scholarly journals Typical dynamics and fluctuation analysis of slow–fast systems driven by fractional Brownian motion

2020 ◽  
pp. 2150030 ◽  
Author(s):  
Solesne Bourguin ◽  
Siragan Gailus ◽  
Konstantinos Spiliopoulos
Keyword(s):  
Slow Component ◽  
Qualitative Difference ◽  
Rates Of Convergence ◽  
Fluctuation Analysis ◽  
Limiting Behavior ◽  
Separation Parameter ◽  
Brownian Noise ◽  
Small Parameters ◽  
Fractional Brownian Noise ◽  
The Relationship

This paper studies typical dynamics and fluctuations for a slow–fast dynamical system perturbed by a small fractional Brownian noise. Based on an ergodic theorem with explicit rates of convergence, which may be of independent interest, we characterize the asymptotic dynamics of the slow component to two orders (i.e. the typical dynamics and the fluctuations). The limiting distribution of the fluctuations turns out to depend upon the manner in which the small-noise parameter is taken to zero relative to the scale-separation parameter. We study also an extension of the original model in which the relationship between the two small parameters leads to a qualitative difference in limiting behavior. The results of this paper provide an approximation, to two orders, to dynamical systems perturbed by small fractional Brownian noise and incorporating multiscale effects.

scholarly journals A Comparative Analysis of Culture Beliefs about Russia’s, Western and Eastern Civilizations among Creative Youth

2021 ◽  
Vol 12 (1) ◽  
pp. 177-197
Author(s):  
V.U. Litvinov ◽  
L.V. Matveeva
Keyword(s):  
Comparative Analysis ◽  
Training Programs ◽  
Qualitative Difference ◽  
Cultural Representations ◽  
Open Questions ◽  
The World ◽  
Important Study ◽  
Moscow City ◽  
The Relationship ◽  
Basic Constituent

Objective. The aim of this research was a comparative analysis of culture beliefs about Russia’s, Eastern and Western civilizations among the youth of Moscow City. Background. Civilization identity is the a basic constituent in forming of individual’s image of the world. Understanding and acceptance of civilization’s cultural particularities helps to save personal and social identity’s stability. But understanding of differences from other civilizations and comparison with them is no less important. Study design. The study examined the relationship between the various components of the cultural representations of civilizations. The presence and nature of the relationship was checked through correlation, qualitative and content analysis. Participants. 200 people (43% of men, 57% of women) from 18 to 2 years old, students of creative universities in Moscow, studying under the training programs for future media workers. Measurements. The study was carried out by the method of questioning, including the associative method, the method of unfinished sentences, closed and open questions. Results. The research’s results proved the hypothesis that culture beliefs of Russia’s youth are qualitatively different for each of the presented civilizations. Besides, the research discovered differences related to gender. Russia’s and Eastern civilizations turned out to be the closest for male according to the research’s results, and for female — Russia’s and Western civilizations respectively. Conclusions. There is a qualitative difference between the cultural ideas of Russian, Western and Eastern civilizations among Russian youth.

Onqelos in Byzantium in the Twelfth and Thirteenth Centuries: The Relationship of R. Samuel of Rossano and R. Meyuhas ben Elijah to the Aramaic Translation

2021 ◽  
Vol 24 (2) ◽  
pp. 231-246
Author(s):  
Jonathan Jacobs
Keyword(s):  
Twelfth Century ◽  
Qualitative Difference ◽  
The Other ◽  
Other Hand ◽  
Explicit Reference ◽  
Relationship Of ◽  
The Relationship

Abstract This study addresses the views of two Byzantine commentators regarding Targum Onqelos: R. Samuel Roshano of the twelfth century and R. Meyuhas ben Elijah of the thirteenth. R. Samuel explicitly refers to the translation forty-six times; R. Meyuhas makes explicit reference to it 104 times. But there are differences between the two commentators in their relation to the Targum: R. Samuel never mentions the name Onqelos, while R. Meyuhas does so explicitly; R. Samuel systematically cites the text of the Targum, while in most cases in R. Meyuhas’ commentary, there is no accurate citation. The qualitative difference is in their respective relationships with the Targum: all of R. Samuel’s references to it signal his agreement; R. Meyuhas, on the other hand, while frequently agreeing with Onqelos, also brings the Targum as one of two possible alternatives and sometimes openly challenges its interpretation.

High Frequency Response of Beams

1975 ◽  
Vol 42 (4) ◽  
pp. 805-808 ◽  
Author(s):  
R. P. Parker ◽  
V. H. Neubert
Keyword(s):  
Experimental Data ◽  
High Frequency ◽  
Rates Of Convergence ◽  
Series Solutions ◽  
Timoshenko Theory ◽  
High Frequency Response ◽  
Lateral Response ◽  
Mode Solution ◽  
Relationship Of ◽  
The Relationship

In developing the relationship of the normal mode solution for a vibrating rod to the pyrotechnic shock problem, a detailed analysis is presented using the Timoshenko theory to obtain the transient lateral response of a cylindrical rod with free ends to a short duration half sine pulse of either moment or shear applied to one end. Two different series solutions are used and the rates of convergence are compared near the boundary. Results are compared with experimental data.

Properties of channels mediating the apamin-insensitive afterhyperpolarization in vagal motoneurons

1995 ◽  
Vol 74 (4) ◽  
pp. 1772-1776 ◽  
Author(s):  
P. Sah
Keyword(s):  
Single Channel ◽  
Slow Component ◽  
Power Spectra ◽  
Corner Frequency ◽  
Equilibrium Potential ◽  
Fluctuation Analysis ◽  
Motor Nucleus ◽  
Small Current ◽  
Calcium Dependent ◽  
Dorsal Motor Nucleus

1. Whole cell recordings were obtained from neurons of the dorsal motor nucleus of the vagus in transverse slices of guinea pig medulla. From a holding potential of -40 mV, short depolarizing voltage steps activated two calcium-dependent potassium currents, Gk(Ca),1 and Gk(Ca),2. 2. Gk(Ca),1 was completely blocked by apamin (100 nM). Gk(Ca),2 was apamin insensitive, voltage independent, and reversed close to the potassium equilibrium potential. 3. Activation of Gk(Ca),2 was associated with an increase in current variance. The channels underlying the slow component were analyzed by stationary and nonstationary fluctuation analysis. Current variance was linearly related to mean current for small current amplitudes but clearly deviated from linearity near the peak of Gk(Ca),2. The predicted single channel conductance was 6.8 +/- 2.5 (SE) pS. Probability of channel opening rose to at most 0.68. The average number of available Gk(Ca),2 channels on vagal neurons was 4,437 +/- 591. 4. Power spectra were constructed from the peak current. Spectra were well fitted with a single Lorentzian with a corner frequency of 72 +/- 7 Hz. The mean burst duration of the channels was 3.8 +/- 0.5 ms. These results indicate that a new type of calcium-activated channel underlies Gk(Ca),2.

scholarly journals Multiscale modelling for tokamak pedestals

2018 ◽  
Vol 84 (2) ◽  
Author(s):  
I. G. Abel ◽  
A. Hallenbert
Keyword(s):  
First Principles ◽  
Detailed Comparison ◽  
Multiscale Approach ◽  
Systems Of Equations ◽  
Line Region ◽  
Open Field Line ◽  
Small Parameters ◽  
The Relationship ◽  
Kinetic Physics ◽  
Current Modelling

Pedestal modelling is crucial to predict the performance of future fusion devices. Current modelling efforts suffer either from a lack of kinetic physics, or an excess of computational complexity. To ameliorate these problems, we take a first-principles multiscale approach to the pedestal. We will present three separate sets of equations, covering the dynamics of edge localised modes (ELMs), the inter-ELM pedestal and pedestal turbulence, respectively. Precisely how these equations should be coupled to each other is covered in detail. This framework is completely self-consistent; it is derived from first principles by means of an asymptotic expansion of the fundamental Vlasov–Landau–Maxwell system in appropriate small parameters. The derivation exploits the narrowness of the pedestal region, the smallness of the thermal gyroradius and the low plasma$\unicode[STIX]{x1D6FD}$(the ratio of thermal to magnetic pressures) typical of current pedestal operation to achieve its simplifications. The relationship between this framework and gyrokinetics is analysed, and possibilities to directly match our systems of equations onto multiscale gyrokinetics are explored. A detailed comparison between our model and other models in the literature is performed. Finally, the potential for matching this framework onto an open-field-line region is briefly discussed.

On modes of long-range dependence

2002 ◽  
Vol 39 (4) ◽  
pp. 882-888 ◽  
Author(s):  
C. C. Heyde
Keyword(s):  
Long Range ◽  
Weak Dependence ◽  
Risky Asset ◽  
Long Range Dependence ◽  
Brownian Noise ◽  
Fractional Brownian Noise

This paper aims at enhancing the understanding of long-range dependence (LRD) by focusing on mechanisms for generating this dependence, namely persistence of signs and/or persistence of magnitudes beyond what can be expected under weak dependence. These concepts are illustrated through a discussion of fractional Brownian noise of index H ∈ (0,1) and it is shown that LRD in signs holds if and only if ½ < H < 1 and LRD in magnitudes if and only if ¾ ≤ H < 1. An application to discrimination between two risky asset finance models, the FATGBM model of Heyde and the multifractal model of Mandelbrot, is given to illustrate the use of the ideas.

scholarly journals Price Appreciation and Roughness Duality in Bitcoin: A Multifractal Analysis

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2088
Author(s):  
Cristiana Vaz ◽  
Rui Pascoal ◽  
Helder Sebastião
Keyword(s):  
Fluctuation Analysis ◽  
Informational Efficiency ◽  
Comprehensive Overview ◽  
Multifractal Detrended Fluctuation Analysis ◽  
Long Range Correlations ◽  
The Public ◽  
Long Run ◽  
Short Run ◽  
The Relationship

Since its launch in 2009, bitcoin has thrived, attracting the attention of investors, regulators, academia, and the public in general. Its price dynamics, characterized by extreme volatility, severe jumps, and impressive long-term appreciation, suggest that bitcoin is a new digital asset. This study presents a comprehensive overview of the fractality of bitcoin in a high-frequency framework, namely by applying Multifractal Detrended Fluctuation Analysis (MF-DFA) and a Multifractal Regime Detecting Method (MRDM) to Bitstamp 1 min bitcoin returns from January 2013 to July 2020. The results suggest that bitcoin is multifractal, with smaller and larger fluctuations being persistent and anti-persistent, respectively. Multifractality comes from significant long-range correlations, which cast some doubts on the informational efficiency at this frequency, but mainly comes from fat-tails, which highlights the significant risks undertaken by investors in this market. Our most important result is that the degree and richness of multifractality is time-varying and increased after 2017, when volumes and prices experienced an explosive behaviour. This complexity puts into perspective the duality of bitcoin: while it is characterized by long-run attractiveness and increasing valuation, it also has a high short-run instability. Hence, this study provides some empirical evidence supporting the relationship between these two observable features.

scholarly journals Proof Theory and Computational Analysis

1997 ◽  
Vol 4 (30) ◽  
Author(s):  
Ulrich Kohlenbach
Keyword(s):  
Proof Theory ◽  
Computational Analysis ◽  
Numerical Data ◽  
Expressive Power ◽  
Rates Of Convergence ◽  
Uniform Bounds ◽  
Survey Paper ◽  
Constructive Proofs ◽  
Polynomial Bounds ◽  
The Relationship

In this survey paper we start with a discussion how functionals of finite type can be used for the proof-theoretic extraction of numerical data (e.g. effective<br />uniform bounds and rates of convergence) from non-constructive proofs in numerical analysis. We focus on the case where the extractability of polynomial bounds is guaranteed.<br />This leads to the concept of hereditarily polynomial bounded analysis (PBA). We indicate the mathematical range of PBA which turns out to be surprisingly large. Finally we discuss the relationship between PBA and so-called feasible analysis<br />FA. It turns out that both frameworks are incomparable. We argue in favor of the thesis that PBA offers the more useful approach for the purpose of extracting mathematically interesting bounds from proofs. In a sequel of appendices to this paper we indicate the expressive power of PBA.

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