NIELSEN COINCIDENCE THEORY OF FIBRE-PRESERVING MAPS AND DOLD`S FIXED POINT INDEX

Let M -> B, N -> B be fibrations and f(1), f(2): M -> N be a pair of fibre-preserving maps. Using normal bordism techniques we define an invariant which is an obstruction to deforming the pair f(1), f(2) over B to a coincidence free pair of maps. In the special case where the two fibrations axe the same and one of the maps is the identity, a weak version of our omega-invariant turns out to equal Dold`s fixed point index of fibre-preserving maps. The concepts of Reidemeister classes and Nielsen coincidence classes over B are developed. As an illustration we compute e.g. the minimal number of coincidence components for all homotopy classes of maps between S(1)-bundles over S(1) as well as their Nielsen and Reidemeister numbers.

Myeloperoxidase activity is increased in gingival crevicular fluid and whole saliva after fixed orthodontic appliance activation

Introduction: Orthodontic tooth movement uses mechanical forces that result in inflammation in the first days. Myeloperoxidase (MPO) is an enzyme found in polymorphonuclear neutrophil (PMN) granules, and it is used to estimate the number of PMN granules in tissues. So far, MPO has not been used to study the inflammatory alterations after the application of orthodontic tooth movement forces. The aim of this study was to determine MPO activity in the gingival crevicular fluid (GCF) and saliva (whole stimulated saliva) of orthodontic patients at different time points after fixed appliance activation. Methods: MPO was determined in the GCF and collected by means of periopaper from the saliva of 14 patients with orthodontic fixed appliances. GCF and saliva samples were collected at baseline, 2 hours, and 7 and 14 days after application of the orthodontic force. Results: Mean MPO activity was increased in both the GCF and saliva of orthodontic patients at 2 hours after appliance activation (P<0.02 for all comparisons). At 2 hours, PMN infiltration into the periodontal ligament from the orthodontic force probably results in the increased MPO level observed at this time point. Conclusions: MPO might be a good marker to assess inflammation in orthodontic movement; it deserves further studies in orthodontic therapy. (Am J Orthod Dentofacial Orthop 2010;138:613-6)

Hierarchical spherical model from a geometric point of view

A continuous version of the hierarchical spherical model at dimension d=4 is investigated. Two limit distributions of the block spin variable X(gamma), normalized with exponents gamma = d + 2 and gamma=d at and above the critical temperature, are established. These results are proven by solving certain evolution equations corresponding to the renormalization group (RG) transformation of the O(N) hierarchical spin model of block size L(d) in the limit L down arrow 1 and N ->infinity. Starting far away from the stationary Gaussian fixed point the trajectories of these dynamical system pass through two different regimes with distinguishable crossover behavior. An interpretation of this trajectories is given by the geometric theory of functions which describe precisely the motion of the Lee-Yang zeroes. The large-N limit of RG transformation with L(d) fixed equal to 2, at the criticality, has recently been investigated in both weak and strong (coupling) regimes by Watanabe (J. Stat. Phys. 115:1669-1713, 2004) . Although our analysis deals only with N = infinity case, it complements various aspects of that work.

Statistical coupling analysis of aspartic proteinases based on crystal structures of the Trichoderma reesei enzyme and its complex with pepstatin A

The crystal structures of an aspartic proteinase from Trichoderma reesei (TrAsP) and of its complex with a competitive inhibitor, pepstatin A, were solved and refined to crystallographic R-factors of 17.9% (R(free)=21.2%) at 1.70 angstrom resolution and 15.81% (R(free) = 19.2%) at 1.85 angstrom resolution, respectively. The three-dimensional structure of TrAsP is similar to structures of other members of the pepsin-like family of aspartic proteinases. Each molecule is folded in a predominantly beta-sheet bilobal structure with the N-terminal and C-terminal domains of about the same size. Structural comparison of the native structure and the TrAsP-pepstatin complex reveals that the enzyme undergoes an induced-fit, rigid-body movement upon inhibitor binding, with the N-terminal and C-terminal lobes tightly enclosing the inhibitor. Upon recognition and binding of pepstatin A, amino acid residues of the enzyme active site form a number of short hydrogen bonds to the inhibitor that may play an important role in the mechanism of catalysis and inhibition. The structures of TrAsP were used as a template for performing statistical coupling analysis of the aspartic protease family. This approach permitted, for the first time, the identification of a network of structurally linked residues putatively mediating conformational changes relevant to the function of this family of enzymes. Statistical coupling analysis reveals coevolved continuous clusters of amino acid residues that extend from the active site into the hydrophobic cores of each of the two domains and include amino acid residues from the flap regions, highlighting the importance of these parts of the protein for its enzymatic activity. (C) 2008 Elsevier Ltd. All rights reserved.

ABELIANIZED OBSTRUCTION FOR FIXED POINTS OF FIBER-PRESERVING MAPS OF SURFACE BUNDLES

Let f: M -> M be a fiber-preserving map where S -> M -> B is a bundle and S is a closed surface. We study the abelianized obstruction, which is a cohomology class in dimension 2, to deform f to a fixed point free map by a fiber-preserving homotopy. The vanishing of this obstruction is only a necessary condition in order to have such deformation, but in some cases it is sufficient. We describe this obstruction and we prove that the vanishing of this class is equivalent to the existence of solution of a system of equations over a certain group ring with coefficients given by Fox derivatives.

Gravimetric study of a potential mineral deposit in the Itapororoca region, Brazil

A semi-detailed gravity survey was carried out over an area of 650 km(2) localized in the Eo-Neoproterozoic coastal zone of Paraiba State where 548 new gravity stations were added to the existing database. Gravity measurements were made with a LaCoste and Romberg model G meter with a precision of 0.04 mGal. The altitude was determined by barometric levelling with a fixed base achieving a 1.2 m measure of uncertainty, corresponding to an overall accuracy of 0.24 mGal for the Bouguer anomaly. The residual Bouguer map for a 7th degree regional polynomial showed a circumscribed negative anomaly coincident with a localized aero-magnetic anomaly and with hydro-thermally altered outcrops, near the city of Itapororoca. The 3D gravity modelling, constrained by geologic mapping was interpreted as a low density, fractured and/or altered material with a most probable volume of approximately 23 km(3), extending to about 8,500 m depth. This result is in accordance with a volcanic body associated with hydrothermal processes accompanied by surface mineralization evidence, which may be of interest to the mining industry.

Opinion dynamics of learning agents: does seeking consensus lead to disagreement?

We study opinion dynamics in a population of interacting adaptive agents voting on a set of issues represented by vectors. We consider agents who can classify issues into one of two categories and can arrive at their opinions using an adaptive algorithm. Adaptation comes from learning and the information for the learning process comes from interacting with other neighboring agents and trying to change the internal state in order to concur with their opinions. The change in the internal state is driven by the information contained in the issue and in the opinion of the other agent. We present results in a simple yet rich context where each agent uses a Boolean perceptron to state their opinion. If the update occurs with information asynchronously exchanged among pairs of agents, then the typical case, if the number of issues is kept small, is the evolution into a society torn by the emergence of factions with extreme opposite beliefs. This occurs even when seeking consensus with agents with opposite opinions. If the number of issues is large, the dynamics becomes trapped, the society does not evolve into factions and a distribution of moderate opinions is observed. The synchronous case is technically simpler and is studied by formulating the problem in terms of differential equations that describe the evolution of order parameters that measure the consensus between pairs of agents. We show that for a large number of issues and unidirectional information flow, global consensus is a fixed point; however, the approach to this consensus is glassy for large societies.

Three-dimensional quantitative structure-activity relationships for a large series of potent antitubercular agents

Comparative molecular field analysis (CoMFA) studies were conducted on a series of 100 isoniazid derivatives as anti-tuberculosis agents using two receptor-independent structural data set alignment strategies: (1) rigid-body fit, and (2) pharmacophore-based. Significant cross-validated correlation coefficients were obtained (CoMFA(1), q(2) = 0,75 and CoMFA(2), q(2) = 0.74), indicating the potential of the models for untested compounds. The models were then used to predict the inhibitory potency of 20 test set compounds that were not included in the training set, and the predicted values were in good agreement with the experimental results.

Tectonic implications of a paleomagnetic study of the Sarmiento Ophiolitic Complex, southern Chile

A paleomagnetic study was carried out on the Late Jurassic Sarmiento Ophiolitic Complex (SOC) exposed in the Magallanes fold and thrust belt in the southern Patagonian Andes (southern Chile). This complex, mainly consisting of a thick succession of pillow-lavas, sheeted dikes and gabbros, is a seafloor remnant of the Late Jurassic to Early Cretaceous Rocas Verdes basin that developed along the south-western margin of South America. Stepwise thermal and alternating field demagnetization permitted the isolation of a post-folding characteristic remanence, apparently carried by fine grain (SD?) magnetite, both in the pillow-lavas and dikes. The mean ""in situ"" direction for the SOC is Dec: 286.9 degrees, Inc: -58.5 degrees, alpha-95: 6.9 degrees, N: 11 (sites). Rock magnetic properties, petrography and whole-rock K-Ar ages in the same rocks are interpreted as evidence of correlation between remanence acquisition and a greenschist facies metamorphic overprint that must have occurred during latest stages or after closure and tectonic inversion of the basin in the Late Cretaceous. The mean remanence direction is anomalous relative to the expected Late Cretaceous direction from stable South America. Particularly, a declination anomaly over 50 degrees is suggestively similar to paleomagnetically interpreted counter clockwise rotations found in thrust slices of the Jurassic El Quemado Fm. located over 100 km north of the study area in Argentina. Nevertheless, a significant ccw rotation of the whole SOC is difficult to reconcile with geologic evidence and paleogeographic models that suggest a narrow back-arc basin sub-parallel to the continental margin. A rigid-body 30 degrees westward tilting of the SOC block around a horizontal axis trending NNW, is considered a much simpler explanation, being consistent with geologic evidence. This may have occurred as a consequence of inverse reactivation of old normal faults, which limit both the SOC exposures and the Cordillera Sarmiento to the East. The age of tilting is unknown but it must postdate remanence acquisition in the Late Cretaceous. Two major orogenic events of the southern Patagonian Andes, in the Eocene (ca. 42 Ma) and Middle Miocene (ca. 12 Ma), respectively, could have caused the proposed tilting. (C) 2008 Elsevier B.V. All rights reserved.

Density-Profile Processes Describing Biological Signaling Networks: Almost Sure Convergence to Deterministic Trajectories

We introduce jump processes in R(k), called density-profile processes, to model biological signaling networks. Our modeling setup describes the macroscopic evolution of a finite-size spin-flip model with k types of spins with arbitrary number of internal states interacting through a non-reversible stochastic dynamics. We are mostly interested on the multi-dimensional empirical-magnetization vector in the thermodynamic limit, and prove that, within arbitrary finite time-intervals, its path converges almost surely to a deterministic trajectory determined by a first-order (non-linear) differential equation with explicit bounds on the distance between the stochastic and deterministic trajectories. As parameters of the spin-flip dynamics change, the associated dynamical system may go through bifurcations, associated to phase transitions in the statistical mechanical setting. We present a simple example of spin-flip stochastic model, associated to a synthetic biology model known as repressilator, which leads to a dynamical system with Hopf and pitchfork bifurcations. Depending on the parameter values, the magnetization random path can either converge to a unique stable fixed point, converge to one of a pair of stable fixed points, or asymptotically evolve close to a deterministic orbit in Rk. We also discuss a simple signaling pathway related to cancer research, called p53 module.

EQUIVARIANT PATH FIELDS ON TOPOLOGICAL MANIFOLDS

A classical theorem of H. Hopf asserts that a closed connected smooth manifold admits a nowhere vanishing vector field if and only if its Euler characteristic is zero. R. Brown generalized Hopf`s result to topological manifolds, replacing vector fields with path fields. In this note, we give an equivariant analog of Brown`s theorem for locally smooth G-manifolds where G is a finite group.

Fixed points on Klein bottle fiber bundles over the circle

The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S(1) for spaces which are fiber bundles over S(1) and the fiber is the Klein bottle K. We classify all such maps which can be deformed fiberwise to a fixed point free map. The similar problem for torus fiber bundles over S(1) has been solved recently.

Coincidence theorems and its applications to equilibrium problems

Given two maps h : X x K -> R and g : X -> K such that, for all x is an element of X, h(x, g(x)) = 0, we consider the equilibrium problem of finding (x) over tilde is an element of X such that h((x) over tilde, g(x)) >= 0 for every x is an element of X. This question is related to a coincidence problem.

An unstructured CVFEM and moving interface algorithm for non-Newtonian Hele-Shaw flows in injection molding

Purpose - The purpose of this paper is to develop a novel unstructured simulation approach for injection molding processes described by the Hele-Shaw model. Design/methodology/approach - The scheme involves dual dynamic meshes with active and inactive cells determined from an initial background pointset. The quasi-static pressure solution in each timestep for this evolving unstructured mesh system is approximated using a control volume finite element method formulation coupled to a corresponding modified volume of fluid method. The flow is considered to be isothermal and non-Newtonian. Findings - Supporting numerical tests and performance studies for polystyrene described by Carreau, Cross, Ellis and Power-law fluid models are conducted. Results for the present method are shown to be comparable to those from other methods for both Newtonian fluid and polystyrene fluid injected in different mold geometries. Research limitations/implications - With respect to the methodology, the background pointset infers a mesh that is dynamically reconstructed here, and there are a number of efficiency issues and improvements that would be relevant to industrial applications. For instance, one can use the pointset to construct special bases and invoke a so-called ""meshless"" scheme using the basis. This would require some interesting strategies to deal with the dynamic point enrichment of the moving front that could benefit from the present front treatment strategy. There are also issues related to mass conservation and fill-time errors that might be addressed by introducing suitable projections. The general question of ""rate of convergence"" of these schemes requires analysis. Numerical results here suggest first-order accuracy and are consistent with the approximations made, but theoretical results are not available yet for these methods. Originality/value - This novel unstructured simulation approach involves dual meshes with active and inactive cells determined from an initial background pointset: local active dual patches are constructed ""on-the-fly"" for each ""active point"" to form a dynamic virtual mesh of active elements that evolves with the moving interface.

Generation of nonground-state condensates and adiabatic paradox

The problem of resonant generation of nonground-state condensates is addressed aiming at resolving the seeming paradox that arises when one resorts to the adiabatic representation. In this picture, the eigenvalues and eigenfunctions of a time-dependent Gross-Pitaevskii Hamiltonian are also functions of time. Since the level energies vary in time, no definite transition frequency can be introduced. Hence no external modulation with a fixed frequency can be made resonant. Thus, the resonant generation of adiabatic coherent modes is impossible. However, this paradox occurs only in the frame of the adiabatic picture. It is shown that no paradox exists in the properly formulated diabatic representation. The resonant generation of diabatic coherent modes is a well defined phenomenon. As an example, the equations are derived, describing the generation of diabatic coherent modes by the combined resonant modulation of the trapping potential and atomic scattering length.