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.

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.

Positive solutions for a fourth order equation with nonlinear boundary conditions

Existence of positive solutions for a fourth order equation with nonlinear boundary conditions, which models deformations of beams on elastic supports, is considered using fixed points theorems in cones of ordered Banach spaces. Iterative and numerical solutions are also considered. (C) 2010 IMACS. Published by Elsevier B.V. All rights reserved.

Integrable maps with non-trivial topology: application to divertor configurations

We explore a method for constructing two-dimensional area-preserving, integrable maps associated with Hamiltonian systems, with a given set of fixed points and given invariant curves. The method is used to find an integrable Poincare map for the field lines in a large aspect ratio tokamak with a poloidal single-null divertor. The divertor field is a superposition of a magnetohydrodynamic equilibrium with an arbitrarily chosen safety factor profile, with a wire carrying an electric current to create an X-point. This integrable map is perturbed by an impulsive perturbation that describes non-axisymmetric magnetic resonances at the plasma edge. The non-integrable perturbed map is applied to study the structure of the open field lines in the scrape-off layer, reproducing the main transport features obtained by integrating numerically the magnetic field line equations, such as the connection lengths and magnetic footprints on the divertor plate.

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.

Homeomorphisms of the annulus with a transitive lift

Let f be a homeomorphism of the closed annulus A that preserves the orientation, the boundary components and that has a lift (f) over tilde to the infinite strip (A) over tilde which is transitive. We show that, if the rotation numbers of both boundary components of A are strictly positive, then there exists a closed nonempty unbounded set B(-) subset of (A) over tilde such that B(-) is bounded to the right, the projection of B to A is dense, B - (1, 0) subset of B and (f) over tilde (B) subset of B. Moreover, if p(1) is the projection on the first coordinate of (A) over tilde, then there exists d > 0 such that, for any (z) over tilde is an element of B(-), lim sup (n ->infinity) p1((f) over tilde (n)((z) over tilde)) - p(1) ((z) over tilde)/n < - d. In particular, using a result of Franks, we show that the rotation set of any homeomorphism of the annulus that preserves orientation, boundary components, which has a transitive lift without fixed points in the boundary is an interval with 0 in its interior.

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.

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)

Instability of equilibrium points of some Lagrangian systems

In this work we show that, if L is a natural Lagrangian system such that the k-jet of the potential energy ensures it does not have a minimum at the equilibrium and such that its Hessian has rank at least n - 2, then there is an asymptotic trajectory to the associated equilibrium point and so the equilibrium is unstable. This applies, in particular, to analytic potentials with a saddle point and a Hessian with at most 2 null eigenvalues. The result is proven for Lagrangians in a specific form, and we show that the class of Lagrangians we are interested can be taken into this specific form by a subtle change of spatial coordinates. We also consider the extension of this results to systems subjected to gyroscopic forces. (C) 2008 Elsevier Inc. All rights reserved.

Genericity of Nondegenerate Critical Points and Morse Geodesic Functionals

We consider a family of variational problems on a Hilbert manifold parameterized by an open subset of a Banach manifold, and we discuss the genericity of the nondegeneracy condition for the critical points. Using classical techniques, we prove an abstract genericity result that employs the infinite dimensional Sard-Smale theorem, along the lines of an analogous result of B. White [29]. Applications are given by proving the genericity of metrics without degenerate geodesics between fixed endpoints in general (non compact) semi-Riemannian manifolds, in orthogonally split semi-Riemannian manifolds and in globally hyperbolic Lorentzian manifolds. We discuss the genericity property also in stationary Lorentzian manifolds.

Role of MMP9 on Invadopodia Formation in Cells From Adenoid Cystic Carcinoma. Study by Laser Scanning Confocal Microscopy

Migration, invasion and protease activity are essential for tumor progression and metastasis. Metastatic cells rely on invadopodia to degrade and invade extracellular matrix (ECM). Invadopodia are membrane protrusions with enzymes required for ECM degradation. These protrusions contain cortactin and membrane type I matrix metalloproteinase (MT1-MMP) superimposed to areas of digested matrix. Here we characterized invadopodia in a cell line (CAC2) derived from human adenoid cystic carcinoma. We carried out fluorescent-substrate degradation assay to assess in situ protease activity of CAC2 cells. Digestion spots in fluorescent substrate appear as black areas in green background. Cells were cultured on Matrigel-gelatin-FITC and fixed after 1 h and 3 h. CAC2 cells were double labeled to actin and cortactin. Cells were also double stained to actin and MT1-MMR Samples were studied by laser scanning confocal microscopy. In all time points CAC2 cells showed actin, cortactin, and MT1-MMP colocalized with digestion spots in fluorescent substrate. We searched for other proteases involved in invadopodia activity. We have previously demonstrated that MMP9 influences adenoid cystic carcinoma behavior. This prompted us to investigate role played by MMP9 on invadopodia formation. CAC2 cells had MMP9 silenced by siRNA. After I h in fluorescent substrate, cells with silenced MMP9 showed clear decrease in matrix digestion compared with controls. No differences were found in cells with silenced MMP9 grown for 3 h on fluorescent substrate. Our results showed that CAC2 cells exhibit functional invadopodia containing cortactin and MT1-MMR Furthermore, MMP9 would be required in the initial steps of invadopodia formation. Microsc. Res. Tech. 73:99-108, 2010. (C) 2009 Wiley-Liss, Inc.

Using non-homogeneous Poisson models with multiple change-points to estimate the number of ozone exceedances in Mexico City

In this paper, we consider some non-homogeneous Poisson models to estimate the probability that an air quality standard is exceeded a given number of times in a time interval of interest. We assume that the number of exceedances occurs according to a non-homogeneous Poisson process (NHPP). This Poisson process has rate function lambda(t), t >= 0, which depends on some parameters that must be estimated. We take into account two cases of rate functions: the Weibull and the Goel-Okumoto. We consider models with and without change-points. When the presence of change-points is assumed, we may have the presence of either one, two or three change-points, depending of the data set. The parameters of the rate functions are estimated using a Gibbs sampling algorithm. Results are applied to ozone data provided by the Mexico City monitoring network. In a first instance, we assume that there are no change-points present. Depending on the adjustment of the model, we assume the presence of either one, two or three change-points. Copyright (C) 2009 John Wiley & Sons, Ltd.

A scenario for torus T(2) destruction via a global bifurcation

We show a scenario of a two-frequeney torus breakdown, in which a global bifurcation occurs due to the collision of a quasi-periodic torus T(2) with saddle points, creating a heteroclinic saddle connection. We analyze the geometry of this torus-saddle collision by showing the local dynamics and the invariant manifolds (global dynamics) of the saddle points. Moreover, we present detailed evidences of a heteroclinic saddle-focus orbit responsible for the type-if intermittency induced by this global bifurcation. We also characterize this transition to chaos by measuring the Lyapunov exponents and the scaling laws. (C) 2007 Elsevier Ltd. All rights reserved.

CASPT2 Study of the Potential Energy Surface of the HSO(2) System

The importance of the HSO(2) system in atmospheric and combustion chemistry has motivated several works dedicated to the study of associated structures and chemical reactions. Nevertheless controversy still exists in connection with the reaction SH + O(2) -> H + SO(2) and also related to the role of the HSOO isomers in the potential energy surface (PES). Here we report high-level ab initio calculation for the electronic ground state of the HSO(2) system. Energetic, geometric, and frequency properties for the major stationary states of the PES are reported at the same level of calculations:,CASPT2/aug-cc-pV(T+d)Z. This study introduces three new stationary points (two saddle points and one minimum). These structures allow the connection of the skewed HSOOs and the HSO(2) minima defining new reaction paths for SH + O(2) -> H + SO(2) and SH + O(2) -> OH + SO. In addition, the location of the HSOO isomers in the reaction pathways have been clarified.

Field on Poincare Group and Quantum Description of Orientable Objects

We propose an approach to the quantum-mechanical description of relativistic orientable objects. It generalizes Wigner`s ideas concerning the treatment of nonrelativistic orientable objects (in particular, a nonrelativistic rotator) with the help of two reference frames (space-fixed and body-fixed). A technical realization of this generalization (for instance, in 3+1 dimensions) amounts to introducing wave functions that depend on elements of the Poincar, group G. A complete set of transformations that test the symmetries of an orientable object and of the embedding space belongs to the group I =GxG. All such transformations can be studied by considering a generalized regular representation of G in the space of scalar functions on the group, f(x,z), that depend on the Minkowski space points xaG/Spin(3,1) as well as on the orientation variables given by the elements z of a matrix ZaSpin(3,1). In particular, the field f(x,z) is a generating function of the usual spin-tensor multi-component fields. In the theory under consideration, there are four different types of spinors, and an orientable object is characterized by ten quantum numbers. We study the corresponding relativistic wave equations and their symmetry properties.