On the upper bound of the number of limit cycles obtained by the second order averaging method I

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On the upper bound of the number of limit cycles obtained by the second order averaging method II

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Geometric tools to determine the hyperbolicity of limit cycles

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Multiplicity of limit cycles and analytic m-solutions for planar differential systems

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The Experience of European Integration and the Potential for Integration in South America

The experience of the European Union is the most significant and far-reaching among all attempts at regional integration. It is, therefore, the most likely to provide some lessons for those world regions that are just beginning this complex process. In turn, the Common Market of the South (MERCOSUR) and the Andean Community (CAN) are among the regional integration projects that have reached the greatest level of formal accomplishment after the EU. MERCOSUR is a customs union that aspires to become a common market, while avowing the commitment to advance towards political integration. For its part, CAN is a customs union that has already developed supranational institutions such as a Commission, a Parliament and a Court of Justice. In both cases, however, words have progressively tended to wander far from deeds. One reason underlying this phenomenon may be a misunderstanding of the European experience with integration. In this article, we discuss the theories that have been developed to account for integration in Europe and may prove useful to understand integration elsewhere and put forward a set of lessons that could be drawn from the European experience. Subsequently, we introduce a description of the experience of integration in South America and reflect (critically) on how the theories and lessons drawn from the EU could be applied to this region –and beyond.

On the existence and uniqueness of limit cycles in Liénard differential equations allowing discontinuities

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Trypanosoma cruzi: vertebrate and invertebrate cycles in the same mammal host, the opossum Didelphis marsupialis

Epimastigotes multiplying extracellularly and metacyclic trypomastigotes, stages that correspond to the cycle of Trypanosoma cruzi in the intestinal lumen of its insect vector, were consistently found in the lumen of the anal glands of opossums Didelphis marsupialis inoculated subcutaneously with infective feces of triatomid bugs.

Understanding sources of the change in international business cycles

Macroeconomic activity has become less volatile over the past three decades in most G7 economies. Current literature focuses on the characterization of the volatility reduction and explanations for this so called "moderation" in each G7 economy separately. In opposed to individual country analysis and individual variable analysis, this paper focuses on common characteristics of the reduction and common explanations for the moderation in G7 countries. In particular, we study three explanations: structural changes in the economy, changes in common international shocks and changes in domestic shocks. We study these explanations in a unified model structure. To this end, we propose a Bayesian factor structural vector autoregressive model. Using the proposed model, we investigate whether we can find common explanations for all G7 economies when information is pooled from multiple domestic and international sources. Our empirical analysis suggests that volatility reductions can largely be attributed to the decline in the magnitudes of the shocks in most G7 countries while only for the U.K., the U.S. and Italy they can partially be attributed to structural changes in the economy. Analyzing the components of the volatility, we also find that domestic shocks rather than common international shocks can account for a large part of the volatility reduction in most of the G7 countries. Finally, we find that after mid-1980s the structure of the economy changes substantially in five of the G7 countries: Germany, Italy, Japan, the U.K. and the U.S..

Biological materials in colorectal surgery: current applications and potential for the future.

Biological materials are increasingly used in abdominal surgery for ventral, pelvic and perineal reconstructions, especially in contaminated fields. Future applications are multi-fold and include prevention and one-step closure of infected areas. This includes prevention of abdominal, parastomal and pelvic hernia, but could also include prevention of separation of multiple anastomoses, suture- or staple-lines. Further indications could be a containment of infected and/or inflammatory areas and protection of vital implants such as vascular grafts. Reinforcement patches of high-risk anastomoses or unresectable perforation sites are possibilities at least. Current applications are based mostly on case series and better data is urgently needed. Clinical benefits need to be assessed in prospective studies to provide reliable proof of efficacy with a sufficient follow-up. Only superior results compared with standard treatment will justify the higher costs of these materials. To date, the use of biological materials is not standard and applications should be limited to case-by-case decision.

Acute flare induced by the calcific tendonitis of the rotator cuff: inhibition of IL-1 a potential therapeutic target?

Introduction: Calcific tendonitis of rotator cuff is observed on plainradiographs in 10% of adults, but remains asymptomatic in half thesecases. Sometimes, these calcifications induce acute flares withmassive inflammation similar to gout or CPPD crisis. Analgesics/anti-inflammatory medications are usually not sufficient to controlssymptoms in these situations. Local steroid infiltration with or withoutremoval of the calcific deposition with a needle aspiration may beuseful. A new approach could be IL-1 inhibitors. Indeed, basic calciumphosphate crystals are capable of stimulating the release of activeIL-1β in vitro. These crystals trigger IL-1β release, in an analogousmanner to MSU crystals in acute gout, suggesting that IL-1β blockademay be clinically useful.Case presentation: This report describes a 70-year old woman withacute rest pain of the right shoulder since 48 hours. On examination,we found massive limitations of active and passive movements. Thepatient evaluated, on the visual scale, her symptoms at 10/10 the nightand 5/10 the day. The radiography and showed a rounded, 8 mmcalcification in the subscapularis tendon. The ultrasound aspectrevealed a heterogeneous calcification partially non solid, surroundedby massive inflammation on Doppler. C-reactive protein anderythrocyte sedimentation rate were high (74 mg/ml, 54 mm/hour).The patient received subcutaneous injections of anakinra: 100 mgdaily for 3 days (D1-D3). We evaluated the patient in our consult at dayD1, D2, D3, D7, D16 and by phone at D70.This treatment rapidly relieved the inflammatory symptoms (within afew hours with no relapse). The mobility of the shoulder, the biologicsparameters improved and the size of the calcification as well thedegree of inflammation regressed on ultrasound after 3 days.Conclusion: This is the first report of a woman with an acute flareinduced by calcific tendonitis who received anakinra. IL-1 inhibitionmay be a therapeutic target in calcific tendonitis. To analyse thisresponse more precisely and elaborate definitive conclusions, aprospective pilot study is on-going in our ambulatory institute.

On the applicability of mathematics : philosophical and historical perspectives

The present thesis is a contribution to the debate on the applicability of mathematics; it examines the interplay between mathematics and the world, using historical case studies. The first part of the thesis consists of four small case studies. In chapter 1, I criticize "ante rem structuralism", proposed by Stewart Shapiro, by showing that his so-called "finite cardinal structures" are in conflict with mathematical practice. In chapter 2, I discuss Leonhard Euler's solution to the Königsberg bridges problem. I propose interpreting Euler's solution both as an explanation within mathematics and as a scientific explanation. I put the insights from the historical case to work against recent philosophical accounts of the Königsberg case. In chapter 3, I analyze the predator-prey model, proposed by Lotka and Volterra. I extract some interesting philosophical lessons from Volterra's original account of the model, such as: Volterra's remarks on mathematical methodology; the relation between mathematics and idealization in the construction of the model; some relevant details in the derivation of the Third Law, and; notions of intervention that are motivated by one of Volterra's main mathematical tools, phase spaces. In chapter 4, I discuss scientific and mathematical attempts to explain the structure of the bee's honeycomb. In the first part, I discuss a candidate explanation, based on the mathematical Honeycomb Conjecture, presented in Lyon and Colyvan (2008). I argue that this explanation is not scientifically adequate. In the second part, I discuss other mathematical, physical and biological studies that could contribute to an explanation of the bee's honeycomb. The upshot is that most of the relevant mathematics is not yet sufficiently understood, and there is also an ongoing debate as to the biological details of the construction of the bee's honeycomb. The second part of the thesis is a bigger case study from physics: the genesis of GR. Chapter 5 is a short introduction to the history, physics and mathematics that is relevant to the genesis of general relativity (GR). Chapter 6 discusses the historical question as to what Marcel Grossmann contributed to the genesis of GR. I will examine the so-called "Entwurf" paper, an important joint publication by Einstein and Grossmann, containing the first tensorial formulation of GR. By comparing Grossmann's part with the mathematical theories he used, we can gain a better understanding of what is involved in the first steps of assimilating a mathematical theory to a physical question. In chapter 7, I introduce, and discuss, a recent account of the applicability of mathematics to the world, the Inferential Conception (IC), proposed by Bueno and Colyvan (2011). I give a short exposition of the IC, offer some critical remarks on the account, discuss potential philosophical objections, and I propose some extensions of the IC. In chapter 8, I put the Inferential Conception (IC) to work in the historical case study: the genesis of GR. I analyze three historical episodes, using the conceptual apparatus provided by the IC. In episode one, I investigate how the starting point of the application process, the "assumed structure", is chosen. Then I analyze two small application cycles that led to revisions of the initial assumed structure. In episode two, I examine how the application of "new" mathematics - the application of the Absolute Differential Calculus (ADC) to gravitational theory - meshes with the IC. In episode three, I take a closer look at two of Einstein's failed attempts to find a suitable differential operator for the field equations, and apply the conceptual tools provided by the IC so as to better understand why he erroneously rejected both the Ricci tensor and the November tensor in the Zurich Notebook.

Microbiota abnormalities in inflammatory airway diseases - Potential for therapy.

Increasingly the development of novel therapeutic strategies is taking into consideration the contribution of the intestinal microbiota to health and disease. Dysbiosis of the microbial communities colonizing the human intestinal tract has been described for a variety of chronic diseases, such as inflammatory bowel disease, obesity and asthma. In particular, reduction of several so-called probiotic species including Lactobacilli and Bifidobacteria that are generally considered to be beneficial, as well as an outgrowth of potentially pathogenic bacteria is often reported. Thus a tempting therapeutic approach is to shape the constituents of the microbiota in an attempt to restore the microbial balance towards the growth of 'health-promoting' bacterial species. A twist to this scenario is the recent discovery that the respiratory tract also harbors a microbiota under steady-state conditions. Investigators have shown that the microbial composition of the airway flora is different between healthy lungs and those with chronic lung diseases, such as asthma, chronic obstructive pulmonary disease as well as cystic fibrosis. This is an emerging field, and thus far there is very limited data showing a direct contribution of the airway microbiota to the onset and progression of disease. However, should future studies provide such evidence, the airway microbiota might soon join the intestinal microbiota as a target for therapeutic intervention. In this review, we highlight the major advances that have been made describing the microbiota in chronic lung disease and discuss current and future approaches concerning manipulation of the microbiota for the treatment and prevention of disease.

Membrane potential dynamics of neocortical projection neurons driving target-specific signals.

Primary sensory cortex discriminates incoming sensory information and generates multiple processing streams toward other cortical areas. However, the underlying cellular mechanisms remain unknown. Here, by making whole-cell recordings in primary somatosensory barrel cortex (S1) of behaving mice, we show that S1 neurons projecting to primary motor cortex (M1) and those projecting to secondary somatosensory cortex (S2) have distinct intrinsic membrane properties and exhibit markedly different membrane potential dynamics during behavior. Passive tactile stimulation evoked faster and larger postsynaptic potentials (PSPs) in M1-projecting neurons, rapidly driving phasic action potential firing, well-suited for stimulus detection. Repetitive active touch evoked strongly depressing PSPs and only transient firing in M1-projecting neurons. In contrast, PSP summation allowed S2-projecting neurons to robustly signal sensory information accumulated during repetitive touch, useful for encoding object features. Thus, target-specific transformation of sensory-evoked synaptic potentials by S1 projection neurons generates functionally distinct output signals for sensorimotor coordination and sensory perception.