Inversion of heavy metal content in soil using hyperspectral characteristic bands-based machine learning method.

The global concern regarding the adverse effects of heavy metal pollution in soil has grown significantly. Accurate prediction of heavy metal content in soil is crucial for environmental protection. This study proposes an inversion analysis method for heavy metals (As, Cd, Cr, Cu, Ni, Pb) in soil based on hyperspectral and machine learning algorithms for 21 soil reference materials from multiple provinces in China. On this basis, an integrated learning model called Stacked RF (the base model is XGBoost, LightGBM, CatBoost, and the meta-model is RF) was established to perform soil heavy metal inversion. Specifically, three popular algorithms were initially employed to preprocess the spectral data, then Random Forest (RF) was used to select the best feature bands to reduce the impact of noise, finally Stacking and four basic machine learning algorithms were used to establish comparisons and analysis of inversion model. Compared with traditional machine learning methods, the stacking model showcases enhanced stability and superior accuracy. Research results indicate that machine learning algorithms, especially ensemble learning models, have better inversion effects on heavy metals in soil. Overall, the MF-RF-Stacking model performed best in the inversion of the six heavy metals. The research results will provide a new perspective on the ensemble learning model method for soil heavy metal content inversion using data of hyperspectral characteristic bands collected from soil reference materials.

A Feasibility Study on Enhanced Oil Recovery of Modified Janus Nano Calcium Carbonate-Assisted Alkyl Polyglycoside to Form Nanofluids in Emulsification Flooding.

Emulsification flooding can effectively enhance crude oil recovery to solve the problem of petroleum shortage. In this work, a modified Janus Nano Calcium carbonate (JNC-12) with a particle size of 30-150 nm was synthesized, and an in situ emulsification nanofluid (ISEN) was prepared with JNC-12 and alkyl polyglycoside (APG). Scanning electron microscope (SEM) showed that the dispersion of JNC-12 in air or APG solution was better than Nano Calcium carbonate (Nano CaCO3). The emulsification properties, interfacial tension, and expansion modulus of ISEN were studied, and the result showed that with the increase in salinity, the emulsification rate decreased, the water yield rate increased, the interfacial tension first decreased and then increased, and the expansion modulus first increased and then decreased. With the increase in temperature, the emulsification rate, emulsion viscosity, and interfacial tension decreased. With the increased oil-water volume, the water yield rate and the emulsion viscosity increased. With increase in the concentration of JNC-12, the water yield rate, the emulsion viscosity, and the interfacial tension decreased but the expansion modulus increased. The emulsion generated by emulsifying ISEN with crude oil was an O/W emulsion, the crude oil viscosity was 4-10 times that of emulsion, and the average particle size of emulsion was 1.107 µm. The addition of ISEN caused the decrease in interfacial tension of oil-water to 0.01-0.1 mN/m. The wettability alteration experiment found that ISEN could change the lipophilic rock to hydrophilic rock. Finally, the core displacement experiments showed that compared with the first water flooding, the oil recovery of the second water flooding after ISEN flooding enhanced by 17.6%. This research has important guiding significance for in situ emulsified nanofluid flooding to enhance oil recovery.

Surface hydrolysis-designed AuNPs-zwitterionic-glucose as a novel tool for targeting macrophage visualization and delivery into infarcted hearts.

Macrophages, innate immune cells, are key players in the maintenance of myocardial homeostasis under normal conditions and tissue repair after injury. The infiltration of macrophages into the injured heart makes them a potentially appealing vehicle for noninvasive imaging and targeted drug delivery of myocardial infarction (MI). In this study, we demonstrated the use of surface hydrolysis-designed AuNPs-zwitterionic-glucose to label macrophages and track their infiltration into isoproterenol hydrochloride (ISO)-induced MI sites noninvasively using CT. The AuNPs-zwitterionic-glucose did not affect the viability or cytokine release of macrophages and were highly taken up by these cells. The in vivo CT images were obtained on Day 4, Day 6, Day 7, and Day 9, and the attenuation was seen to increase in the heart over time compared to the Day 4 scan. In vitro analysis also confirmed the presence of macrophages around injured cardiomyocytes. Additionally, we also addressed the concern of cell tracking or merely AuNP tracking, which is the inherent problem for any form of nanoparticle-labeled cell tracking by using zwitterionic and glucose-functionalized AuNPs. The glucose coated on the surface of AuNPs-zwit-glucose will be hydrolyzed in macrophages, forming only zwitterionic protected AuNPs that cannot be taken up again by endogenous cells in vivo. This will greatly improve the accuracy and precision of imaging and target delivery. We believe this is the first study to noninvasively visualize the infiltration of macrophages into MI hearts using CT, which could be used for imaging and evaluating the possibility of macrophage-mediated delivery in infarcted hearts.

Detection of peanut seed vigor based on hyperspectral imaging and chemometrics.

Rapid nondestructive testing of peanut seed vigor is of great significance in current research. Before seeds are sown, effective screening of high-quality seeds for planting is crucial to improve the quality of crop yield, and seed vitality is one of the important indicators to evaluate seed quality, which can represent the potential ability of seeds to germinate quickly and whole and grow into normal seedlings or plants. Meanwhile, the advantage of nondestructive testing technology is that the seeds themselves will not be damaged. In this study, hyperspectral technology and superoxide dismutase activity were used to detect peanut seed vigor. To investigate peanut seed vigor and predict superoxide dismutase activity, spectral characteristics of peanut seeds in the wavelength range of 400-1000 nm were analyzed. The spectral data are processed by a variety of hot spot algorithms. Spectral data were preprocessed with Savitzky-Golay (SG), multivariate scatter correction (MSC), and median filtering (MF), which can effectively to reduce the effects of baseline drift and tilt. CatBoost and Gradient Boosted Decision Tree were used for feature band extraction, the top five weights of the characteristic bands of peanut seed vigor classification are 425.48nm, 930.8nm, 965.32nm, 984.0nm, and 994.7nm. XGBoost, LightGBM, Support Vector Machine and Random Forest were used for modeling of seed vitality classification. XGBoost and partial least squares regression were used to establish superoxide dismutase activity value regression model. The results indicated that MF-CatBoost-LightGBM was the best model for peanut seed vigor classification, and the accuracy result was 90.83%. MSC-CatBoost-PLSR was the optimal regression model of superoxide dismutase activity value. The results show that the R2 was 0.9787 and the RMSE value was 0.0566. The results suggested that hyperspectral technology could correlate the external manifestation of effective peanut seed vigor.

Rapid nondestructive detection of peanut varieties and peanut mildew based on hyperspectral imaging and stacked machine learning models.

Moldy peanut seeds are damaged by mold, which seriously affects the germination rate of peanut seeds. At the same time, the quality and variety purity of peanut seeds profoundly affect the final yield of peanuts and the economic benefits of farmers. In this study, hyperspectral imaging technology was used to achieve variety classification and mold detection of peanut seeds. In addition, this paper proposed to use median filtering (MF) to preprocess hyperspectral data, use four variable selection methods to obtain characteristic wavelengths, and ensemble learning models (SEL) as a stable classification model. This paper compared the model performance of SEL and extreme gradient boosting algorithm (XGBoost), light gradient boosting algorithm (LightGBM), and type boosting algorithm (CatBoost). The results showed that the MF-LightGBM-SEL model based on hyperspectral data achieves the best performance. Its prediction accuracy on the data training and data testing reach 98.63% and 98.03%, respectively, and the modeling time was only 0.37s, which proved that the potential of the model to be used in practice. The approach of SEL combined with hyperspectral imaging techniques facilitates the development of a real-time detection system. It could perform fast and non-destructive high-precision classification of peanut seed varieties and moldy peanuts, which was of great significance for improving crop yields.

Predicting simultaneously fields of soot temperature and volume fraction in laminar sooting flames from soot radiation measurements - a convolutional neural networks approach.

An original convolutional neural network, i.e. U-net approach, has been designed to retrieve simultaneously local soot temperature and volume fraction fields from line-of-sight measurements of soot radiation fields. A five-stage U-net architecture is established and detailed. Based on a set of N2 diluted ethylene non-premixed flames, the minimum batch size requirement for U-net model training is discussed and the U-net model prediction ability is validated for the first time by fields provided by the modulated absorption emission (MAE) technique documenting the N2 diluted flame. Additionally, the U-net model's flexibility and robustness to noise are also quantitatively studied by introducing 5% & 10% Gaussian random noises into training together with the testing data. Eventually, the U-net predictive results are directly contrasted with those of Bayesian optimized back propagation neural network (BPNN) in terms of testing score, prediction absolute error (AE), soot parameter field smoothness, and time cost.

Noninvasive Prognosis of Postmyocardial Infarction Using Urinary miRNA Ultratrace Detection Based on Single-Target DNA-Functionalized AuNPs.

Urine is the most appropriate body fluid for analysis because it is easily and less-invasively obtained than blood; thus, urinary miRNAs can better represent the local stage of the disease and might grow up to be a new class of noninvasive biomarkers of postmyocardial infarction (MI). Monofunctionalized Au nanoparticles (AuNPs) with only one selective DNA at a specific location are more promising in nanotechnology. This study developed a urinary miRNA ultratrace detection strategy based on single-target DNA-functionalized AuNPs for the noninvasive prognosis of post-MI. The AuNPs were designed with only single-stranded biotinylated DNA complementary to the target miRNA through a ratio-optimized stoichiometric method for the first time. Combined with the duplex specific nuclease-assisted target recycling amplification, the single-target DNA-functionalized AuNPs for the first time were used in inductively coupled plasma-mass spectrometry for the determination of urinary miRNA with high sensitivity. After optimizing the reaction conditions, a linear detection range between 1 fM and 10 pM for miR-155 and a detection limit of 0.47 fM were obtained. Finally, the target miR-155 in urine samples collected from MI rats was quantified and the level of miR-155 in MI groups was 30 times higher than in the control groups. The results suggest that urinary miR-155 could be a novel biomarker for the noninvasive diagnosis of MI.

Application of serum exosomal hypoxia-inducible factor-1 alpha (HIF-1α) as potential circulating biomarker for bacterial peritonitis.

Bacterial peritonitis is a severe disease that diagnosis remains challenging for clinicians. Measuring biomarkers might be a rapid diagnostic method. The objective of this study was to analyze and evaluate the dynamic changes in HIF-1α concentration in serum exosomes during bacterial peritonitis. The pre-clinical application value of serum exosomal HIF-1α was evaluated via imipenem and cilastatin sodium (ICS) intervention in the bacterial peritonitis model. The new colorimetric method to quantitate dynamic expression changes of HIF-1α in serum exosomes during bacterial peritonitis was established by our team via using the gold seed-coated with aptamer-functionalized Au @ Au core-shell peroxidase mimic. The typical inflammatory cytokines of bacterial peritonitis were also measured. Following intramuscular administration with ICS, In-Vivo Xtreme imaging system was used to visualize abdominal infection extent. Meanwhile, HIF-1α concentration in rat serum exosomes and pro-inflammatory factors levels in serum were detected. The serum typical inflammatory cytokines levels were elevated in GFP-labeled E.coli induced bacterial peritonitis. The serum exosomal HIF-1α levels clearly increased at 12 h, reached the peak during 24-48 h, and then gradually decreased at 72 h. Following intramuscular administration with ICS, the abdominal infection extent, HIF-1α concentration in serum exosomes, and the serum pro-inflammatory factors levels were reduced at 24 h in GFP-labeled E. coli induced bacterial peritonitis model. The serum exosomal HIF-1α can be used as a biomarker in the early stage of bacterial peritonitis, which might provide the basic research in the pre-clinical for further predicting and monitoring the pathological process of bacterial peritonitis.

Simultaneous soot multi-parameter fields predictions in laminar sooting flames from neural network-based flame luminosity measurement I: methodology.

We originally report the use of a neural network-based method for diagnosing multiple key parameters in axis-symmetric laminar sooting flames. A Bayesian optimized back propagation neural network (BPNN) is developed and applied to flame luminosity to predict the planar distribution of soot volume fraction, temperature, and primary particle diameter. The feasibility and robustness of this approach are firstly assessed using numerical modeling results and then further validated with experimental results of a series of laminar diffusion sooting flames. This proposed BPNN model-based flame luminosity approach shows high prediction accuracies, typically up to 114 K, 0.25 ppm, and 2.56 nm for soot temperature, volume fraction, and primary particle diameter, respectively. We believe that the present machine learning-assisted optical diagnostics paves a more efficient, lower costing, and high-fidelity way for multi-parameters simultaneous diagnosis in combustion and reacting flows.

Computed tomography imaging spectrometry based on superiorization and guided image filtering.

Computed tomography imaging spectrometry (CTIS) is a snapshot hyperspectral imaging technique that can obtain a three-dimensional (${2D +}\lambda$) data cube of the target scene within a single exposure. Previous studies of CTIS suggest that reconstructions usually suffer from severe artifacts due to the limited number of projections available. To overcome this limitation, an iterative algorithm combining superiorization and guided image filtering is proposed to explore the intrinsic properties of the hyperspectral data cube as well as the characteristics of zero-order diffraction for the first time, to the best of our knowledge. Results from both simulative studies and proof-of-concept experiments demonstrate its superiority in suppressing artifacts and improving precision over the frequently used expectation maximization algorithm.

Machine learning-assisted soot temperature and volume fraction fields predictions in the ethylene laminar diffusion flames.

Inferring local soot temperature and volume fraction distributions from radiation emission measurements of sooting flames may involve solving nonlinear, ill-posed and high-dimensional problems, which are typically conducted by solving ill-posed problems with big matrices with regularization methods. Due to the high data throughput, they are usually inefficient and tedious. Machine learning approaches allow solving such problems, offering an alternative way to deal with complex and dynamic systems with good flexibility. In this study, we present an original and efficient machine learning approach for retrieving soot temperature and volume fraction fields simultaneously from single-color near-infrared emission measurements of dilute ethylene diffusion flames. The machine learning model gathers information from existing data and builds connections between combustion scalars (soot temperature and volume fraction) and emission measurements of flames. Numerical studies were conducted first to show the feasibility and robustness of the method. The experimental Multi-Layer Perceptron (MLP) neural network model was fostered and validated by the N2 diluted ethylene diffusion flames. Furthermore, the model capability tests were carried out as well for CO2 diluted ethylene diffusion flames. Eventually, the model performance subjected to the Modulated Absorption/Emission (MAE) technique measurement uncertainties were detailed.

Toward Combatting COVID-19: A Risk Assessment System.

The coronavirus disease 2019 (COVID-19) has rapidly become a significant public health emergency all over the world since it was first identified in Wuhan, China, in December 2019. Until today, massive disease-related data have been collected, both manually and through the Internet of Medical Things (IoMT), which can be potentially used to analyze the spread of the disease. On the other hand, with the help of IoMT, the analysis results of the current status of COVID-19 can be delivered to people in real time to enable situational awareness, which may help mitigate the disease spread in communities. However, current accessible data on COVID-19 are mostly at a macrolevel, such as for each state, county, or metropolitan area. For fine-grained areas, such as for each city, community, or geographical coordinate, COVID-19 data are usually not available, which prevents us from obtaining information on the disease spread in closer neighborhoods around us. To address this problem, in this article, we propose a two-level risk assessment system. In particular, we define a "risk index." Then, we develop a risk assessment model, called MK-DNN, by taking advantage of the multikernel density estimation (MKDE) and deep neural network (DNN). We train MK-DNN at the macrolevel (for each metro area), which subsequently enables us to obtain the risk indices at the microlevel (for each geographic coordinate). Moreover, a heuristic validation method is further designed to help validate the obtained microlevel risk indices. Simulations conducted on real-world data demonstrate the accuracy and validity of our proposed risk assessment system.

Astragaloside IV Derivative (LS-102) Alleviated Myocardial Ischemia Reperfusion Injury by Inhibiting Drp1Ser616 Phosphorylation-Mediated Mitochondrial Fission.

Our previous studies showed that Astragaloside IV derivative (LS-102) exhibited potent protective function against ischemia reperfusion (I/R) injury, but little is known about the mechanisms. Mitochondrial fission regulated by dynamin-related protein1 (Drp1) is a newly recognized determinant of mitochondrial function. This study aimed to investigate the protection of LS-102 on mitochondrial structure and function by regulating the activity of Drp1 using models of H9c2 cardiomyocyte injury induced by hypoxia-reperfusion (H/R), and rat heart injury induced by I/R. The results showed that LS-102 significantly decreased apoptosis, levels of ROS, CK, LDH, and calcium, upregulating MMP, and the Bax/Bcl-2 ratio in cardiomyocytes during I/R injury. Furthermore, LS-102 prevented I/R-induced mitochondrial fission by decreasing Drp1's mitochondrial localization through decreasing the phosphorylation of Drp1 at Ser616 (Drp1Ser616) and increasing the phosphorylation of Drp1 at Ser637 (Drp1Ser637) in H9c2 cells. Importantly, we also robustly confirmed Drp1Ser616 as a novel GSK-3ß phosphorylation site. GSK-3ß-mediated phosphorylation at Drp1Ser616 may be associated with mitochondrial fission during I/R of cardiomyocytes. In conclusion, LS-102 exerts cardio protection against I/R-induced injury by inhibiting mitochondrial fission via blocking GSK-3ß-mediated phosphorylation at Ser616 of Drp1.

Urinary bladder stone due to retained indwelling ureteral stent: A case report.

RATIONALE: The indwelling ureteral stents is a common procedure in routine urological practice. The double-J (D-J) stent is the most common type of stents used and is indicated mainly for short-term urinary drainage and prevention of obstruction and infection. However, prolonged indwelling stents may result in disastrous complications, such as hematuria, infection, encrustation, and stone formation. In this context, the persistence of stent in situ might play a key role as a nidus in deposition of urinary sediment, then forming calculus. Although the encrustation may become more serious as time goes on, large bladder stones are relatively rare. However, the serious encrustation and giant stone may complicate or exacerbate the conditions in turn. PATIENT CONCERNS: A 45-year-old female patient who underwent right ureteral stent placement after open ureterolithotomy 6 years ago complained of dysuria, urinary frequency, and urgency over 2 months. DIAGNOSIS: The kidney ureter bladder (KUB) x-ray showed the presence of a giant stone in the bladder and an entire D-J stent. The computed tomography (CT) urography scans revealed normal left kidney, right hydronephrosis, and an encrusted D-J stent with the significant stone, diameter 4.2 cm with a CT value of 1211.0 ±â€Š221.6 HU, on the vesical coil. On the basis of these auxiliary examinations, the case was diagnosed as cystolith and prolonged-indwelling stents. INTERVENTIONS: Pneumatic ballistic lithotripsy was used for crushing the bladder calculi followed by the successful extraction of intact D-J ureteral stent. OUTCOMES: No residual stone was detected on postoperative KUB x-ray and CT urography scans. Patient recovered well and was discharged 10 days after surgery. Semi-annual ultrasound examination was suggested to monitor the effect of therapy. LESSONS: This case reminds us that it is crucial to take various measures to avoid the forgotten ureteral stent and its unfortunate late complication.

Access to 4-Alkenylated Coumarins via Ruthenium-Catalyzed Olefinic C-H Alkenylation of Coumarins with Modifiable and Removable Directing Groups.

The ruthenium-catalyzed activation of the C4 position of coumarins for coupling with acrylates was described using modifiable ketone as a directing group. The alkenylation reaction provided a direct approach to prepare previously inaccessible 4-alkenylated coumarins with operational simplicity and high atom-economy. This protocol also worked well with coumarin-3-carboxylic acids to unveil a rare instance of a tandem alkenylation/decarboxylation reaction. The potential value of this approach was further highlighted by the efficient synthesis of several heterocyclic fused coumarin derivatives.

High conductive graphene assembled films with porous micro-structure for freestanding and ultra-low power strain sensors.

Graphene emerges as an ideal material for constructing high-performance strain sensors, due to its superior mechanical property and high conductivity. However, in the process of assembling graphene into macroscopic materials, its conductivity decreases significantly. Also, tedious fabrication process hinders the application of graphene-based strain sensors. In this work, we report a freestanding graphene assembled film (GAF) with high conductivity ((2.32 ± 0.08) × 105 S m-1). For the sensitive materials of strain sensors, it is higher than most of reported carbon nanotube and graphene materials. These advantages enable the GAF to be an ultra-low power consumption strain sensor for detecting airflow and vocal vibrations. The resistance of the GAF remains unchanged with increasing temperature (20-100 ℃), exhibiting a good thermal stability. Also, the GAF can be used as a strain sensor directly without any flexible substrates, which greatly simplifies the fabrication process in comparison with most reported strain sensors. Additionally, the GAF used as a pressure sensor with only ~4.7 µW power is investigated. This work provides a new direction for the preparation of advanced sensors with ultra-low power consumption, and the development of flexible and energy-saving electronic devices.

Colorimetric determination of the early biomarker hypoxia-inducible factor-1 alpha (HIF-1α) in circulating exosomes by using a gold seed-coated with aptamer-functionalized Au@Au core-shell peroxidase mimic.

An ultra-sensitive method is described here for the determination of HIF-1α (an early biomarker for myocardial infarction) in circulating exosomes in serum. Gold nanospheres were functionalized with a HIF-1α-binding aptamer via sulfydryl chemistry. The apt-AuNP-coated gold seeds were grown by seed-mediated growth, and this significantly increased the peroxidase-mimicking property the nanoparticles. A chromogenic system composed of 3,3'5,5'-tetramethylbenzidine and hydrogen peroxide was used. Absorbance at 652 nm increases linearly in the 0.3 to 200 ng L-1 HIF-1α concentration range, and the limit of detection is 0.2 ng L-1. The method was tested by analyzing rat serum from isoproterenol (ISO)-induced myocardial infarction. It allows HIF-1α to be directly determined in a 25 µL sample without preconcentration. The assay is not interfered by the polydispersity of exosomes released under either health and disease conditions. Graphical abstractGold nanospheres were functionalized with a HIF-1α-binding aptamer via sulfydryl chemistry. Nanosized gold seed particles were then modified with the functionalized gold nanospheres, and this strongly increases the peroxidase-mimicking activity of the nanomaterial. By using the tetramethylbenzidine/H2O2 chromogenic system, the absorbance at 652 nm increases linearly in the 0.3 to 200 ng L-1 HIF-1α concentration range.

Competitive Protein Binding Assay of Naproxen by Human Serum Albumin Functionalized Silicon Dioxide Nanoparticles.

We have developed a new competitive protein binding assay (CPBA) based on human serum albumin functionalized silicon dioxide nanoparticles (nano-SiO2-HSA) that can be used for naproxen determination in urine. Compared with a conventional multi-well reaction plate, nano-SiO2 with a high surface-area-to-volume ratio could be introduced as a stationary phase, markedly improving the analytical performance. Nano-SiO2-HSA and horseradish peroxidase-labeled-naproxen (HRP-naproxen) were prepared for the present CPBA method. In this study, a direct competitive binding to nano-SiO2-HSAwas performed between the free naproxen in the sample and HRP-naproxen. Thus, the catalytic color reactions were investigated on an HRP/3,3'5,5'-tetramethylbenzidine (TMB)/H2O2 system by the HRP-naproxen/nano-SiO2-HSA composite for quantitative measurement via an ultraviolet spectrophotometer. A series of validation experiments indicated that our proposed methods can be applied satisfactorily to the determination of naproxen in urine samples. As a proof of principle, the newly developed nano-CPBA method for the quantification of naproxen in urine can be expected to have the advantages of low costs, fast speed, high accuracy, and relatively simple instrument requirements. Our method could be capable of expanding the analytical applications of nanomaterials and of determining other small-molecule compounds from various biological samples.

Assessment of plenoptic imaging for reconstruction of 3D discrete and continuous luminous fields.

Volumetric tomography has become an indispensable tool for flow diagnostics. However, it usually suffers from high experimental costs as multiple cameras are required in a typical tomographic system. Plenoptic imaging (PI) is a promising alternative which can simultaneously record spatial and angular information using only one single camera. Although PI has been pioneered by a few groups for 3D flow imaging, this particular application is still at its early stage of development and there are some aspects that need further investigation. In this work, we will systematically assess three representative tomographic algorithms for PI via numerical studies. In addition, we show here how 3D PI inversion can be interpreted from a tomographic perspective and how to conveniently perform the calibration with an existing well-established method which can take into account the effect of lens distortion. A proof-of-concept experiment was also conducted, and the conclusions drawn were consistent with those from numerical studies. Although this work was discussed under the context of flow/flame imaging, the general conclusions are also applicable to other application fields, such as biomedical imaging.

Dynamical scaling in the Ohmic spin-boson model studied by extended hierarchical equations of motion.

Through a decomposition of the bath correlation function, the hierarchical equations of motion are extended to the Ohmic spin-boson model at zero temperature. For two typical cutoff functions of the bath spectral density, the rate kernel of spin dynamics is numerically extracted by a time-convolution equation of the average magnetic moment. A characteristic time is defined accordingly as the inverse of the zeroth-order moment of the rate kernel. For a given Kondo parameter in the incoherent regime, the time evolution of average magnetic moments gradually collapses onto a master curve after rescaling the time variable with the characteristic time. The rescaled spin dynamics is nearly independent of the cutoff frequency and the form of cutoff functions. For a given cutoff frequency, the characteristic time with the change of the Kondo parameter is fitted excellently as a function of the renormalized tunneling amplitude. Despite a significant difference in definition, our result is in good agreement with the characteristic time of the noninteracting blip approximation.