An Algorithm for the Automatisation of Pseudo Reductions of PDE Systems Arising from the Uniform-approximation Technique

We construct a wavelet-based almost-sure uniform approximation of fractional Brownian motion (FBM) (Bt(H))_t∈[0,1] of Hurst index H ∈ (0, 1). Our results show that, by Haar wavelets which merely have one vanishing moment, an almost-sure uniform expansion of FBM for H ∈ (0, 1) can be established. The convergence rate of our approximation is derived. We also describe a parallel algorithm that generates sample paths of an FBM efficiently.

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The minimum zone fitting and error evaluation for the logarithmic curve based on geometry optimization approximation algorithm

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331219858855 ◽

2019 ◽

Vol 41 (15) ◽

pp. 4380-4386

Author(s):

Tu Xianping ◽

Lei Xianqing ◽

Ma Wensuo ◽

Wang Xiaoyi ◽

Hu Luqing ◽

...

Keyword(s):

Approximation Algorithm ◽

Evaluation Method ◽

Geometry Optimization ◽

Reference Points ◽

Approximation Technique ◽

Error Evaluation ◽

Iterative Approximation ◽

Logarithmic Curve ◽

Normal Distance ◽

Minimum Zone

The minimum zone fitting and error evaluation for the logarithmic curve has important applications. Based on geometry optimization approximation algorithm whilst considering geometric characteristics of logarithmic curves, a new fitting and error evaluation method for the logarithmic curve is presented. To this end, two feature points, to serve as reference, are chosen either from those located on the least squares logarithmic curve or from amongst measurement points. Four auxiliary points surrounding each of the two reference points are then arranged to resemble vertices of a square. Subsequently, based on these auxiliary points, a series of auxiliary logarithmic curves (16 curves) are constructed, and the normal distance and corresponding range of values between each measurement point and all auxiliary logarithmic curves are calculated. Finally, by means of an iterative approximation technique consisting of comparing, evaluating, and changing reference points; determining new auxiliary points; and constructing corresponding auxiliary logarithmic curves, minimum zone fitting and evaluation of logarithmic curve profile errors are implemented. The example results show that the logarithmic curve can be fitted, and its profile error can be evaluated effectively and precisely using the presented method.

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Robust Cooperative Output Regulation for a Network of Parabolic PDE Systems

IEEE Transactions on Automatic Control ◽

10.1109/tac.2021.3079352 ◽

2021 ◽

pp. 1-1

Author(s):

Joachim Deutscher

Keyword(s):

Output Regulation ◽

Parabolic Pde ◽

Pde Systems ◽

Cooperative Output Regulation

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Approximation of continuous random variables for the evaluation of the reliability parameter of complex stress–strength models

Annals of Operations Research ◽

10.1007/s10479-021-04010-6 ◽

2021 ◽

Author(s):

Alessandro Barbiero ◽

Asmerilda Hitaj

Keyword(s):

Order Approximation ◽

Linear Optimization ◽

Closed Form Solution ◽

Random Variables ◽

Discrete Distribution ◽

Computation Time ◽

Form Solution ◽

Engineering Problem ◽

Approximation Technique ◽

Reliability Parameter

AbstractIn many management science or economic applications, it is common to represent the key uncertain inputs as continuous random variables. However, when analytic techniques fail to provide a closed-form solution to a problem or when one needs to reduce the computational load, it is often necessary to resort to some problem-specific approximation technique or approximate each given continuous probability distribution by a discrete distribution. Many discretization methods have been proposed so far; in this work, we revise the most popular techniques, highlighting their strengths and weaknesses, and empirically investigate their performance through a comparative study applied to a well-known engineering problem, formulated as a stress–strength model, with the aim of weighting up their feasibility and accuracy in recovering the value of the reliability parameter, also with reference to the number of discrete points. The results overall reward a recently introduced method as the best performer, which derives the discrete approximation as the numerical solution of a constrained non-linear optimization, preserving the first two moments of the original distribution. This method provides more accurate results than an ad-hoc first-order approximation technique. However, it is the most computationally demanding as well and the computation time can get even larger than that required by Monte Carlo approximation if the number of discrete points exceeds a certain threshold.

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Treatment of Pediatric Sternotomy Wound Complications: A Minimally Invasive Approach

The Thoracic and Cardiovascular Surgeon ◽

10.1055/s-0040-1722733 ◽

2021 ◽

Author(s):

Taehee Jo ◽

Joon Hur ◽

Eun Key Kim

Keyword(s):

Negative Pressure Wound Therapy ◽

Wound Dehiscence ◽

Surgical Debridement ◽

Wound Complications ◽

Approximation Technique ◽

Invasive Approach ◽

Nonsurgical Management ◽

Single Use ◽

Sternal Wound Infections ◽

Deep Sternal Wound Infections

Abstract Background Pediatric sternal wound complications (SWCs) include sterile wound dehiscence (SWD) and superficial/deep sternal wound infections (SSWI/DSWI), and are generally managed by repetitive debridement and surgical wound approximation. Here, we report a novel nonsurgical management strategy of pediatric sternotomy wound complications, using serial noninvasive wound approximation technique combined with single-use negative pressure wound therapy (PICO) device. Methods Nine children with SWCs were managed by serial approximation with adhesive skin tapes and serial PICO device application. Thorough surgical debridement or surgical approximations were not performed. Results Three patients were clinically diagnosed as SWD, two patients as SSWI, and four patients as DSWI. None of the wounds demonstrated apparent mediastinitis or bone destructions. PICO device was applied at 16.1 days (range: 6–26 days) postoperatively, together with serial wound approximation by skin tapes. The average duration of PICO use was 16.9 days (range: 11–29 days) and the wound approximation was achieved in all patients. None of the patients underwent aggressive surgical debridement or invasive surgical approximation by sutures. Conclusion We report our successful management of selected pediatric SWCs, using serial noninvasive wound approximation technique combined with PICO device.

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