This paper focuses on the ideological and political construction of the course“Probability Theory and Mathematical Statistics.”Aiming at the current situation in teaching where emphasis is placed on knowledge impart...This paper focuses on the ideological and political construction of the course“Probability Theory and Mathematical Statistics.”Aiming at the current situation in teaching where emphasis is placed on knowledge imparting while value guidance is neglected,and combined with the requirements of ideological and political education policies in the new era,this paper explores the integration path between professional courses and ideological and political education.Through literature analysis,case comparison,and empirical research,the study proposes a systematic implementation plan covering the design of teaching objectives,the reconstruction of teaching content,and the optimization of the evaluation system.The purpose is to cultivate students’sense of social responsibility and innovative awareness by excavating the ideological and political elements in mathematics.The research results provide practical reference for colleges and universities to deepen the reform of ideological and political education in courses,and promote the implementation of the fundamental task of fostering virtue through education in STEM education.展开更多
With the rapid development of higher education in China,colleges and universities are facing new challenges and impacts in talent training.Probability Theory and Mathematical Statistics is one of the important courses...With the rapid development of higher education in China,colleges and universities are facing new challenges and impacts in talent training.Probability Theory and Mathematical Statistics is one of the important courses in higher education for science and engineering majors and economics and management majors.Its critical role in cultivating students’thinking skills and improving their problem-solving skills is self-evident.Course ideological and political education construction is an important link in college talent training work.Combining ideological and political education with course teaching can help students establish correct value concepts and play a certain role in improving their comprehensive ability and quality.At present,the construction of ideological and political education in the Probability Theory and Mathematical Statistics course still faces some problems,mainly manifested in the lack of attention paid by teachers to course ideological and political education,insufficient exploitation of ideological and political elements,and the simplification of ideological and political education implementation methods.In order to comprehensively deepen the construction of course ideological and political education in line with the actual needs of Probability Theory and Mathematical Statistics course teaching,we should strengthen the construction of teacher teams,improve teachers’ability to carry out course ideological and political education,integrate educational resources,develop educational resources for ideological and political education,and innovate teaching methods to improve the overall effect of ideological and political education integration.展开更多
The probability calculus and statistics as well permeate nearly every discipline and professional sector, while no theories underpinning this wide spreading field reached universal consensus so far. The probability in...The probability calculus and statistics as well permeate nearly every discipline and professional sector, while no theories underpinning this wide spreading field reached universal consensus so far. The probability interpretations present irreconcilable traits, so the concept of probability is still substantially unclear. Purpose of this work: The present paper intends to demonstrate how the different models of probability constitute the facial problem which conceals another hidden and more fundamental question. Method: We show how authors do not agree with the concept of probability P and moreover they have different ideas about the precise object qualified by P, which has priority from the point of logic. It is clear how the element X measured by P(X) influences its meaning. In consequence of the conflicting opinions, theorists tend toward a compromise. They use the outcome or result of an experiment as the argument X of P(X) and represent X as a subset of the event space. This paper suggests replacing the outcome-subset with the event-triad E, which provides a comprehensive mathematical support. Results: The last section shows how the triadic model is formally consistent with the conventional theories and can integrate the conflicting views on probability. This unifying result can help mathematicians to go beyond the present theoretical deadlock. In summary, this paper advocates a more explicit notation system for probability and points out how probability can be ambiguous without rigorous specification of the sample space and the experiment in general.展开更多
The knowledge of probability is fully reflected in people's daily life and production. People know the world. By using the tools of probability and mathematical statistics, people can scientifically and reasonably...The knowledge of probability is fully reflected in people's daily life and production. People know the world. By using the tools of probability and mathematical statistics, people can scientifically and reasonably analyze various complex problems and data, thus significantly improving people's quality of life. At the same time, they can accurately predict the law and trend of things development based on the existing data. Because of these advantages, probability theory and mathematical statistics have become the direction of many complicated problems. At present, people are in great need of big data analysis. Similarly, people also need a better way for big data analysis to deal with various difficult problems in actual production and life.展开更多
Outcome_Based Education(OBE)is an educational philosophy based on learning outcomes,emphasizing the development of students’learning outcomes and abilities.Based on the OBE concept,this article proposes reform object...Outcome_Based Education(OBE)is an educational philosophy based on learning outcomes,emphasizing the development of students’learning outcomes and abilities.Based on the OBE concept,this article proposes reform objectives for probability theory and mathematical statistics courses,revises the curriculum outline,develops personalized after-school learning materials,emphasizes mathematical modeling,focuses on the use of data analysis software,reforms traditional teaching methods,and constructs new teaching models to comprehensively improve the quality of classroom teaching.展开更多
Taking the advantage of Internet of Things(IoT)enabled measurements,this paper formulates the event detection problem as an information-plus-noise model,and detects events in power systems based on free probability th...Taking the advantage of Internet of Things(IoT)enabled measurements,this paper formulates the event detection problem as an information-plus-noise model,and detects events in power systems based on free probability theory(FPT).Using big data collected from phasor measurement units(PMUs),we construct the event detection matrix to reflect both spatial and temporal characteristics of power gird states.The event detection matrix is further described as an information matrix plus a noise matrix,and the essence of event detection is to extract event information from the event detection matrix.By associating the event detection problem with FPT,the empirical spectral distributions(ESDs)related moments of the sample covariance matrix of the information matrix are computed,to distinguish events from“noises”,including normal fluctuations,background noises,and measurement errors.Based on central limit theory(CLT),the alarm threshold is computed using measurements collected in normal states.Additionally,with the aid of sliding window,this paper builds an event detection architecture to reflect power grid state and detect events online.Case studies with simulated data from Anhui,China,and real PMU data from Guangdong,China,verify the effectiveness of the proposed method.Compared with other data-driven methods,the proposed method is more sensitive and has better adaptability to the normal fluctuations,background noises,and measurement errors in real PMU cases.In addition,it does not require large number of training samples as needed in the training-testing paradigm.展开更多
In the evaluation of some simulation systems, only small samples data are gotten due to the limited conditions. In allusion to the evaluation problem of small sample data, an interval estimation approach with the impr...In the evaluation of some simulation systems, only small samples data are gotten due to the limited conditions. In allusion to the evaluation problem of small sample data, an interval estimation approach with the improved grey confidence degree is proposed.On the basis of the definition of grey distance, three kinds of definition of the grey weight for every sample element in grey estimated value are put forward, and then the improved grey confidence degree is designed. In accordance with the new concept, the grey interval estimation for small sample data is deduced. Furthermore,the bootstrap method is applied for more accurate grey confidence interval. Through resampling of the bootstrap, numerous small samples with the corresponding confidence intervals can be obtained. Then the final confidence interval is calculated from the union of these grey confidence intervals. In the end, the simulation system evaluation using the proposed method is conducted. The simulation results show that the reasonable confidence interval is acquired, which demonstrates the feasibility and effectiveness of the proposed method.展开更多
Steganalysis attack is to statistically estimate the embedded watermark in the watermarked multimedia,and the estimated watermark may be destroyed by the attacker.The existing methods of false negative probability,how...Steganalysis attack is to statistically estimate the embedded watermark in the watermarked multimedia,and the estimated watermark may be destroyed by the attacker.The existing methods of false negative probability,however,do not consider the influence of steganalysis attack.This paper proposed the game theory based false negative probability to estimate the impacts of steganalysis attack,as well as unintentional attack.Specifically,game theory was used to model the collision between the embedment and steganalysis attack,and derive the optimal building embedding/attacking strategy.Such optimal playing strategies devote to calculating the attacker destructed watermark,used for calculation of the game theory based false negative probability.The experimental results show that watermark detection reliability measured using our proposed method,in comparison,can better reflect the real scenario in which the embedded watermark undergoes unintentional attack and the attacker using steganalysis attack.This paper provides a foundation for investigating countermeasures of digital watermarking community against steganalysis attack.展开更多
Relations between statistical residence time series and effective shooting are analyzed in accordance with the properties of the random residence time of maneuver targets crossing shot area in a given time. An estimat...Relations between statistical residence time series and effective shooting are analyzed in accordance with the properties of the random residence time of maneuver targets crossing shot area in a given time. An estimation method for kill probability is proposed, which solves the probability of number of residence times satisfied effective shooting in given time. Some expressions and their approximate formulae of kill probability are derived, under known the distribution of residence time series. Theoretical analysis and simulation results show that this method is suitable for evaluating the hit ability of fire system for maneuver targets in random shooting.展开更多
Aiming at the characteristics of complex logic relation and multiple dynamic gates in system,its failure probability model is established based on dynamic fault tree. For the multi-state dynamic fault tree,it can be t...Aiming at the characteristics of complex logic relation and multiple dynamic gates in system,its failure probability model is established based on dynamic fault tree. For the multi-state dynamic fault tree,it can be transferred into Markov chain with continuous parameters. The state transfer diagram can be decomposed into several state transfer chains,and the failure probability models can be derived according to the lengths of the chains. Then,the failure probability of the dynamic fault tree analysis(DFTA) can be obtained by adding each chain's probability. The failure probability calculation of DFTA based on the continuous parameter Markov chain is proposed and proved. Given an example,the analytic method is compared with the conventional methods which have to solve the differential equation. It is known from the results that the analytic method can be applied to engineering easily.展开更多
An algorithm for automatically extracting feature points is developed after the area of feature points in 2-dimensional (2D) imagebeing located by probability theory, correlated methods and criterion for abnormity. Fe...An algorithm for automatically extracting feature points is developed after the area of feature points in 2-dimensional (2D) imagebeing located by probability theory, correlated methods and criterion for abnormity. Feature points in 2D image can be extracted only by calculating standard deviation of gray within sampled pixels area in our approach statically. While extracting feature points, the limitation to confirm threshold by tentative method according to some a priori information on processing image can be avoided. It is proved that the proposed algorithm is valid and reliable by extracting feature points on actual natural images with abundant and weak texture, including multi-object with complex background, respectively. It can meet the demand of extracting feature points of 2D image automatically in machine vision system.展开更多
In this paper, we conduct research on the applications of advanced mathematics on the mathematical modeling and the inner connections with linear algebra and the probability statistics. Aiming at model in mathematical...In this paper, we conduct research on the applications of advanced mathematics on the mathematical modeling and the inner connections with linear algebra and the probability statistics. Aiming at model in mathematical modeling and solving and model of evaluation and promotion of the two links, put forward the ＂bystander＂ and ＂the authorities＂ this two characters, and points out that excellent mathematical modeling participants should have ＂from a bystander to the authorities＂ and ＂from the authorities to return to bystanders＂ two-way role transformation ability. Great situation in mathematics teaching, by means of the mathematical modeling formed in the development of the teachers, as well as the teaching thought, teaching experience and achievements, the onward march of mathematical experiment should be faster than mathematical modeling. Our research provides the new paradigm for the math development which will be meaningful.展开更多
The purpose of the present study is to investigate the presence of multi-fractal behaviours in the traffic time series not only by statistical approaches but also by geometrical approaches. The pointwisc Hǒlder expon...The purpose of the present study is to investigate the presence of multi-fractal behaviours in the traffic time series not only by statistical approaches but also by geometrical approaches. The pointwisc Hǒlder exponent of a function is calculated by developing an algorithm for the numerical evaluation of HSlder exponent of time series. The traffic time series observed on the Beijing Yuquanying highway are analysed. The results from all these methods indicate that the traffic data exhibit the multi-fractal behaviour.展开更多
While the conventional forensic scientists routinely validate and express the results of their investigations quantitatively using statistical measures from probability theory,digital forensics examiners rarely if eve...While the conventional forensic scientists routinely validate and express the results of their investigations quantitatively using statistical measures from probability theory,digital forensics examiners rarely if ever do so.In this paper,we review some of the quantitative tools and techniques which are available for use in digital forensic investigations,including Bayesian networks,complexity theory,information theory and probability theory,and indicate how they may be used to obtain likelihood ratios or odds ratios for the relative plausibility of alternative explanations for the creation of the recovered digital evidence.The potential benefits of such quantitative measures for modern digital forensics are also outlined.展开更多
Correspondence imaging is a new modality of ghost imaging, which can retrieve a positive/negative image by simple conditional averaging of the reference frames that correspond to relatively large/small values of the t...Correspondence imaging is a new modality of ghost imaging, which can retrieve a positive/negative image by simple conditional averaging of the reference frames that correspond to relatively large/small values of the total intensity measured at the bucket detector. Here we propose and experimentally demonstrate a more rigorous and general approach in which a ghost image is retrieved by calculating a Pearson correlation coefficient between the bucket detector intensity and the brightness at a given pixel of the reference frames, and at the next pixel, and so on. Furthermore, we theoretically provide a statistical interpretation of these two imaging phenomena, and explain how the error depends on the sample size and what kind of distribution the error obeys. According to our analysis, the image signal-to-noise ratio can be greatly improved and the sampling number reduced by means of our new method.展开更多
We study the stochastic motion of a Brownian particle driven by a constant force over a static periodic potential. We show that both the effective diffusion and the effective drag coefficient are mathematically well-d...We study the stochastic motion of a Brownian particle driven by a constant force over a static periodic potential. We show that both the effective diffusion and the effective drag coefficient are mathematically well-defined and we derive analytic expressions for these two quantities. We then investigate the asymptotic behaviors of the effective diffusion and the effective drag coefficient, respectively, for small driving force and for large driving force. In the case of small driving force, the effective diffusion is reduced from its Brownian value by a factor that increases exponentially with the amplitude of the potential. The effective drag coefficient is increased by approximately the same factor. As a result, the Einstein relation between the diffusion coefficient and the drag coefficient is approximately valid when the driving force is small. For moderately large driving force, both the effective diffusion and the effective drag coefficient are increased from their Brownian values, and the Einstein relation breaks down. In the limit of very large driving force, both the effective diffusion and the effective drag coefficient converge to their Brownian values and the Einstein relation is once again valid.展开更多
With the bias between the predetermined planting location and the fact mine position,slant range of SLMM(submarine launch mobile mine)appears randomly scattered.The normal distribution model of slant range was propose...With the bias between the predetermined planting location and the fact mine position,slant range of SLMM(submarine launch mobile mine)appears randomly scattered.The normal distribution model of slant range was proposed by the distribution theory of multivariate random variables,and the simplified model based on key parameters was present,and the laws of slant range distribution parameters such as mean and variance were given,which were affected by key parameters.The conclusions ensure that slant range of SLMM can be controlled when laying mines and provide the basis for tactical decision-making.展开更多
基金Shaanxi Provincial 14th Five-Year Plan for Educational Science Research(SGH24Q481)。
文摘This paper focuses on the ideological and political construction of the course“Probability Theory and Mathematical Statistics.”Aiming at the current situation in teaching where emphasis is placed on knowledge imparting while value guidance is neglected,and combined with the requirements of ideological and political education policies in the new era,this paper explores the integration path between professional courses and ideological and political education.Through literature analysis,case comparison,and empirical research,the study proposes a systematic implementation plan covering the design of teaching objectives,the reconstruction of teaching content,and the optimization of the evaluation system.The purpose is to cultivate students’sense of social responsibility and innovative awareness by excavating the ideological and political elements in mathematics.The research results provide practical reference for colleges and universities to deepen the reform of ideological and political education in courses,and promote the implementation of the fundamental task of fostering virtue through education in STEM education.
基金2023 General Project of Philosophy and Social Science Research in Universities of Jiangsu Province“Exploration and Practice of Mixed Teaching Model Oriented by Curriculum Ideology and Politics in the Course of Probability Theory and Mathematical Statistics”(2023SJYB1499)。
文摘With the rapid development of higher education in China,colleges and universities are facing new challenges and impacts in talent training.Probability Theory and Mathematical Statistics is one of the important courses in higher education for science and engineering majors and economics and management majors.Its critical role in cultivating students’thinking skills and improving their problem-solving skills is self-evident.Course ideological and political education construction is an important link in college talent training work.Combining ideological and political education with course teaching can help students establish correct value concepts and play a certain role in improving their comprehensive ability and quality.At present,the construction of ideological and political education in the Probability Theory and Mathematical Statistics course still faces some problems,mainly manifested in the lack of attention paid by teachers to course ideological and political education,insufficient exploitation of ideological and political elements,and the simplification of ideological and political education implementation methods.In order to comprehensively deepen the construction of course ideological and political education in line with the actual needs of Probability Theory and Mathematical Statistics course teaching,we should strengthen the construction of teacher teams,improve teachers’ability to carry out course ideological and political education,integrate educational resources,develop educational resources for ideological and political education,and innovate teaching methods to improve the overall effect of ideological and political education integration.
文摘The probability calculus and statistics as well permeate nearly every discipline and professional sector, while no theories underpinning this wide spreading field reached universal consensus so far. The probability interpretations present irreconcilable traits, so the concept of probability is still substantially unclear. Purpose of this work: The present paper intends to demonstrate how the different models of probability constitute the facial problem which conceals another hidden and more fundamental question. Method: We show how authors do not agree with the concept of probability P and moreover they have different ideas about the precise object qualified by P, which has priority from the point of logic. It is clear how the element X measured by P(X) influences its meaning. In consequence of the conflicting opinions, theorists tend toward a compromise. They use the outcome or result of an experiment as the argument X of P(X) and represent X as a subset of the event space. This paper suggests replacing the outcome-subset with the event-triad E, which provides a comprehensive mathematical support. Results: The last section shows how the triadic model is formally consistent with the conventional theories and can integrate the conflicting views on probability. This unifying result can help mathematicians to go beyond the present theoretical deadlock. In summary, this paper advocates a more explicit notation system for probability and points out how probability can be ambiguous without rigorous specification of the sample space and the experiment in general.
文摘The knowledge of probability is fully reflected in people's daily life and production. People know the world. By using the tools of probability and mathematical statistics, people can scientifically and reasonably analyze various complex problems and data, thus significantly improving people's quality of life. At the same time, they can accurately predict the law and trend of things development based on the existing data. Because of these advantages, probability theory and mathematical statistics have become the direction of many complicated problems. At present, people are in great need of big data analysis. Similarly, people also need a better way for big data analysis to deal with various difficult problems in actual production and life.
基金Research Project on Education and Teaching Reform of Xi’an University of Technology in 2024(xjy2450).
文摘Outcome_Based Education(OBE)is an educational philosophy based on learning outcomes,emphasizing the development of students’learning outcomes and abilities.Based on the OBE concept,this article proposes reform objectives for probability theory and mathematical statistics courses,revises the curriculum outline,develops personalized after-school learning materials,emphasizes mathematical modeling,focuses on the use of data analysis software,reforms traditional teaching methods,and constructs new teaching models to comprehensively improve the quality of classroom teaching.
基金supported by the National Key Research and Development Program of China(No.2021YFB2401302)。
文摘Taking the advantage of Internet of Things(IoT)enabled measurements,this paper formulates the event detection problem as an information-plus-noise model,and detects events in power systems based on free probability theory(FPT).Using big data collected from phasor measurement units(PMUs),we construct the event detection matrix to reflect both spatial and temporal characteristics of power gird states.The event detection matrix is further described as an information matrix plus a noise matrix,and the essence of event detection is to extract event information from the event detection matrix.By associating the event detection problem with FPT,the empirical spectral distributions(ESDs)related moments of the sample covariance matrix of the information matrix are computed,to distinguish events from“noises”,including normal fluctuations,background noises,and measurement errors.Based on central limit theory(CLT),the alarm threshold is computed using measurements collected in normal states.Additionally,with the aid of sliding window,this paper builds an event detection architecture to reflect power grid state and detect events online.Case studies with simulated data from Anhui,China,and real PMU data from Guangdong,China,verify the effectiveness of the proposed method.Compared with other data-driven methods,the proposed method is more sensitive and has better adaptability to the normal fluctuations,background noises,and measurement errors in real PMU cases.In addition,it does not require large number of training samples as needed in the training-testing paradigm.
文摘In the evaluation of some simulation systems, only small samples data are gotten due to the limited conditions. In allusion to the evaluation problem of small sample data, an interval estimation approach with the improved grey confidence degree is proposed.On the basis of the definition of grey distance, three kinds of definition of the grey weight for every sample element in grey estimated value are put forward, and then the improved grey confidence degree is designed. In accordance with the new concept, the grey interval estimation for small sample data is deduced. Furthermore,the bootstrap method is applied for more accurate grey confidence interval. Through resampling of the bootstrap, numerous small samples with the corresponding confidence intervals can be obtained. Then the final confidence interval is calculated from the union of these grey confidence intervals. In the end, the simulation system evaluation using the proposed method is conducted. The simulation results show that the reasonable confidence interval is acquired, which demonstrates the feasibility and effectiveness of the proposed method.
基金supported by the National Natural Science Foundation of China（No. 71020107027） in part by the Doctoral Startup Fundation of Xinjiang University of Finace and Economics
文摘Steganalysis attack is to statistically estimate the embedded watermark in the watermarked multimedia,and the estimated watermark may be destroyed by the attacker.The existing methods of false negative probability,however,do not consider the influence of steganalysis attack.This paper proposed the game theory based false negative probability to estimate the impacts of steganalysis attack,as well as unintentional attack.Specifically,game theory was used to model the collision between the embedment and steganalysis attack,and derive the optimal building embedding/attacking strategy.Such optimal playing strategies devote to calculating the attacker destructed watermark,used for calculation of the game theory based false negative probability.The experimental results show that watermark detection reliability measured using our proposed method,in comparison,can better reflect the real scenario in which the embedded watermark undergoes unintentional attack and the attacker using steganalysis attack.This paper provides a foundation for investigating countermeasures of digital watermarking community against steganalysis attack.
基金Sponsored by the National Defense Funds under Grant(9140C300602080C30)Natural Science Foundation of Shanxi Province China(2008011011)
文摘Relations between statistical residence time series and effective shooting are analyzed in accordance with the properties of the random residence time of maneuver targets crossing shot area in a given time. An estimation method for kill probability is proposed, which solves the probability of number of residence times satisfied effective shooting in given time. Some expressions and their approximate formulae of kill probability are derived, under known the distribution of residence time series. Theoretical analysis and simulation results show that this method is suitable for evaluating the hit ability of fire system for maneuver targets in random shooting.
文摘Aiming at the characteristics of complex logic relation and multiple dynamic gates in system,its failure probability model is established based on dynamic fault tree. For the multi-state dynamic fault tree,it can be transferred into Markov chain with continuous parameters. The state transfer diagram can be decomposed into several state transfer chains,and the failure probability models can be derived according to the lengths of the chains. Then,the failure probability of the dynamic fault tree analysis(DFTA) can be obtained by adding each chain's probability. The failure probability calculation of DFTA based on the continuous parameter Markov chain is proposed and proved. Given an example,the analytic method is compared with the conventional methods which have to solve the differential equation. It is known from the results that the analytic method can be applied to engineering easily.
文摘An algorithm for automatically extracting feature points is developed after the area of feature points in 2-dimensional (2D) imagebeing located by probability theory, correlated methods and criterion for abnormity. Feature points in 2D image can be extracted only by calculating standard deviation of gray within sampled pixels area in our approach statically. While extracting feature points, the limitation to confirm threshold by tentative method according to some a priori information on processing image can be avoided. It is proved that the proposed algorithm is valid and reliable by extracting feature points on actual natural images with abundant and weak texture, including multi-object with complex background, respectively. It can meet the demand of extracting feature points of 2D image automatically in machine vision system.
文摘In this paper, we conduct research on the applications of advanced mathematics on the mathematical modeling and the inner connections with linear algebra and the probability statistics. Aiming at model in mathematical modeling and solving and model of evaluation and promotion of the two links, put forward the ＂bystander＂ and ＂the authorities＂ this two characters, and points out that excellent mathematical modeling participants should have ＂from a bystander to the authorities＂ and ＂from the authorities to return to bystanders＂ two-way role transformation ability. Great situation in mathematics teaching, by means of the mathematical modeling formed in the development of the teachers, as well as the teaching thought, teaching experience and achievements, the onward march of mathematical experiment should be faster than mathematical modeling. Our research provides the new paradigm for the math development which will be meaningful.
文摘The purpose of the present study is to investigate the presence of multi-fractal behaviours in the traffic time series not only by statistical approaches but also by geometrical approaches. The pointwisc Hǒlder exponent of a function is calculated by developing an algorithm for the numerical evaluation of HSlder exponent of time series. The traffic time series observed on the Beijing Yuquanying highway are analysed. The results from all these methods indicate that the traffic data exhibit the multi-fractal behaviour.
文摘While the conventional forensic scientists routinely validate and express the results of their investigations quantitatively using statistical measures from probability theory,digital forensics examiners rarely if ever do so.In this paper,we review some of the quantitative tools and techniques which are available for use in digital forensic investigations,including Bayesian networks,complexity theory,information theory and probability theory,and indicate how they may be used to obtain likelihood ratios or odds ratios for the relative plausibility of alternative explanations for the creation of the recovered digital evidence.The potential benefits of such quantitative measures for modern digital forensics are also outlined.
基金supported by the National Key Scientific Instrument and Equipment Development Project of China(Grant No.2013YQ030595)the National High Technology Research and Development Program of China(Grant No.2013AA122902)
文摘Correspondence imaging is a new modality of ghost imaging, which can retrieve a positive/negative image by simple conditional averaging of the reference frames that correspond to relatively large/small values of the total intensity measured at the bucket detector. Here we propose and experimentally demonstrate a more rigorous and general approach in which a ghost image is retrieved by calculating a Pearson correlation coefficient between the bucket detector intensity and the brightness at a given pixel of the reference frames, and at the next pixel, and so on. Furthermore, we theoretically provide a statistical interpretation of these two imaging phenomena, and explain how the error depends on the sample size and what kind of distribution the error obeys. According to our analysis, the image signal-to-noise ratio can be greatly improved and the sampling number reduced by means of our new method.
文摘We study the stochastic motion of a Brownian particle driven by a constant force over a static periodic potential. We show that both the effective diffusion and the effective drag coefficient are mathematically well-defined and we derive analytic expressions for these two quantities. We then investigate the asymptotic behaviors of the effective diffusion and the effective drag coefficient, respectively, for small driving force and for large driving force. In the case of small driving force, the effective diffusion is reduced from its Brownian value by a factor that increases exponentially with the amplitude of the potential. The effective drag coefficient is increased by approximately the same factor. As a result, the Einstein relation between the diffusion coefficient and the drag coefficient is approximately valid when the driving force is small. For moderately large driving force, both the effective diffusion and the effective drag coefficient are increased from their Brownian values, and the Einstein relation breaks down. In the limit of very large driving force, both the effective diffusion and the effective drag coefficient converge to their Brownian values and the Einstein relation is once again valid.
基金Sponsored by the Science Research Development Foundation of Dalian Naval Academy(2009032)
文摘With the bias between the predetermined planting location and the fact mine position,slant range of SLMM(submarine launch mobile mine)appears randomly scattered.The normal distribution model of slant range was proposed by the distribution theory of multivariate random variables,and the simplified model based on key parameters was present,and the laws of slant range distribution parameters such as mean and variance were given,which were affected by key parameters.The conclusions ensure that slant range of SLMM can be controlled when laying mines and provide the basis for tactical decision-making.
