TOPOLOGY OF SINPLE SINGULARITIES OF RULED SURFACES IN R-p

In this work we compare the simple singularities of germs from R-2 to R-p with multiplicity 2 or 3 with the singularities appearing in the set of 2-ruled surfaces. We also study the topological type of all finitely determined singularities by studying generic projections of these singularities in R-3. (C) 2011 Elsevier B.V. All rights reserved.

Topological analysis of singularity loci for serial and parallel manipulators

Singularities of robot manipulators have been intensely studied in the last decades by researchers of many fields. Serial singularities produce some local loss of dexterity of the manipulator, therefore it might be desirable to search for singularityfree trajectories in the jointspace. On the other hand, parallel singularities are very dangerous for parallel manipulators, for they may provoke the local loss of platform control, and jeopardize the structural integrity of links or actuators. It is therefore utterly important to avoid parallel singularities, while operating a parallel machine. Furthermore, there might be some configurations of a parallel manipulators that are allowed by the constraints, but nevertheless are unreachable by any feasible path. The present work proposes a numerical procedure based upon Morse theory, an important branch of differential topology. Such procedure counts and identify the singularity-free regions that are cut by the singularity locus out of the configuration space, and the disjoint regions composing the configuration space of a parallel manipulator. Moreover, given any two configurations of a manipulator, a feasible or a singularity-free path connecting them can always be found, or it can be proved that none exists. Examples of applications to 3R and 6R serial manipulators, to 3UPS and 3UPU parallel wrists, to 3UPU parallel translational manipulators, and to 3RRR planar manipulators are reported in the work.

Topology of the ambient boundary and the convergence of causal curves

We discuss the topological nature of the boundary spacetime, the conformal infinity of the ambient cosmological metric. Due to the existence of a homothetic group, the bounding spacetime must be equipped not with the usual Euclidean metric topology but with the Zeeman fine topology. This then places severe constraints to the convergence of a sequence of causal curves and the extraction of a limit curve, and also to our ability to formulate conditions for singularity formation.

Undulating matter : a topology of the studio

With specific reference to the writing of Dan Graham and the experiences of creative practice, this paper will elaborate an account of studio practice as a topology - a theory drawn from mathematics in which space is understood not as a static field but in terms of properties of connectedness, movement and differentiation. This paper will trace a brief sequence of topological formulations to draw together the expression of topology as form and its structural dimension as a methodology in the specific context of the author’s studio practice. In so doing, this paper seeks to expand the notion of topology in art beyond its association with Conceptual Art of the 1960s and 70s to propose that topology provides a dynamic theoretical model for apprehending the generative ‘logic’ that gives direction and continuity to the art-making process.

Permanent shift: the topology of Didier Vermeiren's Cariatide à la Pierre

Photographic documentation of sculpture produces significant consequences for the way in which sculptural space is conceived. When viewed as discrete mediums the interaction of the photograph and its sculptural subject is always framed by notions of loss. However, when taken as a composite system, the sculpture-photograph proposes a new ontology of space. In place of the fixity of medium, we can observe a topology at play: a theory drawn from mathematics in which space is understood not as a static field but in terms of properties of connectedness, movement and differentiation. Refracted through the photographic medium, sculpture becomes not a field of fixed points in space, but rather as a fluid set of relations - a continuous sequence of multiple ‘surfaces’, a network of shifting views. This paper will develop a topological account of studio practice through an examination of the work of the contemporary Belgian sculptor Didier Vermeiren (b. 1951). Since the 1980s, Vermeiren has made extensive use of photography in his sculptural practice. By analysing a series of iterations of his work Cariatide à la Pierre (1997-1998), this paper proposes that Vermeiren’s use of photography reveals patterns of connection that expand and complicate the language of sculpture, while also emphasising the broader topology of the artist’s practice as a network of ‘backward glances’ to previous works from the artist’s oeuvre and the art-historical canon. In this context, photography is not simply a method of documentation, but rather a means of revealing the intrinsic condition of sculpture as medium shaped by dynamic patterns of connection and change. In Vermeiren’s work the sculpture-photograph, has a composite identity that exceeds straightforward categories of medium. In their place, we can observe a practice based upon the complex interactions of objects whose ontology is always underpinned by a certain contingency. It is in this fundamental mobility, that the topology of Vermeiren’s practice can be said to rest.

Hierarchical clustering of the genetic connectivity matrix reveals the network topology of gene action on brain microstructure: An N=531 twin study

Genetic correlation (rg) analysis determines how much of the correlation between two measures is due to common genetic influences. In an analysis of 4 Tesla diffusion tensor images (DTI) from 531 healthy young adult twins and their siblings, we generalized the concept of genetic correlation to determine common genetic influences on white matter integrity, measured by fractional anisotropy (FA), at all points of the brain, yielding an NxN genetic correlation matrix rg(x,y) between FA values at all pairs of voxels in the brain. With hierarchical clustering, we identified brain regions with relatively homogeneous genetic determinants, to boost the power to identify causal single nucleotide polymorphisms (SNP). We applied genome-wide association (GWA) to assess associations between 529,497 SNPs and FA in clusters defined by hubs of the clustered genetic correlation matrix. We identified a network of genes, with a scale-free topology, that influences white matter integrity over multiple brain regions.

On The Topology Of Manifolds With Positive Isotropic Curvature

We show that a closed orientable Riemannian n-manifold, n >= 5, with positive isotropic curvature and free fundamental group is homeomorphic to the connected sum of copies of Sn-1 x S-1.

Topology of wolfgram proteins and 2?, 3?-cyclic nucleotide 3?-phosphodiesterase in CNS myelin: Studies with proteases

The topological disposition of Wolfgram proteins (WP) and their relationship with 2', 3'-cyclic nucleotide 3'-phosphodiesterase (CNPase) in human, rat, sheep, bovine, guinea pig and chicken CNS myelin was investigated. Controlled digestion of myelin with trypsin gave a 35KDa protein band (WP-t) when electrophoresed on dodecyl sulfate-polyacrylamide gel in all species. Western blot analysis showed that the WP-t was derived from WP. WP-t was also formed when rat myelin was treated with other proteases such as kallikrein, thermolysin and leucine aminopeptidase. Staining for CNPase activity on nitrocellulose blots showed that WP-t is enzymatically active. Much of the CNPase activity remained with the membrane fraction even after treatment with high concentrations of trypsin when WP were completely hydrolysed and no protein bands with M.W > 14KDa were detected on the gels. Therefore protein fragments of WP with M.W < 14KDa may contain CNPase activity. From these results, it is suggested that the topological disposition of all the various WP is such that a 35KDa fragment is embedded in the lipid bilayer and the remaining fragment exposed at the intraperiod line in the myelin structure which may play a role in the initiation of myelinogenesis.

Molecular topology of three ring nematogens from C-13-H-1 dipolar couplings

Molecules in their liquid crystalline phase undergo rotational motion about the long axis of the molecule and the shape adopted by the rotating molecule plays an important role in influencing the mesophase morphology. In this context, obtaining the topology and the relative orientation of the different sub-units are important steps. For studying the liquid crystalline phase, C-13 NMR spectroscopy is a convenient method and for certain specifically designed nematogens, 2-dimensional separated local field (2D-SLF) NMR spectroscopy provides a particularly simple and straightforward means of arriving at the molecular topology. We demonstrate this approach on two three ring based nematogens designed with a phenyl or a thiophene ring at one of the termini. From the C-13-H-1 dipolar couplings of the terminal carbon obtained using the 2D-SLF NMR technique, the order parameter of the local symmetry axis of the terminal phenyl ring as well as of the long molecular axis could be easily estimated. For the thiophene nematogen, the lack of symmetry of the thiophene moiety necessitates some additional computational steps. The results indicate that the thiophene unit has its local ordering axis oriented away from the long molecular axis by a small angle, consistent with a bent structure expected in view of the thiophene geometry. The experiment also demonstrates the ability of 2D-SLF NMR to provide high resolution spectra by separation of several overlapped resonances in terms of their C-13-H-1 dipolar couplings. The results are consistent with a rod-like topology of the core of the investigated mesogens. The investigation demonstrates the potential of 2D-SLF NMR C-13 spectroscopy for obtaining atomistic level information and its utility for topological studies of different mesogens.

MS3ALIGN: an efficient molecular surface aligner using the topology of surface curvature

Background: Aligning similar molecular structures is an important step in the process of bio-molecular structure and function analysis. Molecular surfaces are simple representations of molecular structure that are easily constructed from various forms of molecular data such as 3D atomic coordinates (PDB) and Electron Microscopy (EM) data. Methods: We present a Multi-Scale Morse-Smale Molecular-Surface Alignment tool, MS3ALIGN, which aligns molecular surfaces based on significant protrusions on the molecular surface. The input is a pair of molecular surfaces represented as triangle meshes. A key advantage of MS3ALIGN is computational efficiency that is achieved because it processes only a few carefully chosen protrusions on the molecular surface. Furthermore, the alignments are partial in nature and therefore allows for inexact surfaces to be aligned. Results: The method is evaluated in four settings. First, we establish performance using known alignments with varying overlap and noise values. Second, we compare the method with SurfComp, an existing surface alignment method. We show that we are able to determine alignments reported by SurfComp, as well as report relevant alignments not found by SurfComp. Third, we validate the ability of MS3ALIGN to determine alignments in the case of structurally dissimilar binding sites. Fourth, we demonstrate the ability of MS3ALIGN to align iso-surfaces derived from cryo-electron microscopy scans. Conclusions: We have presented an algorithm that aligns Molecular Surfaces based on the topology of surface curvature. Awebserver and standalone software implementation of the algorithm available at http://vgl.serc.iisc.ernet. in/ms3align.

Topology of toroidal helical fields in non-circular cross-sectional tokamaks

The ordinary differential magnetic field line equations are solved numerically; the tokamak magnetic structure is studied on Hefei Tokamak-7 Upgrade (HT-7U) when the equilibrium field with a monotonic q-profile is perturbed by a helical magnetic field. We find that a single mode (m, n) helical perturbation can cause the formation of islands on rational surfaces with q = m/n and q = (m +/- 1, +/- 2, +/- 3,...)/n due to the toroidicity and plasma shape (i.e. elongation and triangularity), while there are many undestroyed magnetic surfaces called Kolmogorov-Arnold-Moser (KAM) barriers on irrational surfaces. The islands on the same rational surface do not have the same size. When the ratio between the perturbing magnetic field B-r(r) and the toroidal magnetic field amplitude B(phi)0 is large enough, the magnetic island chains on different rational surfaces will overlap and chaotic orbits appear in the overlapping area, and the magnetic field becomes stochastic. It is remarkable that the stochastic layer appears first in the plasma edge region.

Functional characterization and membrane topology of Escherichia coli WecA, a sugar-phosphate transferase initiating the biosynthesis of enterobacterial common antigen and O-antigen lipopolysaccharide

WecA is an integral membrane protein that initiates the biosynthesis of enterobacterial common antigen and O-antigen lipopolysaccharide (LPS) by catalyzing the transfer of N-acetylglucosamine (GlcNAc)-1-phosphate onto undecaprenyl phosphate (Und-P) to form Und-P-P-GlcNAc. WecA belongs to a large family of eukaryotic and prokaryotic prenyl sugar transferases. Conserved aspartic acids in putative cytoplasmic loops 2 (Asp90 and Asp91) and 3 (Asp156 and Asp159) were targeted for replacement mutagenesis with either glutamic acid or asparagine. We examined the ability of each mutant protein to complement O-antigen LPS synthesis in a wecA-deficient strain and also determined the steady-state kinetic parameters of the mutant proteins in an in vitro transfer assay. Apparent K(m) and V(max) values for UDP-GlcNAc, Mg(2+), and Mn(2+) suggest that Asp156 is required for catalysis, while Asp91 appears to interact preferentially with Mg(2+), possibly playing a role in orienting the substrates. Topological analysis using the substituted cysteine accessibility method demonstrated the cytosolic location of Asp90, Asp91, and Asp156 and provided a more refined overall topological map of WecA. Also, we show that cells expressing a WecA derivative C terminally fused with the green fluorescent protein exhibited a punctate distribution of fluorescence on the bacterial surface, suggesting that WecA localizes to discrete regions in the bacterial plasma membrane.