The Dynamics of Cumulative Step Size Adaptation on the Ellipsoid Model

2016 ◽  
Vol 24 (1) ◽  
pp. 25-57 ◽  
Author(s):  
Hans-Georg Beyer ◽  
Michael Hellwig
Keyword(s):  
Steady State ◽  
Linear Convergence ◽  
Search Space ◽  
Mean Value ◽  
Superior Performance ◽  
Noisy Environments ◽  
Step Size ◽  
State Behavior ◽  
Closed Form Solutions ◽  
The Mean

The behavior of the [Formula: see text]-Evolution Strategy (ES) with cumulative step size adaptation (CSA) on the ellipsoid model is investigated using dynamic systems analysis. At first a nonlinear system of difference equations is derived that describes the mean value evolution of the ES. This system is successively simplified to finally allow for deriving closed-form solutions of the steady state behavior in the asymptotic limit case of large search space dimensions. It is shown that the system exhibits linear convergence order. The steady state mutation strength is calculated, and it is shown that compared to standard settings in [Formula: see text] self-adaptive ESs, the CSA control rule allows for an approximately [Formula: see text]-fold larger mutation strength. This explains the superior performance of the CSA in non-noisy environments. The results are used to derive a formula for the expected running time. Conclusions regarding the choice of the cumulation parameter c and the damping constant D are drawn.

scholarly journals Analysis of the (μ/μI,λ)-CSA-ES with Repair by Projection Applied to a Conically Constrained Problem

2020 ◽  
Vol 28 (3) ◽  
pp. 463-488 ◽  
Author(s):  
Patrick Spettel ◽  
Hans-Georg Beyer
Keyword(s):  
Steady State ◽  
Linear Optimization ◽  
Deep Understanding ◽  
Mean Value ◽  
Step Size ◽  
Analytical Treatment ◽  
Constrained Problems ◽  
Iterative System ◽  
The Mean ◽  
Theoretical Analyses

Theoretical analyses of evolution strategies are indispensable for gaining a deep understanding of their inner workings. For constrained problems, rather simple problems are of interest in the current research. This work presents a theoretical analysis of a multi-recombinative evolution strategy with cumulative step size adaptation applied to a conically constrained linear optimization problem. The state of the strategy is modeled by random variables and a stochastic iterative mapping is introduced. For the analytical treatment, fluctuations are neglected and the mean value iterative system is considered. Nonlinear difference equations are derived based on one-generation progress rates. Based on that, expressions for the steady state of the mean value iterative system are derived. By comparison with real algorithm runs, it is shown that for the considered assumptions, the theoretical derivations are able to predict the dynamics and the steady state values of the real runs.

Sickle cell crisis as evaluated from measurements of hydroxybutyrate dehydrogenase and myoglobin in plasma.

1981 ◽  
Vol 27 (2) ◽  
pp. 314-316 ◽  
Author(s):  
E F Roth ◽  
P A Bardfeld ◽  
S J Goldsmith ◽  
E Radel ◽  
J C Williams
Keyword(s):  
Steady State ◽  
Sickle Cell Disease ◽  
Sickle Cell ◽  
High Specificity ◽  
Mean Value ◽  
Cell Disease ◽  
Sickle Cell Crisis ◽  
The Mean ◽  
Low Sensitivity ◽  
Sickle Cell Crises

Abstract Data on plasma hydroxybutyrate dehydrogenase activity (I) and myoglobin concentration were used to evaluate painful sickle cell crises. I was increased during non-crisis steady state in patients with sickle cell disease as compared to normal values (232, SD 79.7 vs 85, SD 33 Sigma units/mL). During crisis, the mean value for I increased further to 379 (SD 139) Sigma units/mL. For 12 patients evaluated both during steady state and crisis, there was a mean increase in plasma I of 131% (SD 76%). Repeated determinations of I in sickle cell disease patients during several months while they were in steady state showed that baseline I varied by no more than 20% from the mean. Plasma myoglobin in patients with sickle cell disease was not above normal, but during crisis 21 of 39 patients tested had increased plasma myoglobin concentrations. Our data suggest that I may be a useful indicator of sickle cell crisis when the patient's own baseline value is available for comparison. Plasma myoglobin measurements give evidence of muscle damage during crisis with high specificity but low sensitivity.

scholarly journals Advanced Variable Step Size Incremental Conductance MPPT for a Standalone PV System Utilizing a GA-Tuned PID Controller

Energies ◽  
2020 ◽  
Vol 13 (16) ◽  
pp. 4153 ◽  
Author(s):  
Adeel Feroz Mirza ◽  
Majad Mansoor ◽  
Qiang Ling ◽  
Muhammad Imran Khan ◽  
Omar M. Aldossary
Keyword(s):  
Steady State ◽  
Pid Controller ◽  
Superior Performance ◽  
Variable Step Size ◽  
Step Size ◽  
Pv System ◽  
Fast Tracking ◽  
Point Tracking ◽  
Incremental Conductance ◽  
Variable Step

In this article, a novel maximum power point tracking (MPPT) controller for the fast-changing irradiance of photovoltaic (PV) systems is introduced. Our technique utilizes a modified incremental conductance (IC) algorithm for the efficient and fast tracking of MPP. The proposed system has a simple implementation, fast tracking, and achieved steady-state oscillation. Traditional MPPT techniques use a tradeoff between steady-state and transition-state parameters. The shortfalls of various techniques are studied. A comprehensive comparative study is done to test various existing techniques against the proposed technique. The common parameters discussed in this study are fast convergence, efficiency, and reduced oscillations. The proposed method successfully addresses these issues and improves the results significantly by using a proportional integral deferential (PID) controller with a genetic algorithm (GA) to predict the variable step size of the IC-based MPPT technique. The system is designed and tested against the perturbation and observation (P&O)-based MPPT technique. Our technique effectively detects global maxima (GM) for fast-changing irradiance due to the adopted GA-based tuning of the controller. A comparative analysis of the results proves the superior performance and capabilities to track GM in fewer iterations.

Some explicit formulas for the steady-state behavior of the queue with semi-Markovian service times

1977 ◽  
Vol 9 (1) ◽  
pp. 141-157 ◽  
Author(s):  
Marcel F. Neuts
Keyword(s):  
Steady State ◽  
Continuous Time ◽  
Explicit Formulas ◽  
State Behavior ◽  
Virtual Waiting Time ◽  
Poisson Arrivals ◽  
Queue Lengths ◽  
The Mean ◽  
Service Times ◽  
Recursive Matrix

This paper discusses a number of explicit formulas for the steady-state features of the queue with Poisson arrivals in groups of random sizes and semi-Markovian service times. Computationally useful formulas for the expected duration of the various busy periods, for the mean numbers of customers served during them, as well as for the lower order moments of the queue lengths, both in discrete and in continuous time, and of the virtual waiting time are obtained. The formulas are recursive matrix expressions, which generalize the analogous but much simpler results for the classical M/G/1 model.

Some explicit formulas for the steady-state behavior of the queue with semi-Markovian service times

1977 ◽  
Vol 9 (01) ◽  
pp. 141-157 ◽  
Author(s):  
Marcel F. Neuts
Keyword(s):  
Steady State ◽  
Continuous Time ◽  
Explicit Formulas ◽  
State Behavior ◽  
Virtual Waiting Time ◽  
Poisson Arrivals ◽  
Queue Lengths ◽  
The Mean ◽  
Service Times ◽  
Recursive Matrix

This paper discusses a number of explicit formulas for the steady-state features of the queue with Poisson arrivals in groups of random sizes and semi-Markovian service times. Computationally useful formulas for the expected duration of the various busy periods, for the mean numbers of customers served during them, as well as for the lower order moments of the queue lengths, both in discrete and in continuous time, and of the virtual waiting time are obtained. The formulas are recursive matrix expressions, which generalize the analogous but much simpler results for the classical M/G/1 model.

A probabilistic analogue of the mean value theorem and its applications to reliability theory

1999 ◽  
Vol 36 (3) ◽  
pp. 706-719 ◽  
Author(s):  
Antonio Di Crescenzo
Keyword(s):  
Steady State ◽  
Order Statistic ◽  
Arbitrary Order ◽  
Queueing Systems ◽  
Mean Value ◽  
Reliability Theory ◽  
Maintenance Cost ◽  
Mean Value Theorem ◽  
Probabilistic Generalization ◽  
The Mean

In a similar spirit to the probabilistic generalization of Taylor's theorem by Massey and Whitt [13], we give a probabilistic analogue of the mean value theorem. The latter is shown to be useful in various contexts of reliability theory. In particular, we provide various applications to the evaluation of the mean total profits of devices having random lifetimes, to the mean total-time-on-test at an arbitrary order statistic of a random sample of lifetimes, and to the mean maintenance cost for the second room of queueing systems in steady state characterized by two serial waiting rooms.

Diffusing capacity of the lung in pulmonary emphysema

1964 ◽  
Vol 19 (5) ◽  
pp. 981-989 ◽  
Author(s):  
Stephen M. Ayres ◽  
Meta E. Buehler ◽  
Ruth G. Armstrong
Keyword(s):  
Gas Chromatography ◽  
Carbon Monoxide ◽  
Steady State ◽  
Body Size ◽  
Normal Subjects ◽  
Mean Value ◽  
Diffusing Capacity ◽  
Common Cause ◽  
Abnormal Distribution ◽  
The Mean

Steady-state CO and O2 methods for measuring pulmonary diffusing capacity may be affected by abnormal distribution of inspired gas relative to perfusion. These methods frequently fail to separate abnormalities in diffusion from abnormalities in distribution in patients with obstructive emphysema. A rebreathing CO method has been developed which, in theory, is less sensitive to inequalities in distribution. The DlCO by this method in 41 normal subjects averaged 20.8 ± 8.6 ml/min mm Hg and was closely correlated with body size and lung volume. Only 3 of 25 patients with obstructive emphysema had a DlCO less than the 95% confidence level although the mean value for all of the patients (16.8 ml/min mm Hg) was significantly lower than that of the normal group. It is concluded that loss of diffusing surface is not a common cause of oxyhemoglobin desaturation in obstructive emphysema. diffusion; carbon monoxide; ventilation-to-perfusion; gas chromatography Submitted on December 27, 1963

scholarly journals A Smoothed Algorithm with Convergence Analysis under Generalized Maximum Correntropy Criteria in Impulsive Interference

Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1099
Author(s):  
Hua Qu ◽  
Youwei Shi ◽  
Jihong Zhao
Keyword(s):  
Steady State ◽  
Impulsive Noise ◽  
Weighted Average ◽  
Variable Step Size ◽  
Gradient Vector ◽  
Step Size ◽  
State Behavior ◽  
Mean Square Stability ◽  
Variable Step ◽  
Steady State Behavior

The generalized maximum correntropy criterion (GMCC) algorithm is computationally simple and robust against impulsive noise but it suffers from slow convergence speed as it is derived and based on stochastic gradient, which only use the current data sample. In order to deal with this issue, a smoothed GMCC algorithm (SGMCC) is proposed. In the SGMCC algorithm, instead of taking the exponential weighted average of gradient vector to approximate the expectation of the gradient vector, we take the exponential weighted average of the variable step-size so that the SGMCC algorithm can be viewed as a sign GMCC algorithm with smoothed variable step-size. Moreover, convergence performance analyses are derived in terms of variable step-size, mean-square stability and steady-state behavior to demonstrate the robustness of the proposed algorithm. At last, simulation comparisons show that the proposed algorithm is robust against impulsive noise and converges fast with lower computational complexity. Also, for the steady-state behavior, simulation results verify that the simulated value matches well with the theoretical one.

FRACTAL LIMIT DISTRIBUTIONS IN RANDOM TRANSPORTS

Fractals ◽  
1996 ◽  
Vol 04 (03) ◽  
pp. 257-264 ◽  
Author(s):  
HIDEKI TAKAYASU ◽  
TAKUO KAWAKAMI ◽  
Y. -H. TAGUCHI ◽  
TOMOO KATSUYAMA
Keyword(s):  
Steady State ◽  
Transport Model ◽  
Mean Value ◽  
Symmetric Case ◽  
Continuous Change ◽  
Steady State Distribution ◽  
State Distribution ◽  
Fluid Turbulence ◽  
Scalar Quantity ◽  
The Mean

We analyze a random transport model of a scalar quantity on a discrete space-time. By changing a parameter which is a portion of the quantity transported at a time, we observe a continuous change of steady-state distribution of fluctuations from Gaussian to a power-law when the mean value of the scalar quantity is not zero. In the symmetric case with zero mean, the steady-state converges either to a trivial no fluctuation state or to a Lorentzian fluctuation state with diverging variance independent of the parameter. We discuss a possible origin of the intermittent behaviors of fully-developed fluid turbulence as an application.

A Computational Fluid Dynamics Study of Propulsion Due to the Orientation Effects of Swimmer’s Hand

2013 ◽  
Vol 29 (6) ◽  
pp. 817-823 ◽  
Author(s):  
Milda Bilinauskaite ◽  
Vishveshwar R. Mantha ◽  
Abel I. Rouboa ◽  
Pranas Ziliukas ◽  
António J. Silva
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Steady State ◽  
Angle Of Attack ◽  
Mean Value ◽  
Hydrodynamic Characteristics ◽  
Front Crawl ◽  
Hand Model ◽  
The Mean ◽  
Drag And Lift

The aim of the article is to determine the hydrodynamic characteristics of a swimmer’s scanned hand model for various possible combinations of both the angle of attack and the sweepback angle, simulating separate underwater arm stroke phases of front crawl swimming. An actual swimmer’s hand with thumb adducted was scanned using an Artec L 3D scanner. ANSYS Fluent code was applied for carrying out steady-state computational fluid dynamics (CFD) analysis. The hand model was positioned in nine different positions corresponding to the swimmer’s hand orientations (angle of attack and sweepback angle) and velocities observed during the underwater hand stroke of front crawl. Hydrodynamic forces and coefficients were calculated. Results showed significantly higher drag coefficient values in the pull phase, when compared with previous studies under a steady-state flow condition. The mean value of the ratio of drag and lift coefficients was 2.67 ± 2.3 in underwater phases. The mean value of the ratio of drag and lift forces was 2.73 ± 2.4 in underwater phases. Moreover, hydrodynamic coefficients were not almost constant throughout different flow velocities, and variation was observed for different hand positions corresponding to different stroke phases. The current study suggests that the realistic variation of both the orientation angles influenced higher values of drag, lift and resultant coefficients and forces.

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