Identification method for a fractional-order system in terms of equivalent dynamic properties.

In this paper, we introduce an efficient method for identifying fractional dynamic systems using extended sparse regression and cross-validation techniques. The former identifies equations that fit the data with varying candidate functions, while the latter determines the optimal equation with the fewest terms yet ensuring accuracy. The identified optimal equation is expected to share the same dynamic properties as the original fractional system. Unlike previous studies focusing on efficiently computing fractional terms, this strategy addresses dynamic analysis from a data perspective. Importantly, in the proposed method, we treat the fractional order as a variable to account for its impact on the dynamic properties of the identified equation. This treatment enables the identified equation to successfully capture dynamic behaviors when the fractional order changes. We validate the effectiveness of the method using three classical fractional-order systems as well as an energy harvesting system. Interestingly, we find that, although the identified equations do not contain non-local terms like the original fractional-order systems, they exhibit the same stochastic P-bifurcation phenomena. In other words, we construct an equivalent equation without memory properties, sharing the dynamic properties with the original system.

New insight into the nano-fluid flow in a channel with tempered fractional operators.

While studying time fractional fluid flow problems it is typical to consider the Caputo derivative, however, these models have limitations including a singular kernel and an infinite waiting time from a random walk perspective. To help remedy this problem, this paper considers a tempered Caputo derivative, giving the system a finite waiting time. Initially, a fast approximation to a generalised tempered diffusion problem is developed using a sum of exponential approximation. The scheme is then proven to be unconditionally stable and convergent. The convergence properties are also tested on a sample solution. The fast scheme is then applied to a system of coupled tempered equations which describes the concentration, temperature and velocity of a nanofluid under the Boussinesq approximation. The most notable finding is that increasing both the fractional and tempering parameters reduces the heat transfer ability of the nanofluid system.

Molecular cloning and characterization of Cinnamoyl-CoA reductase promoter gene from Asarum sieboldii Miq.

Asarum sieboldii Miq., a perennial herb of the family Aristolochiaceae, is widely used in China to treat cold, fever, aphthous stomatitis, toothache, gingivitis, and rheumatoid arthritis. Methyleugenol is the most representative pharmacological constituent of this medicinal herb. Cinnamoyl-CoA reductase (CCR), which has been well known for occupying a critical position in the lignin biosynthesis pathway, is also shared with the biosynthesis of methyleugenol. To better understand the regulatory mechanisms of methyleugenol biosynthesis, a 1530-bp long promoter region of the AsCCR1 gene was isolated. PLACE and PlantCARE analysis affirmed the existence of the core promoter elements such as TATA and CAAT boxes, abiotic stress-responsive cis-regulation elements like abscisic acid-responsive element, G-box, and MBS in the isolated sequence. The histochemical assay suggested that it was a constitutive promoter, highly expressed in the root tissue. Moreover, the region of -200 bp to ATG (start codon) was enough to drive the expression of It GUS gene. Treatments with low temperature and high concentration of gibberellin or abscisic acid demonstrated the abiotic stress-induced expression of the AsCCR1 promoter. Overall, this study revealed the isolation and characterization of the AsCCR1 promoter. Moreover, it also provided a candidate gene for molecular breeding in A. sieboldii to enhance its pharmacological potential.

Physiological, Biochemical and Transcriptomic Analysis of the Aerial Parts (Leaf-Blade and Petiole) of Asarum sieboldii Responding to Drought Stress.

Asarum sieboldii Miq. is a leading economic crop and a traditional medicinal herb in China. Leaf-blade and petiole are the only aerial tissues of A. sieboldii during the vegetative growth, playing a vital role in the accumulation and transportation of biomass energy. They also act as critical indicators of drought in agricultural management, especially for crops having underground stems. During drought, variations in the morphology and gene expression of the leaves and petioles are used to control agricultural irrigation and production. Besides, such stress can also alter the differential gene expression in these tissues. However, little is known about the drought-tolerant character of the aerial parts of A. sieboldii. In this study, we examined the physiological, biochemical and transcriptomic responses to the drought stress in the leaf blades and petioles of A. sieboldii. The molecular mechanism, involving in drought stress response, was elucidated by constructing the cDNA libraries and performing transcriptomic sequencing. Under drought stress, a total of 2912 and 2887 unigenes were differentially expressed in the leaf blade and petiole, respectively. The detection of many transcription factors and functional genes demonstrated that multiple regulatory pathways were involved in drought tolerance. In response to drought, the leaf blade and petiole displayed a general physiological character, a higher SOD and POD activity, a higher MDA content and lower chlorophyll content. Three unigenes encoding POD were up-regulated, which can improve POD activity. Essential oil in petiole was extracted. The relative contents of methyleugenol and safrole in essential oil were increased from 0.01% to 0.05%, and 3.89% to 16.97%, respectively, while myristicin slightly reduced from 24.87% to 21.52%. Additionally, an IGS unigene, involved in eugenol biobiosynthesis, was found up-regulated under drought stress, which was predicated to be responsible for the accumulation of methyleugenol and safrole. Simple sequence repeats (SSRs) were characterized in of A. sieboldii, and a total of 5466 SSRs were identified. Among them, mono-nucleotides were the most abundant repeat units, accounting for 44.09% followed by tri-, tetra-, penta and hexa-nucleotide repeats. Overall, the present work provides a valuable resource for the population genetics studies of A. sieboldii. Besides, it provides much genomic information for the functional dissection of the drought-resistance in A. sieboldii, which will be useful to understand the bio-regulatory mechanisms linked with drought-tolerance to enhance its yield.

Review of fractional epidemic models.

The global impact of corona virus (COVID-19) has been profound, and the public health threat it represents is the most serious seen in a respiratory virus since the 1918 influenza A(H1N1) pandemic. In this paper, we have focused on reviewing the results of epidemiological modelling especially the fractional epidemic model and summarized different types of fractional epidemic models including fractional Susceptible-Infective-Recovered (SIR), Susceptible-Exposed-Infective-Recovered (SEIR), Susceptible-Exposed-Infective-Asymptomatic-Recovered (SEIAR) models and so on. Furthermore, we propose a general fractional SEIAR model in the case of single-term and multi-term fractional differential equations. A feasible and reliable parameter estimation method based on modified hybrid Nelder-Mead simplex search and particle swarm optimisation is also presented to fit the real data using fractional SEIAR model. The effective methods to solve the fractional epidemic models we introduced construct a simple and effective analytical technique that can be easily extended and applied to other fractional models, and can help guide the concerned bodies in preventing or controlling, even predicting the infectious disease outbreaks.

Multi-term time fractional diffusion equations and novel parameter estimation techniques for chloride ions sub-diffusion in reinforced concrete.

In this paper, searching for a better chloride ions sub-diffusion system, a multi-term time-fractional derivative diffusion model is proposed for the description of the time-dependent chloride ions penetration in reinforced concrete structures exposed to chloride environments. We prove the stability and convergence of the model. We use the modified grid approximation method (MGAM) to estimate the fractional orders and chloride ions diffusion coefficients in the reinforced concrete for the multi-term time fractional diffusion system. And then to verify the efficiency and accuracy of the proposed methods in dealing with the fractional inverse problem, two numerical examples with real data are investigated. Meanwhile, we use two methods of fixed chloride ions diffusion coefficient and variable diffusion coefficient with diffusion depth to simulate chloride ions sub-diffusion system. The result shows that with the new fractional orders and parameters, our multi-term fractional order chloride ions sub-diffusion system is capable of providing numerical results that agree better with the real data than other models. On the other hand, it is also noticed from the numerical solution of the chloride ions sub-diffusion system that setting the variable diffusion coefficient with diffusion depth is more reasonable. And it is also found that chloride ions diffusion coefficients in reinforced concrete should be decreased with diffusion depth which is completely consistent with the theory. In addition, the model can be used to predict the chloride profiles with a time-dependent property. This article is part of the theme issue 'Advanced materials modelling via fractional calculus: challenges and perspectives'.

Fluostatins M-Q Featuring a 6-5-6-6 Ring Skeleton and High Oxidized A-Rings from Marine Streptomyces sp. PKU-MA00045.

Aromatic polyketides from marine actinomycetes have received increasing attention due to their unusual structures and potent bioactivities. Compared to their terrestrial counterparts, marine aromatic polyketides have been less discovered and their structural and biological diversities are far from being fully investigated. In this study, we employed a PCR-based genome mining method to discover aromatic polyketides in our marine bacteria collection. Five new atypical angucyclinones, fluostatins M-Q (1-5) featuring a unique 6-5-6-6 ring skeleton, were discovered from one "positive" Streptomyces sp. PKU-MA00045. The structures of fluostatins M-Q (1-5) were elucidated based on comprehensive spectroscopic analyses and the crystallographic structure of fluostatin P (4), which contains the most oxidized A-ring, was solved by X-ray diffraction analysis with Cu Kα radiation. Compared to the published 16 fluostatin analogues, fluostatins M-Q (1-5) contained a different methoxy group attached at C-7 and hydroxy group attached at C-4, enriching the structural diversity of aromatic polyketides from marine actinomycetes. Genome sequencing of Streptomyces sp. PKU-MA00045 revealed the biosynthetic gene cluster of fluostatins M-Q (1-5), which contained different genes and gene organizations compared to known fluostatin gene clusters, facilitating the investigation of the biosynthesis of the unique 6-5-6-6 ring skeleton in all fluostatins.

Bacillibactin and Bacillomycin Analogues with Cytotoxicities against Human Cancer Cell Lines from Marine Bacillus sp. PKU-MA00093 and PKU-MA00092.

Nonribosomal peptides from marine Bacillus strains have received considerable attention for their complex structures and potent bioactivities. In this study, we carried out PCR-based genome mining for potential nonribosomal peptides producers from our marine bacterial library. Twenty-one "positive" strains were screened out from 180 marine bacterial strains, and subsequent small-scale fermentation, HPLC and phylogenetic analysis afforded Bacillus sp. PKU-MA00092 and PKU-MA00093 as two candidates for large-scale fermentation and isolation. Ten nonribosomal peptides, including four bacillibactin analogues (1-4) and six bacillomycin D analogues (5-10) were discovered from Bacillus sp. PKU-MA00093 and PKU-MA00092, respectively. Compounds 1 and 2 are two new compounds and the ¹H NMR and 13C NMR data of compounds 7 and 9 is first provided. All compounds 1-10 were assayed for their cytotoxicities against human cancer cell lines HepG2 and MCF7, and the bacillomycin D analogues 7-10 showed moderate cytotoxicities with IC50 values from 2.9 ± 0.1 to 8.2 ± 0.2 µM. The discovery of 5-10 with different fatty acid moieties gave us the opportunity to reveal the structure-activity relationships of bacillomycin analogues against these human cancer cell lines. These results enrich the structural diversity and bioactivity properties of nonribosomal peptides from marine Bacillus strains.

Comparative Transcriptomics Analysis for Gene Mining and Identification of a Cinnamyl Alcohol Dehydrogenase Involved in Methyleugenol Biosynthesis from Asarum sieboldii Miq.

Asarum sieboldii Miq., one of the three original plants of TCM ASARI RADIX ET RHIZOMA, is a perennial herb distributed in central and eastern China, the Korean Peninsula, and Japan. Methyleugenol has been considered as the most important constituent of Asarum volatile oil, meanwhile asarinin is also employed as the quality control standard of ASARI RADIX ET RHIZOMA in Chinese Pharmacopeia. They both have shown wide range of biological activities. However, little was known about genes involved in biosynthesis pathways of either methyleugenol or asarinin in Asarum plants. In the present study, we performed de novo transcriptome analysis of plant tissues (e.g., roots, rhizomes, and leaves) at different developmental stages. The sequence assembly resulted in 311,597 transcripts from these plant materials, among which 925 transcripts participated in 'secondary metabolism' with particularly up to 20.22% of them falling into phenylpropanoid biosynthesis pathway. The corresponding enzymes belong to seven families potentially encoding phenylalanine ammonia-lyase (PAL), trans-cinnamate 4-monooxygenase (C4H), p-coumarate 3-hydroxylase (C3H), caffeoyl-CoA O-methyltransferase (CCoAOMT), cinnamoyl-CoA reductase (CCR), cinnamyl alcohol dehydrogenase (CAD), and eugenol synthase (EGS). Moreover, 5 unigenes of DIR (dirigent protein) and 11 unigenes of CYP719A (719A subfamily of cytochrome P450 oxygenases) were speculated to be involved in asarinin pathway. Of the 15 candidate CADs, four unigenes that possessed high FPKM (fragments per transcript kilobase per million fragments mapped) value in roots were cloned and characterized. Only the recombinant AsCAD5 protein efficiently converted p-coumaryl, coniferyl, and sinapyl aldehydes to their corresponding alcohols, which are key intermediates employed not only in biosynthesis of lignin but also in that of methyleugenol and asarinin. qRT-PCR revealed that AsCAD5 had a high expression level in roots at three developmental stages. Our study will provide insight into the potential application of molecular breeding and metabolic engineering for improving the quality of TCM ASARI RADIX ET RHIZOMA.

Characterization of anomalous relaxation using the time-fractional Bloch equation and multiple echo T2 *-weighted magnetic resonance imaging at 7 T.

PURPOSE: To study the utility of fractional calculus in modeling gradient-recalled echo MRI signal decay in the normal human brain. METHODS: We solved analytically the extended time-fractional Bloch equations resulting in five model parameters, namely, the amplitude, relaxation rate, order of the time-fractional derivative, frequency shift, and constant offset. Voxel-level temporal fitting of the MRI signal was performed using the classical monoexponential model, a previously developed anomalous relaxation model, and using our extended time-fractional relaxation model. Nine brain regions segmented from multiple echo gradient-recalled echo 7 Tesla MRI data acquired from five participants were then used to investigate the characteristics of the extended time-fractional model parameters. RESULTS: We found that the extended time-fractional model is able to fit the experimental data with smaller mean squared error than the classical monoexponential relaxation model and the anomalous relaxation model, which do not account for frequency shift. CONCLUSIONS: We were able to fit multiple echo time MRI data with high accuracy using the developed model. Parameters of the model likely capture information on microstructural and susceptibility-induced changes in the human brain. Magn Reson Med 77:1485-1494, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Comparative Transcriptomic Analysis Reveals the Effects of Drought on the Biosynthesis of Methyleugenol in Asarum sieboldii Miq.

Asarum sieboldii Miq., a perennial herb in the family Aristolochiaceae, is widely used to treat colds, fever, headache and toothache in China. However, little is known about the drought-tolerance characteristics of A. sieboldii. In this study, to elucidate the molecular-genetic mechanisms of drought-stress tolerance of A. sieboldii, RNA-seq was conducted. In total, 53,344 unigenes were assembled, and 28,715 unigenes were annotated. A total of 6444 differential-expression unigenes (DEGs) were found, which were mainly enriched in phenylpropanoid, starch and sucrose metabolic pathways. Drought stress revealed significant up-regulation of the unigenes encoding PAL, C4H, HCT, C3H, CCR and IGS in the methyleugenol-biosynthesis pathway. Under the condition of maintaining drought for 15 days and 30 days, drought stress reduced the biosynthesis of volatile oil by 24% and 38%, respectively, while the production of key medicinal ingredients (such as methyl eugenol) was increased. These results provide valuable information about the diverse mechanisms of drought resistance in the A. sieboldii, and the changes in the expression of the genes involved in methyleugenol biosynthesis in response to drought stress.

A Variable Order Fractional Differential-Based Texture Enhancement Algorithm with Application in Medical Imaging.

Texture enhancement is one of the most important techniques in digital image processing and plays an essential role in medical imaging since textures discriminate information. Most image texture enhancement techniques use classical integral order differential mask operators or fractional differential mask operators using fixed fractional order. These masks can produce excessive enhancement of low spatial frequency content, insufficient enhancement of large spatial frequency content, and retention of high spatial frequency noise. To improve upon existing approaches of texture enhancement, we derive an improved Variable Order Fractional Centered Difference (VOFCD) scheme which dynamically adjusts the fractional differential order instead of fixing it. The new VOFCD technique is based on the second order Riesz fractional differential operator using a Lagrange 3-point interpolation formula, for both grey scale and colour image enhancement. We then use this method to enhance photographs and a set of medical images related to patients with stroke and Parkinson's disease. The experiments show that our improved fractional differential mask has a higher signal to noise ratio value than the other fractional differential mask operators. Based on the corresponding quantitative analysis we conclude that the new method offers a superior texture enhancement over existing methods.

Stability and convergence of an implicit numerical method for the space and time fractional Bloch-Torrey equation.

Fractional-order dynamics in physics, particularly when applied to diffusion, leads to an extension of the concept of Brownian motion through a generalization of the Gaussian probability function to what is termed anomalous diffusion. As magnetic resonance imaging is applied with increasing temporal and spatial resolution, the spin dynamics is being examined more closely; such examinations extend our knowledge of biological materials through a detailed analysis of relaxation time distribution and water diffusion heterogeneity. Here, the dynamic models become more complex as they attempt to correlate new data with a multiplicity of tissue compartments, where processes are often anisotropic. Anomalous diffusion in the human brain using fractional-order calculus has been investigated. Recently, a new diffusion model was proposed by solving the Bloch-Torrey equation using fractional-order calculus with respect to time and space. However, effective numerical methods and supporting error analyses for the fractional Bloch-Torrey equation are still limited. In this paper, the space and time fractional Bloch-Torrey equation (ST-FBTE) in both fractional Laplacian and Riesz derivative form is considered. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we derive an analytical solution for the ST-FBTE in fractional Laplacian form with initial and boundary conditions on a finite domain. Secondly, we propose an implicit numerical method (INM) for the ST-FBTE based on the Riesz form, and the stability and convergence of the INM are investigated. We prove that the INM for the ST-FBTE is unconditionally stable and convergent. Finally, we present some numerical results that support our theoretical analysis.