Although much has been known about how humans psychologically perform data-driven scientific discovery,less has been known about its brain mechanism.The number series completion is a typical data-driven scientific dis...Although much has been known about how humans psychologically perform data-driven scientific discovery,less has been known about its brain mechanism.The number series completion is a typical data-driven scientific discovery task,and has been demonstrated to possess the priming effect,which is attributed to the regularity identification and its subsequent extrapolation.In order to reduce the heterogeneities and make the experimental task proper for a brain imaging study,the number magnitude and arithmetic operation involved in number series completion tasks are further restricted.Behavioral performance in Experiment 1 shows the reliable priming effect for targets as expected.Then,a factorial design (the priming effect:prime vs.target;the period length:simple vs.complex) of event-related functional magnetic resonance imaging (fMRI) is used in Experiment 2 to examine the neural basis of data-driven scientific discovery.The fMRI results reveal a double dissociation of the left DLPFC (dorsolateral prefrontal cortex) and the left APFC (anterior prefrontal cortex) between the simple (period length=1) and the complex (period length=2) number series completion task.The priming effect in the left DLPFC is more significant for the simple task than for the complex task,while the priming effect in the left APFC is more significant for the complex task than for the simple task.The reliable double dissociation may suggest the different roles of the left DLPFC and left APFC in data-driven scientific discovery.The left DLPFC (BA 46) may play a crucial role in rule identification,while the left APFC (BA 10) may be related to mental set maintenance needed during rule identification and extrapolation.展开更多
This article studies the existence of analytic invariant curves for a nonlinear second order difference equation which was modeled from macroeconomics of the business cycle. The author not only discusses the case of t...This article studies the existence of analytic invariant curves for a nonlinear second order difference equation which was modeled from macroeconomics of the business cycle. The author not only discusses the case of the eigenvalue off the unit circle S^1 and the case on S^1 with the Diophantine condition but also considers the case of the eigenvalue at a root of the unity, which obviously violates the Diophantine condition.展开更多
This paper examines the causal relationship between oil prices and the Gross Domestic Product(GDP)in the Kingdom of Saudi Arabia.The study is carried out by a data set collected quarterly,by Saudi Arabian Monetary Aut...This paper examines the causal relationship between oil prices and the Gross Domestic Product(GDP)in the Kingdom of Saudi Arabia.The study is carried out by a data set collected quarterly,by Saudi Arabian Monetary Authority,over a period from 1974 to 2016.We seek how a change in real crude oil price affects the GDP of KSA.Based on a new technique,we treat this data in its continuous path.Precisely,we analyze the causality between these two variables,i.e.,oil prices and GDP,by using their yearly curves observed in the four quarters of each year.We discuss the causality in the sense of Granger,which requires the stationarity of the data.Thus,in the first Step,we test the stationarity by using the Monte Carlo test of a functional time series stationarity.Our main goal is treated in the second step,where we use the functional causality idea to model the co-variability between these variables.We show that the two series are not integrated;there is one causality between these two variables.All the statistical analyzes were performed using R software.展开更多
We study the local analytic solutions f of the functional equation f（ψ（zf（z））） = φ（f（z）） for z in some neighborhood of the origin. Whether the solution f vanishes at z = 0 or not plays a critical role for ...We study the local analytic solutions f of the functional equation f（ψ（zf（z））） = φ（f（z）） for z in some neighborhood of the origin. Whether the solution f vanishes at z = 0 or not plays a critical role for local analytic solutions of this equation. In this paper, we obtain results of analytic solutions not only in the case f（0） = 0 but also for f（0） ≠ 0. When assuming f（0） = 0, for technical reasons, we just get the result for f′（0）≠ 0. Then when assuming f（0） = ω0 ≠ 0, ψ（0） = s # 0, ψ（z） is analytic at z = 0 and ψ（z） is analytic at z = ω0, we give the existence of local analytic solutions f in the case of 0 〈 ｜sω0｜ 〈 1 and the case of ｜sω0｜ = 1 with the Brjuno condition.展开更多
Background： Breast cancer is the most common female cancer in Pakistan. The incidence of breast cancer in Pakistan is about 2.5 times higher than that in the neighboring countries India and Iran. In Karachi, the most...Background： Breast cancer is the most common female cancer in Pakistan. The incidence of breast cancer in Pakistan is about 2.5 times higher than that in the neighboring countries India and Iran. In Karachi, the most populated city of Pakistan, the age-standardized rate of breast cancer was 69.1 per 100,000 women during 1998-2002, which is the highest recorded rate in Asia. The carcinoma of breast in Pakistan is an enormous public health concern. In this study, we examined the recent trends of breast cancer incidence rates among the women in Karachi. Methods： We obtained the secondary data of breast cancer incidence from various hospitals. They included Jinnah Hospital, KIRAN （Karachi Institute of Radiotherapy and Nuclear Medicine）, and Civil hospital, where the data were available for the years 2004-2011. A total of 5331 new cases of female breast cancer were registered during this period. We analyzed the data in 5-year age groups 15-19, 20-24, 25-29, 30-34, 35-39, 40-44, 45-49, 50-54, 55-59, 60-64, 65-69, 70-74, 75＋. Nonparametric smoothing were used to obtained age-specific incidence curves, and then the curves are decomposed using principal components analysis to fit FTS （functional time series） model. We then used exponential smoothing statspace models to estimate the forecasts of incidence curve and construct prediction intervals. Results： The breast cancer incidence rates in Karachi increased with age for all available years. The rates increased monotonically and are relatively sharp with the age from 15 years to 50 years and then they show variability after the age of 50 years. 10-year forecasts for the female breast cancer incidence rates in Karachi show that the future rates are expected to remain stable for the age-groups 15-50 years, but they will increase for the females of 50-years and over. Hence in future, the newly diagnosed breast cancer cases in the older women in Karachi are expected to increase. Conclusion： Prediction of age related changes in breast cancer incidence rates w展开更多
We study the Eisenstein series for a convex cocompact discrete subgroup on a two-dimen- sional complex hyperbolic space Hc^2. We find an inner product formula which gives the connection between Eisenstein series and a...We study the Eisenstein series for a convex cocompact discrete subgroup on a two-dimen- sional complex hyperbolic space Hc^2. We find an inner product formula which gives the connection between Eisenstein series and automorphic Green functions on a two-dimensional complex hyperbolic space HC^2. As an application of our inner product formula, we obtain the functional equations of Eisenstein series.展开更多
The article presents the proof of the validity of the generalized Riemann hypothesis on the basis of adjustment and correction of the proof of the Riemanns hypothesis in the work?[1], obtained by a finite exponential ...The article presents the proof of the validity of the generalized Riemann hypothesis on the basis of adjustment and correction of the proof of the Riemanns hypothesis in the work?[1], obtained by a finite exponential functional series and finite exponential functional progression.展开更多
The uniform mathematical model of distortion signals in power grid has been setup with the theory of Wiener-G Functional. Firstly,the Matlab simulation models were established. Secondly,the Wiener kernel of power load...The uniform mathematical model of distortion signals in power grid has been setup with the theory of Wiener-G Functional. Firstly,the Matlab simulation models were established. Secondly,the Wiener kernel of power load was found based on the Gaussian white noise as input. And then the uniform mathematical model of the power grid signal was established according to the homogeneous of the same order of Wiener functional series. Finally,taking three typical distortion sources which are semiconductor rectifier,electric locomotive and electric arc furnace in power grid as examples,we have validated the model through the Matlab simulation and analyzed the simulation errors. The results show that the uniform mathematical model of distortion signals in power grid can approximation the actual model by growing the items of the series under the condition of the enough storage space and computing speed.展开更多
Let is the Walsh generalized system. In the paper constructed a weighted space , and series in the Walsh generalized system with monotonically decreasing coefficient such that for each function in the space one can fi...Let is the Walsh generalized system. In the paper constructed a weighted space , and series in the Walsh generalized system with monotonically decreasing coefficient such that for each function in the space one can find a subseries that converges to in the weighted and almost everywhere on [0,1].展开更多
Using the properties of theta-series and Schwarz reflection principle, a proof for Riemann hypothesis (RH) is directly presented and the first ten nontrivial zeros are easily obtained. From now on RH becomes Riemann T...Using the properties of theta-series and Schwarz reflection principle, a proof for Riemann hypothesis (RH) is directly presented and the first ten nontrivial zeros are easily obtained. From now on RH becomes Riemann Theorem (RT) and all its equivalent results and the consequences assuming RH are true.展开更多
Multiple change-points estimation for functional time series is studied in this paper.The change-point problem is first transformed into a high-dimensional sparse estimation problem via basis functions.Group least abs...Multiple change-points estimation for functional time series is studied in this paper.The change-point problem is first transformed into a high-dimensional sparse estimation problem via basis functions.Group least absolute shrinkage and selection operator(LASSO)is then applied to estimate the number and the locations of possible change points.However,the group LASSO(GLASSO)always overestimate the true points.To circumvent this problem,a further Information Criterion(IC)is applied to eliminate the redundant estimated points.It is shown that the proposed two-step procedure estimates the number and the locations of the change-points consistently.Simulations and two temperature data examples are also provided to illustrate the finite sample performance of the proposed method.展开更多
Two-dimensional(2D)semiconducting materials and transition-metal oxides are promising materials for nonvolatile memory and brain-inspired neuromorphic computing applications.However,it remains chal-lenging to obtain h...Two-dimensional(2D)semiconducting materials and transition-metal oxides are promising materials for nonvolatile memory and brain-inspired neuromorphic computing applications.However,it remains chal-lenging to obtain high-quality stacked 2D films with low energy consumptions(or drive currents)be-cause of their high interfacial resistance.In this study,we synthesized 2D Ti_(3)C_(2)T_(x)MXene-derived three-dimensional(3D)TiO_(2)nanoflowers(NFs)as a feasible resistive switching(RS)material with outstanding electronic properties and synaptic learning capabilities.The electrical and optical characteristics of the synthesized material were determined through density functional theory calculations.Electrical measure-ments of the Al/Ti_(3)C_(2)T_(x)-TiO_(2)NF/Pt memory device indicated the occurrence of forming-free switching phenomena with extremely low switching voltages(0.68-0.53 V),stable ON/OFF ratio(2.3×103),and retention greater than 105 s.The Holt-Winters exponential smoothing technique was used for mod-eling and predicting the switching voltages of the RS device.The mechanism underlying the reliable RS was confirmed by observing the dense conductive filaments through conductive atomic force mi-croscopy.Interestingly,the 2D Ti_(3)C_(2)T_(x)MXene-derived 3D TiO_(2)NF-based RS device mimicked the po-tentiation/depression and spike-time-dependent plasticity of a biological synapse.Finally,a convolutional neural network was implemented based on the observed synaptic weights of Al/Ti_(3)C_(2)T_(x)-TiO_(2)NF/Pt for image-edge detection.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos.60775039 and 60875075)supported by the Grant-in-aid for Scientific Research (Grant No.18300053) from the Japanese Society for the Promotion of Science+2 种基金Support Center for Advanced Telecommunications Technology Research,Foundationthe Open Foundation of Key Laboratory of Multimedia and Intelligent Software Technology (Beijing University of Technology) Beijingthe Doctoral Research Fund of Beijing University of Technology (Grant No.00243)
文摘Although much has been known about how humans psychologically perform data-driven scientific discovery,less has been known about its brain mechanism.The number series completion is a typical data-driven scientific discovery task,and has been demonstrated to possess the priming effect,which is attributed to the regularity identification and its subsequent extrapolation.In order to reduce the heterogeneities and make the experimental task proper for a brain imaging study,the number magnitude and arithmetic operation involved in number series completion tasks are further restricted.Behavioral performance in Experiment 1 shows the reliable priming effect for targets as expected.Then,a factorial design (the priming effect:prime vs.target;the period length:simple vs.complex) of event-related functional magnetic resonance imaging (fMRI) is used in Experiment 2 to examine the neural basis of data-driven scientific discovery.The fMRI results reveal a double dissociation of the left DLPFC (dorsolateral prefrontal cortex) and the left APFC (anterior prefrontal cortex) between the simple (period length=1) and the complex (period length=2) number series completion task.The priming effect in the left DLPFC is more significant for the simple task than for the complex task,while the priming effect in the left APFC is more significant for the complex task than for the simple task.The reliable double dissociation may suggest the different roles of the left DLPFC and left APFC in data-driven scientific discovery.The left DLPFC (BA 46) may play a crucial role in rule identification,while the left APFC (BA 10) may be related to mental set maintenance needed during rule identification and extrapolation.
基金supported by the Fund of Educational Reform Project of Guangxi Province of China (200710961)the Scientific Research Foundation of the Education Department of Guangxi Province of China (200707MS112)+1 种基金the Natural Science Fund of Hechi University (2006N001)the fund of Key discipline of applied mathematics of Hechi University (200725)
文摘This article studies the existence of analytic invariant curves for a nonlinear second order difference equation which was modeled from macroeconomics of the business cycle. The author not only discusses the case of the eigenvalue off the unit circle S^1 and the case on S^1 with the Diophantine condition but also considers the case of the eigenvalue at a root of the unity, which obviously violates the Diophantine condition.
基金the financial support through the General Research Program under project number GRP-73-41.
文摘This paper examines the causal relationship between oil prices and the Gross Domestic Product(GDP)in the Kingdom of Saudi Arabia.The study is carried out by a data set collected quarterly,by Saudi Arabian Monetary Authority,over a period from 1974 to 2016.We seek how a change in real crude oil price affects the GDP of KSA.Based on a new technique,we treat this data in its continuous path.Precisely,we analyze the causality between these two variables,i.e.,oil prices and GDP,by using their yearly curves observed in the four quarters of each year.We discuss the causality in the sense of Granger,which requires the stationarity of the data.Thus,in the first Step,we test the stationarity by using the Monte Carlo test of a functional time series stationarity.Our main goal is treated in the second step,where we use the functional causality idea to model the co-variability between these variables.We show that the two series are not integrated;there is one causality between these two variables.All the statistical analyzes were performed using R software.
基金supported by National Natural Science Foundation of China(11101295)
文摘We study the local analytic solutions f of the functional equation f（ψ（zf（z））） = φ（f（z）） for z in some neighborhood of the origin. Whether the solution f vanishes at z = 0 or not plays a critical role for local analytic solutions of this equation. In this paper, we obtain results of analytic solutions not only in the case f（0） = 0 but also for f（0） ≠ 0. When assuming f（0） = 0, for technical reasons, we just get the result for f′（0）≠ 0. Then when assuming f（0） = ω0 ≠ 0, ψ（0） = s # 0, ψ（z） is analytic at z = 0 and ψ（z） is analytic at z = ω0, we give the existence of local analytic solutions f in the case of 0 〈 ｜sω0｜ 〈 1 and the case of ｜sω0｜ = 1 with the Brjuno condition.
文摘Background： Breast cancer is the most common female cancer in Pakistan. The incidence of breast cancer in Pakistan is about 2.5 times higher than that in the neighboring countries India and Iran. In Karachi, the most populated city of Pakistan, the age-standardized rate of breast cancer was 69.1 per 100,000 women during 1998-2002, which is the highest recorded rate in Asia. The carcinoma of breast in Pakistan is an enormous public health concern. In this study, we examined the recent trends of breast cancer incidence rates among the women in Karachi. Methods： We obtained the secondary data of breast cancer incidence from various hospitals. They included Jinnah Hospital, KIRAN （Karachi Institute of Radiotherapy and Nuclear Medicine）, and Civil hospital, where the data were available for the years 2004-2011. A total of 5331 new cases of female breast cancer were registered during this period. We analyzed the data in 5-year age groups 15-19, 20-24, 25-29, 30-34, 35-39, 40-44, 45-49, 50-54, 55-59, 60-64, 65-69, 70-74, 75＋. Nonparametric smoothing were used to obtained age-specific incidence curves, and then the curves are decomposed using principal components analysis to fit FTS （functional time series） model. We then used exponential smoothing statspace models to estimate the forecasts of incidence curve and construct prediction intervals. Results： The breast cancer incidence rates in Karachi increased with age for all available years. The rates increased monotonically and are relatively sharp with the age from 15 years to 50 years and then they show variability after the age of 50 years. 10-year forecasts for the female breast cancer incidence rates in Karachi show that the future rates are expected to remain stable for the age-groups 15-50 years, but they will increase for the females of 50-years and over. Hence in future, the newly diagnosed breast cancer cases in the older women in Karachi are expected to increase. Conclusion： Prediction of age related changes in breast cancer incidence rates w
文摘We study the Eisenstein series for a convex cocompact discrete subgroup on a two-dimen- sional complex hyperbolic space Hc^2. We find an inner product formula which gives the connection between Eisenstein series and automorphic Green functions on a two-dimensional complex hyperbolic space HC^2. As an application of our inner product formula, we obtain the functional equations of Eisenstein series.
文摘The article presents the proof of the validity of the generalized Riemann hypothesis on the basis of adjustment and correction of the proof of the Riemanns hypothesis in the work?[1], obtained by a finite exponential functional series and finite exponential functional progression.
基金Sponsored by the National Natural Science Foundation of China(Grant No.51277043)
文摘The uniform mathematical model of distortion signals in power grid has been setup with the theory of Wiener-G Functional. Firstly,the Matlab simulation models were established. Secondly,the Wiener kernel of power load was found based on the Gaussian white noise as input. And then the uniform mathematical model of the power grid signal was established according to the homogeneous of the same order of Wiener functional series. Finally,taking three typical distortion sources which are semiconductor rectifier,electric locomotive and electric arc furnace in power grid as examples,we have validated the model through the Matlab simulation and analyzed the simulation errors. The results show that the uniform mathematical model of distortion signals in power grid can approximation the actual model by growing the items of the series under the condition of the enough storage space and computing speed.
文摘Let is the Walsh generalized system. In the paper constructed a weighted space , and series in the Walsh generalized system with monotonically decreasing coefficient such that for each function in the space one can find a subseries that converges to in the weighted and almost everywhere on [0,1].
文摘Using the properties of theta-series and Schwarz reflection principle, a proof for Riemann hypothesis (RH) is directly presented and the first ten nontrivial zeros are easily obtained. From now on RH becomes Riemann Theorem (RT) and all its equivalent results and the consequences assuming RH are true.
基金NSFC(Grant No.12171427/U21A20426/11771390)Zhejiang Provincial Natural Science Foundation(Grant No.LZ21A010002)the Fundamental Research Funds for the Central Universities(Grant No.2021XZZX002)。
文摘Multiple change-points estimation for functional time series is studied in this paper.The change-point problem is first transformed into a high-dimensional sparse estimation problem via basis functions.Group least absolute shrinkage and selection operator(LASSO)is then applied to estimate the number and the locations of possible change points.However,the group LASSO(GLASSO)always overestimate the true points.To circumvent this problem,a further Information Criterion(IC)is applied to eliminate the redundant estimated points.It is shown that the proposed two-step procedure estimates the number and the locations of the change-points consistently.Simulations and two temperature data examples are also provided to illustrate the finite sample performance of the proposed method.
基金supported by the National Research Foundation of Korea (NRF)grant funded by the Korean government (No.2016R1A3B 1908249)the Samsung Semiconductor Research Center at Korea University for their support (No.IO201211-08116-01).
文摘Two-dimensional(2D)semiconducting materials and transition-metal oxides are promising materials for nonvolatile memory and brain-inspired neuromorphic computing applications.However,it remains chal-lenging to obtain high-quality stacked 2D films with low energy consumptions(or drive currents)be-cause of their high interfacial resistance.In this study,we synthesized 2D Ti_(3)C_(2)T_(x)MXene-derived three-dimensional(3D)TiO_(2)nanoflowers(NFs)as a feasible resistive switching(RS)material with outstanding electronic properties and synaptic learning capabilities.The electrical and optical characteristics of the synthesized material were determined through density functional theory calculations.Electrical measure-ments of the Al/Ti_(3)C_(2)T_(x)-TiO_(2)NF/Pt memory device indicated the occurrence of forming-free switching phenomena with extremely low switching voltages(0.68-0.53 V),stable ON/OFF ratio(2.3×103),and retention greater than 105 s.The Holt-Winters exponential smoothing technique was used for mod-eling and predicting the switching voltages of the RS device.The mechanism underlying the reliable RS was confirmed by observing the dense conductive filaments through conductive atomic force mi-croscopy.Interestingly,the 2D Ti_(3)C_(2)T_(x)MXene-derived 3D TiO_(2)NF-based RS device mimicked the po-tentiation/depression and spike-time-dependent plasticity of a biological synapse.Finally,a convolutional neural network was implemented based on the observed synaptic weights of Al/Ti_(3)C_(2)T_(x)-TiO_(2)NF/Pt for image-edge detection.
