The presence of invasive plant species poses a substantial ecological impact,thus comprehensive evaluation of their potential range and risk under the influence of climate change is necessary.This study uses maximum e...The presence of invasive plant species poses a substantial ecological impact,thus comprehensive evaluation of their potential range and risk under the influence of climate change is necessary.This study uses maximum entropy(MaxEnt)modeling to forecast the likelihood of Leucaena leucocephala(Lam.)de Wit invasion in Saudi Arabia under present and future climate change scenarios.Utilizing the MaxEnt modeling,we integrated climatic and soil data to predict habitat suitability for the invasive species.We conducted a detailed analysis of the distribution patterns of the species,using climate variables and ecological factors.We focused on the important influence of temperature seasonality,temperature annual range,and precipitation seasonality.The distribution modeling used robust measures of area under the curve(AUC)and receiver-operator characteristic(ROC)curves,to map the invasion extent,which has a high level of accuracy in identifying appropriate habitats.The complex interaction that influenced the invasion of L.leucocephala was highlighted by the environmental parameters using Jackknife test.Presently,the actual geographic area where L.leucocephala was found in Saudi Arabia was considerably smaller than the theoretical maximum range,suggesting that it had the capacity to expand further.The MaxEnt model exhibited excellent prediction accuracy and produced reliable results based on the data from the ROC curve.Precipitation and temperature were the primary factors influencing the potential distribution of L.leucocephala.Currently,an estimated area of 216,342 km^(2)in Saudi Arabia was at a high probability of invasion by L.leucocephala.We investigated the potential for increased invasion hazards in the future due to climate change scenarios(Shared Socioeconomic Pathways(SSPs)245 and 585).The analysis of key climatic variables,including temperature seasonality and annual range,along with soil properties such as clay composition and nitrogen content,unveiled their substantial influence on the distribution dynamic of L.leucocephala.Our findings indicated a significant expansion of high risk zones.High-risk zones for L.leucocephala invasion in the current climate conditions had notable expansions projected under future climate scenarios,particularly evident in southern Makkah,Al Bahah,Madina,and Asir areas.The results,backed by thorough spatial studies,emphasize the need to reduce the possible ecological impacts of climate change on the spread of L.leucocephala.Moreover,the study provides valuable strategic insights for the management of invasion,highlighting the intricate relationship between climate change,habitat appropriateness,and the risks associated with invasive species.Proactive techniques are suggested to avoid and manage the spread of L.leucocephala,considering its high potential for future spread.This study enhances the overall comprehension of the dynamics of invasive species by combining modeling techniques with ecological knowledge.It also provides valuable information for decision-making to implement efficient conservation and management strategies in response to changing environmental conditions.展开更多
To preliminarily determine the appropriate dosage of carboplatin (CBP) at AUC of 5 mg-M1^-1·min^-1 in the combination chemotherapy for Chinese senile patients with non-small cell lung cancer (NSCLC). Thirty-f...To preliminarily determine the appropriate dosage of carboplatin (CBP) at AUC of 5 mg-M1^-1·min^-1 in the combination chemotherapy for Chinese senile patients with non-small cell lung cancer (NSCLC). Thirty-five Chinese senile patients with NSCLC in advanced stage (Ⅲ/Ⅳ) were given 96 cycles of combination chemotherapy. Chemotherapy schedules included Taxol+CBP, Gemzar+CBP and NVB+CBE The dose of CBP was at 5 mg.mL^-1·min^-1 of area under the concentration-time curve (AUC). Side effects and quality of life were observed before and after the chemotherapy. Myelosuppression was severe and commonly observed. Grade 3/4 of granulocytopenia was found in 47.9% (46/96) of the patients and grade 3/4 of thrombocytopenia was noted in 28.1% (27/96) of the subjects. However, other side effects were slight. The mean score of quality of life (QOL), according to the criteria of QOL for Chinese cancer patients had reduced 6.8. At 5 mg.mL^-1·min^-1 by AUC, the hematological toxicity of CBP was severe and it had some negative effects on the QOL. The administration of CBP at 5 mg.mL^-1·min^-1 by AUC may be too high for Chinese senile patients with non-small cell lung cancer.展开更多
Although high-dose methotrexate(HD-MTX)is the most effective drug against primary CNS lymphomas(PCNSL),outcome-de-termining variables related to its administration schedule have not been defined.The impact on toxicity...Although high-dose methotrexate(HD-MTX)is the most effective drug against primary CNS lymphomas(PCNSL),outcome-de-termining variables related to its administration schedule have not been defined.The impact on toxicity and outcome of the area under thecurve(AUC(MTX)),dose intensity(DI(MTX))and infusion rate(IR(MTX))of MTX and plsamatic creatinine clearance(CL(crea))was investigated in a retrospective series of 45 PCNSL patients treated with three different HD-MTX-basedcombinations.Anticon-vulsants were administered in 31 pts(69%).Age>60 years,anticonvulsant therapy,slow IR(MTX)(</=800 mgm(-2)h(-1)),and reduced DI(MTX)(</=1000 mgm(-2)wk(-1))were significantly correlated with low AUC(MTX)values.Seven pa-展开更多
BACKGROUND Ulcerative colitis(UC)is an immune-mediated chronic inflammatory condition with a worldwide distribution.Although the etiology of this disease is still unknown,the understanding of the role of the microbiot...BACKGROUND Ulcerative colitis(UC)is an immune-mediated chronic inflammatory condition with a worldwide distribution.Although the etiology of this disease is still unknown,the understanding of the role of the microbiota is becoming increasingly strong.AIM To investigate the predictive power of the gut microbiota for the diagnosis of UC in a cohort of newly diagnosed treatment-naïve Saudi children with UC.METHODS The study population included 20 children with a confirmed diagnosis of UC and 20 healthy controls.Microbial DNA was extracted and sequenced,and shotgun metagenomic analysis was performed for bacteria and bacteriophages.Biostatistics and bioinformatics demonstrated significant dysbiosis in the form of reduced alpha diversity,beta diversity,and significant difference of abundance of taxa between children with UC and control groups.The receiver operating characteristic curve,a probability curve,was used to determine the difference between the UC and control groups.The area under the curve(AUC)represents the degree of separability between the UC group and the control group.The AUC was calculated for all identified bacterial species and for bacterial species identified by the random forest classification algorithm as important potential biomarkers of UC.A similar method of AUC calculation for all bacteriophages and important species was used.RESULTS The median age and range were 14(0.5-21)and 12.9(6.8-16.3)years for children with UC and controls,respectively,and 40%and 35%were male for children with UC and controls,respectively.The AUC for all identified bacterial species was 89.5%.However,when using the bacterial species identified as important by random forest classification algorithm analysis, the accuracy increased to 97.6%. Similarly, the AUC for all theidentified bacteriophages was 87.4%, but this value increased to 94.5% when the important bacteriophagebiomarkers were used.CONCLUSIONThe very high to excellent AUCs of fecal bacterial and viral species suggest the potential use of noninvasivemicrobiota-based tests for the diagnosis of unusual cases of UC in children. In addition, the identification ofimportant bacteria and bacteriophages whose abundance is reduced in children with UC suggests the potential ofpreventive and adjuvant microbial therapy for UC.展开更多
Using Picard's theorem and the Leray-Schauder fixed point theorem to reinvestigate the area-preserving convex curve flow in the plane which is considered as a coupled system and thus different from the setting han...Using Picard's theorem and the Leray-Schauder fixed point theorem to reinvestigate the area-preserving convex curve flow in the plane which is considered as a coupled system and thus different from the setting handled by Gage.展开更多
The relationship between the specific surface area(SSA) of rust and the electrochemical behavior of rusted steel under wet-dry acid corrosion conditions was investigated. The results showed that the corrosion curren...The relationship between the specific surface area(SSA) of rust and the electrochemical behavior of rusted steel under wet-dry acid corrosion conditions was investigated. The results showed that the corrosion current density first increased and then decreased with increasing SSA of the rust during the corrosion process. The structure of the rust changed from single-layer to double-layer, and the γ-FeOOH content decreased in the inner layer of the rust with increasing corrosion time; by contrast, the γ-FeOOH content in the outer layer was constant. When the SSA of the rust was lower than the critical SSA corresponding to the relative humidity during the drying period, condensed water in the micropores of the rust could evaporate, which prompted the diffusion of O_2 into the rust and the following formation process of γ-FeOOH, leading to an increase of corrosion current density with increasing corrosion time. However, when the SSA of the rust reached or exceeded the critical SSA, condensate water in the micro-pores of the inner layer of the rust could not evaporate which inhibited the diffusion of O_2 and decreased the γ-FeOOH content in the inner rust, leading to a decrease of corrosion current density with increasing corrosion time.展开更多
The security of wireless local area network (WLAN) becomes a bottleneck for its further applications. At present, many standard organizations and manufacturers of WLAN try to solve this problem. However, owing to the ...The security of wireless local area network (WLAN) becomes a bottleneck for its further applications. At present, many standard organizations and manufacturers of WLAN try to solve this problem. However, owing to the serious secure leak in IEEE802.11 standards, it is impossible to utterly solve the problem by simply adding some remedies. Based on the analysis on the security mechanism of WLAN and the latest techniques of WLAN security, a solution to WLAN security was presented. The solution makes preparation for the further combination of WLAN and Internet.展开更多
In Vietnam,rainfall data usually received using daily rainfall at all hydrology stations with higher time resolution are scarce.However,its analyses to achieve IDF(Intensity-Duration-Frequency)curves are often require...In Vietnam,rainfall data usually received using daily rainfall at all hydrology stations with higher time resolution are scarce.However,its analyses to achieve IDF(Intensity-Duration-Frequency)curves are often required at a finer scale such as hourly.Therefore,it needs to develop and apply methods to derive the IDF characteristics of short-duration events from daily rainfall statistics in Vietnam.In recent years,the need for new insights into the rainfall process leading to new approaches to model the distribution of rainfall intensities in time and space was recognized.This research aims to establish IDF curves for monsoon climate area in Vietnam based on scaling method.Scaling properties of extreme rainfall are examined in the Red River Delta of Vietnam in order to establish scaling behavior of statistical moments over different durations.Such scaling or scale-invariant models enable us to scale data from one temporal resolution to another,and thus,help to overcome the lack of the extreme rainfall data of sub-daily durations.The disaggregation or downscaling techniques are used to obtain sub-daily rainfall data from daily rainfall data for the derivation of scaled IDF curves.Research results show that most of rainfall amount(approximately 70%)received from rains occurring between 6:0 pm to 6:0 am of the day after that,the daytime usually less rainfall occurrence with only 30%.The peak rainfall is usually occurred during 0:0 am to 4:0 am having approximately 42.98%of rainfall amount over a day.The peak rainfall likely happen earlier in the recent year(36%rainfall amount over a day occurrence from 6:00 pm to 10:00 pm in 2008).The analysis also illustrated that approximately 40%of rainfall events have duration less than 60 minutes.In contrast,only approximately 9%of rainfall events have duration more than 6 hours but total rainfall depths of these events is approximately.展开更多
Our aim in this paper is to interest retinal eye specialists in preventing dry macula degeneration by a special flurry vector field through open or closed curved surfaces. The flux of vector fields through surfaces is...Our aim in this paper is to interest retinal eye specialists in preventing dry macula degeneration by a special flurry vector field through open or closed curved surfaces. The flux of vector fields through surfaces is based on vector element area and volume element. Therefore, we explain a few geometrical derivations of area and volume elements in curved orthogonal coordinate systems. We hope that by derivation of a spatial vector field flurry against drusen through open or closed surfaces due to the Gauss theorem might select drusen under eye retina cells without destroying the cells and prevent macula degeneration. A changed flurry of a magnetic or electric vector field through a closed line causes an electric or magnetic vector field on the surface closed by the line. We also hope that derivation by Stokes’ and Greens’ theorems, with the help of iron, might help eye cells to get in life.展开更多
Climate change is the most serious causes and has a direct impact on biodiversity.According to the world’s biodiversity conservation organization,rep-tile species are most affected since their biological and ecologic...Climate change is the most serious causes and has a direct impact on biodiversity.According to the world’s biodiversity conservation organization,rep-tile species are most affected since their biological and ecological qualities are directly linked to climate.Due to a lack of time frame in existing works,conser-vation adoption affects the performance of existing works.The proposed research presents a knowledge-driven Decision Support System(DSS)including the assisted translocation to adapt to future climate change to conserving from its extinction.The Dynamic approach is used to develop a knowledge-driven DSS using machine learning by applying an ecological and biological variable that characterizes the model and mitigation processes for species.However,the frame-work demonstrates the huge difference in the estimated significance of climate change,the model strategy helps to recognize the probable risk of threatened spe-cies translocation to future climate change.The proposed system is evaluated using various performance metrics and this framework can comfortably adapt to the decisions support to reintroduce the species for conservation in the future.展开更多
An approach is presented for computing integral values, such as areas and volumes of revo-lution . of regions bounded by rational plane B zier curves. The method approximates rational curveswith polynomial curves, an...An approach is presented for computing integral values, such as areas and volumes of revo-lution . of regions bounded by rational plane B zier curves. The method approximates rational curveswith polynomial curves, and then computes the integral values on those polynomial curves. Errorbounds are provided. For high precision, this new algorithm performs much more quickly than con-ventional numerical methods.展开更多
基金the Researchers Supporting Project(RSP2024R347),King Saud University,Riyadh,Saudi Arabia.
文摘The presence of invasive plant species poses a substantial ecological impact,thus comprehensive evaluation of their potential range and risk under the influence of climate change is necessary.This study uses maximum entropy(MaxEnt)modeling to forecast the likelihood of Leucaena leucocephala(Lam.)de Wit invasion in Saudi Arabia under present and future climate change scenarios.Utilizing the MaxEnt modeling,we integrated climatic and soil data to predict habitat suitability for the invasive species.We conducted a detailed analysis of the distribution patterns of the species,using climate variables and ecological factors.We focused on the important influence of temperature seasonality,temperature annual range,and precipitation seasonality.The distribution modeling used robust measures of area under the curve(AUC)and receiver-operator characteristic(ROC)curves,to map the invasion extent,which has a high level of accuracy in identifying appropriate habitats.The complex interaction that influenced the invasion of L.leucocephala was highlighted by the environmental parameters using Jackknife test.Presently,the actual geographic area where L.leucocephala was found in Saudi Arabia was considerably smaller than the theoretical maximum range,suggesting that it had the capacity to expand further.The MaxEnt model exhibited excellent prediction accuracy and produced reliable results based on the data from the ROC curve.Precipitation and temperature were the primary factors influencing the potential distribution of L.leucocephala.Currently,an estimated area of 216,342 km^(2)in Saudi Arabia was at a high probability of invasion by L.leucocephala.We investigated the potential for increased invasion hazards in the future due to climate change scenarios(Shared Socioeconomic Pathways(SSPs)245 and 585).The analysis of key climatic variables,including temperature seasonality and annual range,along with soil properties such as clay composition and nitrogen content,unveiled their substantial influence on the distribution dynamic of L.leucocephala.Our findings indicated a significant expansion of high risk zones.High-risk zones for L.leucocephala invasion in the current climate conditions had notable expansions projected under future climate scenarios,particularly evident in southern Makkah,Al Bahah,Madina,and Asir areas.The results,backed by thorough spatial studies,emphasize the need to reduce the possible ecological impacts of climate change on the spread of L.leucocephala.Moreover,the study provides valuable strategic insights for the management of invasion,highlighting the intricate relationship between climate change,habitat appropriateness,and the risks associated with invasive species.Proactive techniques are suggested to avoid and manage the spread of L.leucocephala,considering its high potential for future spread.This study enhances the overall comprehension of the dynamics of invasive species by combining modeling techniques with ecological knowledge.It also provides valuable information for decision-making to implement efficient conservation and management strategies in response to changing environmental conditions.
基金a grant from a key research program of the Education Bureau of Hubei Province (D2006-02-002).
文摘To preliminarily determine the appropriate dosage of carboplatin (CBP) at AUC of 5 mg-M1^-1·min^-1 in the combination chemotherapy for Chinese senile patients with non-small cell lung cancer (NSCLC). Thirty-five Chinese senile patients with NSCLC in advanced stage (Ⅲ/Ⅳ) were given 96 cycles of combination chemotherapy. Chemotherapy schedules included Taxol+CBP, Gemzar+CBP and NVB+CBE The dose of CBP was at 5 mg.mL^-1·min^-1 of area under the concentration-time curve (AUC). Side effects and quality of life were observed before and after the chemotherapy. Myelosuppression was severe and commonly observed. Grade 3/4 of granulocytopenia was found in 47.9% (46/96) of the patients and grade 3/4 of thrombocytopenia was noted in 28.1% (27/96) of the subjects. However, other side effects were slight. The mean score of quality of life (QOL), according to the criteria of QOL for Chinese cancer patients had reduced 6.8. At 5 mg.mL^-1·min^-1 by AUC, the hematological toxicity of CBP was severe and it had some negative effects on the QOL. The administration of CBP at 5 mg.mL^-1·min^-1 by AUC may be too high for Chinese senile patients with non-small cell lung cancer.
文摘Although high-dose methotrexate(HD-MTX)is the most effective drug against primary CNS lymphomas(PCNSL),outcome-de-termining variables related to its administration schedule have not been defined.The impact on toxicity and outcome of the area under thecurve(AUC(MTX)),dose intensity(DI(MTX))and infusion rate(IR(MTX))of MTX and plsamatic creatinine clearance(CL(crea))was investigated in a retrospective series of 45 PCNSL patients treated with three different HD-MTX-basedcombinations.Anticon-vulsants were administered in 31 pts(69%).Age>60 years,anticonvulsant therapy,slow IR(MTX)(</=800 mgm(-2)h(-1)),and reduced DI(MTX)(</=1000 mgm(-2)wk(-1))were significantly correlated with low AUC(MTX)values.Seven pa-
基金Supported by Researchers Supporting Project,King Saud University,Riyadh,Saudi Arabia,No.RSPD2024R864.
文摘BACKGROUND Ulcerative colitis(UC)is an immune-mediated chronic inflammatory condition with a worldwide distribution.Although the etiology of this disease is still unknown,the understanding of the role of the microbiota is becoming increasingly strong.AIM To investigate the predictive power of the gut microbiota for the diagnosis of UC in a cohort of newly diagnosed treatment-naïve Saudi children with UC.METHODS The study population included 20 children with a confirmed diagnosis of UC and 20 healthy controls.Microbial DNA was extracted and sequenced,and shotgun metagenomic analysis was performed for bacteria and bacteriophages.Biostatistics and bioinformatics demonstrated significant dysbiosis in the form of reduced alpha diversity,beta diversity,and significant difference of abundance of taxa between children with UC and control groups.The receiver operating characteristic curve,a probability curve,was used to determine the difference between the UC and control groups.The area under the curve(AUC)represents the degree of separability between the UC group and the control group.The AUC was calculated for all identified bacterial species and for bacterial species identified by the random forest classification algorithm as important potential biomarkers of UC.A similar method of AUC calculation for all bacteriophages and important species was used.RESULTS The median age and range were 14(0.5-21)and 12.9(6.8-16.3)years for children with UC and controls,respectively,and 40%and 35%were male for children with UC and controls,respectively.The AUC for all identified bacterial species was 89.5%.However,when using the bacterial species identified as important by random forest classification algorithm analysis, the accuracy increased to 97.6%. Similarly, the AUC for all theidentified bacteriophages was 87.4%, but this value increased to 94.5% when the important bacteriophagebiomarkers were used.CONCLUSIONThe very high to excellent AUCs of fecal bacterial and viral species suggest the potential use of noninvasivemicrobiota-based tests for the diagnosis of unusual cases of UC in children. In addition, the identification ofimportant bacteria and bacteriophages whose abundance is reduced in children with UC suggests the potential ofpreventive and adjuvant microbial therapy for UC.
文摘Using Picard's theorem and the Leray-Schauder fixed point theorem to reinvestigate the area-preserving convex curve flow in the plane which is considered as a coupled system and thus different from the setting handled by Gage.
基金the National Natural Science Foundation of China(Project No.51571027)for funding support
文摘The relationship between the specific surface area(SSA) of rust and the electrochemical behavior of rusted steel under wet-dry acid corrosion conditions was investigated. The results showed that the corrosion current density first increased and then decreased with increasing SSA of the rust during the corrosion process. The structure of the rust changed from single-layer to double-layer, and the γ-FeOOH content decreased in the inner layer of the rust with increasing corrosion time; by contrast, the γ-FeOOH content in the outer layer was constant. When the SSA of the rust was lower than the critical SSA corresponding to the relative humidity during the drying period, condensed water in the micropores of the rust could evaporate, which prompted the diffusion of O_2 into the rust and the following formation process of γ-FeOOH, leading to an increase of corrosion current density with increasing corrosion time. However, when the SSA of the rust reached or exceeded the critical SSA, condensate water in the micro-pores of the inner layer of the rust could not evaporate which inhibited the diffusion of O_2 and decreased the γ-FeOOH content in the inner rust, leading to a decrease of corrosion current density with increasing corrosion time.
基金The National Natural Science Foundation ofChina(No60703031)The Natural Science Foundation of Shaanxi Province ( No2007F50)
文摘The security of wireless local area network (WLAN) becomes a bottleneck for its further applications. At present, many standard organizations and manufacturers of WLAN try to solve this problem. However, owing to the serious secure leak in IEEE802.11 standards, it is impossible to utterly solve the problem by simply adding some remedies. Based on the analysis on the security mechanism of WLAN and the latest techniques of WLAN security, a solution to WLAN security was presented. The solution makes preparation for the further combination of WLAN and Internet.
文摘In Vietnam,rainfall data usually received using daily rainfall at all hydrology stations with higher time resolution are scarce.However,its analyses to achieve IDF(Intensity-Duration-Frequency)curves are often required at a finer scale such as hourly.Therefore,it needs to develop and apply methods to derive the IDF characteristics of short-duration events from daily rainfall statistics in Vietnam.In recent years,the need for new insights into the rainfall process leading to new approaches to model the distribution of rainfall intensities in time and space was recognized.This research aims to establish IDF curves for monsoon climate area in Vietnam based on scaling method.Scaling properties of extreme rainfall are examined in the Red River Delta of Vietnam in order to establish scaling behavior of statistical moments over different durations.Such scaling or scale-invariant models enable us to scale data from one temporal resolution to another,and thus,help to overcome the lack of the extreme rainfall data of sub-daily durations.The disaggregation or downscaling techniques are used to obtain sub-daily rainfall data from daily rainfall data for the derivation of scaled IDF curves.Research results show that most of rainfall amount(approximately 70%)received from rains occurring between 6:0 pm to 6:0 am of the day after that,the daytime usually less rainfall occurrence with only 30%.The peak rainfall is usually occurred during 0:0 am to 4:0 am having approximately 42.98%of rainfall amount over a day.The peak rainfall likely happen earlier in the recent year(36%rainfall amount over a day occurrence from 6:00 pm to 10:00 pm in 2008).The analysis also illustrated that approximately 40%of rainfall events have duration less than 60 minutes.In contrast,only approximately 9%of rainfall events have duration more than 6 hours but total rainfall depths of these events is approximately.
文摘Our aim in this paper is to interest retinal eye specialists in preventing dry macula degeneration by a special flurry vector field through open or closed curved surfaces. The flux of vector fields through surfaces is based on vector element area and volume element. Therefore, we explain a few geometrical derivations of area and volume elements in curved orthogonal coordinate systems. We hope that by derivation of a spatial vector field flurry against drusen through open or closed surfaces due to the Gauss theorem might select drusen under eye retina cells without destroying the cells and prevent macula degeneration. A changed flurry of a magnetic or electric vector field through a closed line causes an electric or magnetic vector field on the surface closed by the line. We also hope that derivation by Stokes’ and Greens’ theorems, with the help of iron, might help eye cells to get in life.
文摘Climate change is the most serious causes and has a direct impact on biodiversity.According to the world’s biodiversity conservation organization,rep-tile species are most affected since their biological and ecological qualities are directly linked to climate.Due to a lack of time frame in existing works,conser-vation adoption affects the performance of existing works.The proposed research presents a knowledge-driven Decision Support System(DSS)including the assisted translocation to adapt to future climate change to conserving from its extinction.The Dynamic approach is used to develop a knowledge-driven DSS using machine learning by applying an ecological and biological variable that characterizes the model and mitigation processes for species.However,the frame-work demonstrates the huge difference in the estimated significance of climate change,the model strategy helps to recognize the probable risk of threatened spe-cies translocation to future climate change.The proposed system is evaluated using various performance metrics and this framework can comfortably adapt to the decisions support to reintroduce the species for conservation in the future.
文摘An approach is presented for computing integral values, such as areas and volumes of revo-lution . of regions bounded by rational plane B zier curves. The method approximates rational curveswith polynomial curves, and then computes the integral values on those polynomial curves. Errorbounds are provided. For high precision, this new algorithm performs much more quickly than con-ventional numerical methods.