Robustness to Algorithmic Singularities and Sensitivity in Computational Kinematics

A robust approach to computational kinematics intended to cope with algorithmic singularities is introduced in this article. The approach is based on the reduction of the original system of equations to a subsystem of bivariate equations, as opposed to the multivariate polynomial reduction leading to the characteristic univariate polynomial. The effectiveness of the approach is illustrated for the exact function-generation synthesis of planar, spherical, and spatial four-bar linkages. Some numerical examples are provided for the case of the spherical four-bar function generator with six precision points to show the benefits of the proposed method with respect to methods reported in the literature.The first author acknowledges the support of Universidad Politecnica de Valencia, research project PAID-00-09. The second author acknowledges the support of McGill University by means of a James McGill Professorship.Gracia Calandin, LI.; Angeles, J. (2011). Robustness to Algorithmic Singularities and Sensitivity in Computational Kinematics. Proceedings of the Institution of Mechanical Engineers part C - Journal of Mechanical Engineering Science. 225(4):987-999. doi:10.1243/09544062JMES2464S9879992254Raghavan, M., & Roth, B. (1993). Inverse Kinematics of the General 6R Manipulator and Related Linkages. Journal of Mechanical Design, 115(3), 502-508. doi:10.1115/1.2919218Lee, H. Y., Woernle, C., & Hiller, M. (1991). A Complete Solution for the Inverse Kinematic Problem of the General 6R Robot Manipulator. Journal of Mechanical Design, 113(4), 481-486. doi:10.1115/1.2912808Innocenti, C., & Parenti-Castelli, V. (1993). Echelon form solution of direct kinematics for the general fully-parallel spherical wrist. Mechanism and Machine Theory, 28(4), 553-561. doi:10.1016/0094-114x(93)90035-tGosselin, C. M., Sefrioui, J., & Richard, M. J. (1994). On the Direct Kinematics of Spherical Three-Degree-of-Freedom Parallel Manipulators of General Architecture. Journal of Mechanical Design, 116(2), 594-598. doi:10.1115/1.2919419Alizade, R. I., & Kilit, Ö. (2005). Analytical synthesis of function generating spherical four-bar mechanism for the five precision points. Mechanism and Machine Theory, 40(7), 863-878. doi:10.1016/j.mechmachtheory.2004.12.010Cervantes-Sánchez, J. J., Gracia, L., Rico-Martínez, J. M., Medellín-Castillo, H. I., & González-Galván, E. J. (2009). A novel and efficient kinematic synthesis approach of the spherical 4R function generator for five and six precision points. Mechanism and Machine Theory, 44(11), 2020-2037. doi:10.1016/j.mechmachtheory.2009.05.006Angeles, J. (2007). Fundamentals of Robotic Mechanical Systems. Mechanical Engineering Series. doi:10.1007/978-0-387-34580-2Bai, S., Hansen, M. R., & Angeles, J. (2009). A robust forward-displacement analysis of spherical parallel robots. Mechanism and Machine Theory, 44(12), 2204-2216. doi:10.1016/j.mechmachtheory.2009.07.005Sommese, A. J., & Wampler, C. W. (2005). The Numerical Solution of Systems of Polynomials Arising in Engineering and Science. doi:10.1142/5763Forsythe, G. E. (1970). Pitfalls in Computation, or why a Math Book isn’t Enough. The American Mathematical Monthly, 77(9), 931. doi:10.2307/2318109Angeles, J., Hommel, G., & Kovács, P. (Eds.). (1993). Computational Kinematics. Solid Mechanics and Its Applications. doi:10.1007/978-94-015-8192-9Yang, A. T., & Freudenstein, F. (1964). Application of Dual-Number Quaternion Algebra to the Analysis of Spatial Mechanisms. Journal of Applied Mechanics, 31(2), 300-308. doi:10.1115/1.3629601Gupta, K. C., & Beloiu, A. S. (1998). Branch and circuit defect elimination in spherical four-bar linkages. Mechanism and Machine Theory, 33(5), 491-504. doi:10.1016/s0094-114x(97)00078-

Mitochondrial Data in Monocot Phylologenetics

Mitochondrial sequences are an important source of data in animal phylogenetics, equivalent in importance to plastid sequences in plants. However, in recent years plant systematists have begun exploring the mitochondrial genome as a source of phylogenetically useful characters. The plant mitochondrial genome is renowned for its variability in size, structure, and gene organization, but this need not be of concern for the application of sequence data in phylogenetics. However, the incorporation of reverse transcribed mitochondrial genes ( processed paralogs ) and the recurring transfer of genes from the mitochondrion to the nucleus are evolutionary events that must be taken into account. RNA editing of mitochondrial genes is sometimes considered a problem in phylogenetic reconstruction, but we regard it only as a mechanism that may increase variability at edited sites and change the codon position bias accordingly. Additionally, edited sites may prove a valuable tool in identifying processed paralogs. An overview of genes and sequences used in phylogenetic studies of angiosperms is presented. In the monocots, a large amount of mitochondrial sequence data is being collected together with sequence data from plastid and nuclear genes, thus offering an opportunity to compare data from different genomic compartments. The mitochondrial and plastid data are incongruent when organelle gene trees are reconstructed. Possible reasons for the observed incongruence involve sampling of paralogous sequences and highly divergent substitution rates, potentially leading to longbranch attraction. The above problems are addressed in Acorales, Alismatales, Poales, Liliaceae, the Anthericum clade (in Agavaceae), and in some achlorophyllous taxa

Rate accelerations in nuclear 18S rDNA of mycoheterotrophic and parasitic angiosperms

Rate variation in genes from all three genomes has been observed frequently in plant lineages with a parasitic and mycoheterotrophic mode of life. While the loss of photosynthetic ability leads to a relaxation of evolutionary constraints in genes involved in the photosynthetic apparatus, it remains to be determined how prevalent increased substitution rates are in nuclear DNA of non-photosynthetic angiosperms. In this study we infer rates of molecular evolution of 18S rDNA of all parasitic and mycoheterotorphic plant families (except Lauraceae and Polygalaceae) using relative rate tests. In several holoparasitic and mycoheterotrophic plant lineages extremely high substitution rates are observed compared to other photosynthetic angiosperms. The position and frequency of these substitutions have been identified to understand the mutation dynamics of 18S rRNA in achlorophyllous plants. Despite the presence of significantly elevated substitution rates, very few mutations occur in major functional and structural regions of the small ribosomal molecule, providing evidence that the efficiency of the translational apparatus in non-photosynthetic plants has not been affected

DNA Barcode Sequence Identification Incorporating Taxonomic Hierarchy and within Taxon Variability

For DNA barcoding to succeed as a scientific endeavor an accurate and expeditious query sequence identification method is needed. Although a global multiple–sequence alignment can be generated for some barcoding markers (e.g. COI, rbcL), not all barcoding markers are as structurally conserved (e.g. matK). Thus, algorithms that depend on global multiple–sequence alignments are not universally applicable. Some sequence identification methods that use local pairwise alignments (e.g. BLAST) are unable to accurately differentiate between highly similar sequences and are not designed to cope with hierarchic phylogenetic relationships or within taxon variability. Here, I present a novel alignment–free sequence identification algorithm–BRONX–that accounts for observed within taxon variability and hierarchic relationships among taxa. BRONX identifies short variable segments and corresponding invariant flanking regions in reference sequences. These flanking regions are used to score variable regions in the query sequence without the production of a global multiple–sequence alignment. By incorporating observed within taxon variability into the scoring procedure, misidentifications arising from shared alleles/haplotypes are minimized. An explicit treatment of more inclusive terminals allows for separate identifications to be made for each taxonomic level and/or for user–defined terminals. BRONX performs better than all other methods when there is imperfect overlap between query and reference sequences (e.g. mini–barcode queries against a full–length barcode database). BRONX consistently produced better identifications at the genus–level for all query types

Beyond quantitative and qualitative traits: three telling cases in the life sciences

This paper challenges the common assumption that some phenotypic traits are quantitative while others are qualitative. The distinction between these two kinds of traits is widely influential in biological and biomedical research as well as in scientific education and communication. This is probably due to both historical and epistemological reasons. However, the quantitative/qualitative distinction involves a variety of simplifications on the genetic causes of phenotypic variability and on the development of complex traits. Here, I examine three cases from the life sciences that show inconsistencies in the distinction: Mendelian traits (dwarfism and pigmentation in plant and animal models), Mendelian diseases (phenylketonuria), and polygenic mental disorders (schizophrenia). I show that these traits can be framed both quantitatively and qualitatively depending, for instance, on the methods through which they are investigated and on specific epistemic purposes (e.g., clinical diagnosis versus causal explanation). This suggests that the received view of quantitative and qualitative traits has a limited heuristic power—limited to some local contexts or to the specific methodologies adopted. Throughout the paper, I provide directions for framing phenotypes beyond the quantitative/qualitative distinction. I conclude by pointing at the necessity of developing a principled characterisation of what phenotypic traits, in general, are