The classical power law relaxation, i.e. relaxation of current with inverse of power of time for a step-voltage excitation to dielectric—as popularly known as Curie-von Schweidler law is empirically derived and is ob...The classical power law relaxation, i.e. relaxation of current with inverse of power of time for a step-voltage excitation to dielectric—as popularly known as Curie-von Schweidler law is empirically derived and is observed in several relaxation experiments on various dielectrics studies since late 19th Century. This relaxation law is also regarded as “universal-law” for dielectric relaxations;and is also termed as power law. This empirical Curie-von Schewidler relaxation law is then used to derive fractional differential equations describing constituent expression for capacitor. In this paper, we give simple mathematical treatment to derive the distribution of relaxation rates of this Curie-von Schweidler law, and show that the relaxation rate follows Zipf’s power law distribution. We also show the method developed here give Zipfian power law distribution for relaxing time constants. Then we will show however mathematically correct this may be, but physical interpretation from the obtained time constants distribution are contradictory to the Zipfian rate relaxation distribution. In this paper, we develop possible explanation that as to why Zipfian distribution of relaxation rates appears for Curie-von Schweidler Law, and relate this law to time variant rate of relaxation. In this paper, we derive appearance of fractional derivative while using Zipfian power law distribution that gives notion of scale dependent relaxation rate function for Curie-von Schweidler relaxation phenomena. This paper gives analytical approach to get insight of a non-Debye relaxation and gives a new treatment to especially much used empirical Curie-von Schweidler (universal) relaxation law.展开更多
It is shown that time asymmetry is essential for deriving thermodynamic law and arises from the turnover of energy while reducing its information content and driving entropy increase. A dynamically interpreted princip...It is shown that time asymmetry is essential for deriving thermodynamic law and arises from the turnover of energy while reducing its information content and driving entropy increase. A dynamically interpreted principle of least action enables time asymmetry and time flow as a generation of action and redefines useful energy as an information system which implements a form of acting information. This is demonstrated using a basic formula, originally applied for time symmetry/energy conservation considerations, relating time asymmetry (which is conventionally denied but here expressly allowed), to energy behaviour. The results derived then explained that a dynamic energy is driving time asymmetry. It is doing it by decreasing the information content of useful energy, thus generating action and entropy increase, explaining action-time as an information phenomenon. Thermodynamic laws follow directly. The formalism derived readily explains what energy is, why it is conserved (1st law of thermodynamics), why entropy increases (2nd law) and that maximum entropy production within the restraints of the system controls self-organized processes of non-linear irreversible thermodynamics. The general significance of the principle of least action arises from its role of controlling the action generating oriented time of nature. These results contrast with present understanding of time neutrality and clock-time, which are here considered a source of paradoxes, intellectual contradictions and dead-end roads in models explaining nature and the universe.展开更多
This paper examines the enduring impact of Jean-Baptiste Say’s A Treatise on Political Economy on classical economic theory and modern economic policy.It highlights Say’s Law,which posits that supply creates its own...This paper examines the enduring impact of Jean-Baptiste Say’s A Treatise on Political Economy on classical economic theory and modern economic policy.It highlights Say’s Law,which posits that supply creates its own demand,challenging mercantilist views and emphasizing the intrinsic link between production and consumption.The paper also discusses Say’s vision of the entrepreneur as a catalyst for economic growth through innovation and resource allocation,distinguishing him from his contemporaries.It also explores his concept of self-regulating markets,tracing its origins to Adam Smith and its development through Say’s work,which suggests that individual actions in pursuit of self-interest lead to efficient resource allocation without significant government intervention.The paper acknowledges the critiques on Say’s Law,particularly during economic downturns,and the subsequent rise of Keynesian economics,which advocates government intervention to stimulate demand.Finally,it reflects on Say’s legacy,including his influence on subsequent economic thought,and the global application of his principles in various economic policies.The paper concludes that Say’s insights,while contested and flawed,remain important to understand market economies and shaping economic policy in the face of contemporary challenges.展开更多
Background:Against the backdrop of the complex interplay between global migration flows and the European Union’s governance system,immigrants’subjective well-being(SWB)has become a crucial indicator for assessing bo...Background:Against the backdrop of the complex interplay between global migration flows and the European Union’s governance system,immigrants’subjective well-being(SWB)has become a crucial indicator for assessing both their social integration and the effectiveness of integration policies.However,few studies have systematically linked immigration law and policy to SWB through a structured framework of human needs.This study aims to assess how European Union(EU)immigration policies influence immigrants’SWB by facilitating the fulfillment of hierarchical needs based on Maslow’s theory.Methods:Using data from the European Social Survey(ESS,2010–2023),this study analyzed 28,854 first-generation and second-generation immigrants across 24 EU member states.This study employed hierarchical regression models to assess the relative contribution of five levels of needs-physiological,safety,social,esteem,and self-actualization-in predicting life satisfaction and happiness,controlling for sociodemographic factors.Results:Safety needs-comprising perceived safety and institutional trust-produced the largest model improvement(ΔR^(2)≈0.06–0.07).Physiological needs(stable income and self-rated health)also had significant positive effect(β=0.06–0.25,p<0.001).Social and esteem needs showed moderate associations(β≈0.09–0.17,p<0.001),while self-actualization needs(education and union membership)displayed generational variation(β=0.02–0.10,p<0.01).Conclusion:This study not only validates the applicability of Maslow’s theory in migration research but also empirically establishes a policy hierarchy:ensuring physiological and safety needs as a foundation,supporting social and esteem needs,and enabling self-actualization pathways are essential for enhancing immigrant well-being.The findings offer valuable theoretical insights and practical guidance for refining immigrant integration policies within the EU’s multi-level governance structure.展开更多
From a basic probabilistic argumentation, the Zipfian distribution and Benford’s law are derived. It is argued that Zipf’s law fits to calculate the rank probabilities of identical indistinguishable objects and that...From a basic probabilistic argumentation, the Zipfian distribution and Benford’s law are derived. It is argued that Zipf’s law fits to calculate the rank probabilities of identical indistinguishable objects and that Benford’s distribution fits to calculate the rank probabilities of distinguishable objects. i.e. in the distribution of words in long texts all the words in a given rank are identical, therefore, the rank distribution is Zipfian. In logarithmic tables, the objects with identical 1st digits are distinguishable as there are many different digits in the 2nd, 3rd… places, etc., and therefore the distribution is according to Benford’s law. Pareto 20 - 80 rule is shown to be an outcome of Benford’s distribution as when the number of ranks is about 10 the probability of 20% of the high probability ranks is equal to the probability of the rest of 80% low probability ranks. It is argued that all these distributions, including the central limit theorem, are outcomes of Planck’s law and are the result of the quantization of energy. This argumentation may be considered a physical origin of probability.展开更多
Urban Agglomeration(UA)is regarded as an emerging complex urban system in China.The development of UA demands a reasonable scale structure,which can be investigated by Zipf’s law.However,few studies have been conduct...Urban Agglomeration(UA)is regarded as an emerging complex urban system in China.The development of UA demands a reasonable scale structure,which can be investigated by Zipf’s law.However,few studies have been conducted to quantify the optimal scale of UA and how its development deviates from the optimal scale.With the continuous urban expansion,the problem of UAs’scale structure has received increasing attention.In this study,we propose a method based on Zipf’s law for estimating the theoretical optimal scale of UAs in China and assessing the deviation rate from their optimal scales.Twelve typical UAs in China are selected,and their development is assessed via urban impervious surface data from 2000 to 2018.The results show that the average deviation rate of the investigated UAs decreased from 3.40%in 2000 to 2.32%in 2018,demonstrating that these UAs are on a positive evolution trajectory.Furthermore,according to the development stage,we make recommendations on“large cities vs.medium/small-sized cities and promoting vs.restraining”to each UA based on its size.The conceptual and analytical knowledge,as well as the results from this study,are expected to offer valuable insights and new references for regulating and managing UAs’development in China.展开更多
Introduction: The law of Zipf-Mandelbrot is a power law, which has been observed in natural languages. A mathematical diagnosis of fetal cardiac dynamics has been developed with this law. Objective: To develop a metho...Introduction: The law of Zipf-Mandelbrot is a power law, which has been observed in natural languages. A mathematical diagnosis of fetal cardiac dynamics has been developed with this law. Objective: To develop a methodology for diagnostic aid to assess the degree of complexity of adult cardiac dynamics by Zipf-Mandelbrot law. Methodology: A mathematical induction was done for this;two groups of Holter recordings were selected: 11 with normal diagnosis and 11 with acute disease of each group, one Holter of each group was chosen for the induction, the law of Zipf-Mandelbrot was applied to evaluate the degree of complexity of each Holter, searching similarities or differences between the dynamics. A blind study was done with 20 Holters calculating sensitivity, specificity and the coefficient kappa. Results: The complexity grade of a normal cardiac dynamics varied between 0.9483 and 0.7046, and for an acute dynamic between 0.6707 and 0.4228. Conclusions: A new physical mathematical methodology for diagnostic aid was developed;it showed that the degree of complexity of normal cardiac dynamics was higher than those with acute disease, showing quantitatively how cardiac dynamics can evolve to acute state.展开更多
Generalised reduced masses with a set of equations governing the three relative motions between two of 3-bodies in their gravitational field are established,of which the dynamic characteristics of 3-body dynamics,fund...Generalised reduced masses with a set of equations governing the three relative motions between two of 3-bodies in their gravitational field are established,of which the dynamic characteristics of 3-body dynamics,fundamental bases of this paper,are revealed.Based on these findings,an equivalent system is developed,which is a 2-body system with its total mass,constant angular momentum,kinetic and potential energies same as the total ones of three relative motions,so that it can be solved using the well-known theory of the 2-body system.From the solution of an equivalent system with the revealed characteristics of three relative motions,the general theoretical solutions of the 3-body system are obtained in the curve-integration forms along the orbits in the imaged radial motion space.The possible periodical orbits with generalised Kepler’s law are presented.Following the description and mathematical demonstrations of the proposed methods,the examples including Euler’s/Lagrange’s problems,and a reported numerical one are solved to validate the proposed methods.The methods derived from the 3-body system are extended to N-body problems.展开更多
The basic physics of unsteady Hele-Shaw flow at high Reynolds numbers is mainly studied by an experimental measurement. In order to confirm the Darcy′s law in Hele-Shaw cell, since there is an analogy between flow in...The basic physics of unsteady Hele-Shaw flow at high Reynolds numbers is mainly studied by an experimental measurement. In order to confirm the Darcy′s law in Hele-Shaw cell, since there is an analogy between flow in cells and that in porous media, progressive water waves are utilized to build an unsteady flow in a Hele-Shaw cell, and which complex wave number is measured by a wave height gauge. Meanwhile, theoretical analyses are used to compare with experimental data. Result shows Darcy′s Law is not exactly correct for unsteady Hele-Shaw flows, and it is expected to conduct a modified Darcy′s Law.展开更多
Let{Xn;n≥1}be a sequence of i.i.d, random variables with finite variance,Q（n）be the related R/S statistics. It is proved that lim ε↓0 ε^2 ∑n=1 ^8 n log n/1 P{Q（n）≥ε√2n log log n}=2/1 EY^2,where Y=sup0≤t...Let{Xn;n≥1}be a sequence of i.i.d, random variables with finite variance,Q（n）be the related R/S statistics. It is proved that lim ε↓0 ε^2 ∑n=1 ^8 n log n/1 P{Q（n）≥ε√2n log log n}=2/1 EY^2,where Y=sup0≤t≤1B（t）-inf0≤t≤sB（t）,and B（t） is a Brownian bridge.展开更多
We give some theorems of strong law of large numbers and complete convergence for sequences of φ-mixing random variables. In particular, Wittmann＇s strong law of large numbers and Teicher＇s strong law of large nnum...We give some theorems of strong law of large numbers and complete convergence for sequences of φ-mixing random variables. In particular, Wittmann＇s strong law of large numbers and Teicher＇s strong law of large nnumbers for independent random variables are generalized to the case of φ -minxing random variables.展开更多
As the advent and growing popularity of image rendering software,photorealistic computer graphics are becoming more and more perceptually indistinguishable from photographic images.If the faked images are abused,it ma...As the advent and growing popularity of image rendering software,photorealistic computer graphics are becoming more and more perceptually indistinguishable from photographic images.If the faked images are abused,it may lead to potential social,legal or private consequences.To this end,it is very necessary and also challenging to find effective methods to differentiate between them.In this paper,a novel leading digit law,also called Benford's law,based method to identify computer graphics is proposed.More specifically,statistics of the most significant digits are extracted from image's Discrete Cosine Transform(DCT) coefficients and magnitudes of image's gradient,and then the Support Vector Machine(SVM) based classifiers are built.Results of experiments on the image datasets indicate that the proposed method is comparable to prior works.Besides,it possesses low dimensional features and low computational complexity.展开更多
This paper focuses on the Noether symmetries and the conserved quantities for both holonomic and nonholonomic systems based on a new non-conservative dynamical model introduced by E1-Nabulsi. First, the E1-Nabulsi dyn...This paper focuses on the Noether symmetries and the conserved quantities for both holonomic and nonholonomic systems based on a new non-conservative dynamical model introduced by E1-Nabulsi. First, the E1-Nabulsi dynamical model which is based on a fractional integral extended by periodic laws is introduced, and E1-Nabulsi-Hamilton＇s canoni- cal equations for non-conservative Hamilton system with holonomic or nonholonomic constraints are established. Second, the definitions and criteria of E1-Nabulsi-Noether symmetrical transformations and quasi-symmetrical transformations are presented in terms of the invariance of E1-Nabulsi-Hamilton action under the infinitesimal transformations of the group. Fi- nally, Noether＇s theorems for the non-conservative Hamilton system under the E1-Nabulsi dynamical system are established, which reveal the relationship between the Noether symmetry and the conserved quantity of the system.展开更多
Beverloo's scaling law can describe the flow rate of grains discharging from hoppers. In this paper, we show that the Beverloo's scaling law is valid for varying material parameters. The flow rates from a hopp...Beverloo's scaling law can describe the flow rate of grains discharging from hoppers. In this paper, we show that the Beverloo's scaling law is valid for varying material parameters. The flow rates from a hopper with different hopper and orifice sizes(D, D_0) are studied by running large-scale simulations. When the hopper size is fixed, the numerical results show that Beverloo's law is valid even if the orifice diameter is very large and then the criteria for this law are discussed.To eliminate the effect of walls, it is found that the criteria can be suggested as D-D_0≥ 40 d or D/D_0≥ 2. Interestingly,it is found that there is still a scaling relation between the flow rate and orifice diameter if D/D_0 is fixed and less than 2.When the orifice diameter is close to the hopper size, the velocity field changes and the vertical velocities of grains above the free fall region are much larger. Then, the free fall arch assumption is invalid and Beverloo's law is inapplicable.展开更多
文摘The classical power law relaxation, i.e. relaxation of current with inverse of power of time for a step-voltage excitation to dielectric—as popularly known as Curie-von Schweidler law is empirically derived and is observed in several relaxation experiments on various dielectrics studies since late 19th Century. This relaxation law is also regarded as “universal-law” for dielectric relaxations;and is also termed as power law. This empirical Curie-von Schewidler relaxation law is then used to derive fractional differential equations describing constituent expression for capacitor. In this paper, we give simple mathematical treatment to derive the distribution of relaxation rates of this Curie-von Schweidler law, and show that the relaxation rate follows Zipf’s power law distribution. We also show the method developed here give Zipfian power law distribution for relaxing time constants. Then we will show however mathematically correct this may be, but physical interpretation from the obtained time constants distribution are contradictory to the Zipfian rate relaxation distribution. In this paper, we develop possible explanation that as to why Zipfian distribution of relaxation rates appears for Curie-von Schweidler Law, and relate this law to time variant rate of relaxation. In this paper, we derive appearance of fractional derivative while using Zipfian power law distribution that gives notion of scale dependent relaxation rate function for Curie-von Schweidler relaxation phenomena. This paper gives analytical approach to get insight of a non-Debye relaxation and gives a new treatment to especially much used empirical Curie-von Schweidler (universal) relaxation law.
文摘It is shown that time asymmetry is essential for deriving thermodynamic law and arises from the turnover of energy while reducing its information content and driving entropy increase. A dynamically interpreted principle of least action enables time asymmetry and time flow as a generation of action and redefines useful energy as an information system which implements a form of acting information. This is demonstrated using a basic formula, originally applied for time symmetry/energy conservation considerations, relating time asymmetry (which is conventionally denied but here expressly allowed), to energy behaviour. The results derived then explained that a dynamic energy is driving time asymmetry. It is doing it by decreasing the information content of useful energy, thus generating action and entropy increase, explaining action-time as an information phenomenon. Thermodynamic laws follow directly. The formalism derived readily explains what energy is, why it is conserved (1st law of thermodynamics), why entropy increases (2nd law) and that maximum entropy production within the restraints of the system controls self-organized processes of non-linear irreversible thermodynamics. The general significance of the principle of least action arises from its role of controlling the action generating oriented time of nature. These results contrast with present understanding of time neutrality and clock-time, which are here considered a source of paradoxes, intellectual contradictions and dead-end roads in models explaining nature and the universe.
文摘This paper examines the enduring impact of Jean-Baptiste Say’s A Treatise on Political Economy on classical economic theory and modern economic policy.It highlights Say’s Law,which posits that supply creates its own demand,challenging mercantilist views and emphasizing the intrinsic link between production and consumption.The paper also discusses Say’s vision of the entrepreneur as a catalyst for economic growth through innovation and resource allocation,distinguishing him from his contemporaries.It also explores his concept of self-regulating markets,tracing its origins to Adam Smith and its development through Say’s work,which suggests that individual actions in pursuit of self-interest lead to efficient resource allocation without significant government intervention.The paper acknowledges the critiques on Say’s Law,particularly during economic downturns,and the subsequent rise of Keynesian economics,which advocates government intervention to stimulate demand.Finally,it reflects on Say’s legacy,including his influence on subsequent economic thought,and the global application of his principles in various economic policies.The paper concludes that Say’s insights,while contested and flawed,remain important to understand market economies and shaping economic policy in the face of contemporary challenges.
文摘Background:Against the backdrop of the complex interplay between global migration flows and the European Union’s governance system,immigrants’subjective well-being(SWB)has become a crucial indicator for assessing both their social integration and the effectiveness of integration policies.However,few studies have systematically linked immigration law and policy to SWB through a structured framework of human needs.This study aims to assess how European Union(EU)immigration policies influence immigrants’SWB by facilitating the fulfillment of hierarchical needs based on Maslow’s theory.Methods:Using data from the European Social Survey(ESS,2010–2023),this study analyzed 28,854 first-generation and second-generation immigrants across 24 EU member states.This study employed hierarchical regression models to assess the relative contribution of five levels of needs-physiological,safety,social,esteem,and self-actualization-in predicting life satisfaction and happiness,controlling for sociodemographic factors.Results:Safety needs-comprising perceived safety and institutional trust-produced the largest model improvement(ΔR^(2)≈0.06–0.07).Physiological needs(stable income and self-rated health)also had significant positive effect(β=0.06–0.25,p<0.001).Social and esteem needs showed moderate associations(β≈0.09–0.17,p<0.001),while self-actualization needs(education and union membership)displayed generational variation(β=0.02–0.10,p<0.01).Conclusion:This study not only validates the applicability of Maslow’s theory in migration research but also empirically establishes a policy hierarchy:ensuring physiological and safety needs as a foundation,supporting social and esteem needs,and enabling self-actualization pathways are essential for enhancing immigrant well-being.The findings offer valuable theoretical insights and practical guidance for refining immigrant integration policies within the EU’s multi-level governance structure.
文摘From a basic probabilistic argumentation, the Zipfian distribution and Benford’s law are derived. It is argued that Zipf’s law fits to calculate the rank probabilities of identical indistinguishable objects and that Benford’s distribution fits to calculate the rank probabilities of distinguishable objects. i.e. in the distribution of words in long texts all the words in a given rank are identical, therefore, the rank distribution is Zipfian. In logarithmic tables, the objects with identical 1st digits are distinguishable as there are many different digits in the 2nd, 3rd… places, etc., and therefore the distribution is according to Benford’s law. Pareto 20 - 80 rule is shown to be an outcome of Benford’s distribution as when the number of ranks is about 10 the probability of 20% of the high probability ranks is equal to the probability of the rest of 80% low probability ranks. It is argued that all these distributions, including the central limit theorem, are outcomes of Planck’s law and are the result of the quantization of energy. This argumentation may be considered a physical origin of probability.
基金supported in part by the National Natural Science Foundation of China[Grants number 42090012]03 Special Research and 5G Project of Jiangxi Province in China[Grants number 20212ABC03A09]Zhuhai Industry University Research Cooperation Project of China[Grants number ZH22017001210098PWC].
文摘Urban Agglomeration(UA)is regarded as an emerging complex urban system in China.The development of UA demands a reasonable scale structure,which can be investigated by Zipf’s law.However,few studies have been conducted to quantify the optimal scale of UA and how its development deviates from the optimal scale.With the continuous urban expansion,the problem of UAs’scale structure has received increasing attention.In this study,we propose a method based on Zipf’s law for estimating the theoretical optimal scale of UAs in China and assessing the deviation rate from their optimal scales.Twelve typical UAs in China are selected,and their development is assessed via urban impervious surface data from 2000 to 2018.The results show that the average deviation rate of the investigated UAs decreased from 3.40%in 2000 to 2.32%in 2018,demonstrating that these UAs are on a positive evolution trajectory.Furthermore,according to the development stage,we make recommendations on“large cities vs.medium/small-sized cities and promoting vs.restraining”to each UA based on its size.The conceptual and analytical knowledge,as well as the results from this study,are expected to offer valuable insights and new references for regulating and managing UAs’development in China.
文摘Introduction: The law of Zipf-Mandelbrot is a power law, which has been observed in natural languages. A mathematical diagnosis of fetal cardiac dynamics has been developed with this law. Objective: To develop a methodology for diagnostic aid to assess the degree of complexity of adult cardiac dynamics by Zipf-Mandelbrot law. Methodology: A mathematical induction was done for this;two groups of Holter recordings were selected: 11 with normal diagnosis and 11 with acute disease of each group, one Holter of each group was chosen for the induction, the law of Zipf-Mandelbrot was applied to evaluate the degree of complexity of each Holter, searching similarities or differences between the dynamics. A blind study was done with 20 Holters calculating sensitivity, specificity and the coefficient kappa. Results: The complexity grade of a normal cardiac dynamics varied between 0.9483 and 0.7046, and for an acute dynamic between 0.6707 and 0.4228. Conclusions: A new physical mathematical methodology for diagnostic aid was developed;it showed that the degree of complexity of normal cardiac dynamics was higher than those with acute disease, showing quantitatively how cardiac dynamics can evolve to acute state.
文摘Generalised reduced masses with a set of equations governing the three relative motions between two of 3-bodies in their gravitational field are established,of which the dynamic characteristics of 3-body dynamics,fundamental bases of this paper,are revealed.Based on these findings,an equivalent system is developed,which is a 2-body system with its total mass,constant angular momentum,kinetic and potential energies same as the total ones of three relative motions,so that it can be solved using the well-known theory of the 2-body system.From the solution of an equivalent system with the revealed characteristics of three relative motions,the general theoretical solutions of the 3-body system are obtained in the curve-integration forms along the orbits in the imaged radial motion space.The possible periodical orbits with generalised Kepler’s law are presented.Following the description and mathematical demonstrations of the proposed methods,the examples including Euler’s/Lagrange’s problems,and a reported numerical one are solved to validate the proposed methods.The methods derived from the 3-body system are extended to N-body problems.
文摘The basic physics of unsteady Hele-Shaw flow at high Reynolds numbers is mainly studied by an experimental measurement. In order to confirm the Darcy′s law in Hele-Shaw cell, since there is an analogy between flow in cells and that in porous media, progressive water waves are utilized to build an unsteady flow in a Hele-Shaw cell, and which complex wave number is measured by a wave height gauge. Meanwhile, theoretical analyses are used to compare with experimental data. Result shows Darcy′s Law is not exactly correct for unsteady Hele-Shaw flows, and it is expected to conduct a modified Darcy′s Law.
基金Project Supported by NSFC (10131040)SRFDP (2002335090)
文摘A law of iterated logarithm for R/S statistics with the help of the strong approximations of R/S statistics by functions of a Wiener process is shown.
文摘Let{Xn;n≥1}be a sequence of i.i.d, random variables with finite variance,Q（n）be the related R/S statistics. It is proved that lim ε↓0 ε^2 ∑n=1 ^8 n log n/1 P{Q（n）≥ε√2n log log n}=2/1 EY^2,where Y=sup0≤t≤1B（t）-inf0≤t≤sB（t）,and B（t） is a Brownian bridge.
文摘数据增广是提升深度学习模型性能的有效方法之一。针对多类别目标检测任务中检测性能不平衡问题,提出一种针对“短板类别”(检测性能远低于模型平均检测性能的类别)的离线数据增广方法。受Cannikin’s Law的启发,采用基于复制粘贴(copy-paste)机制的场景多样性增广方法。随机采集训练集中“短板类别”实例区域,通过相似性度量机制选取训练集中增广目标样本进行随机粘贴。为了降低随机粘贴导致的遮挡问题,采用基于自遮挡(cut-replace)机制的增广方法提升模型遮挡表达能力。通过截取样本自身区域,对特征表达最显著区域进行遮挡。实验表明,FCOS目标检测框架在PASCAL VOC数据上的平均检测精度(mean average precision,mAP)从79.10%提升到83.90%,其中短板类别更为显著,提升了20.8个百分点。在MS-COCO数据上平均检测精度提升了0.9个百分点。
基金Supported by the National Natural Science Foundation of China (10671149)
文摘We give some theorems of strong law of large numbers and complete convergence for sequences of φ-mixing random variables. In particular, Wittmann＇s strong law of large numbers and Teicher＇s strong law of large nnumbers for independent random variables are generalized to the case of φ -minxing random variables.
文摘As the advent and growing popularity of image rendering software,photorealistic computer graphics are becoming more and more perceptually indistinguishable from photographic images.If the faked images are abused,it may lead to potential social,legal or private consequences.To this end,it is very necessary and also challenging to find effective methods to differentiate between them.In this paper,a novel leading digit law,also called Benford's law,based method to identify computer graphics is proposed.More specifically,statistics of the most significant digits are extracted from image's Discrete Cosine Transform(DCT) coefficients and magnitudes of image's gradient,and then the Support Vector Machine(SVM) based classifiers are built.Results of experiments on the image datasets indicate that the proposed method is comparable to prior works.Besides,it possesses low dimensional features and low computational complexity.
基金supported by the National Natural Science Foundation of China(Grant Nos.10972151 and 11272227)the Innovation Program for Postgraduate in Higher Education Institutions of Jiangsu Province,China(Grant No.CXLX11_0961)
文摘This paper focuses on the Noether symmetries and the conserved quantities for both holonomic and nonholonomic systems based on a new non-conservative dynamical model introduced by E1-Nabulsi. First, the E1-Nabulsi dynamical model which is based on a fractional integral extended by periodic laws is introduced, and E1-Nabulsi-Hamilton＇s canoni- cal equations for non-conservative Hamilton system with holonomic or nonholonomic constraints are established. Second, the definitions and criteria of E1-Nabulsi-Noether symmetrical transformations and quasi-symmetrical transformations are presented in terms of the invariance of E1-Nabulsi-Hamilton action under the infinitesimal transformations of the group. Fi- nally, Noether＇s theorems for the non-conservative Hamilton system under the E1-Nabulsi dynamical system are established, which reveal the relationship between the Noether symmetry and the conserved quantity of the system.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11705256 and 11605264)
文摘Beverloo's scaling law can describe the flow rate of grains discharging from hoppers. In this paper, we show that the Beverloo's scaling law is valid for varying material parameters. The flow rates from a hopper with different hopper and orifice sizes(D, D_0) are studied by running large-scale simulations. When the hopper size is fixed, the numerical results show that Beverloo's law is valid even if the orifice diameter is very large and then the criteria for this law are discussed.To eliminate the effect of walls, it is found that the criteria can be suggested as D-D_0≥ 40 d or D/D_0≥ 2. Interestingly,it is found that there is still a scaling relation between the flow rate and orifice diameter if D/D_0 is fixed and less than 2.When the orifice diameter is close to the hopper size, the velocity field changes and the vertical velocities of grains above the free fall region are much larger. Then, the free fall arch assumption is invalid and Beverloo's law is inapplicable.
