Effect of architecture on the phase behavior of AB-type block copolymer melts

Equilibrium phase diagrams are calculated for a selection of two-component block copolymer architectures using self-consistent field theory (SCFT). The topology of the phase diagrams is relatively unaffected by differences in architecture, but the phase boundaries shift significantly in composition. The shifts are consistent with the decomposition of architectures into constituent units as proposed by Gido and coworkers, but there are significant quantitative deviations from this principle in the intermediate-segregation regime. Although the complex phase windows continue to be dominated by the gyroid (G) phase, the regions of the newly discovered Fddd (O^70) phase become appreciable for certain architectures and the perforated-lamellar (PL) phase becomes stable when the complex phase windows shift towards high compositional asymmetry.

On the existence of two-dimensional Euler flows satisfying energy-Casimir stability criteria

The energy-Casimir stability method, also known as the Arnold stability method, has been widely used in fluid dynamical applications to derive sufficient conditions for nonlinear stability. The most commonly studied system is two-dimensional Euler flow. It is shown that the set of two-dimensional Euler flows satisfying the energy-Casimir stability criteria is empty for two important cases: (i) domains having the topology of the sphere, and (ii) simply-connected bounded domains with zero net vorticity. The results apply to both the first and the second of Arnold’s stability theorems. In the spirit of Andrews’ theorem, this puts a further limitation on the applicability of the method. © 2000 American Institute of Physics.

Following the creation of active gold nanocatalysts from phosphine-stabilized molecular clusters

The phosphine-stabilised gold cluster [Au6(Ph2P-o-tolyl)6](NO3)2 is converted into an active nanocatalyst for the oxidation of benzyl alcohol through low-temperature peroxide-assisted removal of the phosphines, avoiding the high-temperature calcination process. The process was monitored using in-situ X-ray absorption spectroscopy, which revealed that after a certain period of the reaction with tertiary butyl hydrogen peroxide, the phosphine ligands are removed to form nanoparticles of gold which matches with the induction period seen in the catalytic reaction. Density functional theory calculations show that the energies required to remove the ligands from the [Au6Ln]2+ increase significantly with successive removal steps, suggesting that the process does not occur at once but sequentially. The calculations also reveal that ligand removal is accompanied by dramatic re-arrangements in the topology of the cluster core.

On universal and periodic β-expansions, and the Hausdorff dimension of the set of all expansions

We study the topology of a set naturally arising from the study of β-expansions. After proving several elementary results for this set we study the case when our base is Pisot. In this case we give necessary and sufficient conditions for this set to be finite. This finiteness property will allow us to generalise a theorem due to Schmidt and will provide the motivation for sufficient conditions under which the growth rate and Hausdorff dimension of the set of β-expansions are equal and explicitly calculable.

Changes of a mutualistic network over time: reanalysis over a 10-year period

We analyzed the structure of a multispecific network or interacting ants and plants bearing extrafloral nectaries recorded in 1990 and again in 2000 in La Mancha, Veracruz, Mexico. We assessed the replicability of the number of interactions found among species and also whether there had been changes in the network structure associated with appearance of new ant and plant species during. that 10-year period. Our results show that the nested topology of the network was similar between sampling dates, group dissimilarity increased, mean number of interactions for ant species increased, the frequency distribution of standardized degrees reached higher values for plant species, more ant species and fewer plant species constituted the core of the more recent network, and the presence of new ant and plant species increased while their contribution to nestedness remained the same. Generalist species (i.e., those with the most links or interactions) appeared to maintain the stability of the network because the new species incorporated into the communities were linked to this core of generalists. Camponotus planatus was the most extreme generalist ant species (the one with the most links) in both networks, followed by four other ant species; but other species changed either their position along the continuum of generalists relative to specialists or their presence or absence within the network. Even though new species moved into the area during the decade between the surveys, the overall network structure remained unmodified.

Insights into the Specificity of Thioredoxin Reductase-Thioredoxin Interactions. A Structural and Functional Investigation of the Yeast Thioredoxin System

The enzymatic activity of thioredoxin reductase enzymes is endowed by at least two redox centers: a flavin and a dithiol/disulfide CXXC motif. The interaction between thioredoxin reductase and thioredoxin is generally species-specific, but the molecular aspects related to this phenomenon remain elusive. Here, we investigated the yeast cytosolic thioredoxin system, which is composed of NADPH, thioredoxin reductase (ScTrxR1), and thioredoxin 1 (ScTrx1) or thioredoxin 2 (ScTrx2). We showed that ScTrxR1 was able to efficiently reduce yeast thioredoxins (mitochondrial and cytosolic) but failed to reduce the human and Escherichia coli thioredoxin counterparts. To gain insights into this specificity, the crystallographic structure of oxidized ScTrxR1 was solved at 2.4 angstrom resolution. The protein topology of the redox centers indicated the necessity of a large structural rearrangement for FAD and thioredoxin reduction using NADPH. Therefore, we modeled a large structural rotation between the two ScTrxR1 domains (based on the previously described crystal structure, PDB code 1F6M). Employing diverse approaches including enzymatic assays, site-directed mutagenesis, amino acid sequence alignment, and structure comparisons, insights were obtained about the features involved in the species-specificity phenomenon, such as complementary electronic parameters between the surfaces of ScTrxR1 and yeast thioredoxin enzymes and loops and residues (such as Ser(72) in ScTrx2). Finally, structural comparisons and amino acid alignments led us to propose a new classification that includes a larger number of enzymes with thioredoxin reductase activity, neglected in the low/high molecular weight classification.

Plane curve diagrams and geometrical applications

We look at plane curve diagrams (f,alpha), which are given by a plane curve multigerm alpha : (R, S) -> R(2) and a function on it f : (R, S) -> R. We obtain a classification of all such diagrams, where alpha has e-codimension <= 2 and f has finite order. Then we define an equivalence between plane curves which we call Ah(alpha)-equivalence and which is determined by the class of the diagram (h(alpha), alpha). Here, h alpha denotes the height function of alpha with respect to its normal vector. This is an equivalence which not only takes into account the topology of the singularity of alpha, but also its flat geometry. Finally, we apply our results in order to obtain a classification of all the plane projections of a generic space curve gamma embedded in R(3).

Coherent states of a particle in a magnetic field and the Stieltjes moment problem

A solution to a version of the Stieltjes moment. problem is presented. Using this solution, we construct a family of coherent states of a charged particle in a uniform magnetic field. We prove that these states form an overcomplete set that is normalized and resolves the unity. By the help of these coherent states we construct the Fock-Bergmann representation related to the particle quantization. This quantization procedure takes into account a circle topology of the classical motion. (C) 2009 Elsevier B.V. All rights reserved.

MODELING THE EVOLUTION OF COMPLEX NETWORKS THROUGH THE PATH-STAR TRANSFORMATION AND OPTIMAL MULTIVARIATE METHODS

The topology of real-world complex networks, such as in transportation and communication, is always changing with time. Such changes can arise not only as a natural consequence of their growth, but also due to major modi. cations in their intrinsic organization. For instance, the network of transportation routes between cities and towns ( hence locations) of a given country undergo a major change with the progressive implementation of commercial air transportation. While the locations could be originally interconnected through highways ( paths, giving rise to geographical networks), transportation between those sites progressively shifted or was complemented by air transportation, with scale free characteristics. In the present work we introduce the path-star transformation ( in its uniform and preferential versions) as a means to model such network transformations where paths give rise to stars of connectivity. It is also shown, through optimal multivariate statistical methods (i.e. canonical projections and maximum likelihood classification) that while the US highways network adheres closely to a geographical network model, its path-star transformation yields a network whose topological properties closely resembles those of the respective airport transportation network.

Sensitivity of complex networks measurements

Complex networks obtained from real-world networks are often characterized by incompleteness and noise, consequences of imperfect sampling as well as artifacts in the acquisition process. Because the characterization, analysis and modeling of complex systems underlain by complex networks are critically affected by the quality and completeness of the respective initial structures, it becomes imperative to devise methodologies for identifying and quantifying the effects of the sampling on the network structure. One way to evaluate these effects is through an analysis of the sensitivity of complex network measurements to perturbations in the topology of the network. In this paper, measurement sensibility is quantified in terms of the relative entropy of the respective distributions. Three particularly important kinds of progressive perturbations to the network are considered, namely, edge suppression, addition and rewiring. The measurements allowing the best balance of stability (smaller sensitivity to perturbations) and discriminability (separation between different network topologies) are identified with respect to each type of perturbation. Such an analysis includes eight different measurements applied on six different complex networks models and three real-world networks. This approach allows one to choose the appropriate measurements in order to obtain accurate results for networks where sampling bias cannot be avoided-a very frequent situation in research on complex networks.

Collapse of rho (xx) Ringlike Structures in 2DEGs Under Tilted Magnetic Fields

In the quantum Hall regime, the longitudinal resistivity rho (xx) plotted as a density-magnetic-field (n (2D) -B) diagram displays ringlike structures due to the crossings of two sets of spin split Landau levels from different subbands [see, e.g., Zhang et al., in Phys. Rev. Lett. 95:216801, 2005. For tilted magnetic fields, some of these ringlike structures ""shrink"" as the tilt angle is increased and fully collapse at theta (c) a parts per thousand 6A degrees. Here we theoretically investigate the topology of these structures via a non-interacting model for the 2DEG. We account for the inter Landau-level coupling induced by the tilted magnetic field via perturbation theory. This coupling results in anticrossings of Landau levels with parallel spins. With the new energy spectrum, we calculate the corresponding n (2D) -B diagram of the density of states (DOS) near the Fermi level. We argue that the DOS displays the same topology as rho (xx) in the n (2D) -B diagram. For the ring with filling factor nu=4, we find that the anticrossings make it shrink for increasing tilt angles and collapse at a large enough angle. Using effective parameters to fit the theta=0A degrees data, we find a collapsing angle theta (c) a parts per thousand 3.6A degrees. Despite this factor-of-two discrepancy with the experimental data, our model captures the essential mechanism underlying the ring collapse.

The Hilbert space of the Chern-Simons theory on a cylinder: a loop quantum gravity approach

As a laboratory for loop quantum gravity, we consider the canonical quantization of the three-dimensional Chern-Simons theory on a noncompact space with the topology of a cylinder. Working within the loop quantization formalism, we define at the quantum level the constraints appearing in the canonical approach and completely solve them, thus constructing a gauge and diffeomorphism invariant physical Hilbert space for the theory. This space turns out to be infinite dimensional, but separable.

Periodic geodesics and geometry of compact Lorentzian manifolds with a Killing vector field

We study the geometry and the periodic geodesics of a compact Lorentzian manifold that has a Killing vector field which is timelike somewhere. Using a compactness argument for subgroups of the isometry group, we prove the existence of one timelike non self-intersecting periodic geodesic. If the Killing vector field is nowhere vanishing, then there are at least two distinct periodic geodesics; as a special case, compact stationary manifolds have at least two periodic timelike geodesics. We also discuss some properties of the topology of such manifolds. In particular, we show that a compact manifold M admits a Lorentzian metric with a nowhere vanishing Killing vector field which is timelike somewhere if and only if M admits a smooth circle action without fixed points.

Insights into the Specificity of Thioredoxin Reductase-Thioredoxin Interactions. A Structural and Functional Investigation of the Yeast Thioredoxin System

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Determining the shape of the universe using discrete sources

Suppose we have identified three clusters of galaxies as being topological copies of the same object. How does this information constrain the possible models for the shape of our universe? It is shown here that, if our universe has flat spatial sections, these multiple images can be accommodated within any of the six classes of compact orientable three-dimensional flat space forms. Moreover, the discovery of two more triples of multiple images in the neighbourhood of the first one would allow the determination of the topology of the universe, and in most cases the determination of its size.