Developmental basis of limb homology in Pleurodiran turtles, and the identity of the hooked element in the chelonian tarsus

Although Pleurodiran turtles represent an important component of extant turtle radiation, our knowledge of the development and homology of limb bones in turtles rests mostly upon observations made on derived members of the Cryptodiran clade. Herein, we describe limb development in three pleurodirans: Podocnemis unifilis Troschel, 1848, Podocnemis sextuberculata Cornalia, 1849 and Phrynops hilarii (Dumeril and Bibron, 1835), in an effort to contribute to filling this anatomical gap. For earlier stages of limb development, we described the Y-shaped condensation that gave rise to the zeugopodial cartilages, and differentiation of the primary axis/digital arch that reveals the invariant pattern common to tetrapods. There are up to four central cartilaginous foci in the carpus, and the proximal tarsale is formed by the fusion of the fibulare, intermedium, and centrale 4. Digital development is similar for the five digits. Changes in toe V occur predominantly in the distal tarsale 5. Ontogenetic reduction of phalanges is observed in toe V of Podocnemis. Based on these results, we suggest that the hooked element present in the chelonian tarsus, and traditionally recognized as a modified fifth metatarsale, is actually the fifth distal tarsale. Additionally, our data on limb development of pleurodiran turtles supply more taxonomically comprehensive information to interpret limb configuration within the chelonian clade. (C) 2009 The Linnean Society of London, Zoological Journal of the Linnean Society, 2009, 155, 845-866.

The identity of Sertularia reptans Linnaeus, 1758 (Bryozoa, Candidae)

This paper includes a reassessment of Scrupocellaria reptans (Linnaeus, 1758) (basionym Sertularia reptans), the lectotype of which is selected and figured from among herbarium-sheet specimens held at the Linnean Society of London. Material previously assigned to S. reptans was examined, providing morphological characteristics to distinguish Scrupocellaria ellisi n. sp. Scrupocellaria reptans has a geographically limited distribution in the United Kingdom, while S. ellisi is more widespread in the North Sea, Northeast Atlantic, Adriatic and Tasmania.

Higher identities for the ternary commutator

We use computer algebra to study polynomial identities for the trilinear operation [a, b, c] = abc - acb - bac + bca + cab - cba in the free associative algebra. It is known that [a, b, c] satisfies the alternating property in degree 3, no new identities in degree 5, a multilinear identity in degree 7 which alternates in 6 arguments, and no new identities in degree 9. We use the representation theory of the symmetric group to demonstrate the existence of new identities in degree 11. The only irreducible representations of dimension <400 with new identities correspond to partitions 2(5), 1 and 2(4), 1(3) and have dimensions 132 and 165. We construct an explicit new multilinear identity for partition 2(5), 1 and we demonstrate the existence of a new non-multilinear identity in which the underlying variables are permutations of a(2)b(2)c(2)d(2)e(2) f.

Special identities for Bol algebras

Bol algebras appear as the tangent algebra of Bol loops. A (left) Bol algebra is a vector space equipped with a binary operation [a, b] and a ternary operation {a, b, c} that satisfy five defining identities. If A is a left or right alternative algebra then A(b) is a Bol algebra, where [a, b] := ab - ba is the commutator and {a, b, c} := < b, c, a > is the Jordan associator. A special identity is an identity satisfied by Ab for all right alternative algebras A, but not satisfied by the free Bol algebra. We show that there are no special identities of degree <= 7, but there are special identities of degree 8. We obtain all the special identities of degree 8 in partition six-two. (C) 2011 Elsevier Inc. All rights reserved.

STABLE PIECEWISE POLYNOMIAL VECTOR FIELDS

Let N = {y > 0} and S = {y < 0} be the semi-planes of R-2 having as common boundary the line D = {y = 0}. Let X and Y be polynomial vector fields defined in N and S, respectively, leading to a discontinuous piecewise polynomial vector field Z = (X, Y). This work pursues the stability and the transition analysis of solutions of Z between N and S, started by Filippov (1988) and Kozlova (1984) and reformulated by Sotomayor-Teixeira (1995) in terms of the regularization method. This method consists in analyzing a one parameter family of continuous vector fields Z(epsilon), defined by averaging X and Y. This family approaches Z when the parameter goes to zero. The results of Sotomayor-Teixeira and Sotomayor-Machado (2002) providing conditions on (X, Y) for the regularized vector fields to be structurally stable on planar compact connected regions are extended to discontinuous piecewise polynomial vector fields on R-2. Pertinent genericity results for vector fields satisfying the above stability conditions are also extended to the present case. A procedure for the study of discontinuous piecewise vector fields at infinity through a compactification is proposed here.

A new species of Paralychnophora (Asteraceae: Vernonieae), and comments on the identity of Paralychnophora bicolor

The type of Paralychnophora bicolor was found to represent another species recently described as P. santosii. The misapplication of the name P. bicolor is reviewed. Also, a new species is here proposed, P. glaziouana, for plants previously identified as P. bicolor, since the only available name, P. schwackei, is an illegitimate combination. A key to Paralychnophora is given.

Germline-Specific MATH-BTB Substrate Adaptor MAB1 Regulates Spindle Length and Nuclei Identity in Maize

Germline and early embryo development constitute ideal model systems to study the establishment of polarity, cell identity, and asymmetric cell divisions (ACDs) in plants. We describe here the function of the MATH-BTB domain protein MAB1 that is exclusively expressed in the germ lineages and the zygote of maize (Zea mays). mab1 (RNA interference [RNAi]) mutant plants display chromosome segregation defects and short spindles during meiosis that cause insufficient separation and migration of nuclei. After the meiosis-to-mitosis transition, two attached nuclei of similar identity are formed in mab1 (RNAi) mutants leading to an arrest of further germline development. Transient expression studies of MAB1 in tobacco (Nicotiana tabacum) Bright Yellow-2 cells revealed a cell cycle-dependent nuclear localization pattern but no direct colocalization with the spindle apparatus. MAB1 is able to form homodimers and interacts with the E3 ubiquitin ligase component Cullin 3a (CUL3a) in the cytoplasm, likely as a substrate-specific adapter protein. The microtubule-severing subunit p60 of katanin was identified as a candidate substrate for MAB1, suggesting that MAB1 resembles the animal key ACD regulator Maternal Effect Lethal 26 (MEL-26). In summary, our findings provide further evidence for the importance of posttranslational regulation for asymmetric divisions and germline progression in plants and identified an unstable key protein that seems to be involved in regulating the stability of a spindle apparatus regulator(s).

Polynomial and Poisson dependence in free Poisson algebras and free Poisson fields

We prove that any two Poisson dependent elements in a free Poisson algebra and a free Poisson field of characteristic zero are algebraically dependent, thus answering positively a question from Makar-Limanov and Umirbaev (2007) [8]. We apply this result to give a new proof of the tameness of automorphisms for free Poisson algebras of rank two (see Makar-Limanov and Umirbaev (2011) [9], Makar-Limanov et al. (2009) [10]). (C) 2011 Elsevier Inc. All rights reserved.

Modeling random corrosion processes via polynomial chaos expansion

Polynomial Chaos Expansion (PCE) is widely recognized as a flexible tool to represent different types of random variables/processes. However, applications to real, experimental data are still limited. In this article, PCE is used to represent the random time-evolution of metal corrosion growth in marine environments. The PCE coefficients are determined in order to represent data of 45 corrosion coupons tested by Jeffrey and Melchers (2001) at Taylors Beach, Australia. Accuracy of the representation and possibilities for model extrapolation are considered in the study. Results show that reasonably accurate smooth representations of the corrosion process can be obtained. The representation is not better because a smooth model is used to represent non-smooth corrosion data. Random corrosion leads to time-variant reliability problems, due to resistance degradation over time. Time variant reliability problems are not trivial to solve, especially under random process loading. Two example problems are solved herein, showing how the developed PCE representations can be employed in reliability analysis of structures subject to marine corrosion. Monte Carlo Simulation is used to solve the resulting time-variant reliability problems. However, an accurate and more computationally efficient solution is also presented.