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.

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.

Bourgin-Yang version of the Borsuk-Ulam theorem for Z(pk)-equivariant maps

Let G = Z(pk) be a cyclic group of prime power order and let V and W be orthogonal representations of G with V-G = W-G = W-G = {0}. Let S(V) be the sphere of V and suppose f: S(V) -> W is a G-equivariant mapping. We give an estimate for the dimension of the set f(-1){0} in terms of V and W. This extends the Bourgin-Yang version of the Borsuk-Ulam theorem to this class of groups. Using this estimate, we also estimate the size of the G-coincidences set of a continuous map from S(V) into a real vector space W'.

Solvability near the characteristic set for a special class of complex vector fields

This work deals with the solvability near the characteristic set Sigma = {0} x S-1 of operators of the form L = partial derivative/partial derivative t+(x(n) a(x)+ ix(m) b(x))partial derivative/partial derivative x, b not equivalent to 0 and a(0) not equal 0, defined on Omega(epsilon) = (-epsilon, epsilon) x S-1, epsilon > 0, where a and b are real-valued smooth functions in (-epsilon, epsilon) and m >= 2n. It is shown that given f belonging to a subspace of finite codimension of C-infinity (Omega(epsilon)) there is a solution u is an element of L-infinity of the equation Lu = f in a neighborhood of Sigma; moreover, the L-infinity regularity is sharp.

Characterization of the procera Tomato Mutant Shows Novel Functions of the SlDELLA Protein in the Control of Flower Morphology, Cell Division and Expansion, and the Auxin-Signaling Pathway during Fruit-Set and Development

procera (pro) is a tall tomato (Solanum lycopersicum) mutant carrying a point mutation in the GRAS region of the gene encoding SlDELLA, a repressor in the gibberellin (GA) signaling pathway. Consistent with the SlDELLA loss of function, pro plants display a GA-constitutive response phenotype, mimicking wild-type plants treated with GA(3). The ovaries from both nonemasculated and emasculated pro flowers had very strong parthenocarpic capacity, associated with enhanced growth of preanthesis ovaries due to more and larger cells. pro parthenocarpy is facultative because seeded fruits were obtained by manual pollination. Most pro pistils had exserted stigmas, thus preventing self-pollination, similar to wild-type pistils treated with GA(3) or auxins. However, Style2.1, a gene responsible for long styles in noncultivated tomato, may not control the enhanced style elongation of pro pistils, because its expression was not higher in pro styles and did not increase upon GA(3) application. Interestingly, a high percentage of pro flowers had meristic alterations, with one additional petal, sepal, stamen, and carpel at each of the four whorls, respectively, thus unveiling a role of SlDELLA in flower organ development. Microarray analysis showed significant changes in the transcriptome of preanthesis pro ovaries compared with the wild type, indicating that the molecular mechanism underlying the parthenocarpic capacity of pro is complex and that it is mainly associated with changes in the expression of genes involved in GA and auxin pathways. Interestingly, it was found that GA activity modulates the expression of cell division and expansion genes and an auxin signaling gene (tomato AUXIN RESPONSE FACTOR7) during fruit-set.

A novel set of ss-N-biaryl ether sulfonamide hydroxamates as potential MMPs inhibitors: Molecular dynamics simulations and molecular properties evaluation

Matrix metalloproteinases (MMPs) constitute a family of zinc-dependent proteases involved in the extracellular matrix degradation. MMP-2 and MMP9 are overexpressed in several human cancer types, including melanoma, thus the development of new compounds to inhibit MMPs' activity is desirable. Molecular dynamic simulation and molecular properties calculations were performed on a set of novel beta-N-biaryl ether sulfonamide-based hydroxamates, reported as MMP-2 and MMP-9 inhibitors, for providing data to develop an exploratory analysis. Thermodynamic, electronic, and steric descriptors have significantly discriminated highly active from moderately and less active inhibitors of MMP-2 whereas apparent partition coefficient at pH 1.5 was also significant for the MMP-9 data set. Compound 47 was considered an outlier in all analysis, indicating the presence of a bulky substituent group in R3 is crucial to this set of inhibitors for the establishment of molecular interactions with the S1 subsite of both enzymes, but there is a limit. (C) 2012 Wiley Periodicals, Inc.

Optimal Code Set Selection and Security Issues in Spectral Phase-Encoded Time Spreading (SPECTS) OCDMA Systems

In this paper, we perform a thorough analysis of a spectral phase-encoded time spreading optical code division multiple access (SPECTS-OCDMA) system based on Walsh-Hadamard (W-H) codes aiming not only at finding optimal code-set selections but also at assessing its loss of security due to crosstalk. We prove that an inadequate choice of codes can make the crosstalk between active users to become large enough so as to cause the data from the user of interest to be detected by other user. The proposed algorithm for code optimization targets code sets that produce minimum bit error rate (BER) among all codes for a specific number of simultaneous users. This methodology allows us to find optimal code sets for any OCDMA system, regardless the code family used and the number of active users. This procedure is crucial for circumventing the unexpected lack of security due to crosstalk. We also show that a SPECTS-OCDMA system based on W-H 32(64) fundamentally limits the number of simultaneous users to 4(8) with no security violation due to crosstalk. More importantly, we prove that only a small fraction of the available code sets is actually immune to crosstalk with acceptable BER (<10(-9)) i.e., approximately 0.5% for W-H 32 with four simultaneous users, and about 1 x 10(-4)% for W-H 64 with eight simultaneous users.

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.

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.

Designing piezoresistive plate-based sensors with distribution of piezoresistive material using topology optimization

Piezoresistive sensors are commonly made of a piezoresistive membrane attached to a flexible substrate, a plate. They have been widely studied and used in several applications. It has been found that the size, position and geometry of the piezoresistive membrane may affect the performance of the sensors. Based on this remark, in this work, a topology optimization methodology for the design of piezoresistive plate-based sensors, for which both the piezoresistive membrane and the flexible substrate disposition can be optimized, is evaluated. Perfect coupling conditions between the substrate and the membrane based on the `layerwise' theory for laminated plates, and a material model for the piezoresistive membrane based on the solid isotropic material with penalization model, are employed. The design goal is to obtain the configuration of material that maximizes the sensor sensitivity to external loading, as well as the stiffness of the sensor to particular loads, which depend on the case (application) studied. The proposed approach is evaluated by studying two distinct examples: the optimization of an atomic force microscope probe and a pressure sensor. The results suggest that the performance of the sensors can be improved by using the proposed approach.

Accumulation of the SET protein in HEK293T cells and mild oxidative stress: cell survival or death signaling

SET protein (I2PP2A) is an inhibitor of PP2A, which regulates the phosphorylated Akt (protein kinase B) levels. We assessed the effects of SET overexpression in HEK293T cells, both in the presence and the absence of mild oxidative stress induced by 50 mu M tert-butyl hydroperoxide. Immunoblotting assays demonstrated that SET accumulated in HEK293T cells and increased the levels of phosphorylated Akt and PTEN; in addition, SET decreased glutathione antioxidant defense of cell and increased expression of genes encoding antioxidant defense proteins. Immunofluorescence analysis demonstrated that accumulated SET was equally distributed in cytoplasm and nucleus; however, in cells that had been exposed to oxidative stress, SET was found in large aggregates in the cytoplasm. SET accumulation in HEK293T cells correlated with inhibition of basal apoptosis as evidenced by a decrease in annexin V staining and activity of caspases; under mild oxidative stress, SET accumulation correlated with caspase-independent cell death, as evidenced by increased PI and annexin V/PI double staining. The results suggest that accumulated SET could act via Akt/PTEN either as cell survival signal or as oxidative stress sensor for cell death.

Axioms for the coincidence index of maps between manifolds of the same dimension

We study the coincidence theory of maps between two manifolds of the same dimension from an axiomatic viewpoint. First we look at coincidences of maps between manifolds where one of the maps is orientation true, and give a set of axioms such that characterizes the local index (which is an integer valued function). Then we consider coincidence theory for arbitrary pairs of maps between two manifolds. Similarly we provide a set of axioms which characterize the local index, which in this case is a function with values in Z circle plus Z(2). We also show in each setting that the group of values for the index (either Z or Z circle plus Z(2)) is determined by the axioms. Finally, for the general case of coincidence theory for arbitrary pairs of maps between two manifolds we provide a set of axioms which characterize the local Reidemeister trace which is an element of an abelian group which depends on the pair of functions. These results extend known results for coincidences between orientable differentiable manifolds. (C) 2012 Elsevier B.V. All rights reserved.

Regularity at infinity of real mappings and a Morse-Sard theorem

We prove a new Morse-Sard-type theorem for the asymptotic critical values of semi-algebraic mappings and a new fibration theorem at infinity for C-2 mappings. We show the equivalence of three different types of regularity conditions which have been used in the literature in order to control the asymptotic behaviour of mappings. The central role of our picture is played by the p-regularity and its bridge toward the rho-regularity which implies topological triviality at infinity.

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.

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.