To address the issues of unknown target size,blurred edges,background interference and low contrast in infrared small target detection,this paper proposes a method based on density peaks searching and weighted multi-f...To address the issues of unknown target size,blurred edges,background interference and low contrast in infrared small target detection,this paper proposes a method based on density peaks searching and weighted multi-feature local difference.Firstly,an improved high-boost filter is used for preprocessing to eliminate background clutter and high-brightness interference,thereby increasing the probability of capturing real targets in the density peak search.Secondly,a triple-layer window is used to extract features from the area surrounding candidate targets,addressing the uncertainty of small target sizes.By calculating multi-feature local differences between the triple-layer windows,the problems of blurred target edges and low contrast are resolved.To balance the contribution of different features,intra-class distance is used to calculate weights,achieving weighted fusion of multi-feature local differences to obtain the weighted multi-feature local differences of candidate targets.The real targets are then extracted using the interquartile range.Experiments on datasets such as SIRST and IRSTD-IK show that the proposed method is suitable for various complex types and demonstrates good robustness and detection performance.展开更多
Let {(D n, FFFn),n/->1} be a sequence of martingale differences and {a ni, 1≤i≤n,n≥1} be an array of real constants. Almost sure convergence for the row sums ?i = 1n ani D1\sum\limits_{i = 1}^n {a_{ni} D_1 } are...Let {(D n, FFFn),n/->1} be a sequence of martingale differences and {a ni, 1≤i≤n,n≥1} be an array of real constants. Almost sure convergence for the row sums ?i = 1n ani D1\sum\limits_{i = 1}^n {a_{ni} D_1 } are discussed. We also discuss complete convergence for the moving average processes underB-valued martingale differences assumption.展开更多
In the study by Baliarsingh and Dutta [Internat. J.Anal., Vol.2014（2014）, Article ID 786437], the authors computed the spectrum and the fine spectrum of the product operator G （u, v; A） over the sequence space e1....In the study by Baliarsingh and Dutta [Internat. J.Anal., Vol.2014（2014）, Article ID 786437], the authors computed the spectrum and the fine spectrum of the product operator G （u, v; A） over the sequence space e1. The product operator G （u, v; △） over l1 is defined by （G（u,v;△）x）k=^k∑i=0ukvi（xi- xi-1） with xk = 0 for all k 〈 0, where x = （xk）∈e1,and u and v axe either constant or strictly decreasing sequences of positive real numbers satisfying certain conditions. In this article we give some improvements of the computation of the spectrum of the operator G （u, v; △） on the sequence space gl.展开更多
A dual-time method is introduced to calculate the unsteady flow in a certain vibrating flat cascade. An implicit lower-upper symmetric-gauss-seidel scheme（LU-SGS） is applied for time stepping in pseudo time domains,...A dual-time method is introduced to calculate the unsteady flow in a certain vibrating flat cascade. An implicit lower-upper symmetric-gauss-seidel scheme（LU-SGS） is applied for time stepping in pseudo time domains, and the convection items are discretized with the spatial three-order weighted non-oscillatory and non-free-parameter dissipation difference （WNND） scheme. The turbulence model adopts q-co low-Reynolds-number model. The frequency specmuns of lift coefficients and the unsteady pressure-difference coefficients at different spanwise heights as well as the entropy contours at blade tips on different vibrating instants, are obtained. By the analysis of frequency specmuns of lift coefficients at three spanwise heights, it is considered that there exist obvious non-linear perturbations in the flow induced by the vibrating, and the perturbation frequencies are higher than the basic frequency. The entropy contours at blade tips at different times display an intensively unsteady attribute of the flow under large amplitudes.展开更多
At present,a growing number of consumer products contain engineered nanoparticle TiO2(nano⁃TiO2),which has resulted in the consequences of nano⁃TiO2 entering the aquatic environment directly or indirectly at some stag...At present,a growing number of consumer products contain engineered nanoparticle TiO2(nano⁃TiO2),which has resulted in the consequences of nano⁃TiO2 entering the aquatic environment directly or indirectly at some stage.The fate of nano⁃TiO2 in the aquatic environment has become the key factor which affects its safety application and nanoecotoxicology.This paper aims to investigate how the dissolved organic matters(DOM),especially the molecular weight fractions in the aquatic environment,affect the aggregation,stability,and fate of nano⁃TiO2,and the interaction mechanism of DOM and nano⁃TiO2.Results of dynamic light scattering(DLS)showed that the molecular weight of DOM molecules caused different aggregation rates of nano⁃TiO2 in aqueous solution.Fourier Transform infrared spectroscopy(FTIR)results indicated the molecular structure is characteristics of DOM fractions and the mechanisms of bonds formation between DOM and nano⁃TiO2.Results of three⁃dimensional excitation⁃emission matrices(3D⁃EEM)confirmed the FTIR results and implied the increase of the stability of theπ-πconjugated system in the presence of DOM.In addition,low molecular weight of DOM fractions appeared to show more affinity with nano⁃TiO2 than high molecular weight fractions.展开更多
BACKGROUND Gestational diabetes mellitus(GDM)is characterized by glucose intolerance that is first diagnosed during pregnancy,making it the most common complication associated with this period.Early detection and targ...BACKGROUND Gestational diabetes mellitus(GDM)is characterized by glucose intolerance that is first diagnosed during pregnancy,making it the most common complication associated with this period.Early detection and targeted treatment of GDM can minimize foetal exposure to maternal hyperglycaemia and subsequently reduce the associated adverse pregnancy outcomes.Previous studies have inconsistently suggested that the level of glycated albumin(GA)might predict GDM.AIM To review and synthesize existing evidence to evaluate the relationship between GA levels and the development of GDM.METHODS We sought to compare GA levels between GDM and control groups in this metaanalysis by systematically searching the Web of Science,PubMed,Cochrane Library,and Embase databases for articles published up to June 2023.The analysis utilized the weighted mean difference(WMD)as the primary metric.The data were meticulously extracted,and the quality of the included studies was assessed.Additionally,we conducted a subgroup analysis based on study region and sample size.We assessed heterogeneity using I2 statistics and evaluated publication bias through funnel plots.Additionally,trim-and-fill analysis was employed to detect and address any potential publication bias.RESULTS The meta-analysis included a total of 11 studies involving 5477 participants,comprising 1900 patients with GDM and 3577 control individuals.The synthesized results revealed a notable correlation between elevated GA levels and increased susceptibility to GDM.The calculated WMD was 0.42,with a 95%confidence interval(95%CI)ranging from 0.11 to 0.74,yielding a P value less than 0.001.Concerning specific GA levels,the mean GA level in the GDM group was 12.6,while for the control group,it was lower,at 11.6.This discrepancy underscores the potential of GA as a biomarker for assessing GDM risk.Moreover,we explored the levels of glycated haemoglobin(HbA1c)in both cohorts.The WMD for HbA1c was 0.19,with a 95%CI ranging from 0.15 to 0.22 and a P value less than 0.001.This observation suggested that both GA and HbA1c levels were elevated in individuals in the GDM group compared to those in the control group.CONCLUSION Our meta-analysis revealed a substantial correlation between elevated GA levels and increased GDM risk.Furthermore,our findings revealed elevated levels of HbA1c in GDM patients,emphasizing the significance of monitoring both GA and HbA1c levels for early GDM detection and effective management.展开更多
High order discretization schemes playmore important role in fractional operators than classical ones.This is because usually for classical derivatives the stencil for high order discretization schemes is wider than l...High order discretization schemes playmore important role in fractional operators than classical ones.This is because usually for classical derivatives the stencil for high order discretization schemes is wider than low order ones;but for fractional operators the stencils for high order schemes and low order ones are the same.Then using high order schemes to solve fractional equations leads to almost the same computational cost with first order schemes but the accuracy is greatly improved.Using the fractional linear multistep methods,Lubich obtains the n-th order(n≤6)approximations of the a-th derivative(a>0)or integral(a<0)[Lubich,SIAM J.Math.Anal.,17,704-719,1986],because of the stability issue the obtained scheme can not be directly applied to the space fractional operator with a∈(1,2)for time dependent problem.By weighting and shifting Lubich’s 2nd order discretization scheme,in[Chen&Deng,SINUM,arXiv:1304.7425]we derive a series of effective high order discretizations for space fractional derivative,called WSLD operators there.As the sequel of the previous work,we further provide new high order schemes for space fractional derivatives by weighting and shifting Lubich’s 3rd and 4th order discretizations.In particular,we prove that the obtained 4th order approximations are effective for space fractional derivatives.And the corresponding schemes are used to solve the space fractional diffusion equation with variable coefficients.展开更多
The weight hierarchy of a linear[n;k;q]code C over GF(q) is the sequence(d_1,d_2,…,d_k)where d_r is the smallest support of any r-dimensional subcode of C. "Determining all possible weight hierarchies of general...The weight hierarchy of a linear[n;k;q]code C over GF(q) is the sequence(d_1,d_2,…,d_k)where d_r is the smallest support of any r-dimensional subcode of C. "Determining all possible weight hierarchies of general linear codes" is a basic theoretical issue and has important scientific significance in communication system.However,it is impossible for g-ary linear codes of dimension k when q and k are slightly larger,then a reasonable formulation of the problem is modified as: "Determine almost all weight hierarchies of general g-ary linear codes of dimension k".In this paper,based on the finite projective geometry method,the authors study g-ary linear codes of dimension 5 in class IV,and find new necessary conditions of their weight hierarchies,and classify their weight hierarchies into6 subclasses.The authors also develop and improve the method of the subspace set,thus determine almost all weight hierarchies of 5-dimensional linear codes in class IV.It opens the way to determine the weight hierarchies of the rest two of 5-dimensional codes(classes III and VI),and break through the difficulties.Furthermore,the new necessary conditions show that original necessary conditions of the weight hierarchies of k-dimensional codes were not enough(not most tight nor best),so,it is important to excogitate further new necessary conditions for attacking and solving the fc-dimensional problem.展开更多
In this research,we summarize the results of a practical study of index options based on the option valuation model which was proposed by Siu and Yang(Acta Math.Appl.Sin.Engl.Ser.,25(3)(2009),pp.339{388),where an EMM ...In this research,we summarize the results of a practical study of index options based on the option valuation model which was proposed by Siu and Yang(Acta Math.Appl.Sin.Engl.Ser.,25(3)(2009),pp.339{388),where an EMM kernel is integrated which takes into account all risk components of a regime-switching model.Further,the regime-switching risk of an economy in the options is priced using a hidden Markov regime-switching model with the risky underlying asset being modulated by a discrete-time,nite-state,hidden Markov chain whose states represent the hidden states of an economy.We apply such a model to the pricing of Hang Seng Index options based on the real-world nancial data from October 2009 to October 2010(i.e.,for the year in which the model was proposed).We employed the entropy martingale measure(EMM)approach proposed by Siu and Yang(Acta Math.Appl.Sin.Engl.Ser.,25(3)(2009),pp.339{388)to determine the optimal martingale measure for the Markov-modulated GBM.In addition,we have proposed a numerical technique called the weighted di erence method to compliment the EMM approach.We have also veri ed the extended jump-di usion model under regime-switching that we proposed recently(Int.J.Finan.Eng.,6(4)(2019),1950038)using the 50ETF options which are obtained from Shanghai Stock Exchange covering a time span from January 2018 to December 2022.Further,we have highlighted the challenges for the EMM kernel-based Markov regime-switching model for pricing the out-of-the-money index options in the real world.展开更多
Recent developments allowed establishing virtual-reality (VR) setups to study multiple aspects of visual learning in honey bees under controlled experimental conditions. Here, we adopted a VR environment to investigat...Recent developments allowed establishing virtual-reality (VR) setups to study multiple aspects of visual learning in honey bees under controlled experimental conditions. Here, we adopted a VR environment to investigate the visual learning in the buff-tailed bumble bee Bombus terrestris. Based on responses to appetitive and aversive reinforcements used for conditioning, we show that bumble bees had the proper appetitive motivation to engage in the VR experiments and that they learned efficiently elemental color discriminations. In doing so, they reduced the latency to make a choice, increased the proportion of direct paths toward the virtual stimuli and walked faster toward them. Performance in a short-term retention test showed that bumble bees chose and fixated longer on the correct stimulus in the absence of reinforcement. Body size and weight, although variable across individuals, did not affect cognitive performances and had a mild impact on motor performances. Overall, we show that bumble bees are suitable experimental subjects for experiments on visual learning under VR conditions, which opens important perspectives for invasive studies on the neural and molecular bases of such learning given the robustness of these insects and the accessibility of their brain.展开更多
This paper proposes and analyzes an efficient finite difference scheme for the two-dimensional nonlinear Schr?dinger(NLS) equation involving fractional Laplacian. The scheme is based on a weighted and shifted Grü...This paper proposes and analyzes an efficient finite difference scheme for the two-dimensional nonlinear Schr?dinger(NLS) equation involving fractional Laplacian. The scheme is based on a weighted and shifted Grünwald-Letnikov difference(WSGD) operator for the spatial fractional Laplacian. We prove that the proposed method preserves the mass and energy conservation laws in semi-discrete formulations. By introducing the differentiation matrices, the semi-discrete fractional nonlinear Schr?dinger(FNLS) equation can be rewritten as a system of nonlinear ordinary differential equations(ODEs) in matrix formulations. Two kinds of time discretization methods are proposed for the semi-discrete formulation. One is based on the Crank-Nicolson(CN) method which can be proved to preserve the fully discrete mass and energy conservation. The other one is the compact implicit integration factor(c IIF) method which demands much less computational effort. It can be shown that the cIIF scheme can approximate CN scheme with the error O(τ~2). Finally numerical results are presented to demonstrate the method’s conservation, accuracy, efficiency and the capability of capturing blow-up.展开更多
基金supported by the National Natural Science Foundation of China (No.52205548)。
文摘To address the issues of unknown target size,blurred edges,background interference and low contrast in infrared small target detection,this paper proposes a method based on density peaks searching and weighted multi-feature local difference.Firstly,an improved high-boost filter is used for preprocessing to eliminate background clutter and high-brightness interference,thereby increasing the probability of capturing real targets in the density peak search.Secondly,a triple-layer window is used to extract features from the area surrounding candidate targets,addressing the uncertainty of small target sizes.By calculating multi-feature local differences between the triple-layer windows,the problems of blurred target edges and low contrast are resolved.To balance the contribution of different features,intra-class distance is used to calculate weights,achieving weighted fusion of multi-feature local differences to obtain the weighted multi-feature local differences of candidate targets.The real targets are then extracted using the interquartile range.Experiments on datasets such as SIRST and IRSTD-IK show that the proposed method is suitable for various complex types and demonstrates good robustness and detection performance.
文摘Let {(D n, FFFn),n/->1} be a sequence of martingale differences and {a ni, 1≤i≤n,n≥1} be an array of real constants. Almost sure convergence for the row sums ?i = 1n ani D1\sum\limits_{i = 1}^n {a_{ni} D_1 } are discussed. We also discuss complete convergence for the moving average processes underB-valued martingale differences assumption.
文摘In the study by Baliarsingh and Dutta [Internat. J.Anal., Vol.2014（2014）, Article ID 786437], the authors computed the spectrum and the fine spectrum of the product operator G （u, v; A） over the sequence space e1. The product operator G （u, v; △） over l1 is defined by （G（u,v;△）x）k=^k∑i=0ukvi（xi- xi-1） with xk = 0 for all k 〈 0, where x = （xk）∈e1,and u and v axe either constant or strictly decreasing sequences of positive real numbers satisfying certain conditions. In this article we give some improvements of the computation of the spectrum of the operator G （u, v; △） on the sequence space gl.
基金This Project is supported by National Natural Science Foundation of China (No.50776056)National Hi-tech Research and Development Program of China (863 Program,No.2006AA05Z250).
文摘A dual-time method is introduced to calculate the unsteady flow in a certain vibrating flat cascade. An implicit lower-upper symmetric-gauss-seidel scheme（LU-SGS） is applied for time stepping in pseudo time domains, and the convection items are discretized with the spatial three-order weighted non-oscillatory and non-free-parameter dissipation difference （WNND） scheme. The turbulence model adopts q-co low-Reynolds-number model. The frequency specmuns of lift coefficients and the unsteady pressure-difference coefficients at different spanwise heights as well as the entropy contours at blade tips on different vibrating instants, are obtained. By the analysis of frequency specmuns of lift coefficients at three spanwise heights, it is considered that there exist obvious non-linear perturbations in the flow induced by the vibrating, and the perturbation frequencies are higher than the basic frequency. The entropy contours at blade tips at different times display an intensively unsteady attribute of the flow under large amplitudes.
基金the National Natural Science Foundation of China(Grant No.51408162)the Special Financial Grant from the China Postdoctoral Science Foundation(Grant No.2016T90303)+1 种基金the China Postdoctoral Science Foundation(Grant No.2014M551258)the Heilongjiang Province Postdoctoral Science Foundation(Grant No.LBH-Z14077)。
文摘At present,a growing number of consumer products contain engineered nanoparticle TiO2(nano⁃TiO2),which has resulted in the consequences of nano⁃TiO2 entering the aquatic environment directly or indirectly at some stage.The fate of nano⁃TiO2 in the aquatic environment has become the key factor which affects its safety application and nanoecotoxicology.This paper aims to investigate how the dissolved organic matters(DOM),especially the molecular weight fractions in the aquatic environment,affect the aggregation,stability,and fate of nano⁃TiO2,and the interaction mechanism of DOM and nano⁃TiO2.Results of dynamic light scattering(DLS)showed that the molecular weight of DOM molecules caused different aggregation rates of nano⁃TiO2 in aqueous solution.Fourier Transform infrared spectroscopy(FTIR)results indicated the molecular structure is characteristics of DOM fractions and the mechanisms of bonds formation between DOM and nano⁃TiO2.Results of three⁃dimensional excitation⁃emission matrices(3D⁃EEM)confirmed the FTIR results and implied the increase of the stability of theπ-πconjugated system in the presence of DOM.In addition,low molecular weight of DOM fractions appeared to show more affinity with nano⁃TiO2 than high molecular weight fractions.
文摘BACKGROUND Gestational diabetes mellitus(GDM)is characterized by glucose intolerance that is first diagnosed during pregnancy,making it the most common complication associated with this period.Early detection and targeted treatment of GDM can minimize foetal exposure to maternal hyperglycaemia and subsequently reduce the associated adverse pregnancy outcomes.Previous studies have inconsistently suggested that the level of glycated albumin(GA)might predict GDM.AIM To review and synthesize existing evidence to evaluate the relationship between GA levels and the development of GDM.METHODS We sought to compare GA levels between GDM and control groups in this metaanalysis by systematically searching the Web of Science,PubMed,Cochrane Library,and Embase databases for articles published up to June 2023.The analysis utilized the weighted mean difference(WMD)as the primary metric.The data were meticulously extracted,and the quality of the included studies was assessed.Additionally,we conducted a subgroup analysis based on study region and sample size.We assessed heterogeneity using I2 statistics and evaluated publication bias through funnel plots.Additionally,trim-and-fill analysis was employed to detect and address any potential publication bias.RESULTS The meta-analysis included a total of 11 studies involving 5477 participants,comprising 1900 patients with GDM and 3577 control individuals.The synthesized results revealed a notable correlation between elevated GA levels and increased susceptibility to GDM.The calculated WMD was 0.42,with a 95%confidence interval(95%CI)ranging from 0.11 to 0.74,yielding a P value less than 0.001.Concerning specific GA levels,the mean GA level in the GDM group was 12.6,while for the control group,it was lower,at 11.6.This discrepancy underscores the potential of GA as a biomarker for assessing GDM risk.Moreover,we explored the levels of glycated haemoglobin(HbA1c)in both cohorts.The WMD for HbA1c was 0.19,with a 95%CI ranging from 0.15 to 0.22 and a P value less than 0.001.This observation suggested that both GA and HbA1c levels were elevated in individuals in the GDM group compared to those in the control group.CONCLUSION Our meta-analysis revealed a substantial correlation between elevated GA levels and increased GDM risk.Furthermore,our findings revealed elevated levels of HbA1c in GDM patients,emphasizing the significance of monitoring both GA and HbA1c levels for early GDM detection and effective management.
基金supported by the National Natural Science Foundation of China under Grant No.11271173,the Fundamental Research Funds for the Central Universities under Grant No.lzujbky-2014-228,and the Program for New Century Excellent Talents in University under Grant No.NCET-09-0438.
文摘High order discretization schemes playmore important role in fractional operators than classical ones.This is because usually for classical derivatives the stencil for high order discretization schemes is wider than low order ones;but for fractional operators the stencils for high order schemes and low order ones are the same.Then using high order schemes to solve fractional equations leads to almost the same computational cost with first order schemes but the accuracy is greatly improved.Using the fractional linear multistep methods,Lubich obtains the n-th order(n≤6)approximations of the a-th derivative(a>0)or integral(a<0)[Lubich,SIAM J.Math.Anal.,17,704-719,1986],because of the stability issue the obtained scheme can not be directly applied to the space fractional operator with a∈(1,2)for time dependent problem.By weighting and shifting Lubich’s 2nd order discretization scheme,in[Chen&Deng,SINUM,arXiv:1304.7425]we derive a series of effective high order discretizations for space fractional derivative,called WSLD operators there.As the sequel of the previous work,we further provide new high order schemes for space fractional derivatives by weighting and shifting Lubich’s 3rd and 4th order discretizations.In particular,we prove that the obtained 4th order approximations are effective for space fractional derivatives.And the corresponding schemes are used to solve the space fractional diffusion equation with variable coefficients.
基金supported by the National Natural Science Foundation of China under Grant No.11171366"the Fundamental Research Funds for the Central Universities"South-Central University for Nationalities under Grant No.CZY12014
文摘The weight hierarchy of a linear[n;k;q]code C over GF(q) is the sequence(d_1,d_2,…,d_k)where d_r is the smallest support of any r-dimensional subcode of C. "Determining all possible weight hierarchies of general linear codes" is a basic theoretical issue and has important scientific significance in communication system.However,it is impossible for g-ary linear codes of dimension k when q and k are slightly larger,then a reasonable formulation of the problem is modified as: "Determine almost all weight hierarchies of general g-ary linear codes of dimension k".In this paper,based on the finite projective geometry method,the authors study g-ary linear codes of dimension 5 in class IV,and find new necessary conditions of their weight hierarchies,and classify their weight hierarchies into6 subclasses.The authors also develop and improve the method of the subspace set,thus determine almost all weight hierarchies of 5-dimensional linear codes in class IV.It opens the way to determine the weight hierarchies of the rest two of 5-dimensional codes(classes III and VI),and break through the difficulties.Furthermore,the new necessary conditions show that original necessary conditions of the weight hierarchies of k-dimensional codes were not enough(not most tight nor best),so,it is important to excogitate further new necessary conditions for attacking and solving the fc-dimensional problem.
文摘In this research,we summarize the results of a practical study of index options based on the option valuation model which was proposed by Siu and Yang(Acta Math.Appl.Sin.Engl.Ser.,25(3)(2009),pp.339{388),where an EMM kernel is integrated which takes into account all risk components of a regime-switching model.Further,the regime-switching risk of an economy in the options is priced using a hidden Markov regime-switching model with the risky underlying asset being modulated by a discrete-time,nite-state,hidden Markov chain whose states represent the hidden states of an economy.We apply such a model to the pricing of Hang Seng Index options based on the real-world nancial data from October 2009 to October 2010(i.e.,for the year in which the model was proposed).We employed the entropy martingale measure(EMM)approach proposed by Siu and Yang(Acta Math.Appl.Sin.Engl.Ser.,25(3)(2009),pp.339{388)to determine the optimal martingale measure for the Markov-modulated GBM.In addition,we have proposed a numerical technique called the weighted di erence method to compliment the EMM approach.We have also veri ed the extended jump-di usion model under regime-switching that we proposed recently(Int.J.Finan.Eng.,6(4)(2019),1950038)using the 50ETF options which are obtained from Shanghai Stock Exchange covering a time span from January 2018 to December 2022.Further,we have highlighted the challenges for the EMM kernel-based Markov regime-switching model for pricing the out-of-the-money index options in the real world.
文摘Recent developments allowed establishing virtual-reality (VR) setups to study multiple aspects of visual learning in honey bees under controlled experimental conditions. Here, we adopted a VR environment to investigate the visual learning in the buff-tailed bumble bee Bombus terrestris. Based on responses to appetitive and aversive reinforcements used for conditioning, we show that bumble bees had the proper appetitive motivation to engage in the VR experiments and that they learned efficiently elemental color discriminations. In doing so, they reduced the latency to make a choice, increased the proportion of direct paths toward the virtual stimuli and walked faster toward them. Performance in a short-term retention test showed that bumble bees chose and fixated longer on the correct stimulus in the absence of reinforcement. Body size and weight, although variable across individuals, did not affect cognitive performances and had a mild impact on motor performances. Overall, we show that bumble bees are suitable experimental subjects for experiments on visual learning under VR conditions, which opens important perspectives for invasive studies on the neural and molecular bases of such learning given the robustness of these insects and the accessibility of their brain.
基金supported by National Natural Science Foundation of China(Grant Nos.61573008 and 61703290)Laboratory of Computational Physics(Grant No.6142A0502020717)National Science Foundation of USA(Grant No.DMS-1620108)
文摘This paper proposes and analyzes an efficient finite difference scheme for the two-dimensional nonlinear Schr?dinger(NLS) equation involving fractional Laplacian. The scheme is based on a weighted and shifted Grünwald-Letnikov difference(WSGD) operator for the spatial fractional Laplacian. We prove that the proposed method preserves the mass and energy conservation laws in semi-discrete formulations. By introducing the differentiation matrices, the semi-discrete fractional nonlinear Schr?dinger(FNLS) equation can be rewritten as a system of nonlinear ordinary differential equations(ODEs) in matrix formulations. Two kinds of time discretization methods are proposed for the semi-discrete formulation. One is based on the Crank-Nicolson(CN) method which can be proved to preserve the fully discrete mass and energy conservation. The other one is the compact implicit integration factor(c IIF) method which demands much less computational effort. It can be shown that the cIIF scheme can approximate CN scheme with the error O(τ~2). Finally numerical results are presented to demonstrate the method’s conservation, accuracy, efficiency and the capability of capturing blow-up.
