scholarly journals On the limit distribution of the normality measure of random binary sequences

2014 ◽  
Vol 46 (5) ◽  
pp. 968-980
Author(s):  
Christoph Aistleitner
Keyword(s):  
Limit Distribution ◽  
Binary Sequences ◽  
Normality Measure

Ensembles of optimal binary sequences of length 22n

2020 ◽  
Vol 1679 ◽  
pp. 042011
Author(s):  
A N Leukhin ◽  
V I Bezrodnyi ◽  
A A Voronin ◽  
A S Merzlyakov ◽  
N V Parsaev
Keyword(s):  
Binary Sequences

On the first zero of an empirical characteristic function

1991 ◽  
Vol 28 (3) ◽  
pp. 593-601 ◽  
Author(s):  
H. U. Bräker ◽  
J. Hüsler
Keyword(s):  
Characteristic Function ◽  
Limit Distribution ◽  
Random Variable ◽  
Empirical Characteristic Function ◽  
The Real ◽  
Exponential Decrease ◽  
Characteristic Process

We deal with the distribution of the first zero Rn of the real part of the empirical characteristic process related to a random variable X. Depending on the behaviour of the theoretical real part of the underlying characteristic function, cases with a slow exponential decrease to zero are considered. We derive the limit distribution of Rn in this case, which clarifies some recent results on Rn in relation to the behaviour of the characteristic function.

scholarly journals Non-local Solvable Birth–Death Processes

2021 ◽  
Author(s):  
Giacomo Ascione ◽  
Nikolai Leonenko ◽  
Enrica Pirozzi
Keyword(s):  
Differential Equations ◽  
Orthogonal Polynomials ◽  
Limit Distribution ◽  
Spectral Decomposition ◽  
Strong Solutions ◽  
Stochastic Representation ◽  
Discrete Approximations ◽  
Local Difference ◽  
Non Local ◽  
Birth Death

AbstractIn this paper, we study strong solutions of some non-local difference–differential equations linked to a class of birth–death processes arising as discrete approximations of Pearson diffusions by means of a spectral decomposition in terms of orthogonal polynomials and eigenfunctions of some non-local derivatives. Moreover, we give a stochastic representation of such solutions in terms of time-changed birth–death processes and study their invariant and their limit distribution. Finally, we describe the correlation structure of the aforementioned time-changed birth–death processes.

scholarly journals Confinement, partial sleep deprivation and defined physical activity–influence on cardiorespiratory regulation and capacity

2021 ◽  
Author(s):  
Jessica Koschate ◽  
Uwe Drescher ◽  
Uwe Hoffmann
Keyword(s):  
Physical Activity ◽  
Cardiorespiratory Fitness ◽  
Space Mission ◽  
Cycle Ergometer ◽  
Work Rate ◽  
Binary Sequences ◽  
Kinetics Parameters ◽  
Slow Heart Rate ◽  
Partial Sleep Deprivation ◽  
Sleep Schedule

Abstract Introduction Adequate cardiorespiratory fitness is of utmost importance during spaceflight and should be assessable via moderate work rate intensities, e.g., using kinetics parameters. The combination of restricted sleep, and defined physical exercise during a 45-day simulated space mission is expected to slow heart rate (HR) kinetics without changes in oxygen uptake ($${\dot{\text{V}}\text{O}}_{{2}}$$ V ˙ O 2 ) kinetics. Methods Overall, 14 crew members (9 males, 5 females, 37 ± 7 yrs, 23.4 ± 3.5 kg m−2) simulated a 45-d-mission to an asteroid. During the mission, the sleep schedule included 5 nights of 5 h and 2 nights of 8 h sleep. The crew members were tested on a cycle ergometer, using pseudo-random binary sequences, changing between 30 and 80 W on day 8 before (MD-8), day 22 (MD22) and 42 (MD42) after the beginning and day 4 (MD + 4) following the end of the mission. Kinetics information was assessed using the maxima of cross-correlation functions (CCFmax). Higher CCFmax indicates faster responses. Results CCFmax(HR) was significantly (p = 0.008) slower at MD-8 (0.30 ± 0.06) compared with MD22 (0.36 ± 0.06), MD42 (0.38 ± 0.06) and MD + 4 (0.35 ± 0.06). Mean HR values during the different work rate steps were higher at MD-8 and MD + 4 compared to MD22 and MD42 (p < 0.001). Discussion The physical training during the mission accelerated HR kinetics, but had no impact on mean HR values post mission. Thus, HR kinetics seem to be sensitive to changes in cardiorespiratory fitness and may be a valuable parameter to monitor fitness. Kinetics and capacities adapt independently in response to confinement in combination with defined physical activity and sleep.

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