Cu2MoS4 Nanocatalyst-Based Electrochemical Sensor for Ofloxacin Electro-Oxidation: Delineating the Combined Roles of Crystallinity and Morphology on the Analytical Performance.

In this study, we demonstrate the influence of crystallinity and morphology on the analytical performance of various Cu2MoS4 (CMS) nanocatalysts-based electrochemical sensors for the high-efficiency detection of Ofloxacin (OFX) antibiotic. The electrochemical kinetics parameters including peak current response (ΔIp), peak-to-peak separation (ΔEp), electrochemically active surface area (ECSA), electron-transfer resistance (Rct), were obtained through the electrochemical analyses, which indicate the single-crystalline nature of CMS nanomaterials (NMs) is beneficial for enhanced electron-transfer kinetics. The morphological features and the electrochemical results for OFX detection substantiate that by tuning the tube-like to plate-like structures of the CMS NMs, it might noticeably enhance multiple adsorption sites and more intrinsic active catalytic sites due to the diffusion of analytes into the interstitial spaces between CMS nanoplates. As results, highly single-crystalline and plate-shaped morphology structures of CMS NMs would significantly enhance the electrocatalytic OFX oxidation in terms of onset potential (Eonset), Tafel slope, catalytic rate constant (kcat), and adsorption capacity (Γ). The CMS NMs-based electrochemical sensing platform showed excellent analytical performance toward the OFX detection with two ultra-wide linear detection concentration ranges from 0.25-100 and 100-1000 µM, a low detection limit of 0.058 µM, and an excellent electrochemical sensitivity (0.743 µA µM-1 cm-2).

Surface ligand modified silver nanoparticles-based SERS sensing platform for ultrasensitive detection of the pesticide thiram in green tea leaves: roles of coating agents in sensing performance.

Silver nanoparticles (AgNPs) have been regarded as a highly promising substrate for surface-enhanced Raman scattering (SERS) sensors. In this study, we focused on the electrochemical synthesis method by developing three kinds of AgNPs using three different electrolytes: citrate (e-Ag-C), oleic acid (e-Ag-O) and fish mint (Houttuynia cordata Thunb.) extract (e-Ag-bio). The as-prepared AgNPs were characterized and then employed as SERS substrates to detect the pesticide thiram. The obtained results show that e-Ag-O exhibits the best SERS performance. The effect of the coating agent was explained by chemical and electromagnetic enhancements (CM and EM). Although thiram could absorb onto e-Ag-C at the highest level, allowing its Raman signal to be best enhanced via the CM, the smallest interparticle distance of e-Ag-O could have resulted in the largest improvement in the EM. Using e-Ag-O to develop SERS-based sensors for thiram, we obtain the impressive detection limit of 1.04 × 10-10 M in standard samples and 10-9 M in tea leaves. The linear ranges are from 10-4 M to 10-7 M and from 10-7 M to 10-9 M, covering the maximum residue levels for plant commodities established by the United States Environment Protection Agency and European Food Safety Authority (2-13 ppm ∼7.7 × 10-6 M to 5 × 10-5 M).

Improving nitrogen content in soil and lemon balm (Melissa officinalis L.) yield by purple nonsulfur bacteria Rhodopseudomonas palustris in two consecutive seasons.

The study was conducted to assess the effects of nitrogen (N)-fixing purple nonsulfur bacteria (PNSB) Rhodopseudomonas palustris TLS06, VNW02, VNW64, and VNS89 on soil fertility, N uptake, essential oil (EO) content, growth, and yield of lemon balm. The experiment followed a completely randomized block design with 9 treatments and 3 replications. The treatments consisted of (i) applying 100% N as the recommended fertilizer rate (RFR), (ii) applying 85% N as RFR, (iii) applying 70% N as RFR, (iv) applying 55% N as RFR, (v) the treatment ii combined with N-PNSB, (vi) the treatment iii combined with N-PNSB, (vii) the treatment iv combined with N-PNSB, (viii) 0% as RFR combined with N-PNSB, and (ix) 0% N as RFR. The results showed that applying N-PNSB increased the plant height, and the number of primary branches in both seasons. In addition, the treatment without N fertilizer combined with N-PNSB increased stem leaf biomass by 41.2 and 50.3% in both seasons as compared with the treatment without neither N fertilizer nor N-PNSB. For soil properties, among treatments without N fertilizer, the treatment with N-PNSB increased concentrations of NH4+, soluble P, and exchangeable K+ by 41.3, 41.4, and 26.8%, respectively, as compared with the treatment without N-PNSB at the end of the second season. Applying 85% N as RFR combined with N-PNSB had a greater yield by 5.78-11.8% as compared with the treatment with 100% N as RFR, and a greater EO content by 23% as compared with the treatment with 85% N as RFR.

Fabrication and characterization of a NiO-ZnO/PANI-CNTs composite for sensing of methanol in an aqueous environment.

In this study, we fabricated a composite of NiO-ZnO/PANI-CNTs on a fluorine tin oxide (FTO) electrode and examined the electrochemical sensing behavior of the modified electrode to detect methanol in aqueous solution. The structural, morphological, and electrochemical properties of the composite were characterized using various methods such as X-ray diffraction (XRD), EDS, FTIR, X-ray photoelectron spectroscopy (XPS), field-emission scanning electron microscopy (FE-SEM), transmission electron microscopy (TEM), selected area electron diffraction (SAED), and electrochemical techniques such as cyclic voltammetry (CV) and chronoamperometry (CA). The composite-based electrode showed excellent electrocatalytic activity and selectivity for methanol oxidation. The calibration equation obtained was ΔI = 0.0003 × CMeOH + 0.02811, with a high correlation coefficient of 0.9993, over a wide detection range of 0 to 500 mM. The material exhibits great potential for the fabrication of sensors to detect methanol in commercial products. Real gasoline samples have been selected to evaluate the practical performance and feasibility of this as-prepared sensor. The experimental data indicated that the recovery of gasoline samples is about 98%, indicating this to be an appropriate detection procedure for effective electrochemical determination of MeOH in real gasoline samples.

Ternary heterogeneous Z-scheme photocatalyst TiO2/CuInS2/OCN incorporated with carbon quantum dots (CQDs) for enhanced photocatalytic degradation efficiency of reactive yellow 145 dye in water.

This study delves into the advanced integration of a ternary heterogeneous Z-scheme photocatalyst, TiO2/CuInS2/OCN (OCN: O-g-C3N4), with carbon quantum dot (CQD) to improve the degradation efficiency of reactive yellow 145 (RY145) dye in water. Through a systematic examination, we elucidated the photocatalytic mechanisms and the role of radicals, electrons, and holes in the treatment process. Our findings revealed that this novel catalyst integration significantly boosted RY145 degradation efficiency, achieving 98.2%, which is markedly higher than the efficiencies which could be achieved using TiO2/CuInS2/OCN alone. Moreover, the TiO2/CuInS2/OCN/CQD photocatalyst demonstrated superior rate performance over its components. Comprehensive evaluations, including photoelectrochemical and radical tests, further confirmed the efficiency of the integrated system, adhering to Z-scheme principles. The catalyst showcased remarkable stability, with over 94% reusability after five reaction cycles. These findings pave the way for the potential use of the TiO2/CuInS2/OCN/CQD photocatalyst as an innovative solution for water pollutant treatment via photocatalytic technology.

An on-site and portable electrochemical sensing platform based on spinel zinc ferrite nanoparticles for the quality control of paracetamol in pharmaceutical samples.

In this study, crystalline spinel zinc ferrite nanoparticles (ZnFe2O4 NPs) were successfully prepared and proposed as a high-performance electrode material for the construction of an electrochemical sensing platform for the detection of paracetamol (PCM). By modifying a screen-printed carbon electrode (SPE) with ZnFe2O4 NPs, the electrochemical characteristics of the ZnFe2O4/SPE and the electrochemical oxidation of PCM were investigated by cyclic voltammetry (CV), electrochemical impedance spectroscopy (EIS), chronoamperometry (CA), and differential pulse voltammetry (DPV) methods. The calculated electrochemical kinetic parameters from these techniques including electrochemically active surface area (ECSA), peak-to-peak separation (ΔEp), charge transfer resistance (Rct), standard heterogeneous electron-transfer rate constants (k0), electron transfer coefficient (α), catalytic rate constant (kcat), adsorption capacity (Γ), and diffusion coefficient (D) proved that the as-synthesized ZnFe2O4 NPs have rapid electron/mass transfer characteristics, intrinsic electrocatalytic activity, and facilitate the adsorption-diffusion of PCM molecules towards the modified electrode surface. As expected, the ZnFe2O4/SPE offered excellent analytical performance towards sensing of PCM with a detection limit of 0.29 µM, a wide linear range of 0.5-400 µM, and high electrochemical sensitivity of 1.1 µA µM-1 cm-2. Moreover, the proposed ZnFe2O4-based electrochemical nanosensor also exhibited good repeatability, high anti-interference ability, and practical feasibility toward PCM sensing in a pharmaceutical tablet. Based on these observations, the designed electrochemical platform not only provides a high-performance nanosensor for the rapid and highly efficient detection of PCM but also opens a new avenue for routine quality control analysis of pharmaceutical formulations.

New Dibenzocyclooctadiene Lignans and Phenolics from Kadsura heteroclite with Anti-Inflammatory Activity.

A chemical investigation of K. heteroclite led to isolation of two new dibenzocyclooctadienes (1 and 2) together with 14 known compounds (3-16) by using multiple chromatographic techniques. New compounds (1 and 2) were obtained and identified by spectroscopic methods (HR-ESI-MS, 1D and 2D NMR, and ECD) as well as by comparison of their experimental data with those reported in the literatures. All the isolates were evaluated for their ability to modulate TNF-α production in lipopolysaccharide (LPS) stimulated RAW264.7 cells. Among them, compound 5 displayed the most inhibition against tumor necrosis factor (TNF)-α production with IC50 value of 6.16±0.14 µM. Whereas, compounds (1, 3, and 6) showed the significant inhibition (IC50 values ranging from 9.41 to 14.54 µM), and compounds (2, 4, 9, 10, 13, 15, and 16) exhibited moderate inhibition (IC50 values ranging from 19.27 to 40.64 µM) toward TNF-α production, respectively.

Prevalence and Factors Affecting Appropriate Inhaler Use in Elderly Patients with Chronic Obstructive Pulmonary Disease: A Prospective Study.

BACKGROUND: Chronic obstructive pulmonary disease (COPD) mainly affects individuals aged 60 and older. The proper use of inhalers is crucial for managing COPD. This study aimed to evaluate the prevalence and factors affecting the appropriate use of inhalers among elderly patients with COPD. METHODS: We enrolled 91 elderly patients with COPD admitted to the Department of Respiratory, University Medical Center HCMC between October 2020 and May 2021. Patients who were capable of using the inhaler would have their inhaler usage recorded through video footage. Two respiratory experts carefully analyzed 133 video-recorded demonstrations for evaluation purposes. RESULTS: 18.7% of the patients demonstrated the correct inhaler technique. Pressurized metered dose inhaler (pMDI) and Turbuhaler had the lowest documented correct usage rates (11.9% and 10.0%, respectively). Two critical steps, namely "holding breath for about five seconds or as long as comfortable" and "breathing out gently," were commonly performed incorrectly when using pMDI, Respimat, Breezhaler, or Turbuhaler. Multivariable logistic regression analysis showed that lower mMRC scores (AOR = 5.3, CI 1.1-25.5, p = 0.037) and receiving inhaler instruction within the past three months (AOR = 5.2, CI 1.3-20.1, p = 0.017) were associated with increased odds of using the inhaler correctly. CONCLUSIONS: Our study found that less than 20% of elderly patients with COPD use inhalers correctly. Common errors include inadequate breath-holding and gentle exhalation. mMRC scores and recent inhaler instruction were predictors of proper use. These findings can aid clinicians in improving inhaler management for elderly patients with COPD.

Stable biogenic silver nanoparticles from Syzygium nervosum bud extract for enhanced catalytic, antibacterial and antifungal properties.

In the present study, the biosynthesis of stable silver nanoparticles (BioAgNPs) was accomplished successfully for the first time by using an aqueous extract derived from the buds of Syzygium nervosum (SN) as both a reducing and a stabilizing agent. Transmission electron microscopy (TEM) and high-resolution transmission electron microscopy (HR-TEM) investigations revealed that the biosynthesized BioAgNPs were predominantly spherical with an average size of 10-30 nm. It was found that the outstanding stability of the BioAgNPs colloidal solution was assigned to the additive effect of the surrounding protective organic layer and the highly negatively charged surface of the nanoparticles. Consequently, good antibacterial activity was demonstrated by the colloidal BioAgNPs solution against four distinct bacterial strains, including Gram-positive S. aureus and B. subtilis as well as Gram-negative E. coli and S. typhi. Interestingly, the biosynthesized BioAgNPs displayed greater antibacterial activity even when tested at low doses against Gram-negative S. typhi. In addition, the biogenic AgNPs demonstrated a significant level of catalytic activity in the process of converting 2-NP, 3-NP, and 4-NP into aminophenols within 15 min, with reaction rate constants of 9.0 × 10-4, 10 × 10-4, and 9.0 × 10-4 s-1, respectively. BioAgNPs formulations were assessed against anthracnose disease in tea plants and were found to be as effective as the positive control at a dose of 20-fold dilution, but less effective at a dose of 30-fold dilution. Both doses of BioAgNPs formulations significantly suppressed Colletotrichum camelliae (anthracnose disease) without affecting the growth of the tea plants.

Targeting mutant dicer tumorigenesis in pleuropulmonary blastoma via inhibition of RNA polymerase I.

DICER1 mutations predispose to increased risk for various cancers, particularly pleuropulmonary blastoma (PPB), the commonest lung malignancy of childhood. There is a paucity of directly actionable molecular targets as these tumors are driven by loss-of-function mutations of DICER1. Therapeutic development for PPB is further limited by a lack of biologically and physiologically-representative disease models. Given recent evidence of Dicer's role as a haploinsufficient tumor suppressor regulating RNA polymerase I (Pol I), Pol I inhibition could abrogate mutant Dicer-mediated accumulation of stalled polymerases to trigger apoptosis. Hence, we developed a novel subpleural orthotopic PPB patient-derived xenograft (PDX) model that retained both RNase IIIa and IIIb hotspot mutations and recapitulated the cardiorespiratory physiology of intra-thoracic disease, and with it evaluated the tolerability and efficacy of first-in-class Pol I inhibitor CX-5461. In PDX tumors, CX-5461 significantly reduced H3K9 di-methylation and increased nuclear p53 expression, within 24 hours' exposure. Following treatment at the maximum tolerated dosing regimen (12 doses, 30 mg/kg), tumors were smaller and less hemorrhagic than controls, with significantly decreased cellular proliferation, and increased apoptosis. As demonstrated in a novel intrathoracic tumor model of PPB, Pol I inhibition with CX-5461 could be a tolerable and clinically-feasible therapeutic strategy for mutant Dicer tumors, inducing antitumor effects by decreasing H3K9 methylation and enhancing p53-mediated apoptosis.

Evaluation of the Effectiveness of the Policy of Holding the Second Dose of Vaccination: Lessons from the Outbreak in Ho Chi Minh City.

The coronavirus disease 2019 (COVID-19) pandemic has caused a lot of ethical controversy in the equal provision of healthcare, including vaccination. Therefore, our study was designed to assess the impact of Ho Chi Minh City's policy to hold the second dose of the COVID-19 vaccine. Using a cross-sectional study design to assess low saturation of peripheral oxygen (SPO2) risk based on vaccination status, we included patients who were confirmed to have SARS-CoV-2 and were treated at home. The stepwise method was used to determine participants' low SPO2 risk-related factors. The average age of the 2836 respondents was 46.43 ± 17.33 (years). Research results have shown that seven factors are related to the low SPO2 status of participants, including age, sneezing, shortness of breath, coughing, and fainting as COVID-19 symptoms, the number of people living with COVID-19, and a history of lung disease. A statistically significant (p = 0.032) finding in this study was that fully vaccinated patients had a 6% lower risk of low SPO2 compared to the first dose less than 21 days group. This result was similar in the vaccine holder group (p < 0.001). Holding the second dose of the COVID-19 vaccine is associated with a lower SPO2 risk than that of fully vaccinated patients. Therefore, this approach should be considered by governments as it could bring a greater benefit to the community.

Three new rotenoids from the stems of Derris elliptica and their anti-microbial activity.

Three new rotenoids, named derieliptosides A-C (1-3), were isolated from the stems of Derris elliptica (Wall.) Benth. Their structures were determined by HR-ESI-MS and NMR spectroscopic methods. Absolute configurations of them were elucidated by analysis of ECD spectra in comparison with TD-DFT calculation. Compounds 1-3 inhibited the growth of fungus Candida albicans and selectively inhibited bacterial strains. Of these, compound 1 showed selective inhibition on the growth of Enterococcus faecalis (MIC: 37.5 µM and IC50: 10.6 µM), Staphylococcus aureus (MIC: 75 µM and IC50: 22.7 µM), and C. albicans (MIC: 37.5 µM and IC50: 11.2 µM).

Effect of Initial Vancomycin Dose and Creatinine Clearance on the Attainment of Target Trough Concentration in Children.

BACKGROUND: Vancomycin is a glycopeptide antibiotic that is used to treat serious grampositive infections. However, therapeutic drug monitoring for vancomycin is not performed routinely in Vietnam in clinical practices. Monitoring of serum vancomycin concentration or trough levels is necessary to ensure the efficacy and safety of vancomycin therapy. OBJECTIVE: This study aims to determine the impact of initial vancomycin dose and creatinine clearance on target trough attainment in hospitalized Vietnamese children. METHODS: A prospective study with patients who received vancomycin for at least three days was conducted. Subsequently, demographic data, clinical diagnosis, vancomycin dosage, and serum creatinine levels were recorded. The vancomycin trough level was collected and creatinine clearance and adjusted vancomycin doses were calculated. RESULTS: A total of 40 eligible patients were enrolled. Patients' mean age, body weight, and height were 1.4 years old, 9.8 kg, and 75.5 cm, respectively. The mean vancomycin dose was 55.83 ± 19.34 mg/kg/day. The mean creatinine clearance was 80.18 ± 29.14 ml/min. The median trough level was 11.09 (7.84 - 16.46) µg/ml. There was no significant difference in the mean initial and the adjusted vancomycin doses (p = 0.062). However, there were statistically significant differences of initial (p = 0.004) or adjusted doses (p = 0.016) between groups of creatinine clearance. The trough vancomycin concentration was not statistically significant (p = 0.406) between these groups. CONCLUSION: Target trough vancomycin level may be associated with creatinine clearance but did not proportionally correspond to the vancomycin dose. Therefore, monitoring vancomycin trough levels is necessary to achieve the target trough and to ensure vancomycin efficacy and safety in treating severely infected Vietnamese children.

Two new norlignans from the aerial parts of Pouzolzia sanguinea (Blume) Merr.

Two new norlignans, pouzolignan N (1) and pouzolignan O (2), together with five known norlignans, pouzolignan F (3), pouzolignan G (4), pouzolignan H (5), pouzolignan L (6), and gnetifolin F (7) were isolated from the aerial parts of Pouzolzia sanguinea (Blume) Merr. Their chemical structures were elucidated via HR-ESI-MS and NMR spectroscopic methods. Absolute configurations at stereocenters were confirmed by comparisons of CD spectra with those of TD-DFT calculations. Compounds 1-6 exhibited chemical structures unique to Pouzolzia species. At a concentration of 30 µM, compounds 1-7 exhibited weak cytotoxic activity toward CAL27 and MDA-MB-231 cell lines (cell viability from 65.3 ± 0.86 to 98.8 ± 1.23%). They also inhibited anoctamin-1 activity with inhibitory rates from 8.1 ± 0.87 to 24.3 ± 1.41%.

Secondary metabolites from Valeriana jatamansi with their anti-inflammatory activity.

Valeriana jatamansi is hired as multiple remedies for treatment of insomnia, blood and circulatory disorders, asthma, dry cough, jaundice, seminal weakness, cardiac debility, and skin diseases in Vietnam. Our research discovered the phytochemical investigation of constituents from this herbal medicine resulted in the isolation of two new compounds (jatamansides A (4) and B (7)) together with 16 known ones from the whole plant. Their structures were established by using spectroscopic techniques (multinuclear and multidimensional nuclear magnetic resonance, infrared, ultraviolet-visible), mass spectrometry, hydrolysis analysis, or comparing their NMR data to those reported in the literature. In addition, all the isolates were evaluated for their inhibitory effect against TNF-α production in LPS-stimulated on RAW264.7 cells with significant inhibition.

Enhancing the chloramphenicol sensing performance of Cu-MoS2 nanocomposite-based electrochemical nanosensors: roles of phase composition and copper loading amount.

The rational design of nanomaterials for electrochemical nanosensors from the perspective of structure-property-performance relationships is a key factor in improving the analytical performance toward residual antibiotics in food. We have investigated the effects of the crystalline phase and copper loading amount on the detection performance of Cu-MoS2 nanocomposite-based electrochemical sensors for the antibiotic chloramphenicol (CAP). The phase composition and copper loading amount on the MoS2 nanosheets can be controlled using a facile electrochemical method. Cu and Cu2O nanoparticle-based electrochemical sensors showed a higher CAP electrochemical sensing performance as compared to CuO nanoparticles due to their higher electrocatalytic activity and conductivity. Moreover, the design of Cu-MoS2 nanocomposites with appropriate copper loading amounts could significantly improve their electrochemical responses for CAP. Under optimized conditions, Cu-MoS2 nanocomposite-based electrochemical nanosensor showed a remarkable sensing performance for CAP with an electrochemical sensitivity of 1.74 µA µM-1 cm-2 and a detection limit of 0.19 µM in the detection range from 0.5-50 µM. These findings provide deeper insight into the effects of nanoelectrode designs on the analytical performance of electrochemical nanosensors.

Skull Fracture Patterns and Morphologies Among Fatal Motorcycle Traffic Accident Victims in Vietnam.

ABSTRACT: We aim to describe morphological structures of skull fractures and relevant factors in motorcycle accident victims in Vietnam. This work represents a retrospective cross-sectional study based on forensic reports of fatal motorcycle accident victims. Between January 2013 and August 2019, a total of 226 fatal motorcycle accident patients with skull fracture diagnoses were enrolled. Linear and depressed fractures were the common patterns (46.0% and 37.2% of cases, respectively), whereas stellate (11.5%) fractures were rare. Fractures of the temporal bone (68.6% of cases) and basilar skull (60.6%) were the most common, whereas fractures of the parietal bone were the least common (9.7%). Two or more patterns of skull fracture were recorded in 25.5% of cases, and 2 or more fracture locations were recorded in 76.6% of cases. Fractures of the parietal bone were associated with victims not wearing a helmet. In addition, fractures of the basilar skull were more likely to occur among victims with alcohol consumption. We found the common pattern of skull fractures was linear and depressed fractures, and the common location of skull fractures was temporal and basilar bone. Further studies that include larger sample sizes and collect more information should be conducted to better understand relationships between skull fractures and related factors.

The Prevalence of Myopia and Factors Associated with It Among Secondary School Children in Rural Vietnam.

PURPOSE: To assess the prevalence of myopia and associated factors among secondary school children in a rural area of Vietnam. METHODS: A school-based cross-sectional study of children in grades six to nine was conducted in four secondary schools in Hoang Mai town, Nghe An Province, Vietnam, during December 2018 and January 2019. The status of myopia was defined as a spherical equivalent objective refractive error of -0.50 D or worse in either eye. A case-control study was conducted to explore factors associated with myopia, where children with myopia were considered to be cases, and children without myopia were considered to be controls. Factors associated with myopia were analyzed using univariate and multivariate logistic regression. RESULTS: The prevalence of myopia among secondary school children was 14.2% (95% CI: 12.7-15.7%) and tended to increase with grade, from 10.5% in grade six to 17.7% in grade nine. Myopia prevalence in girls was significantly higher than in boys. Factors associated with myopia were a mother with a college/university education (OR = 2.5, 95% CI = 1.2-5.3), parents who wore spectacles (OR = 2.0, 95% CI = 1.1-3.8), distance from near work (OR = 5.2, 95% CI = 3.5-7.9), and taking breaks after 30 minutes of continued reading (OR = 1.6, 95% CI = 1.1-2.5). However, there were inverse associations with myopia for children belonging to the wealthiest households (OR = 0.2, 95% CI = 0.1-0.5) and time spent performing outdoor activities (OR = 0.6, 95% CI = 0.4-0.9). CONCLUSION: Our study showed that the prevalence of myopia is considerable among secondary children in rural areas of Vietnam. The prevalence of myopia tended to increase among children in higher grade levels. Thus, appropriate interventions should be developed and conducted to deal with the issue of school-age myopia.

Simulation and Experimental Investigation on Carbonized Tracking Failure of EPDM/BN-based Electrical Insulation.

* Correspondence: tariq [...].

Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations.

For a long time it has been well-known that high-dimensional linear parabolic partial differential equations (PDEs) can be approximated by Monte Carlo methods with a computational effort which grows polynomially both in the dimension and in the reciprocal of the prescribed accuracy. In other words, linear PDEs do not suffer from the curse of dimensionality. For general semilinear PDEs with Lipschitz coefficients, however, it remained an open question whether these suffer from the curse of dimensionality. In this paper we partially solve this open problem. More precisely, we prove in the case of semilinear heat equations with gradient-independent and globally Lipschitz continuous nonlinearities that the computational effort of a variant of the recently introduced multilevel Picard approximations grows at most polynomially both in the dimension and in the reciprocal of the required accuracy.