mm (7%). Conclusions: Low-cost Mark II and ST01 scanners are recommended for obtaining torso geometries because of their accuracy and repeatability. Subject’s breathing/movement affects the resultant geometry around the abdominal and anterolateral regions

Syntaxin 3B is essential for the exocytosis of synaptic vesicles in ribbon synapses of the retina.

Ribbon synapses of the vertebrate retina are specialized synapses that release neurotransmitter by synaptic vesicle exocytosis in a manner that is proportional to the level of depolarization of the cell. This release property is different from conventional neurons, in which the release of neurotransmitter occurs as a short-lived burst triggered by an action potential. Synaptic vesicle exocytosis is a calcium regulated process that is dependent on a set of interacting synaptic proteins that form the so-called SNARE (soluble N-ethylmaleimide sensitive factor attachment protein receptor) complex. Syntaxin 3B has been identified as a specialized SNARE molecule in ribbon synapses of the rodent retina. However, the best physiologically-characterized neuron that forms ribbon-style synapses is the rod-dominant or Mb1 bipolar cell of the goldfish retina. We report here the molecular characterization of syntaxin 3B from the goldfish retina. Using a combination of reverse transcription (RT) polymerase chain reaction (PCR) and immunostaining with a specific antibody, we show that syntaxin 3B is highly enriched in the plasma membrane of bipolar cell synaptic terminals of the goldfish retina. Using membrane capacitance measurements we demonstrate that a peptide derived from goldfish syntaxin 3B inhibits synaptic vesicle exocytosis. These experiments demonstrate that syntaxin 3B is an important factor for synaptic vesicle exocytosis in ribbon synapses of the vertebrate retina

On the eigenvalues of Cayley graphs on the symmetric group generated by a complete multipartite set of transpositions

Given a finite simple graph \cG with $n$ vertices, we can construct the Cayley graph on the symmetric group $S_n$ generated by the edges of \cG, interpreted as transpositions. We show that, if \cG is complete multipartite, the eigenvalues of the Laplacian of \Cay(\cG) have a simple expression in terms of the irreducible characters of transpositions, and of the Littlewood-Richardson coefficients. As a consequence we can prove that the Laplacians of \cG and of \Cay(\cG) have the same first nontrivial eigenvalue. This is equivalent to saying that Aldous's conjecture, asserting that the random walk and the interchange process have the same spectral gap, holds for complete multipartite graphs.Comment: 29 pages. Includes modification which appear on the published version in J. Algebraic Combi