Recurrent Averaging Inequalities in Multi-Agent Control and Social Dynamics Modeling

Many multi-agent control algorithms and dynamic agent-based models arising in natural and social sciences are based on the principle of iterative averaging. Each agent is associated to a value of interest, which may represent, for instance, the opinion of an individual in a social group, the velocity vector of a mobile robot in a flock, or the measurement of a sensor within a sensor network. This value is updated, at each iteration, to a weighted average of itself and of the values of the adjacent agents. It is well known that, under natural assumptions on the network's graph connectivity, this local averaging procedure eventually leads to global consensus, or synchronization of the values at all nodes. Applications of iterative averaging include, but are not limited to, algorithms for distributed optimization, for solution of linear and nonlinear equations, for multi-robot coordination and for opinion formation in social groups. Although these algorithms have similar structures, the mathematical techniques used for their analysis are diverse, and conditions for their convergence and differ from case to case. In this paper, we review many of these algorithms and we show that their properties can be analyzed in a unified way by using a novel tool based on recurrent averaging inequalities (RAIs). We develop a theory of RAIs and apply it to the analysis of several important multi-agent algorithms recently proposed in the literature

Delay Robustness of Consensus Algorithms: Continuous-Time Theory

Consensus among autonomous agents is a key problem in multiagent control. In this article, we consider averaging consensus policies over time-varying graphs in presence of unknown but bounded communication delays. It is known that consensus is established (no matter how large the delays are) if the graph is periodically, or uniformly quasi-strongly connected (UQSC). The UQSC condition is often believed to be the weakest sufficient condition under which consensus can be proved. We show that the UQSC condition can actually be substantially relaxed and replaced by a condition that we call aperiodic quasi-strong connectivity, which, in some sense, proves to be very close to the necessary condition (the so-called integral connectivity). Under the assumption of reciprocity of interactions (e.g., for undirected or type-symmetric graphs), a necessary and sufficient condition for consensus in presence of bounded communication delays is established; the relevant results have been previously proved only in the undelayed case

Recurrent averaging inequalities in multi-agent control and social dynamics modeling

Many multi-agent control algorithms and dynamic agent-based models arising in natural and social sciences are based on the principle of iterative averaging. Each agent is associated to a value of interest, which may represent, for instance, the opinion of an individual in a social group, the velocity vector of a mobile robot in a flock, or the measurement of a sensor within a sensor network. This value is updated, at each iteration, to a weighted average of itself and of the values of the adjacent agents. It is well known that, under natural assumptions on the network's graph connectivity, this local averaging procedure eventually leads to global consensus, or synchronization of the values at all nodes. Applications of iterative averaging include, but are not limited to, algorithms for distributed optimization, for solution of linear and nonlinear equations, for multi-robot coordination and for opinion formation in social groups. Although these algorithms have similar structures, the mathematical techniques used for their analysis are diverse, and conditions for their convergence and differ from case to case. In this paper, we review many of these algorithms and we show that their properties can be analyzed in a unified way by using a novel tool based on recurrent averaging inequalities (RAIs). We develop a theory of RAIs and apply it to the analysis of several important multi-agent algorithms recently proposed in the literature

Control Theory in Engineering

The subject matter of this book ranges from new control design methods to control theory applications in electrical and mechanical engineering and computers. The book covers certain aspects of control theory, including new methodologies, techniques, and applications. It promotes control theory in practical applications of these engineering domains and shows the way to disseminate researchers’ contributions in the field. This project presents applications that improve the properties and performance of control systems in analysis and design using a higher technical level of scientific attainment. The authors have included worked examples and case studies resulting from their research in the field. Readers will benefit from new solutions and answers to questions related to the emerging realm of control theory in engineering applications and its implementation

The Political Economy of Corporate Governance Change in Bulgaria: Washington Consensus, Primitive Accumulation of Capital, and Catching-Up in the 1990

This study examines three key determinants of corporate governance change in Bulgaria: the Washington Consensus policy, primitive accumulation of capital forces, and 'catching-up' factors. The study reveals that in the early transition (1989-96) primitive capital accumulation prevailed over the Washington Consensus impact on corporate governance transformation while since 1997 Washington Consensus has been in the process of becoming the decisive factor for institutional change. The emerging corporate governance system has been neither Anglo-American (market based) nor bank-based, but rather a 'crony' relationship-based one. The striking features of this system are as follows: (i) a dual enterprise sector, (ii) ownership heterogeneity; (iii) fragile capital markets; (iv) pervasive banks lending behavior; (v) globalization factors discretion. The challenge to policy-makers in Bulgaria is how to design institutions for 'catching-up' that would curb both managerial and globalization factors discretion.

Использование сорбента на основе сверхсшитого стирол-дивинилбензольного сополимера с иммобилизованным ЛПС-селективным лигандом при гемоперфузии для лечения пациентов с септическим шоком

Aim of the study: to evaluate safety and feasibility of clinical use of an extracorporeal blood adsorber based on a hypercrosslinked styrene-divinylbenzene copolymer with immobilized lipopolysaccharide (LPS)-selective ligand designed to remove endotoxins from the bloodstream to treat patients with septic shock.Materials and methods. Nine patients (mean age 58 years, 5 men and 4 women, initial median APACHE II score 28 points, SOFA score 10 points) with confirmed Gram-negative bacterial infection and septic shock (SEPSIS-3, 2016) underwent LPS-selective hemoperfusion using an extracorporeal blood adsorber based on a hypercrosslinked styrene divinylbenzene copolymer with immobilized LPS-selective ligand for 6 hours, followed by prolonged veno-venous hemodiafiltration. Before the hemoperfusion (day 0), immediately after it, a day after its end (day 1) and once daily for the next 4 days we assessed the hemodynamic parameters, oxygenation, organ failure signs, white blood cell count, procalcitonin, C-reactive protein, clinical chemistry parameters.Results. Hemoperfusion resulted in a rapid decrease in the endotoxin activity (EAA test), more than twofold decrease in plasma level of interleukin-1 (immunoenzyme test). At the end of the procedure, the plasma lactate level decreased to normal values by day 3, pH values restored to normal within 1-2 days. The noradrenaline requirement rapidly decreased and completely resolved within 1-3 days, which corresponded to the restoration of mean blood pressure values. The values of the PaO2/FiO2 oxygenation index increased significantly after 24 hours, and the median values of 300 were maintained during all subsequent days of observation. During the first day, hemoperfudion caused a rapid decline in APACHE II and SOFA scores, while acute renal failure (estimated by urea and creatinine levels) resolved gradually by day 5. The hemoperfusion did not affect the unchanged coagulation parameters (prothrombin, fibrinogen, INR). During the first day after the procedure, we observed a short-term 1.5-fold decrease in platelet count with subsequent recovery by days 2-3 in most patients. Two patients, both differing from the rest of the patients prior to treatment in the highest values of APACHE II score (above 30), APTT (above 40) and endotoxin activity in EAA test (above 0.9), died on the 4th and 8th days of treatment. The rest of the patients survived, with clinical improvement in all parameters.Conclusion. The results of extracorporeal blood purification using Efferon LPS extracorporeal blood adsorber indicate a high therapeutic potential of the method and suggest the need for extended clinical trials to assess its clinical efficacy in ICU to reduce the high mortality in patients with septic shock.Цель исследования: оценка безопасности и определение возможности применения гемосорбента на основе сверхсшитого стирол-дивинилбензольного сополимера с иммобилизованным липополисахарид (ЛПС)-селективным лигандом, предназначенного для удаления из кровотока эндотоксинов, для лечения пациентов с септическим шоком.Материалы и методы. Девяти пациентам (средний возраст 58 лет, 5 мужчин и 4 женщины, начальные значения медиан для APACHE II 28 баллов, для SOFA 10 баллов) с подтвержденной грам-не-гативной бактериальной инфекцией и септическим шоком (СЕПСИС-3, 2016) проводили ЛПС-селек-тивную гемоперфузию (ЛСГ) с помощью колонки с сорбентом на основе сверхсшитого стирол-дивинилбензольного сополимера с иммобилизованным ЛПС-селективным лигандом в течении 6 часов с последующей продленной вено-венозной гемодиафильтрацией. До ЛСГ (день 0), сразу после нее, через сутки после ее окончания (день 1) и ежедневно на протяжении последующих 4-x суток определяли показатели гемодинамики, оксигенации, органной недостаточности, содержание лейкоцитов, прокальцитонина, С-реактивного белка, биохимические показатели.Результаты. Проведение ЛСГ приводило к быстрому снижению активности эндотоксина (ЕАА тест), более чем двукратному уменьшению содержания интерлейкина-1 (иммуноферментный тест) в плазме крови. По окончании процедуры снижалась концентрация лактата в плазме крови, доходя до нормальных значений на 3-е сутки, восстанавливались до нормальных значения рН на 1-2-е сутки. Потребность в норадреналине быстро снижалась и полностью прекращалась на 1-3-е сутки, что соответствовало восстановлению значений среднего артериального давления. Значения индекса оксигенации PaO2/FiO2 значимо повышались через сутки, значения медианы 300 удерживались на протяжении всех последующих дней наблюдения. Проведение ЛСГ обеспечивало быстрое, в течение первых суток, снижение показателей по шкалам APACHEII и SOFA, в то время как показатели острой почечной недостаточности (содержание мочевины и креатинина) градуально снижались вплоть до нормальных значений к 5- му дню. Проведение ЛСГ не приводило к изменению ненарушенных показателей системы свертывания (протромбина, фибриногена, МНО). В течение первых суток после процедуры наблюдали кратковременное 1,5-кратное снижение содержания тромбоцитов с последующим восстановлением на 2-3-и сутки у большинства пациентов. Двое пациентов, отличающихся до лечения от остальных пациентов наиболее высокими значениями оценки по шкале APACHEII (выше 30), по показателям АЧТВ (свыше 40) и значениям акивности эндотоксина в тесте ЕАА (свыше 0,9), погибли на 4-й и 8-й дни лечения. Остальные пациенты живы, с клиническим улучшением по всем показателям.Заключение. Результаты проведения экстракорпорального очищения крови с помощью колонки с сорбентом на основе сверхсшитого стирол-дивинилбензольного сополимера с иммобилизованным ЛПС-селективным лигандом указывают на высокий терапевтический потенциал примененного метода и обосновывают необходимость проведения расширенных клинических исследований с целью оценки эффективности его использования в клинической практике ОРИТ для снижения высокой летальности пациентов с септическим шоком

Growth in Transition: What We Know, What We Don't, and What We Should

This essay surveys macroeconomic issues that marked the transition from centrally planned to market economy in Central and Eastern European and former Soviet Union countries. We first establish a set of stylized facts of the transition so far, namely: (1) output fell, (2) capital shrank, (3) labor moved, (4) trade reoriented, (5) the structure changed, (6) institutions collapsed, and (7) transition costs. We then critically survey the theoretical literature on transition, discussing various explanations for the initial output fall as well as medium term issues, such as optimal speed of transition, disorganization, institutions and sectoral reallocation as a source of output dynamics. Last, we review the empirical literature to assess how well it translates the theoretical models and explains the stylized facts. The essay concludes with a succinct list of suggestions for future research.http://deepblue.lib.umich.edu/bitstream/2027.42/39854/3/wp470.pd