Intersecções homoclínicas

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

TYPE-ZERO SADDLE-NODE BIFURCATIONS AND STABILITY REGION ESTIMATION OF NONLINEAR AUTONOMOUS DYNAMICAL SYSTEMS

A complete characterization of the stability boundary of a class of nonlinear dynamical systems that admit energy functions is developed in this paper. This characterization generalizes the existing results by allowing the type-zero saddle-node nonhyperbolic equilibrium points on the stability boundary. Conceptual algorithms to obtain optimal estimates of the stability region (basin of attraction) in the form of level sets of a given family of energy functions are derived. The behavior of the stability region and the corresponding estimates are investigated for parameter variation in the neighborhood of a type-zero saddle-node bifurcation value.

Lock-in and quasiperiodicity in a forced hydrodynamically self-excited jet

The ability of hydrodynamically self-excited jets to lock into strong external forcing is well known. Their dynamics before lock-in and the specific bifurcations through which they lock in, however, are less well known. In this experimental study, we acoustically force a low-density jet around its natural global frequency. We examine its response leading up to lock-in and compare this to that of a forced van der Pol oscillator. We find that, when forced at increasing amplitudes, the jet undergoes a sequence of two nonlinear transitions: (i) from periodicity to T{double-struck}2 quasiperiodicity via a torus-birth bifurcation; and then (ii) from T{double-struck}2 quasiperiodicity to 1:1 lock-in via either a saddle-node bifurcation with frequency pulling, if the forcing and natural frequencies are close together, or a torus-death bifurcation without frequency pulling, but with a gradual suppression of the natural mode, if the two frequencies are far apart. We also find that the jet locks in most readily when forced close to its natural frequency, but that the details contain two asymmetries: the jet (i) locks in more readily and (ii) oscillates more strongly when it is forced below its natural frequency than when it is forced above it. Except for the second asymmetry, all of these transitions, bifurcations and dynamics are accurately reproduced by the forced van der Pol oscillator. This shows that this complex (infinite-dimensional) forced self-excited jet can be modelled reasonably well as a simple (three-dimensional) forced self-excited oscillator. This result adds to the growing evidence that open self-excited flows behave essentially like low-dimensional nonlinear dynamical systems. It also strengthens the universality of such flows, raising the possibility that more of them, including some industrially relevant flames, can be similarly modelled. © 2013 Cambridge University Press.

Hero's journey in bifurcation diagram

The hero's journey is a narrative structure identified by several authors in comparative studies on folklore and mythology. This storytelling template presents the stages of inner metamorphosis undergone by the protagonist after being called to an adventure. In a simplified version, this journey is divided into three acts separated by two crucial moments. Here we propose a discrete-time dynamical system for representing the protagonist's evolution. The suffering along the journey is taken as the control parameter of this system. The bifurcation diagram exhibits stationary, periodic and chaotic behaviors. In this diagram, there are transition from fixed point to chaos and transition from limit cycle to fixed point. We found that the values of the control parameter corresponding to these two transitions are in quantitative agreement with the two critical moments of the three-act hero's journey identified in 10 movies appearing in the list of the 200 worldwide highest-grossing films. (C) 2011 Elsevier B.V. All rights reserved.

Stability boundary characterization of nonlinear autonomous dynamical systems in the presence of saddle-node equilibrium points

A dynamical characterization of the stability boundary for a fairly large class of nonlinear autonomous dynamical systems is developed in this paper. This characterization generalizes the existing results by allowing the existence of saddle-node equilibrium points on the stability boundary. The stability boundary of an asymptotically stable equilibrium point is shown to consist of the stable manifolds of the hyperbolic equilibrium points on the stability boundary and the stable, stable center and center manifolds of the saddle-node equilibrium points on the stability boundary.

The impact of lymphadenectomy and lymph node metastasis on the outcomes of radical cystectomy for bladder cancer

CONTEXT: The presence of lymph node metastases and the extent of lymphadenectomy have both been shown to influence the outcome of patients with muscle-invasive bladder cancer. OBJECTIVE: Current standards for detection of lymph node metastases, lymph-node mapping studies, histopathologic techniques, and risk factors in relation to lymph node involvement are discussed. The impact of lymph node metastases and the extent of lymphadenectomy on the outcome of patients treated with radical cystectomy are analyzed. EVIDENCE ACQUISITION: A systematic literature review of bladder cancer and lymph nodes was performed searching the electronic databases Pubmed/Medline, Cochrane, and Embase. Articles were selected based on title, abstract, study format, and content by a consensus of all participating authors. EVIDENCE SYNTHESIS: Lymph node status is highly consequential in bladder cancer patients because the presence of lymph node metastases is predictive of poor outcome. Knowledge of primary landing sites of lymph node metastases is important for optimum therapeutic management. Accurate pathologic work-ups of resected lymph node tissue are mandatory. Molecular markers could potentially guide therapeutic decisions in the future because they may enable the detection of micrometastatic disease. In current series, radical cystectomy with an extended lymphadenectomy seems to provide a clinically meaningful therapeutic benefit compared with a limited approach. However, the anatomic boundaries of lymph node dissection are still under debate. Therefore, large prospective multicenter trials are needed to validate the influence of extended lymph node dissection on disease-specific survival. CONCLUSIONS: An extended pelvic lymph node dissection (encompassing the external iliac vessels, the obturator fossa, the lateral and medial aspects of the internal iliac vessels, and at least the distal half of the common iliac vessels together with its bifurcation) can be curative in patients with metastasis or micrometastasis to a few nodes. Therefore, the procedure may be offered to all patients undergoing radical cystectomy for invasive bladder cancer.

Pulse dynamics in a three-component system : existence analysis

In this article, we analyze the three-component reaction-diffusion system originally developed by Schenk et al. (PRL 78:3781–3784, 1997). The system consists of bistable activator-inhibitor equations with an additional inhibitor that diffuses more rapidly than the standard inhibitor (or recovery variable). It has been used by several authors as a prototype three-component system that generates rich pulse dynamics and interactions, and this richness is the main motivation for the analysis we present. We demonstrate the existence of stationary one-pulse and two-pulse solutions, and travelling one-pulse solutions, on the real line, and we determine the parameter regimes in which they exist. Also, for one-pulse solutions, we analyze various bifurcations, including the saddle-node bifurcation in which they are created, as well as the bifurcation from a stationary to a travelling pulse, which we show can be either subcritical or supercritical. For two-pulse solutions, we show that the third component is essential, since the reduced bistable two-component system does not support them. We also analyze the saddle-node bifurcation in which two-pulse solutions are created. The analytical method used to construct all of these pulse solutions is geometric singular perturbation theory, which allows us to show that these solutions lie in the transverse intersections of invariant manifolds in the phase space of the associated six-dimensional travelling wave system. Finally, as we illustrate with numerical simulations, these solutions form the backbone of the rich pulse dynamics this system exhibits, including pulse replication, pulse annihilation, breathing pulses, and pulse scattering, among others.

Genetic polymorphisms in DPF3 associated with risk of breast cancer and lymph node metastases

Background Several studies have identified rare genetic variations responsible for many cases of familial breast cancer but their contribution to total breast cancer incidence is relatively small. More common genetic variations with low penetrance have been postulated to account for a higher proportion of the population risk of breast cancer. Methods and Results In an effort to identify genes that influence non-familial breast cancer risk, we tested over 25,000 single nucleotide polymorphisms (SNPs) located within approximately 14,000 genes in a large-scale case-control study in 254 German women with breast cancer and 268 age-matched women without malignant disease. We identified a marker on chromosome 14q24.3-q31.1 that was marginally associated with breast cancer status (OR = 1.5, P = 0.07). Genotypes for this SNP were also significantly associated with indicators of breast cancer severity, including presence of lymph node metastases ( P = 0.006) and earlier age of onset ( P = 0.01). The association with breast cancer status was replicated in two independent samples (OR = 1.35, P = 0.05). High-density association fine mapping showed that the association spanned about 80 kb of the zinc-finger gene DPF3 (also known as CERD4 ). One SNP in intron 1 was found to be more strongly associated with breast cancer status in all three sample collections (OR = 1.6, P = 0.003) as well as with increased lymph node metastases ( P = 0.01) and tumor size ( P = 0.01). Conclusion Polymorphisms in the 5' region of DPF3 were associated with increased risk of breast cancer development, lymph node metastases, age of onset, and tumor size in women of European ancestry. This large-scale association study suggests that genetic variation in DPF3 contributes to breast cancer susceptibility and severity.

Prognostic and therapeutic relevance of FLIP and procaspase-8 overexpression in non-small cell lung cancer

Non-small cell lung carcinoma remains by far the leading cause of cancer-related deaths worldwide. Overexpression of FLIP, which blocks the extrinsic apoptotic pathway by inhibiting caspase-8 activation, has been identified in various cancers. We investigated FLIP and procaspase-8 expression in NSCLC and the effect of HDAC inhibitors on FLIP expression, activation of caspase-8 and drug resistance in NSCLC and normal lung cell line models. Immunohistochemical analysis of cytoplasmic and nuclear FLIP and procaspase-8 protein expression was carried out using a novel digital pathology approach. Both FLIP and procaspase-8 were found to be significantly overexpressed in tumours, and importantly, high cytoplasmic expression of FLIP significantly correlated with shorter overall survival. Treatment with HDAC inhibitors targeting HDAC1-3 downregulated FLIP expression predominantly via post-transcriptional mechanisms, and this resulted in death receptor- and caspase-8-dependent apoptosis in NSCLC cells, but not normal lung cells. In addition, HDAC inhibitors synergized with TRAIL and cisplatin in NSCLC cells in a FLIP- and caspase-8-dependent manner. Thus, FLIP and procaspase-8 are overexpressed in NSCLC, and high cytoplasmic FLIP expression is indicative of poor prognosis. Targeting high FLIP expression using HDAC1-3 selective inhibitors such as entinostat to exploit high procaspase-8 expression in NSCLC has promising therapeutic potential, particularly when used in combination with TRAIL receptor-targeted agents.

New Insights into Optimal Discrete Rate Adaptation for Average Power Constrained Single and Multi-Node Systems

The throughput-optimal discrete-rate adaptation policy, when nodes are subject to constraints on the average power and bit error rate, is governed by a power control parameter, for which a closed-form characterization has remained an open problem. The parameter is essential in determining the rate adaptation thresholds and the transmit rate and power at any time, and ensuring adherence to the power constraint. We derive novel insightful bounds and approximations that characterize the power control parameter and the throughput in closed-form. The results are comprehensive as they apply to the general class of Nakagami-m (m >= 1) fading channels, which includes Rayleigh fading, uncoded and coded modulation, and single and multi-node systems with selection. The results are appealing as they are provably tight in the asymptotic large average power regime, and are designed and verified to be accurate even for smaller average powers.

Synchronization of globally coupled two-state stochastic oscillators with a state-dependent refractory period

We present a model of identical coupled two-state stochastic units, each of which in isolation is governed by a fixed refractory period. The nonlinear coupling between units directly affects the refractory period, which now depends on the global state of the system and can therefore itself become time dependent. At weak coupling the array settles into a quiescent stationary state. Increasing coupling strength leads to a saddle node bifurcation, beyond which the quiescent state coexists with a stable limit cycle of nonlinear coherent oscillations. We explicitly determine the critical coupling constant for this transition.

Combined inhibition of FLIP and XIAP induces Bax-independent apoptosis in type II colorectal cancer cells.

Death receptors can directly (type I cells) or indirectly induce apoptosis by activating mitochondrial-regulated apoptosis (type II cells). The level of caspase 8 activation is thought to determine whether a cell is type I or II, with type II cells less efficient at activating this caspase following death receptor activation. FLICE-inhibitory protein (FLIP) blocks death receptor-mediated apoptosis by inhibiting caspase 8 activation; therefore, we assessed whether silencing FLIP could convert type II cells into type I. FLIP silencing-induced caspase 8 activation in Bax wild-type and null HCT116 colorectal cancer cells; however, complete caspase 3 processing and apoptosis were only observed in Bax wild-type cells. Bax-null cells were also more resistant to chemotherapy and tumor necrosis factor-related apoptosis inducing ligand and, unlike the Bax wild-type cells, were not sensitized to these agents by FLIP silencing. Further analyses indicated that release of second mitochondrial activator of caspases from mitochondria and subsequent inhibition of X-linked inhibitor of apoptosis protein (XIAP) was required to induce full caspase 3 processing and apoptosis following FLIP silencing. These results indicate that silencing FLIP does not necessarily bypass the requirement for mitochondrial involvement in type II cells. Furthermore, targeting FLIP and XIAP may represent a therapeutic strategy for the treatment of colorectal tumors with defects in mitochondrial-regulated apoptosis.