An Algorithmic Approach to Limit Cycles of Nonlinear Differential Systems: the Averaging Method Revisited

This paper introduces an algorithmic approach to the analysis of bifurcation of limit cycles from the centers of nonlinear continuous differential systems via the averaging method. We develop three algorithms to implement the averaging method. The first algorithm allows to transform the considered differential systems to the normal formal of averaging. Here, we restricted the unperturbed term of the normal form of averaging to be identically zero. The second algorithm is used to derive the computational formulae of the averaged functions at any order. The third algorithm is based on the first two algorithms that determines the exact expressions of the averaged functions for the considered differential systems. The proposed approach is implemented in Maple and its effectiveness is shown by several examples. Moreover, we report some incorrect results in published papers on the averaging method.Comment: Proc. 44th ISSAC, July 15--18, 2019, Beijing, Chin

Mass Varying Neutrinos, Quintessence, and the Accelerating Expansion of the Universe

We analyze the Mass Varying Neutrino (MaVaN) scenario. We consider a minimal model of massless Dirac fermions coupled to a scalar field, mainly in the framework of finite temperature quantum field theory. We demonstrate that the mass equation we find has non-trivial solutions only for special classes of potentials, and only within certain temperature intervals. We give most of our results for the Ratra-Peebles Dark Energy (DE) potential. The thermal (temporal) evolution of the model is analyzed. Following the time arrow, the stable, metastable and unstable phases are predicted. The model predicts that the present Universe is below its critical temperature and accelerates. At the critical point the Universe undergoes a first-order phase transition from the (meta)stable oscillatory regime to the unstable rolling regime of the DE field. This conclusion agrees with the original idea of quintessence as a force making the Universe roll towards its true vacuum with zero \Lambda-term. The present MaVaN scenario is free from the coincidence problem, since both the DE density and the neutrino mass are determined by the scale M of the potential. Choosing M ~ 10^{-3} eV to match the present DE density, we can obtain the present neutrino mass in the range m ~ 10^{-2}-1 eV and consistent estimates for other parameters of the Universe.Comment: 29 pages, 7 figures. V. 3: Analysis of the dynamics of the Universe and some refs. added; extended version to be published in PR

Cart-O-matic project : autonomous and collaborative multi-robot localization, exploration and mapping

International audienceThe aim of the Cart-O-matic project was to design and build a multi-robot system able to autonomously map an unknown building. This work has been done in the framework of a French robotics contest called Defi CAROTTE organized by the General Delegation for Armaments (DGA) and the French National Research Agency (ANR). The scientific issues of this project deal with Simultaneous Localization And Mapping (SLAM), multi-robot collaboration and object recognition. In this paper, we will mainly focussed on the two first topics : after a general introduction, we will briefly describe the innovative simultaneous localization and mapping algorithm used during the competition. We will next explain how this algorithm can deal with multi-robots systems and 3D mapping. The next part of the paper will be dedicated to the multi-robot pathplanning and exploration strategy. The last section will illustrate the results with 2D and 3D maps, collaborative exploration strategies and example of planned trajectories

Cosmological zoo -- accelerating models with dark energy

ecent observations of type Ia supernovae indicate that the Universe is in an accelerating phase of expansion. The fundamental quest in theoretical cosmology is to identify the origin of this phenomenon. In principle there are two possibilities: 1) the presence of matter which violates the strong energy condition (a substantial form of dark energy), 2) modified Friedmann equations (Cardassian models -- a non-substantial form of dark matter). We classify all these models in terms of 2-dimensional dynamical systems of the Newtonian type. We search for generic properties of the models. It is achieved with the help of Peixoto's theorem for dynamical system on the Poincar{\'e} sphere. We find that the notion of structural stability can be useful to distinguish the generic cases of evolutional paths with acceleration. We find that, while the $\Lambda$CDM models and phantom models are typical accelerating models, the cosmological models with bouncing phase are non-generic in the space of all planar dynamical systems. We derive the universal shape of potential function which gives rise to presently accelerating models. Our results show explicitly the advantages of using a potential function (instead of the equation of state) to probe the origin of the present acceleration. We argue that simplicity and genericity are the best guide in understanding our Universe and its acceleration.Comment: RevTeX4, 23 pages, 10 figure

Оценка риска желудочно-кишечного кровотечения у пациентов с повреждением головного мозга

The aim of the study was to develop a risk model for upper gastrointestinal tract (GIT) bleeding in patients with brain injury of various etiologies.Material and methods. Case histories of 33 patients were included into a retrospective descriptive study: 22 patients had severe brain injury of various etiologies, and 11 patients after elective surgery for cerebral aneurisms with uneventful postop period were taken for comparison. The patients were grouped in two arms: Group 1 included patients with obvious signs of GIT bleeding (N=11) and Group 2 had no obvious signs of bleeding (N=22). Complaints, life and medical history, comorbidities, specialists’ exams data, results of laboratory and instrumental examinations, therapeutic regimens were analyzed. Presence of disproportionate pathologic sympathetic overreaction to acute brain injury, i.e., paroxysmal sympathetic hyperactivity (PSH), was assessed on admission and on Days 1, 3 and 5 after brain injury. Results. A model for upper GIT bleeding risk assessment was designed using logistic regression. The resulting model gains high quality rating: χ²=33,78, 3; p<0,001; OR=315. The risk of upper GIT bleeding exceeded 95% in patients having combination of 4 symptoms in their medical history (presence of PSH on Day 1 after acute brain injury; Karnofsky performance scale index 75; lack of neurovegetative stabilization in the acute period of brain injury; gastric and/or duodenal ulcer).Conclusion. Determining the risk factors thresholds enables stratification of patients by the risk for upper GIT bleeding. Modification of the identified four risk factors (presence of PSH on Day 1after acute brain injury; Karnofsky performance scale index 75; lack of neurovegetative stabilization in the acute period of brain injury; gastric and/or duodenal ulcer) will probably reduce the occurrence of upper GIT bleeding in patients with acute brane injury of various etiology.Цель исследования — построение модели риска развития желудочно-кишечного кровотечения из желудка и двенадцатиперстной кишки у пациентов с повреждением головного мозга различной этиологии. Материал и методы. В ретроспективное описательное исследование включили истории болезни 33-х пациентов: 22 пациентов — с тяжелым повреждением головного мозга различной этиологии и, для сравнения, 11 пациентов — с аневризматической болезнью сосудов головного мозга с неосложненным течением послеоперационного периода после плановых нейрохирургических вмешательств. Всех пациентов разделили на 2 группы: с явными признаками кровотечения из ЖКТ (n=11) и без явных признаков кровотечения (n=22). Проанализировали жалобы, анамнез заболевания и жизни, сопутствующие заболевания, данные осмотров специалистов, результаты лабораторных и инструментальных исследований, особенности терапии. Функции вегетативной нервной системы оценивали по проявлениям пароксизмальной симпатической гиперактивности (ПСГА) при поступлении в стационар, на 1-е, 3-и и 5-е сут после повреждения ГМ. Результаты. Средствами логистической регрессии построили модель оценки риска развития явного кровотечения из верхних отделов желудочно-кишечного тракта. Полученная модель обладает высокой оценкой качества: χ²=33,78, 3; p<0,001; OR=315. При сочетании в анамнезе 4-х признаков (повышение ПСГА в 1-е сут после повреждения головного мозга; индекс Карновского менее 75; отсутствие нейровегетативной стабилизации в остром периоде повреждения головного мозга; язвенная болезнь желудка и двенадцатиперстной кишки (ДПК)) риск развития явного кровотечения из верхних отделов желудочно-кишечного тракта превышал 95%.Заключение. Выделение пороговых значений факторов риска позволяет разделить пациентов на группы риска развития кровотечений из верхних отделов ЖКТ. Воздействие на выявленные 4 фактора риска (проявления ПСГА в 1-е сут после повреждения головного мозга; индекс Карновского менее 75; отсутствие нейровегетативной стабилизации в остром периоде повреждения головного мозга; язвенная болезнь желудка и ДПК) позволит, вероятно, снизить частоту ЖКК из верхних отделов ЖКТ у пациентов с повреждением ГМ различной этиологии.

РАЗЛИЧНОЕ ВЛИЯНИЕ НАРКОТИЧЕСКИХ АНАЛЬГЕТИКОВ НА ДИНАМИКУ АКТИВНОСТИ ЦИТОКИНОВ ВО ВРЕМЯ КАРДИОХИРУРГИЧЕСКИХ ВМЕШАТЕЛЬСТВ В УСЛОВИЯХ ИСКУССТВЕННОГО КРОВООБРАЩЕНИЯ

According to experimental data, morphine possesses certain anti-inflammatory properties, which can reduce the manifestations of system inflammatory response (SIR) after cardiopulmonary bypass. Objective: to investigate the effect of various narcotic analgesics on the activity of some SIR markers during peri-operative period of cardiac surgery with cardiopulmonary bypass. Subjects and methods. During the one-centered randomized prospective study, the changes in the concentration of interleukin-6, (IL-6), interleukin-8 (IL-8) and tumor necrosis factor (TNF) were followed up before cardiopulmonary bypass, and in 1, 3 and 24 hours after it in 60 patients, randomly divided into 2 groups. Patients of Group 1 (n = 30) received anesthesia with phentanyl, those from Group 2 (n = 30) received morphine. The groups did not differ in their clinical and demographic parameters and surgery types, performed in them. Results. The significant increase in the concentration of all inflammatory markers was observed in 1 hour after cardiopulmonary bypass was off, which was the evidence of SIR development. In the Group on morphine, the activity of markers was lower versus the Group on phentanyl. Thus, concentration of IL-6 in 3 hours after cardiopulmonary bypass made 155 (113; 180) versus 178 (102; 236) pg/ml (p = 0.006), IL-8 in 1 hour after cardiopulmonary bypass made 37.4 (25.4; 50.2) versus 52.6 (24; 91.4) pg/ml (p = 0,03), in 1 hour the level of TNF achieved 10.7 (8.6; 15.9) versus 15.7 (11.4; 23.1) pg/ml (p = 0.01), and in 3 hours it made − 9.7 (8.3; 13.8) versus 14.1 (9.6; 18.8) pg/ml (p = 0.04). However, there was no difference in the clinical course parameters between the Groups. Conclusion. The obtained results prove the morphine potential to reduce the expression of pro-inflammatory markers when used during cardiac surgery with cardiopulmonary bypass. Согласно экспериментальным данным, морфин обладает противовоспалительными свойствами, которые могут снизить проявления системного воспалительного ответа (СВО) после процедур искусственного кровообращения (ИК). Цель: изучить влияние различных наркотических анальгетиков на активность некоторых маркеров СВО в периоперационном периоде кардиохирургических вмешательств, выполненных в условиях ИК. Материалы и методы. В ходе одноцентрового, рандомизированного, проспективного исследования изучали динамику концентрации интерлейкина-6 (ИЛ-6), интерлейкина-8 (ИЛ-8) и фактора некроза опухоли (ФНО) до ИК, через 1, 3 и 24 ч после окончания ИК у 60 пациентов, рандомизированных в две группы. Пациенты 1-й группы (n = 30) получали анестезию с использованием фентанила, 2-й (n = 30) − с применением морфина. Группы не различались по клинико-демографическим показателям и характеристикам операций у больных. Результаты. Обнаружено выраженное увеличение концентрации всех маркеров воспаления уже через 1 ч после отключения ИК в обеих группах, что свидетельствовало о развитии СВО. В группе морфина активность маркеров была ниже, чем в группе фентанила. Так, концентрация ИЛ-6 через 3 ч после ИК составляла 155 (113; 180) против 178 (102; 236) пг/мл (p = 0,006), ИЛ-8 через 1 ч после ИК − 37,4 (25,4; 50,2) против 52,6 (24; 91,4) пг/мл (p = 0,03), уровень ФНО через 1 ч достиг 10,7 (8,6; 15,9) против 15,7 (11,4; 23,1) пг/мл (p = 0,01), через 3 ч − 9,7 (8,3; 13,8) против 14,1 (9,6; 18,8) пг/мл (p = 0,04). Однако различий в показателях клинического течения между группами не было. Заключение. Полученные результаты показывают способность морфина снижать экспрессию провоспалительных маркеров при использовании во время кардиохирургических вмешательств в условиях ИК.

Surfactant therapy for pneumonia COVID-19 of obstetric patients

Introduction. Pregnant women may be at increased risk for severe COVID-19 illness. Pregnant women are more likely to be hospitalized at ICU, needed the mechanical ventilation compared to nonpregnant women of childbearing age. Building on the experience of the effective use of the exogenous surfactant for influenza A/H1N1 treatment of pregnant women with COVID-19, the surfactant therapy has also been included in the treatment.The objective. To evaluate the effectiveness of surfactant therapy in the integrated treatment of severe COVID-19 pneumonia of pregnant women and postpartum women.Materials and methods. The study included 135 pregnant and postpartum women with severe COVID-19 pneumonia. All of them received antiviral, anticoagulant, anticytokine and anti-inflammatory therapy. 68 patients (main group) with an initially more severe course of the disease and a greater degree of lung damage (p = 0.026) received inhalations with Surfactant-BL, 67 patients (control group) did not receive the  surfactant therapy. Patients received Surfactant-BL through a  mesh-nebulizer at a  dose of 75 mg 2 times a day for 3–5 days.Result. Patients of the main group showed decreasing risks of requiring the noninvasive ventilation (27.9% vs. 52.2%, р = 0.014) and artificial lung ventilation (2.9% vs. 11.9%, p = 0.047), the length of stay in the intensive care unit (ICU) was reduced (10.6 vs. 13.1 inpatient days, р = 0.045). Сomplications such as pneumomediastinum and pneumothorax occurred less frequently in the surfactant therapy group (24.2% vs. 52.4%, p = 0.037) with a high extent of lung damage (CT-3–4). With early surfactant therapy in the standard oxygen therapy stage or high-flow oxygenation, gas exchange indicators were restored faster, thus avoiding mechanical ventilation and has reduced the duration of intensive care (р = 0.004) and prevented deaths.Conclusion. The use of surfactant therapy for pneumonia associated with COVID-19 in pregnant and postpartum women against the background of ongoing complex therapy helps to prevent further lung damage, reduce the mechanical ventilation risk and improve oxygenation earlier, especially with early start of surfactant therapy