Double point curves for corank 2 map germs from C-2 to C-3

We characterize finite determinacy of map germs f : (C-2, 0) -> (C-3, 0) in terms of the Milnor number mu(D(f)) of the double point curve D(f) in (C-2, 0) and we provide an explicit description of the double point scheme in terms of elementary symmetric functions. Also we prove that the Whitney equisingularity of 1-parameter families of map germs f(t) : (C-2, 0) -> (C-3, 0) is equivalent to the constancy of both mu(D(f(t))) and mu(f(t)(C-2)boolean AND H) with respect to t, where H subset of C-3 is a generic plane. (C) 2011 Elsevier B.V. All rights reserved.

ACTIVE NETWORKS THAT MAXIMIZE THE AMOUNT OF INFORMATION TRANSMISSION

This work clarifies the relationship between network circuit (topology) and behavior (information transmission and synchronization) in active networks, e. g. neural networks. As an application, we show how to determine a network topology that is optimal for information transmission. By optimal, we mean that the network is able to transmit a large amount of information, it possesses a large number of communication channels, and it is robust under large variations of the network coupling configuration. This theoretical approach is general and does not depend on the particular dynamic of the elements forming the network, since the network topology can be determined by finding a Laplacian matrix (the matrix that describes the connections and the coupling strengths among the elements) whose eigenvalues satisfy some special conditions. To illustrate our ideas and theoretical approaches, we use neural networks of electrically connected chaotic Hindmarsh-Rose neurons.

How far is C-0(Gamma, X) with Gamma discrete from C-0(K, X) spaces?

For a locally compact Hausdorff space K and a Banach space X we denote by C-0(K, X) the space of X-valued continuous functions on K which vanish at infinity, provided with the supremum norm. Let n be a positive integer, Gamma an infinite set with the discrete topology, and X a Banach space having non-trivial cotype. We first prove that if the nth derived set of K is not empty, then the Banach-Mazur distance between C-0(Gamma, X) and C-0(K, X) is greater than or equal to 2n + 1. We also show that the Banach-Mazur distance between C-0(N, X) and C([1, omega(n)k], X) is exactly 2n + 1, for any positive integers n and k. These results extend and provide a vector-valued version of some 1970 Cambern theorems, concerning the cases where n = 1 and X is the scalar field.

Base-Paired and Base-Stacked Structures of the Anti-HIV Drug Lamivudine: A Nucleoside DNA-Mimicry with Unprecedented Topology

We have prepared a DNA-mimicry of nucleosides in which the anti-HIV drug lamivudine (beta-L-2',3'-dideoxy-3'-thiacytidine, 3TC) self-assembles into a base-paired and helically base-stacked hexagonal structure. Face-to-face and face-to-tail stacked 3TC=3TC dimers base-paired through two hydrogen bonds between neutral cytosines by either N-H center dot center dot center dot O or N-H center dot center dot center dot N atoms give rise to a right-handed DNA-mimicry of lamivudine with an unusual highly symmetric hexagonal lattice and topology. In addition, a base-paired and base-stacked supramolecular architecture of lamivudine hemihydrochloride hemihydrate was also obtained as a result of our crystal screenings. This structure is formed through partially face-to-face stacked lamivudine pairs held together by protonated and neutral fragments. However, no helical stacking occurs in this structure in which lamivudine also adopts unusual conformations as the C1'-endo and C1'-exo sugar puckers and cytosine orientations intermediate between the anti and syn conformations. As a conclusion drawn from the nucleoside duplex, the hexagonal DNA-mimicry of lamivudine reveals that such double-stranded helices can be assembled without counterions and organic solvents but with higher crystallographic symmetry instead, because only water crystallizes together with lamivudine in this structure.

Three-feature model to reproduce the topology of citation networks and the effects from authors' visibility on their h-index

Various factors are believed to govern the selection of references in citation networks, but a precise, quantitative determination of their importance has remained elusive. In this paper, we show that three factors can account for the referencing pattern of citation networks for two topics, namely "graphenes" and "complex networks", thus allowing one to reproduce the topological features of the networks built with papers being the nodes and the edges established by citations. The most relevant factor was content similarity, while the other two - in-degree (i.e. citation counts) and age of publication - had varying importance depending on the topic studied. This dependence indicates that additional factors could play a role. Indeed, by intuition one should expect the reputation (or visibility) of authors and/or institutions to affect the referencing pattern, and this is only indirectly considered via the in-degree that should correlate with such reputation. Because information on reputation is not readily available, we simulated its effect on artificial citation networks considering two communities with distinct fitness (visibility) parameters. One community was assumed to have twice the fitness value of the other, which amounts to a double probability for a paper being cited. While the h-index for authors in the community with larger fitness evolved with time with slightly higher values than for the control network (no fitness considered), a drastic effect was noted for the community with smaller fitness. (C) 2012 Elsevier Ltd. All rights reserved.

Numeric reconstruction of cytoskeleton with finite element method and topology optimization method

The importance of mechanical aspects related to cell activity and its environment is becoming more evident due to their influence in stem cell differentiation and in the development of diseases such as atherosclerosis. The mechanical tension homeostasis is related to normal tissue behavior and its lack may be related to the formation of cancer, which shows a higher mechanical tension. Due to the complexity of cellular activity, the application of simplified models may elucidate which factors are really essential and which have a marginal effect. The development of a systematic method to reconstruct the elements involved in the perception of mechanical aspects by the cell may accelerate substantially the validation of these models. This work proposes the development of a routine capable of reconstructing the topology of focal adhesions and the actomyosin portion of the cytoskeleton from the displacement field generated by the cell on a flexible substrate. Another way to think of this problem is to develop an algorithm to reconstruct the forces applied by the cell from the measurements of the substrate displacement, which would be characterized as an inverse problem. For these kind of problems, the Topology Optimization Method (TOM) is suitable to find a solution. TOM is consisted of an iterative application of an optimization method and an analysis method to obtain an optimal distribution of material in a fixed domain. One way to experimentally obtain the substrate displacement is through Traction Force Microscopy (TFM), which also provides the forces applied by the cell. Along with systematically generating the distributions of focal adhesion and actin-myosin for the validation of simplified models, the algorithm also represents a complementary and more phenomenological approach to TFM. As a first approximation, actin fibers and flexible substrate are represented through two-dimensional linear Finite Element Method. Actin contraction is modeled as an initial stress of the FEM elements. Focal adhesions connecting actin and substrate are represented by springs. The algorithm was applied to data obtained from experiments regarding cytoskeletal prestress and micropatterning, comparing the numerical results to the experimental ones

Phylogeny and revision of the Neotropical bee genus Rhectomia s.l. Moure (Hymenoptera, Apidae, Augochlorini)

This paper revises the bees currently considered to belong to the genus Rhectomia s.l. and proposes a species phylogeny based on morphological characters, using other Corynurina as outgroups. The results indicate that Rhinocorynura Schrottky renders Rhectomia s.l. paraphyletic. Consequently, Corynurella is removed from synonymy with Rhectomia s.s., and Paracorynurella gen.n. is proposed. The topology among these genera is: outgroup [(Rhectomia s.s. + Rhinocorynura) (Paracorynurella gen.n. + Corynurella)]. Nine species are assigned to Corynurella: C. brokopondoi sp.n., C. caerulea sp.n., C. cognata sp.n., C. decora sp.n., C. harrisoni (Engel), C. mourei Eickwort, C. nigra sp.n., C. singularis sp.n. and C. triangulata sp.n. Three new species are described in Paracorynurella gen.n.: type species P. betoi sp.n., P. excavata sp.n., P. reticulata sp.n.; P. difficillima (Ducke) comb.n. is transferred from Rhinocorynura. Three species are recognized in Rhectomia s.s.: R. catarina sp.n., R. liebherri Engel and R. pumilla Moure. The male of R. liebherri is described for the first time. Keys for the identification of the genera and species are provided.

Topology Verification for Isosurface Extraction

The broad goals of verifiable visualization rely on correct algorithmic implementations. We extend a framework for verification of isosurfacing implementations to check topological properties. Specifically, we use stratified Morse theory and digital topology to design algorithms which verify topological invariants. Our extended framework reveals unexpected behavior and coding mistakes in popular publicly available isosurface codes.

On bifurcation of solutions of the Yamabe problem in product manifolds

We study local rigidity and multiplicity of constant scalar curvature metrics in arbitrary products of compact manifolds. Using (equivariant) bifurcation theory we determine the existence of infinitely many metrics that are accumulation points of pairwise non-homothetic solutions of the Yamabe problem. Using local rigidity and some compactness results for solutions of the Yamabe problem, we also exhibit new examples of conformal classes (with positive Yamabe constant) for which uniqueness holds. (C) 2011 Elsevier Masson SAS. All rights reserved.

Orobothriurus (Scorpiones: Bothriuridae) phylogeny, Andean biogeography, and the relative importance of genitalic and somatic characters

The genus Orobothriurus Maury, 1976 (Bothriuridae Simon, 1880) displays an Andean pattern of distribution, most of its species occurring at high altitudes (over 2000-2500 m to a maximum altitude record of 4910 m) from central Peru to Argentina. The recent discovery of several new species and the uncertain phylogenetic position of Orobothriurus lourencoi Ojanguren Affilastro, 2003, required a reanalysis of Orobothriurus phylogeny. Thirty bothriurid taxa, including all species of Orobothriurus and Pachakutej Ochoa, 2004, were scored for 65 morphological characters and analysed with parsimony under equal and implied weighting. The resulting topology justifies the establishment of a new genus, Rumikiru Ojanguren Affilastro et al., in press, for O. lourencoi and a closely related, new species, Rumikiru atacama Ojanguren Affilastro et al., in press. It also offers new insights about the phylogeny and biogeography of Orobothriurus and related genera. Characters from the male genitalia (i.e. hemispermatophore), comprising approximately 26% of the morphological matrix, were found to be less homoplastic than those from somatic morphology, contradicting suggestions that genitalia are uninformative or potentially misleading in phylogenetic studies.

Local symmetries in gauge theories in a finite-dimensional setting

It is shown that the correct mathematical implementation of symmetry in the geometric formulation of classical field theory leads naturally beyond the concept of Lie groups and their actions on manifolds, out into the realm of Lie group bundles and, more generally, of Lie groupoids and their actions on fiber bundles. This applies not only to local symmetries, which lie at the heart of gauge theories, but is already true even for global symmetries when one allows for fields that are sections of bundles with (possibly) non-trivial topology or, even when these are topologically trivial, in the absence of a preferred trivialization. (C) 2012 Elsevier B.V. All rights reserved.

Influence of pattern gradation on the design of piezocomposite energy harvesting devices using topology optimization

Piezoelectric materials can be used to convert oscillatory mechanical energy into electrical energy. Energy harvesting devices are designed to capture the ambient energy surrounding the electronics and convert it into usable electrical energy. The design of energy harvesting devices is not obvious, requiring optimization procedures. This paper investigates the influence of pattern gradation using topology optimization on the design of piezocomposite energy harvesting devices based on bending behavior. The objective function consists of maximizing the electric power generated in a load resistor. A projection scheme is employed to compute the element densities from design variables and control the length scale of the material density. Examples of two-dimensional piezocomposite energy harvesting devices are presented and discussed using the proposed method. The numerical results illustrate that pattern gradation constraints help to increase the electric power generated in a load resistor and guides the problem toward a more stable solution. (C) 2012 Elsevier Ltd. All rights reserved.

Symmetry insights for design of supercomputer network topologies: roots and weights lattices

We present a family of networks whose local interconnection topologies are generated by the root vectors of a semi-simple complex Lie algebra. Cartan classification theorem of those algebras ensures those families of interconnection topologies to be exhaustive. The global arrangement of the network is defined in terms of integer or half-integer weight lattices. The mesh or torus topologies that network millions of processing cores, such as those in the IBM BlueGene series, are the simplest member of that category. The symmetries of the root systems of an algebra, manifested by their Weyl group, lends great convenience for the design and analysis of hardware architecture, algorithms and programs.

Gauge and integrable theories in loop spaces

We propose an integral formulation of the equations of motion of a large class of field theories which leads in a quite natural and direct way to the construction of conservation laws. The approach is based on generalized non-abelian Stokes theorems for p-form connections, and its appropriate mathematical language is that of loop spaces. The equations of motion are written as the equality of a hyper-volume ordered integral to a hyper-surface ordered integral on the border of that hyper-volume. The approach applies to integrable field theories in (1 + 1) dimensions, Chern-Simons theories in (2 + 1) dimensions, and non-abelian gauge theories in (2 + 1) and (3 + 1) dimensions. The results presented in this paper are relevant for the understanding of global properties of those theories. As a special byproduct we solve a long standing problem in (3 + 1)-dimensional Yang-Mills theory, namely the construction of conserved charges, valid for any solution, which are invariant under arbitrary gauge transformations. (C) 2012 Elsevier B.V. All rights reserved.

Terbium(III) and dysprosium(III) 8-connected 3D networks containing 2,5-thiophenedicarboxylate anion: Crystal structures and photoluminescence studies

Two novel coordination polymers with the formula {[Ln(2)(2,5-tdc)(3)(dmso)(2)].H2O}(n) (Ln = Tb(III) for (1) and Dy(III) for (2)), (2,5-tdc(2-) = 2,5-thiophenedicarboxylate and dmso = dimethylsulfoxide) have been synthesized by the diffusion method and characterized by thermal analysis, vibrational spectroscopy and single crystal X-ray diffraction analysis. Structure analysis reveals that 2,5-tdc(2-) play a versatile role toward different lanthanide ions to form three-dimensional metal-organic frameworks (MOFs) in which the lanthanides ions are heptacoordinated. Photophysical properties were studied using excitation and emission spectra, where the photoluminescence data show the high emission intensity of the characteristic transitions D-5(4 ->) F-7(J) (J= 6, 5, 4 and 3) for (1) and (F9/2 -> HJ)-F-4-H-6 (J = 15/2, 13/2 and 11/2) for (2), indicating that 2,5-tdc(2-) is a good sensitizer. (C) 2012 Elsevier Ltd. All rights reserved.