Stress distribution in bone simulation model with pre-angled implants

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

Endothelium-dependent relaxation in response to poly-L-arginine in canine coronary arteries: implications about hyperpolarization as a mechanism of vasodilatation

OBJECTIVE: To study the mechanism by which poly-L-arginine mediates endothelium-dependent relaxation. METHODS: Vascular segments with and without endothelium were suspended in organ chambers filled with control solution maintained at 37ºC and bubbled with 95% O2 / 5% CO2. Used drugs: indomethacin, acetycholine, EGTA, glybenclamide, ouabain, poly-L-arginine, methylene blue, N G-nitro-L-arginine, and verapamil and N G-monomethyl-L-arginine. Prostaglandin F2á and potassium chloride were used to contract the vascular rings. RESULTS: Poly-L-arginine (10-11 to 10-7 M) induced concentration-dependent relaxation in coronary artery segments with endothelium. The relaxation to poly-L-arginine was attenuated by ouabain, but was unaffected by glybenclamide. L-NOARG and oxyhemoglobin caused attenuation, but did not abolish this relaxation. Also, the relaxations was unaffected by methylene blue, verapamil, or the presence of a calcium-free bathing medium. The endothelium-dependent to poly-L-arginine relaxation was abolished only in vessels contracted with potassium chloride (40 mM) in the presence of L-NOARG and indomethacin. CONCLUSION: These experiments indicate that poly-L-arginine induces relaxation independent of nitric oxide.

Principal curves and principal oriented points

Principal curves have been defined Hastie and Stuetzle (JASA, 1989) assmooth curves passing through the middle of a multidimensional dataset. They are nonlinear generalizations of the first principalcomponent, a characterization of which is the basis for the principalcurves definition.In this paper we propose an alternative approach based on a differentproperty of principal components. Consider a point in the space wherea multivariate normal is defined and, for each hyperplane containingthat point, compute the total variance of the normal distributionconditioned to belong to that hyperplane. Choose now the hyperplaneminimizing this conditional total variance and look for thecorresponding conditional mean. The first principal component of theoriginal distribution passes by this conditional mean and it isorthogonal to that hyperplane. This property is easily generalized todata sets with nonlinear structure. Repeating the search from differentstarting points, many points analogous to conditional means are found.We call them principal oriented points. When a one-dimensional curveruns the set of these special points it is called principal curve oforiented points. Successive principal curves are recursively definedfrom a generalization of the total variance.

Dynamical Systems approach to Saffman-Taylor fingering. A Dynamical Solvability Scenario

A dynamical systems approach to competition of Saffman-Taylor fingers in a Hele-Shaw channel is developed. This is based on global analysis of the phase space flow of the low-dimensional ordinary-differential-equation sets associated with the classes of exact solutions of the problem without surface tension. Some simple examples are studied in detail. A general proof of the existence of finite-time singularities for broad classes of solutions is given. Solutions leading to finite-time interface pinchoff are also identified. The existence of a continuum of multifinger fixed points and its dynamical implications are discussed. We conclude that exact zero-surface tension solutions taken in a global sense as families of trajectories in phase space are unphysical because the multifinger fixed points are nonhyperbolic, and an unfolding does not exist within the same class of solutions. Hyperbolicity (saddle-point structure) of the multifinger fixed points is argued to be essential to the physically correct qualitative description of finger competition. The restoring of hyperbolicity by surface tension is proposed as the key point to formulate a generic dynamical solvability scenario for interfacial pattern selection.

Periodic points of holomorphic maps via Lefschetz numbers

In this paper we study the set of periods of holomorphic maps on compact manifolds, using the periodic Lefschetz numbers introduced by Dold and Llibre, which can be computed from the homology class of the map. We show that these numbers contain information about the existence of periodic points of a given period; and, if we assume the map to be transversal, then they give us the exact number of such periodic orbits. We apply this result to the complex projective space of dimension n and to some special type of Hopf surfaces, partially characterizing their set of periods. In the first case we also show that any holomorphic map of CP(n) of degree greater than one has infinitely many distinct periodic orbits, hence generalizing a theorem of Fornaess and Sibony. We then characterize the set of periods of a holomorphic map on the Riemann sphere, hence giving an alternative proof of Baker's theorem.

Fixed point results for multivalued contractions on graphs and their applications

Nous présentons dans cette thèse des théorèmes de point fixe pour des contractions multivoques définies sur des espaces métriques, et, sur des espaces de jauges munis d’un graphe. Nous illustrons également les applications de ces résultats à des inclusions intégrales et à la théorie des fractales. Cette thèse est composée de quatre articles qui sont présentés dans quatre chapitres. Dans le chapitre 1, nous établissons des résultats de point fixe pour des fonctions multivoques, appelées G-contractions faibles. Celles-ci envoient des points connexes dans des points connexes et contractent la longueur des chemins. Les ensembles de points fixes sont étudiés. La propriété d’invariance homotopique d’existence d’un point fixe est également établie pour une famille de Gcontractions multivoques faibles. Dans le chapitre 2, nous établissons l’existence de solutions pour des systèmes d’inclusions intégrales de Hammerstein sous des conditions de type de monotonie mixte. L’existence de solutions pour des systèmes d’inclusions différentielles avec conditions initiales ou conditions aux limites périodiques est également obtenue. Nos résultats s’appuient sur nos théorèmes de point fixe pour des G-contractions multivoques faibles établis au chapitre 1. Dans le chapitre 3, nous appliquons ces mêmes résultats de point fixe aux systèmes de fonctions itérées assujettis à un graphe orienté. Plus précisément, nous construisons un espace métrique muni d’un graphe G et une G-contraction appropriés. En utilisant les points fixes de cette G-contraction, nous obtenons plus d’information sur les attracteurs de ces systèmes de fonctions itérées. Dans le chapitre 4, nous considérons des contractions multivoques définies sur un espace de jauges muni d’un graphe. Nous prouvons un résultat de point fixe pour des fonctions multivoques qui envoient des points connexes dans des points connexes et qui satisfont une condition de contraction généralisée. Ensuite, nous étudions des systèmes infinis de fonctions itérées assujettis à un graphe orienté (H-IIFS). Nous donnons des conditions assurant l’existence d’un attracteur unique à un H-IIFS. Enfin, nous appliquons notre résultat de point fixe pour des contractions multivoques définies sur un espace de jauges muni d’un graphe pour obtenir plus d’information sur l’attracteur d’un H-IIFS. Plus précisément, nous construisons un espace de jauges muni d’un graphe G et une G-contraction appropriés tels que ses points fixes sont des sous-attracteurs du H-IIFS.

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.

Saddle points and rare collisions under scaling approach in a Fermi accelerator with two nonlinear terms

Rare collisions of a classical particle bouncing between two walls are studied. The dynamics is described by a two-dimensional, nonlinear and area-preserving mapping in the variables velocity and time at the instant that the particle collides with the moving wall. The phase space is of mixed type preventing diffusion of the particle to high energy. Successive and therefore rare collisions are shown to have a histogram of frequency which is scaling invariant with respect to the control parameters. The saddle fixed points are studied and shown to be scaling invariant with respect to the control parameters too. © 2012 Elsevier B.V. All rights reserved.

Separation of particles leading either to decay or unlimited growth of energy in a driven stadium-like billiard

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Convergence towards asymptotic state in 1-D mappings: a scaling investigation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Cavovarus Foot Realignment to Treat Anteromedial Ankle Arthrosis

Background: Adult patients with cavovarus feet were seen with symptomatic anteromedial ankle arthrosis and, frequently, lateral hindfoot instability. Static and dynamic realignment was performed to redistribute joint contact pressures and restore stability. Methods: Thirteen patients with fixed cavovarus feet (6 neurogenic, 7 idiopathic; 6 with hindfoot instability, 7 without) and mild to moderate anteromedial ankle arthrosis were treated by osteotomies and tendon transfers but no lateral ligament reconstruction. Anteromedial cheilectomy of the ankle was added to increase dorsiflexion and alleviate anteromedial impingement. Results: Failure occurred in 2 patients, who required additional procedures. The remaining 11 patients improved from preoperative 45 to 71 points (American Orthopaedic Foot and Ankle Society Ankle-Hindfoot Scale score) at the latest follow-up (average 84 months). Ankle dorsiflexion improved 7 degrees on average. There was no recurrent hindfoot instability and no progression of anteromedial ankle arthrosis over time. Conclusion: Cavovarus foot realignment with anteromedial ankle cheilectomy reliably improved patients’ symptoms related to ankle arthrosis, restored lateral hindfoot stability, and stabilized the extent of anteromedial ankle arthrosis when talar varus tilt was reduced. Level of Evidence: Level IV, retrospective case series.

A generic, hard transition to chaos

A hard-in-amplitude transition to chaos in a class of dissipative flows of broad applicability is presented. For positive values of a parameter F, no matter how small, a fully developed chaotic attractor exists within some domain of additional parameters, whereas no chaotic behavior exists for F < 0. As F is made positive, an unstable fixed point reaches an invariant plane to enter a phase half-space of physical solutions; the ghosts of a line of fixed points and a rich heteroclinic structure existing at F = 0 make the limits t --* +oc, F ~ +0 non-commuting, and allow an exact description of the chaotic flow. The formal structure of flows that exhibit the transition is determined. A subclass of such flows (coupled oscillators in near-resonance at any 2 : q frequency ratio, with F representing linear excitation of the first oscillator) is fully analysed

Universal duality in a Luttinger liquid coupled to a generic environment

We study a Luttinger liquid (LL) coupled to a generic environment consisting of bosonic modes with arbitrary density-density and current-current interactions. The LL can be either in the conducting phase and perturbed by a weak scatterer or in the insulating phase and perturbed by a weak link. The environment modes can also be scattered by the imperfection in the system with arbitrary transmission and reflection amplitudes. We present a general method of calculating correlation functions under the presence of the environment and prove the duality of exponents describing the scaling of the weak scatterer and of the weak link. This duality holds true for a broad class of models and is sensitive to neither interaction nor environmental modes details, thus it shows up as the universal property. It ensures that the environment cannot generate new stable fixed points of the renormalization group flow. Thus, the LL always flows toward either conducting or insulating phase. Phases are separated by a sharp boundary which is shifted by the influence of the environment. Our results are relevant, for example, for low-energy transport in (i) an interacting quantum wire or a carbon nanotube where the electrons are coupled to the acoustic phonons scattered by the lattice defect; (ii) a mixture of interacting fermionic and bosonic cold atoms where the bosonic modes are scattered due to an abrupt local change of the interaction; (iii) mesoscopic electric circuits.

Fixed Point Theorems of Kannan Type for Cyclical Contractive Conditions

The main aim of this paper is to obtain fixed point theorems for Kannan and Zamfirescu operators in the presence of cyclical contractive condition. A method for approximation of the fixed points is also provided, for which both a priori and a posteriori error estimates are given. Our results generalize, unify and extend several important fixed points theorems in literature. In order to illustrate the efficiency of our generalizations five significant examples are also given.