Stability region bifurcations of nonlinear autonomous dynamical systems: Type-zero saddle-node bifurcations

The behavior of stability regions of nonlinear autonomous dynamical systems subjected to parameter variation is studied in this paper. In particular, the behavior of stability regions and stability boundaries when the system undergoes a type-zero sadle-node bifurcation on the stability boundary is investigated in this paper. It is shown that the stability regions suffer drastic changes with parameter variation if type-zero saddle-node bifurcations occur on the stability boundary. A complete characterization of these changes in the neighborhood of a type-zero saddle-node bifurcation value is presented in this paper. Copyright (C) 2010 John Wiley & Sons, Ltd.

Using bifurcations in the determination of lock-in ranges for third-order phase-locked loops

Transmission and switching in digital telecommunication networks require distribution of precise time signals among the nodes. Commercial systems usually adopt a master-slave (MS) clock distribution strategy building slave nodes with phase-locked loop (PLL) circuits. PLLs are responsible for synchronizing their local oscillations with signals from master nodes, providing reliable clocks in all nodes. The dynamics of a PLL is described by an ordinary nonlinear differential equation, with order one plus the order of its internal linear low-pass filter. Second-order loops are commonly used because their synchronous state is asymptotically stable and the lock-in range and design parameters are expressed by a linear equivalent system [Gardner FM. Phaselock techniques. New York: John Wiley & Sons: 1979]. In spite of being simple and robust, second-order PLLs frequently present double-frequency terms in PD output and it is very difficult to adapt a first-order filter in order to cut off these components [Piqueira JRC, Monteiro LHA. Considering second-harmonic terms in the operation of the phase detector for second order phase-locked loop. IEEE Trans Circuits Syst [2003;50(6):805-9; Piqueira JRC, Monteiro LHA. All-pole phase-locked loops: calculating lock-in range by using Evan`s root-locus. Int J Control 2006;79(7):822-9]. Consequently, higher-order filters are used, resulting in nonlinear loops with order greater than 2. Such systems, due to high order and nonlinear terms, depending on parameters combinations, can present some undesirable behaviors, resulting from bifurcations, as error oscillation and chaos, decreasing synchronization ranges. In this work, we consider a second-order Sallen-Key loop filter [van Valkenburg ME. Analog filter design. New York: Holt, Rinehart & Winston; 1982] implying a third order PLL The resulting lock-in range of the third-order PLL is determined by two bifurcation conditions: a saddle-node and a Hopf. (C) 2008 Elsevier B.V. All rights reserved.

Mechanism and model of the oscillatory electro-oxidation of methanol

A mechanism for the kinetic instabilities observed in the galvanostatic electro-oxidation of methanol is suggested and a model developed. The model is investigated using stoichiometric network analysis as well as concepts from algebraic geometry (polynomial rings and ideal theory) revealing the occurrence of a Hopf and a saddle-node bifurcation. These analytical solutions are confirmed by numerical integration of the system of differential equations. (C) 2010 American Institute of Physics

Menopausal status: a possible predictive factor for recurrence in women with cancer of the uterine cervix without pelvic lymph node metastasis

Abstract Objectives to evaluate risk factors for recurrence of carcinoma of the uterine cervix among women who had undergone radical hysterectomy without pelvic lymph node metastasis, while taking into consideration not only the classical histopathological factors but also sociodemographic, clinical and treatment-related factors. Study desin This was an exploratory analysis on 233 women with carcinoma of the uterine cervix (stages IB and IIA) who were treated by means of radical hysterectomy and pelvic lymphadenectomy, with free surgical margins and without lymph node metastases on conventional histopathological examination. Women with histologically normal lymph nodes but with micrometastases in the immunohistochemical analysis (AE1/AE3) were excluded. Disease-free survival for sociodemographic, clinical and histopathological variables was calculated using the Kaplan-Meier method. The Cox proportional hazards model was used to identify the independent risk factors for recurrence. Twenty-seven recurrences were recorded (11.6%), of which 18 were pelvic, four were distant, four were pelvic + distant and one was of unknown location. The five-year disease-free survival rate among the study population was 88.4%. The independent risk factors for recurrence in the multivariate analysis were: postmenopausal status (HR 14.1; 95% CI: 3.7-53.6; P < 0.001), absence of or slight inflammatory reaction (HR 7.9; 95% CI: 1.7-36.5; P = 0.008) and invasion of the deepest third of the cervix (HR 6.1; 95% CI: 1.3-29.1; P = 0.021). Postoperative radiotherapy was identified as a protective factor against recurrence (HR 0.02; 95% CI: 0.001-0.25; P = 0.003). (To continue) Postmenopausal status is a possible independent risk factor for recurrence even when adjusted for classical prognostic factors (such as tumour size, depth of tumour invasion, capillary embolisation) and treatment-related factors (period of treatment and postoperative radiotherapy status)

Lack of Galectin-3 Disturbs Mesenteric Lymph Node Homeostasis and B Cell Niches in the Course of Schistosoma mansoni Infection

Galectin-3 is a beta-galactoside-binding protein that has been shown to regulate pathophysiological processes, including cellular activation, differentiation and apoptosis. Recently, we showed that galectin-3 acts as a potent inhibitor of B cell differentiation into plasma cells. Here, we have investigated whether galectin-3 interferes with the lymphoid organization of B cell compartments in mesenteric lymph nodes (MLNs) during chronic schistosomiasis, using WT and galectin-3(-/-) mice. Schistosoma mansoni synthesizes GalNAc beta 1-4(Fuc alpha 1-3) GlcNAc(Lac-DiNAc) structures (N-acetylgalactosamine beta 1-4 N-acetylglucosamine), which are known to interact with galectin-3 and elicit an intense humoral response. Antigens derived from the eggs and adult worms are continuously drained to MLNs and induce a polyclonal B cell activation. In the present work, we observed that chronically-infected galectin-3(-/-) mice exhibited a significant reduced amount of macrophages and B lymphocytes followed by drastic histological changes in B lymphocyte and plasma cell niches in the MLNs. The lack of galectin-3 favored an increase in the lymphoid follicle number, but made follicular cells more susceptible to apoptotic stimuli. There were an excessive quantity of apoptotic bodies, higher number of annexin V(+)/PI(-) cells, and reduced clearance of follicular apoptotic cells in the course of schistosomiasis. Here, we observed that galectin-3 was expressed in nonlymphoid follicular cells and its absence was associated with severe damage to tissue architecture. Thus, we convey new information on the role of galectin-3 in regulation of histological events associated with B lymphocyte and plasma cell niches, apoptosis, phagocytosis and cell cycle properties in the MLNs of mice challenged with S. mansoni.

Rotation curve bifurcations as indicators of close recent galaxy encounters

Context. Rotation curves of interacting galaxies often show that velocities are either rising or falling in the direction of the companion galaxy. Aims. We seek to reproduce and analyse these features in the rotation curves of simulated equal-mass galaxies suffering a one-to-one encounter as possible indicators of close encounters. Methods. Using simulations of major mergers in 3D, we study the time evolution of these asymmetries in a pair of galaxies during the first passage. Results. Our main results are: (a) the rotation curve asymmetries appear right at pericentre of the first passage, (b) the significant disturbed rotation velocities occur within a small time interval, of similar to 0.5 Gyr h(-1), and, therefore, the presence of bifurcation in the velocity curve could be used as an indicator of the pericentre occurrence. These results are in qualitative agreement with previous findings for minor mergers and flybys.

Transition to chaotic scattering: Signatures in the differential cross section

We show that bifurcations in chaotic scattering manifest themselves through the appearance of an infinitely fine-scale structure of singularities in the cross section. These ""rainbow singularities"" are created in a cascade, which is closely related to the bifurcation cascade undergone by the set of trapped orbits (the chaotic saddle). This cascade provides a signature in the differential cross section of the complex pattern of bifurcations of orbits underlying the transition to chaotic scattering. We show that there is a power law with a universal coefficient governing the sequence of births of rainbow singularities and we verify this prediction by numerical simulations.

Automatic Network Fingerprinting through Single-Node Motifs

Complex networks have been characterised by their specific connectivity patterns (network motifs), but their building blocks can also be identified and described by node-motifs-a combination of local network features. One technique to identify single node-motifs has been presented by Costa et al. (L. D. F. Costa, F. A. Rodrigues, C. C. Hilgetag, and M. Kaiser, Europhys. Lett., 87, 1, 2009). Here, we first suggest improvements to the method including how its parameters can be determined automatically. Such automatic routines make high-throughput studies of many networks feasible. Second, the new routines are validated in different network-series. Third, we provide an example of how the method can be used to analyse network time-series. In conclusion, we provide a robust method for systematically discovering and classifying characteristic nodes of a network. In contrast to classical motif analysis, our approach can identify individual components (here: nodes) that are specific to a network. Such special nodes, as hubs before, might be found to play critical roles in real-world networks.

Node-Depth Encoding and Multiobjective Evolutionary Algorithm Applied to Large-Scale Distribution System Reconfiguration

The power loss reduction in distribution systems (DSs) is a nonlinear and multiobjective problem. Service restoration in DSs is even computationally hard since it additionally requires a solution in real-time. Both DS problems are computationally complex. For large-scale networks, the usual problem formulation has thousands of constraint equations. The node-depth encoding (NDE) enables a modeling of DSs problems that eliminates several constraint equations from the usual formulation, making the problem solution simpler. On the other hand, a multiobjective evolutionary algorithm (EA) based on subpopulation tables adequately models several objectives and constraints, enabling a better exploration of the search space. The combination of the multiobjective EA with NDE (MEAN) results in the proposed approach for solving DSs problems for large-scale networks. Simulation results have shown the MEAN is able to find adequate restoration plans for a real DS with 3860 buses and 632 switches in a running time of 0.68 s. Moreover, the MEAN has shown a sublinear running time in function of the system size. Tests with networks ranging from 632 to 5166 switches indicate that the MEAN can find network configurations corresponding to a power loss reduction of 27.64% for very large networks requiring relatively low running time.

Design constraints for third-order PLL nodes in master-slave clock distribution networks

Clock signal distribution in telecommunication commercial systems usually adopts a master-slave architecture, with a precise time basis generator as a master and phase-locked loops (PLLs) as slaves. In the majority of the networks, second-order PLLs are adopted due to their simplicity and stability. Nevertheless, in some applications better transient responses are necessary and, consequently, greater order PLLs need to be used, in spite of the possibility of bifurcations and chaotic attractors. Here a master-slave network with third-order PLLs is analyzed and conditions for the stability of the synchronous state are derived, providing design constraints for the node parameters, in order to guarantee stability and reachability of the synchronous state for the whole network. Numerical simulations are carried out in order to confirm the analytical results. (C) 2009 Elsevier B.V. All rights reserved.

Route to chaos in a third-order phase-locked loop network

Phase-locked loops (PLLs) are widely used in applications related to control systems and telecommunication networks. Here we show that a single-chain master-slave network of third-order PLLs can exhibit stationary, periodic and chaotic behaviors, when the value of a single parameter is varied. Hopf, period-doubling and saddle-saddle bifurcations are found. Chaos appears in dissipative and non-dissipative conditions. Thus, chaotic behaviors with distinct dynamical features can be generated. A way of encoding binary messages using such a chaos-based communication system is suggested. (C) 2009 Elsevier B.V. All rights reserved.

ASSOCIATION BETWEEN SADDLE NOSE DEFORMITY AND RETRO-ORBITAL MASS IN WEGENER`S GRANULOMATOSIS

Objectives: The relationship between saddle nose deformity (SND) in Wegener`s granulomatosis (WG) and other clinical features, including retro-orbital mass formation (ROM), has been poor described. Therefore, this relationship was analyzed retrospectively from 2000 to 2010. Patients and Methods: Eighteen consecutive WG patients with SND diagnosed by computed tomography were matched to 36 WG patients without SND (control group) for gender, age at WG diagnosis and disease duration. Results: No difference was found between the two groups in relation to WG type (limited and systemic forms), ethnicity, laboratory features, constitutional symptoms or clinical manifestations, including upper respiratory tract, and treatment, except for ROM (33.3 vs. 2.8% in SND(+) and SND(-) groups, respectively; p=0.004) and subglottic stenosis (22.2 vs. 2.8%; p=0.038). However, on multivariate analysis, only ROM (OR 17.15; 95% CI 1.11-265.52) was statistically associated to SND. In addition, in more than half of the cases, SND manifested prior to ROM. Conclusions: Results of this prospective analysis showed that SND was strongly associated to ROM in WG. Since early diagnosis and aggressive treatment of orbital involvement could lead to better prognosis, the presence of SND warrants additional vigilance.

Gene expression profiling of papillary thyroid carcinoma identifies transcripts correlated with BRAF mutational status and lymph node metastasis

Purpose: To identify papillary thyroid carcinoma (PTC)-associated transcripts, we compared the gene expression profiles of three Serial Analysis of Gene Expression libraries generated from thyroid tumors and a normal thyroid tissue. Experimental Design: Selected transcripts were validated in a panel of 57 thyroid tumors using quantitative PCR (qPCR). An independent set of 71 paraffin-embedded sections was used for validation using immunohistochemical analysis. To determine if PTC-associated gene expression could predict lymph node involvement, a separate cohort of 130 primary PTC (54 metastatic and 76 nonmetastatic) was investigated. The BRAF(V600E) mutational status was compared with qPCR data to identify genes that might be regulated by abnormal BRAF/MEK/extracellular signal-regulated kinase signaling. Results: We identified and validated new PTC-associated transcripts. Three genes (CST6, CXCL14, and DHRS3) are strongly associated with PTC. Immunohistochemical analysis of CXCL14 confirmed the qPCR data and showed protein expression in PTC epithelial cells. We also observed that CST6, CXCL14, DHRS3, and SPP1 were associated with PTC lymph node metastasis, with CST6, CXCL14, and SPP1 being positively correlated with metastasis and DHRS3 being negatively correlated. Finally, we found a strong correlation between CST6 and CXCL14 expression and BRAF(V600E) mutational status, suggesting that these genes may be induced subsequently to BRAF activation and therefore may be downstream in the BRAF/MEK/extracellular signal-regulated kinase signaling pathway. Conclusion: CST6, CXCL14, DHRS3, and SPP1 may play a role in PTC pathogenesis and progression and are possible molecular targets for FTC therapy.

The interaction between N-category and N-ratio as a new tool to improve lymph node metastasis staging in gastric cancer: Results of a single cancer center in Brazil

Background: Depth of tumor invasion (T-category) and the number of metastatic lymph nodes (N-category) are the most important prognostic factors in patients with gastric cancer. Recently, the ratio between metastatic and dissected lymph nodes (N-ratio) has been established as one. The aim of this study is to evaluate the impact of N-ratio and its interaction with N-category as a prognostic factor in gastric cancer. Methods: This was a retrospective study in which we reviewed clinical and pathological data of 165 patients who had undergone curative surgery at our institution through a 9-year period. The exclusion criteria included metastases, gastric stump tumors and gastrectomy with less than 15 lymph nodes dissected. Results: The median age of the patients was 63 years and most of them were male. Total gastrectomy was the most common procedure and 92.1% of the patients had a D2-lymphadenectomy. Their 5-year overall survival was 57.7%. T-category, N-category, extended gastrectomy, and N-ratio were prognostic factors in overall and disease-free survival in accordance with univariate analysis. In accordance with TNM staging, N1 patients who have had NR1 had 5-year survival in 75.5% whereas in the NR2 group only 33% of the cases had 5-year survival. In the multivariate analysis, the interaction between N-category and N-ratio was an independent prognostic factor. Conclusion: Our findings confirmed the role of N-ratio as prognostic factor of survival in patients with gastric cancer surgically treated with at least 15 lymph nodes dissected. The relationship between N-category and N-ratio is a better predictor than lymph node metastasis staging. (C) 2010 Elsevier Ltd. All rights reserved.

Mid-humeral sentinel lymph node dissection in patients with primary cutaneous malignant melanoma

In rare cases, lymphatic drainage from the malignant melanomas in the upper extremity may follow an unpredictable pattern (outside the axillary nodes), and these aberrant sentinel nodes may represent the only site of regional lymph node metastases. The precise anatomical landmarks and technical aspects of surgical exploration of these aberrant sentinel lymph nodes are rarely described in the literature, including aberrant sentinel mid-humeral lymph nodes. This report describes a step-by-step dissection of the mid-humeral sentinel lymph nodes in two patients with a primary malignant melanoma in the upper extremity, identified by lymphatic mapping. Recognition of precise regional anatomy and following a special surgical technique makes the procedure safe and successful, thus avoiding local complications and allowing a prompt recovery. Melanoma Res 20:138-140 (C) 2010 Wolters Kluwer Health vertical bar Lippincott Williams & Wilkins.