Self-similarity of rogue wave generation in gyrotrons: Beyond the Peregrine breather

Within the framework of numerical simulations, we study the gyrotron dynamics under conditions of a significant excess of the operating current over the starting value, when the generation of electromagnetic pulses with anomalously large amplitudes ("rogue waves") are realized. We demonstrate that the relation between peak power and duration of rogue waves is self-similar, but does not reproduce the one characteristic for Peregrine breathers. Remarkably, the discovered self-similar relation corresponds to the exponential nonlinearity of an equivalent Schr\"odinger-like evolution equation. This interpretation can be used as a theoretical basis for explaining the giant amplitudes of gyrotron rogue waves

БАЙЕСОВСКИЙ ПОДХОД К ПОВЫШЕНИЮ ДОСТОВЕРНОСТИ КОНТРОЛЯ КАЧЕСТВА ВОД

Increased variability and, at the same time, a reduced frequency of selective measurements of controlled indicators of natural waters increase the probability of erroneous evaluation of their quality. The task is to increase the reliability of such an assessment by analyzing arrays of new data in conjunction with data accumulated in previous periods. To do this, a Bayesian approach was modified using the uniformity measure of the combined data. It is shown that in the latter case the combined estimate shifts from the Bayesian one to the maximum likelihood estimate from the newly obtained experimental data, thus "forgetting" the obsolete data. At the same time, the 90% confidence interval, in which the true values of the monitored indicators are concluded, is narrowed, which increases the reliability of the probabilistic assessment of water quality. The proposed approach is illustrated by the example of a universal nonparametric method for estimating the probability of the concentration of a certain pollutant in compliance with the requirements as the most common indicator of water quality. The example is brought to specific numerical values, allowing both to compare the classical and modified Bayesian approach, and to give recommendations on the rational use of the latter. The proposed approach can find wide application in the problems of analysis of statistical quality indicators in various subject areas with a shortage of experimental data.Keywords: water quality control, probabilistic estimation, Bayesian approach, mixture of distributions, maximum likelihood function DOI: http://dx.doi.org/10.15826/analitika.2018.22.3.001(Russian)O.M. Rozental’1, L.N. Aleksandrovskaya2, A.V. Kirillin21Institute of water problems of RAS, ul. Gubkina, 3, Moscow, 125993, Russian Federation 2Moscow Aviation Institute (MAI), Volokolamskoe shosse, 4, Moscow, 125080, Russian FederationПовышенная изменчивость и одновременно – пониженная частота выборочных измерений контролируемых показателей природных вод повышают вероятность ошибочной оценки их качества. В работе решается задача повышения достоверности такой оценки путем анализа массивов новых данных совместно с данными, накопленными в предыдущие периоды. Для этого  была применена модификация байесовского подхода с использованием показателя степени однородности объединяемых данных. Показано, что в последнем случае объединенная оценка смещается по сравнению с байесовской в сторону оценки максимального правдоподобия по вновь полученным экспериментальным данным, «забывая» таким образом устаревшие данные. При этом 90-процентный доверительный интервал, в котором заключены истинные значения контролируемых показателей, сужается, что повышает достоверность вероятностной оценки качества воды. Предложенный подход проиллюстрирован на примере универсального непараметрического метода оценки вероятности соответствия концентрации некоторого загрязняющего вещества предъявляемым требованиям, как наиболее общего показателя качества воды. Пример доведен до конкретных числовых значений, позволяющих как провести сравнение классического и модифицированного байесовского подхода, так и выдать рекомендации по рациональному использованию последнего. Предложенный подход может найти широкое применение в задачах анализа статистических показателей качества в различных предметных областях при дефиците экспериментальных данных.Ключевые слова: контроль качества вод, вероятностная оценка, байесовский подход, смесь распределений, функция максимального правдоподобияDOI: http://dx.doi.org/10.15826/analitika.2018.22.3.00

Bayesian approach to improve the reliability of control of water quality

Increased variability and, at the same time, a reduced frequency of selective measurements of controlled indicators of natural waters increase the probability of erroneous evaluation of their quality. The task is to increase the reliability of such an assessment by analyzing arrays of new data in conjunction with data accumulated in previous periods. To do this, a Bayesian approach was modified using the uniformity measure of the combined data. It is shown that in the latter case the combined estimate shifts from the Bayesian one to the maximum likelihood estimate from the newly obtained experimental data, thus "forgetting" the obsolete data. At the same time, the 90% confidence interval, in which the true values of the monitored indicators are concluded, is narrowed, which increases the reliability of the probabilistic assessment of water quality. The proposed approach is illustrated by the example of a universal nonparametric method for estimating the probability of the concentration of a certain pollutant in compliance with the requirements as the most common indicator of water quality. The example is brought to specific numerical values, allowing both to compare the classical and modified Bayesian approach, and to give recommendations on the rational use of the latter. The proposed approach can find wide application in the problems of analysis of statistical quality indicators in various subject areas with a shortage of experimental data.Повышенная изменчивость и одновременно - пониженная частота выборочных измерений контролируемых показателей природных вод повышают вероятность ошибочной оценки их качества. В работе решается задача повышения достоверности такой оценки путем анализа массивов новых данных совместно с данными, накопленными в предыдущие периоды. Для этого была применена модификация байесовского подхода с использованием показателя степени однородности объединяемых данных. Показано, что в последнем случае объединенная оценка смещается по сравнению с байесовской в сторону оценки максимального правдоподобия по вновь полученным экспериментальным данным, «забывая» таким образом устаревшие данные. При этом 90-процентный доверительный интервал, в котором заключены истинные значения контролируемых показателей, сужается, что повышает достоверность вероятностной оценки качества воды. Предложенный подход проиллюстрирован на примере универсального непараметрического метода оценки вероятности соответствия концентрации некоторого загрязняющего вещества предъявляемым требованиям, как наиболее общего показателя качества воды. Пример доведен до конкретных числовых значений, позволяющих как провести сравнение классического и модифицированного байесовского подхода, так и выдать рекомендации по рациональному использованию последнего. Предложенный подход может найти широкое применение в задачах анализа статистических показателей качества в различных предметных областях при дефиците экспериментальных данных

Mechanisms explaining transitions between tonic and phasic firing in neuronal populations as predicted by a low dimensional firing rate model

Several firing patterns experimentally observed in neural populations have been successfully correlated to animal behavior. Population bursting, hereby regarded as a period of high firing rate followed by a period of quiescence, is typically observed in groups of neurons during behavior. Biophysical membrane-potential models of single cell bursting involve at least three equations. Extending such models to study the collective behavior of neural populations involves thousands of equations and can be very expensive computationally. For this reason, low dimensional population models that capture biophysical aspects of networks are needed. \noindent The present paper uses a firing-rate model to study mechanisms that trigger and stop transitions between tonic and phasic population firing. These mechanisms are captured through a two-dimensional system, which can potentially be extended to include interactions between different areas of the nervous system with a small number of equations. The typical behavior of midbrain dopaminergic neurons in the rodent is used as an example to illustrate and interpret our results. \noindent The model presented here can be used as a building block to study interactions between networks of neurons. This theoretical approach may help contextualize and understand the factors involved in regulating burst firing in populations and how it may modulate distinct aspects of behavior.Comment: 25 pages (including references and appendices); 12 figures uploaded as separate file

Longitudinal neuronal organization and coordination in a simple vertebrate: a continuous, semi-quantitative computer model of the central pattern generator for swimming in young frog tadpoles

When frog tadpoles hatch their swimming requires co-ordinated contractions of trunk muscles, driven by motoneurons and controlled by a Central Pattern Generator (CPG). To study this co-ordination we used a 3.5 mm long population model of the young tadpole CPG with continuous distributions of neurons and axon lengths as estimated anatomically. We found that: (1) alternating swimming-type activity fails to self-sustain unless some excitatory interneurons have ascending axons, (2) a rostro-caudal (R-C) gradient in the distribution of excitatory premotor interneurons with short axons is required to obtain the R-C gradient in excitation and resulting progression of motoneuron firing necessary for forward swimming, (3) R-C delays in motoneuron firing decrease if excitatory motoneuron to premotor interneuron synapses are present, (4) these feedback connections and the electrical synapses between motoneurons synchronise motoneuron discharges locally, (5) the above findings are independent of the detailed membrane properties of neurons

The fundamental constants and their variation: observational status and theoretical motivations

This article describes the various experimental bounds on the variation of the fundamental constants of nature. After a discussion on the role of fundamental constants, of their definition and link with metrology, the various constraints on the variation of the fine structure constant, the gravitational, weak and strong interactions couplings and the electron to proton mass ratio are reviewed. This review aims (1) to provide the basics of each measurement, (2) to show as clearly as possible why it constrains a given constant and (3) to point out the underlying hypotheses. Such an investigation is of importance to compare the different results, particularly in view of understanding the recent claims of the detections of a variation of the fine structure constant and of the electron to proton mass ratio in quasar absorption spectra. The theoretical models leading to the prediction of such variation are also reviewed, including Kaluza-Klein theories, string theories and other alternative theories and cosmological implications of these results are discussed. The links with the tests of general relativity are emphasized.Comment: 56 pages, l7 figures, submitted to Rev. Mod. Phy

The contribution of metacognitions and attentional control to decisional procrastination

Earlier research has implicated metacognitions and attentional control in procrastination and self-regulatory failure. This study tested several hypotheses: (1) that metacognitions would be positively correlated with decisional procrastination; (2) that attentional control would be negatively correlated with decisional procrastination; (3) that metacognitions would be negatively correlated with attentional control; and (4) that metacognitions and attentional control would predict decisional procrastination when controlling for negative affect. One hundred and twenty-nine participants completed the Depression Anxiety Stress Scale 21, the Meta-Cognitions Questionnaire 30, the Attentional Control Scale, and the Decisional Procrastination Scale. Significant relationships were found between all three attentional control factors (focusing, shifting, and flexible control of thought) and two metacognitions factors (negative beliefs concerning thoughts about uncontrollability and danger, and cognitive confidence). Results also revealed that decisional procrastination was significantly associated with negative affect, all measured metacognitions factors, and all attentional control factors. In the final step of a hierarchical regression analysis only stress, cognitive confidence, and attention shifting were independent predictors of decisional procrastination. Overall these findings support the hypotheses and are consistent with the Self-Regulatory Executive Function model of psychological dysfunction. The implications of these findings are discussed