The Body Plan Concept and Its Centrality in Evo-Devo

A body plan is a suite of characters shared by a group of phylogenetically related animals at some point during their development. The concept of bauplane, or body plans, has played and continues to play a central role in the study of evolutionary developmental biology (evo-devo). Despite the importance of the body plan concept in evo-devo, many researchers may not be familiar with the progression of ideas that have led to our current understanding of body plans, and/or current research on the origin and maintenance of body plans. This lack of familiarity, as well as former ties between the body plan concept and metaphysical ideology is likely responsible for our underappreciation of the body plan concept in its own right, as well as its role in evo-devo. My aim in this review is to outline how we have arrived at our modern definition of body plan, the controversies associated with the concept, its role in evo-devo, and how current research is informing us on body plans. To this end, I integrate concepts such as the nature of phyla, the Cambrian explosion, constraint, evolvability, and results from recent research on gene regulatory networks with the much older concept of the body plan

Bogomol'nyi Decomposition for Vesicles of Arbitrary Genus

We apply the Bogomol'nyi technique, which is usually invoked in the study of solitons or models with topological invariants, to the case of elastic energy of vesicles. We show that spontaneous bending contribution caused by any deformation from metastable bending shapes falls in two distinct topological sets: shapes of spherical topology and shapes of non-spherical topology experience respectively a deviatoric bending contribution a la Fischer and a mean curvature bending contribution a la Helfrich. In other words, topology may be considered to describe bending phenomena. Besides, we calculate the bending energy per genus and the bending closure energy regardless of the shape of the vesicle. As an illustration we briefly consider geometrical frustration phenomena experienced by magnetically coated vesicles.Comment: 8 pages, 1 figure; LaTeX2e + IOPar

Elastic theory of unconstrained non-Euclidean plates

Non-Euclidean plates are a subset of the class of elastic bodies having no stress-free configuration. Such bodies exhibit residual stress when relaxed from all external constraints, and may assume complicated equilibrium shapes even in the absence of external forces. In this work we present a mathematical framework for such bodies in terms of a covariant theory of linear elasticity, valid for large displacements. We propose the concept of non-Euclidean plates to approximate many naturally formed thin elastic structures. We derive a thin plate theory, which is a generalization of existing linear plate theories, valid for large displacements but small strains, and arbitrary intrinsic geometry. We study a particular example of a hemispherical plate. We show the occurrence of a spontaneous buckling transition from a stretching dominated configuration to bending dominated configurations, under variation of the plate thickness

Differential systems associated with tableaux over Lie algebras

We give an account of the construction of exterior differential systems based on the notion of tableaux over Lie algebras as developed in [Comm. Anal. Geom 14 (2006), 475-496; math.DG/0412169]. The definition of a tableau over a Lie algebra is revisited and extended in the light of the formalism of the Spencer cohomology; the question of involutiveness for the associated systems and their prolongations is addressed; examples are discussed.Comment: 16 pages; to appear in: "Symmetries and Overdetermined Systems of Partial Differential Equations" (M. Eastwood and W. Miller, Jr., eds.), IMA Volumes in Mathematics and Its Applications, Springer-Verlag, New Yor

Surfaces immersed in Lie algebras associated with elliptic integrals

The main aim of this paper is to study soliton surfaces immersed in Lie algebras associated with ordinary differential equations (ODE's) for elliptic functions. That is, given a linear spectral problem for such an ODE in matrix Lax representation, we search for the most general solution of the wave function which satisfies the linear spectral problem. These solutions allow for the explicit construction of soliton surfaces by the Fokas-Gel'fand formula for immersion, as formulated in (Grundland and Post 2011) which is based on the formalism of generalized vector fields and their prolongation structures. The problem has been reduced to examining three types of symmetries, namely, a conformal symmetry in the spectral parameter (known as the Sym-Tafel formula), gauge transformations of the wave function and generalized symmetries of the associated integrable ODE. The paper contains a detailed explanation of the immersion theory of surfaces in Lie algebras in connection with ODE's as well as an exposition of the main tools used to study their geometric characteristics. Several examples of the Jacobian and P-Weierstrass elliptic functions are included as illustrations of the theoretical results.Comment: 22 pages, 3 sets of figures. Keywords: Generalized symmetries, integrable models, surfaces immersed in Lie algebra

X-ray time variability across the atoll source states of 4U 1636--53

We have studied the rapid X-ray time variability in 149 pointed observations with the \textit{Rossi X-ray Timing Explorer} (RXTE)'s Proportional Counter Array of the atoll source 4U~1636--53 in the banana state and, for the first time with RXTE, in the island state. We compare the frequencies of the variability components of 4U~1636--53 with those in other atoll and Z-sources and find that 4U~1636--53 follows the universal scheme of correlations previously found for other atoll sources at (sometimes much) lower luminosities. Our results on the hectohertz QPO suggest that the mechanism that sets its frequency differs from that for the other components, while the amplitude setting mechanism is common. A previously proposed interpretation of the narrow low-frequency QPO frequencies in different sources in terms of harmonic mode switching is not supported by our data, nor by some previous data on other sources and the frequency range that this QPO covers is found not to be related to spin, angular momentum or luminosity.Comment: 16 pages, 13 figures, accepted for publication in Ap

Mirax: A Brazilian X-Ray Astronomy Satellite Mission

We describe the ``Monitor e Imageador de Raios-X'' (MIRAX), an X-ray astronomy satellite mission proposed by the high energy astrophysics group at the National Institute for Space Research (INPE) in Brazil to the Brazilian Space Agency. MIRAX is an international collaboration that includes, besides INPE, the University of California San Diego, the University of Tuebingen in Germany, the Massachusetts Institute of Technology and the Space Research Organization Netherlands. The payload of MIRAX will consist in two identical hard X-ray cameras (10 -200 keV) and one soft X-ray camera (2-28 keV), both with angular resolution of ~ 5-6 arcmin. The basic objective of MIRAX is to carry out continuous broadband imaging spectroscopy observations of a large source sample (~ 9 months/yr) in the central Galactic plane region. This will allow the detection, localization, possible identification, and spectral/temporal study of the entire history of transient phenomena to be carried out in one single mission. MIRAX will have sensitivities of ~ 5 mCrab/day in the 2-10 keV band (~2 times better than the All Sky Monitor on Rossi X-ray Timing Explorer) and 2.6 mCrab/day in the 10-100 keV band (~40 times better than the Earth Occultation technique of the Burst and Transient Source Experiment on the Compton Gamma-Ray Observatory). The MIRAX spacecraft will weigh about 200 kg and is expected to be launched in a low-altitude (~ 600 km) circular equatorial orbit around 2007/2008.Comment: 6 pages, 1 table, 3 figures, presented at 2002 COSPAR meeting in Houston. Submitted to Adv. Space Re

Global deletion of Panx3 produces multiple phenotypic effects in mouse humeri and femora

© 2016 Anatomical Society. Pannexins form single-membrane channels that allow passage of small molecules between the intracellular and extracellular compartments. Of the three pannexin family members, Pannexin3 (Panx3) is the least studied but is highly expressed in skeletal tissues and is thought to play a role in the regulation of chondrocyte and osteoblast proliferation and differentiation. The purpose of our study is to closely examine the in vivo effects of Panx3 ablation on long bone morphology using micro-computed tomography. Using Panx3 knockout (KO) and wildtype (WT) adult mice, we measured and compared aspects of phenotypic shape, bone mineral density (BMD), cross-sectional geometric properties of right femora and humeri, and lean mass. We found that KO mice have absolutely and relatively shorter diaphyseal shafts compared with WT mice, and relatively larger areas of muscle attachment sites. No differences in BMD or lean mass were found between WT and KO mice. Interestingly, KO mice had more robust femora and humeri compared with WT mice when assessed in cross-section at the midshaft. Our results clearly show that Panx3 ablation produces phenotypic effects in mouse femora and humeri, and support the premise that Panx3 has a role in regulating long bone growth and development