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Optimization for Software Implementation of Fractional Calculus Numerical Methods in an Embedded System.

ABSTRACT: In this article, some practical software optimization methods for implementations of fractional order backward difference, sum, and differintegral operator based on Grünwald-Letnikov definition are presented. These numerical algorithms are of great interest in the context of the evaluation of fractional-order differential equations in embedded systems, due to their more convenient form compared to Caputo and Riemann-Liouville definitions or Laplace transforms, based on the discrete convolution operation. A well-known difficulty relates to the non-locality of the operator, implying continually increasing numbers of processed samples, which may reach the limits of available memory or lead to exceeding the desired computation time. In the study presented here, several promising software optimization techniques were analyzed and tested in the evaluation of the variable fractional-order backward difference and derivative on two different Arm^® Cortex^®-M architectures. Reductions in computation times of up to 75% and 87% were achieved compared to the initial implementation, depending on the type of Arm^® core.

SUBMITTER: Matusiak M

PROVIDER: S-EPMC7517086 | biostudies-literature | 2020 May

REPOSITORIES: biostudies-literature

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Optimization for Software Implementation of Fractional Calculus Numerical Methods in an Embedded System.

Matusiak Mariusz M

Entropy (Basel, Switzerland) 20200518 5

In this article, some practical software optimization methods for implementations of fractional order backward difference, sum, and differintegral operator based on Grünwald-Letnikov definition are presented. These numerical algorithms are of great interest in the context of the evaluation of fractional-order differential equations in embedded systems, due to their more convenient form compared to Caputo and Riemann-Liouville definitions or Laplace transforms, based on the discrete convolution o ...[more]

PMID: 33286338

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Project description:BackgroundPretreatments are one of the main bottlenecks for the lignocellulose conversion process and the search for cheaper and effective pretreatment methodologies for each biomass is a complex but fundamental task. Here, we used a 2ν5-1 fractional factorial design (FFD) to optimize five pretreatment variables: milling time, temperature, double treatment, chemical concentration, and pretreatment time in acid-alkali (EA) and acid-organosolv (EO) pretreatments, applied to elephant grass leaves.ResultsFFD allowed optimization of the pretreatment conditions using a reduced number of experiments and allowed the identification of secondary interactions between the factors. FFD showed that the temperature can be kept at its lower level and that the first acid step can be eliminated in both pretreatments, without significant losses to enzymatic hydrolysis. EA resulted in the highest release of reducing sugars (maximum of 205 mg/g substrate in comparison to 152 mg/g in EO and 40 mg/g in the untreated sample), using the following conditions in the alkali step: [NaOH] = 4.5% w/v; 85 °C and 100 min after ball milling the sample. The factors statistically significant (P < 0.05) in EA pretreatment were NaOH concentration, which contributes to improved hydrolysis by lignin and silica removal, and the milling time, which has a mechanical effect. For EO samples, the statistically significant factors to improved hydrolysis were ethanol and catalyst concentrations, which are both correlated to higher cellulose amounts in the pretreated substrates. The catalyst is also correlated to lignin removal. The detailed characterization of the main hemicellulosic sugars in the solids after pretreatments revealed their distinct recalcitrance: glucose was typically more recalcitrant than xylose and arabinose, which could be almost completely removed under specific pretreatments. In EA samples, the removal of hemicellulose derivatives was very dependent on the acid step, especially arabinose removal.ConclusionThe results presented herewith contribute to the development of more efficient and viable pretreatments to produce cellulosic ethanol from grass biomasses, saving time, costs and energy. They also facilitate the design of enzymatic cocktails and a more appropriate use of the sugars contained in the pretreatment liquors, by establishing the key recalcitrant polymers in the solids resulting from each processing step.

Dataset Information

Optimization for Software Implementation of Fractional Calculus Numerical Methods in an Embedded System.

Publications

Optimization for Software Implementation of Fractional Calculus Numerical Methods in an Embedded System.

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