Based on the maximum entropy principle, a probability density function (PDF) is derived for the distribution of wave heights in a random wave field, without any more hypothesis. The present PDF, being a non-Rayleigh f...Based on the maximum entropy principle, a probability density function (PDF) is derived for the distribution of wave heights in a random wave field, without any more hypothesis. The present PDF, being a non-Rayleigh form, involves two parameters: the average wave height H— and the state parameter γ. The role of γ in the distribution of wave heights is examined. It is found that γ may be a certain measure of sea state. A least square method for determining γ from measured data is proposed. In virtue of the method, the values of γ are determined for three sea states from the data measured in the East China Sea. The present PDF is compared with the well known Rayleigh PDF of wave height and it is shown that it much better fits the data than the Rayleigh PDF. It is expected that the present PDF would fit some other wave variables, since its derivation is not restricted only to the wave height.展开更多
Marine environmental design parameter extrapolation has important applications in marine engineering and coastal disaster prevention.The distribution models used for environmental design parameter usually pass the hyp...Marine environmental design parameter extrapolation has important applications in marine engineering and coastal disaster prevention.The distribution models used for environmental design parameter usually pass the hypothesis tests in statistical analysis,but the calculation results of different distribution models often vary largely.In this paper,based on the information entropy,the overall uncertainty test criteria were studied for commonly used distributions including Gumbel,Weibull,and Pearson-III distribution.An improved method for parameter estimation of the maximum entropy distribution model is proposed on the basis of moment estimation.The study in this paper shows that the number of sample data and the degree of dispersion are proportional to the information entropy,and the overall uncertainty of the maximum entropy distribution model is minimal compared with other models.展开更多
A new compound distribution model for extreme wave heights of typhoon-affected sea areas is proposed on the basis of the maximum-entropy principle. The new model is formed by nesting a discrete distribution in a conti...A new compound distribution model for extreme wave heights of typhoon-affected sea areas is proposed on the basis of the maximum-entropy principle. The new model is formed by nesting a discrete distribution in a continuous one, having eight parameters which can be determined in terms of observed data of typhoon occurrence-frequency and extreme wave heights by numerically solving two sets of equations derived in this paper. The model is examined by using it to predict the N-year return-period wave height at two hydrology stations in the Yellow Sea, and the predicted results are compared with those predicted by use of some other compound distribution models. Examinations and comparisons show that the model has some advantages for predicting the N-year return-period wave height in typhoon-affected sea areas.展开更多
Tibetan spruce (Picea smithiana) is an endemic species of the Himalayas,and it distributes only in a re-stricted area with very low number.To address the lack of detailed distributional information,we used maximum en-...Tibetan spruce (Picea smithiana) is an endemic species of the Himalayas,and it distributes only in a re-stricted area with very low number.To address the lack of detailed distributional information,we used maximum en-tropy (Maxent) niche-based model to predict the species' potential distribution from limited occurrence-only records.The location data of P.smithiana,relative bioclimatic variables,vegetation data,digital elevation model (DEM),and the derived data were analyzed in Maxent.The receiver operating characteristic (ROC) curve was applied to assess the prediction accuracy.The Maxent jackknife test was performed to quantify the training gains from data layers and the response of P.smithiana distribution to four typical environmental variables was analyzed.Results show that the model performs well at the regional scale.There is a potential for continued expansion of P.smithiana population numbers and distribution in China.P.smithiana potentially distributes in the lower reaches of Gyirong Zangbo and Poiqu rivers in Gyirong and Nyalam counties in Qomolangma (Mount Everest) National Nature Preserve (QNNP),China.The species prefers warm temperate climate in mountain area and mainly distributes in needle-leaved evergreen closed to open forest and mixed forest along the river valley at relatively low altitudes of about 2000-3000 m.Model simulations suggest that distribution patterns of rare species with few species numbers can be well predicted by Max-ent.展开更多
Configurational information entropy(CIE)analysis has been shown to be applicable for determining the neutron skin thickness(δnp)of neutron-rich nuclei from fragment production in projectile fragmentation reactions.Th...Configurational information entropy(CIE)analysis has been shown to be applicable for determining the neutron skin thickness(δnp)of neutron-rich nuclei from fragment production in projectile fragmentation reactions.The BNN+FRACS machine learning model was adopted to predict the fragment mass cross-sections(σ_(A))of the projectile fragmentation reactions induced by calcium isotopes from ^(36)Ca to ^(56)Ca on a ^(9)Be target at 140MeV/u.The fast Fourier transform was adopted to decompose the possible information compositions inσA distributions and determine the quantity of CIE(S_(A)[f]).It was found that the range of fragments significantly influences the quantity of S_(A)[f],which results in different trends of S_(A)[f]~δnp correlation.The linear S_(A)[f]~δnp correlation in a previous study[Nucl.Sci.Tech.33,6(2022)]could be reproduced using fragments with relatively large mass fragments,which verifies that S_(A)[f]determined from fragmentσAis sensitive to the neutron skin thickness of neutron-rich isotopes.展开更多
The new distributions of the statistics of wave groups based on the maximum entropy principle are presented. The maximum entropy distributions appear to be superior to conventional distributions when applied to a limi...The new distributions of the statistics of wave groups based on the maximum entropy principle are presented. The maximum entropy distributions appear to be superior to conventional distributions when applied to a limited amount of information. Its applications to the wave group properties show the effectiveness of the maximum entropy distribution. FFF filtering method is employed to obtain the wave envelope fast and efficiently. Comparisons of both the maximum entropy distribution and the distribution of Longuet-Higgins （1984） with the laboratory wind-wave data show that the former gives a better fit.展开更多
This paper concerns an application of a popular existing law, the maximum entropy principle, to the study of statistical distribution of the ocean wave heights. Under two proper premisses. a conclusion that the wave h...This paper concerns an application of a popular existing law, the maximum entropy principle, to the study of statistical distribution of the ocean wave heights. Under two proper premisses. a conclusion that the wave heights obey the Weibull distribution is drawn by making use of the maximum entropy principle. From this result, we hold that the intnnsic departures using the Rayleigh distribution to describe The realistic wave height must exist, and the Weibull distribution usually used as an empirical one has profound origin in physics. The Gluhovskli's empirical wave heights distribution relying on water depth is also discussed briefly, and a possible physical explanation associated with the maximum entropy principle is carried out.展开更多
The maximum entropy distribution, which consists of various recognized theoretical distributions, is a better curve to estimate the design thickness of sea ice. Method of moment and empirical curve fitting method are ...The maximum entropy distribution, which consists of various recognized theoretical distributions, is a better curve to estimate the design thickness of sea ice. Method of moment and empirical curve fitting method are common-used parameter estimation methods for maximum entropy distribution. In this study, we propose to use the particle swarm optimization method as a new parameter estimation method for the maximum entropy distribution, which has the advantage to avoid deviation introduced by simplifications made in other methods. We conducted a case study to fit the hindcasted thickness of the sea ice in the Liaodong Bay of Bohai Sea using these three parameter-estimation methods for the maximum entropy distribution. All methods implemented in this study pass the K-S tests at 0.05 significant level. In terms of the average sum of deviation squares, the empirical curve fitting method provides the best fit for the original data, while the method of moment provides the worst. Among all three methods, the particle swarm optimization method predicts the largest thickness of the sea ice for a same return period. As a result, we recommend using the particle swarm optimization method for the maximum entropy distribution for offshore structures mainly influenced by the sea ice in winter, but using the empirical curve fitting method to reduce the cost in the design of temporary and economic buildings.展开更多
This paper deals with the Bayesian estimation of Shannon entropy for the generalized inverse exponential distribution.Assuming that the observed samples are taken from the upper record ranked set sampling(URRSS)and up...This paper deals with the Bayesian estimation of Shannon entropy for the generalized inverse exponential distribution.Assuming that the observed samples are taken from the upper record ranked set sampling(URRSS)and upper record values(URV)schemes.Formulas of Bayesian estimators are derived depending on a gamma prior distribution considering the squared error,linear exponential and precautionary loss functions,in addition,we obtain Bayesian credible intervals.The random-walk Metropolis-Hastings algorithm is handled to generate Markov chain Monte Carlo samples from the posterior distribution.Then,the behavior of the estimates is examined at various record values.The output of the study shows that the entropy Bayesian estimates under URRSS are more convenient than the other estimates under URV in the majority of the situations.Also,the entropy Bayesian estimates perform well as the number of records increases.The obtained results validate the usefulness and efficiency of the URV method.Real data is analyzed for more clarifying purposes which validate the theoretical results.展开更多
The maximum entropy principle(MEP) is one of the first methods which have been used to predict droplet size and velocity distributions of liquid sprays. This method needs a mean droplets diameter as an input to predic...The maximum entropy principle(MEP) is one of the first methods which have been used to predict droplet size and velocity distributions of liquid sprays. This method needs a mean droplets diameter as an input to predict the droplet size distribution. This paper presents a new sub-model based on the deterministic aspects of liquid atomization process independent of the experimental data to provide the mean droplets diameter for using in the maximum entropy formulation(MEF). For this purpose, a theoretical model based on the approach of energy conservation law entitled energy-based model(EBM) is presented. Based on this approach, atomization occurs due to the kinetic energy loss. Prediction of the combined model(MEF/EBM) is in good agreement with the available experimental data. The energy-based model can be used as a fast and reliable enough model to obtain a good estimation of the mean droplets diameter of a spray and the combined model(MEF/EBM) can be used to well predict the droplet size distribution at the primary breakup.展开更多
The Argentine shortfin squid Illex argentinus is an economically important short-lived species widely distributed in the southwest Atlantic Ocean.The abundance and distribution of I.argentinus are associated with clim...The Argentine shortfin squid Illex argentinus is an economically important short-lived species widely distributed in the southwest Atlantic Ocean.The abundance and distribution of I.argentinus are associated with climate change and environmental fluctuations.The potential distribution of I.argentinus was modeled with various environmental variables including sea surface temperature(SST),sea surface height(SSH),chlorophyll a,sea surface salinity(SSS),net primary productivity(NPP),mixed layer depth(MLD),eddy kinetic energy(EKE),and photosynthetically active radiation(PAR)using the maximum entropy(MaxEnt)approach during the peak fishing seasons(January–April).The habitat suitability index(HSI)was defined as the probability of species emergence from the MaxEnt model and the area of HSI≥0.6 was regarded as suitable.Results indicate that the predicted habitat correlated with the actual fishing position,with similar trends in the percentages of suitable habitats and catch per unit effort(CPUE)of I.argentinus from January to April.Moreover,SST,SSH,PAR,and MLD were identified critical environmental variables for the distribution of I.argentinus.In addition,the median of preferred ranges of the critical environmental variables were concentrated within the suitable habitats of I.argentinus.The Area under the Receiver Operating Characteristic Curve(AUC)was greater than 0.96 for all four months.Variations in latitudinal and longitudinal gravity centers(LATG and LONG)of fishing effort were consistent with latitudinal and longitudinal gravity centers(LATG_H and LONG_H)of the HSI.Our findings suggest that the MaxEnt model is an effective tool to predict the potential distribution of I.argentinus.Meanwhile,SST,SSH,PAR,and MLD should be given with more extensive attention in predicting the potential distribution of I.argentinus,as they are important environmental indicators that can help decision-makers search for the fishing ground of I.argentinus in the Southwest Atlantic.展开更多
It is generally recognized that the optimal distribution of catalyst activity in a spherical catalyst is a Dirac d-function. However, catalyst with other alternative distribution may accomplish the same reaction task ...It is generally recognized that the optimal distribution of catalyst activity in a spherical catalyst is a Dirac d-function. However, catalyst with other alternative distribution may accomplish the same reaction task without necessarily concentrating the catalyst activity in an inside thin layer. Moreover, the alternative with activity on catalyst surface may offer higher reaction rate and better utilization of reaction heat (higher exergy output). Simple cases of first-order exothermal reactions, in particular when the catalyst is limited by the maximum working temperature, are presented to demonstrate the above advantages and to show the importance of studying the optimal activity distribution with the consideration on exergy maximization and entropy production minimization.展开更多
With temperatures increasing as a result of global warming,extreme high temperatures are becoming more intense and more frequent on larger scale during summer in China.In recent years,a variety of researches have exam...With temperatures increasing as a result of global warming,extreme high temperatures are becoming more intense and more frequent on larger scale during summer in China.In recent years,a variety of researches have examined the high temperature distribution in China.However,it hardly considers the variation of temperature data and systems when defining the threshold of extreme high temperature.In order to discern the spatio-temporal distribution of extreme heat in China,we examined the daily maximum temperature data of 83 observation stations in China from 1950 to 2008.The objective of this study was to understand the distribution characteristics of extreme high temperature events defined by Detrended Fluctuation Analysis(DFA).The statistical methods of Permutation Entropy(PE)were also used in this study to analyze the temporal distribution.The results showed that the frequency of extreme high temperature events in China presented 3 periods of 7,10—13 and 16—20 years,respectively.The abrupt changes generally happened in the 1960s,the end of 1970s and early 1980s.It was also found that the maximum frequency occurred in the early 1950s,and the frequency decreased sharply until the late 1980s when an evidently increasing trend emerged.Furthermore,the annual averaged frequency of extreme high temperature events reveals a decreasing-increasing-decreasing trend from southwest to northeast China,but an increasing-decreasing trend from southeast to northwest China.And the frequency was higher in southern region than that in northern region.Besides,the maximum and minimum of frequencies were relatively concentrated spatially.Our results also shed light on the reasons for the periods and abrupt changes of the frequency of extreme high temperature events in China.展开更多
A probability density function of surface elevation is obtained through improvement of the method introduced by Cieslikiewicz who employed the maximum entropy principle to investigate the surface elevation distributio...A probability density function of surface elevation is obtained through improvement of the method introduced by Cieslikiewicz who employed the maximum entropy principle to investigate the surface elevation distribution. The density function can be easily extended to higher order according to demand and is non-negative everywhere, satisfying the basic behavior of the probability, Moreover because the distribution is derived without any assumption about sea waves, it is found from comparison with several accepted distributions that the new form of distribution can be applied in a wider range of wave conditions, In addition, the density function can be used to fit some observed distributions of surface vertical acceleration although something remains unsolved.展开更多
In this paper, we recall for physicists how it is possible using the principle of maximization of the Boltzmann-Shannon entropy to derive the Burr-Singh-Maddala (BurrXII) double power law probability distribution func...In this paper, we recall for physicists how it is possible using the principle of maximization of the Boltzmann-Shannon entropy to derive the Burr-Singh-Maddala (BurrXII) double power law probability distribution function and its approximations (Pareto, loglogistic.) and extension (GB2…) first used in econometrics. This is possible using a deformation of the power function, as this has been done in complex systems for the exponential function. We give to that distribution a deep stochastic interpretation using the theory of Weron et al. Applied to thermodynamics, the entropy nonextensivity can be accounted for by assuming that the asymptotic exponents are scale dependent. Therefore functions which describe phenomena presenting power-law asymptotic behaviour can be obtained without introducing exotic forms of the entropy.展开更多
The two statistical principles of maximum entropy and maximum likelihood are investigated for the three-parameter kappa distribution. These two methods become equivalent in the discrete case with x, β>0 where 0<...The two statistical principles of maximum entropy and maximum likelihood are investigated for the three-parameter kappa distribution. These two methods become equivalent in the discrete case with x, β>0 where 0<α=1/(2k+1)≤1, k=0,1,2…or the maximum entropy method.展开更多
Spatial variability of soil properties imposes a challenge for practical analysis and design in geotechnical engineering.The latter is particularly true for slope stability assessment,where the effects of uncertainty ...Spatial variability of soil properties imposes a challenge for practical analysis and design in geotechnical engineering.The latter is particularly true for slope stability assessment,where the effects of uncertainty are synthesized in the so-called probability of failure.This probability quantifies the reliability of a slope and its numerical calculation is usually quite involved from a numerical viewpoint.In view of this issue,this paper proposes an approach for failure probability assessment based on Latinized partially stratified sampling and maximum entropy distribution with fractional moments.The spatial variability of geotechnical properties is represented by means of random fields and the Karhunen-Loève expansion.Then,failure probabilities are estimated employing maximum entropy distribution with fractional moments.The application of the proposed approach is examined with two examples:a case study of an undrained slope and a case study of a slope with cross-correlated random fields of strength parameters under a drained slope.The results show that the proposed approach has excellent accuracy and high efficiency,and it can be applied straightforwardly to similar geotechnical engineering problems.展开更多
Background: Hylurgus ligniperda(Fabricius) is native to Europe but has established populations in many countries and regions. H. ligniperda mainly infests Pinus species, and can cause severe weakness and even death of...Background: Hylurgus ligniperda(Fabricius) is native to Europe but has established populations in many countries and regions. H. ligniperda mainly infests Pinus species, and can cause severe weakness and even death of the host through its boring activity;it can also be a vector of various pathogenic fungi. This study was conducted to investigate the environmental variables limiting the distribution of H. ligniperda and the change trend of its suitable areas under climate change.Results: We used a maximum entropy model to predict the potential geographical distribution of H. ligniperda on a global scale under near current and future climatic scenarios using its occurrence data and environmental variables. The result shows that the areas surrounding the Mediterranean region, the eastern coastal areas of Asia, and the southeastern part of Oceania are highly suitable for H. ligniperda. The environmental variables with the greatest effect on the distribution of H. ligniperda were determined using the jackknife method and Pearson’s correlation analysis and included the monthly average maximum temperature in April, precipitation of driest quarter, the monthly average minimum temperature in December, precipitation of coldest quarter, mean temperature of driest quarter and mean diurnal range.Conclusions: Excessive precipitation in winter and low temperatures in spring had a great effect on the distribution of H. ligniperda. The potential geographical distribution of H. ligniperda was predicted to change under future climatic conditions compared with near current climate conditions. Highly suitable areas, moderately suitable areas and low suitable areas were predicted to increase by 59.99%, 44.43% and 22.92%, respectively, under the2081–2100 ssp245 scenario.展开更多
In view of the problem of fine characterization of narrow and thin channels,the maximum entropy criterion is used to enhance the focusing characteristics of Wigner-Ville Distribution.On the basis of effectively improv...In view of the problem of fine characterization of narrow and thin channels,the maximum entropy criterion is used to enhance the focusing characteristics of Wigner-Ville Distribution.On the basis of effectively improving the time-frequency resolution of seismic signal,a new method of microscopic ancient river channel identification is established.Based on the principle of the equivalence between the maximum entropy power spectrum and the AR model power spectrum,the prediction error and the autoregression coefficient of AR model are obtained using the Burg algorithm and Levinson-Durbin recurrence rule.Under the condition of the first derivative of autocorrelation function being 0,the Wigner-Ville Distribution of seismic signal is calculated,and the Wigner-Ville Distribution time-frequency power spectrum(MEWVD)is obtained under the maxi-mum entropy criterion of the microscopic ancient river channel.Through analysis of emulational seismic signal and forward numerical simulation signal of narrow thin model,it is found that MEWVD can effectively avoid the interference of cross term of Wigner-Ville Distribution,and obtain more accurate spectral characteristics than STFT and CWT signal analysis methods.It is also proved that the narrow and thin river channels of different scales can be identified effectively by MEWVD of different frequencies.The method is applied to the third member of Jurassic Shaximiao Formation(J2s33-2)gas reservoir of the Zhongji-ang gas field in Sichuan Basin.The spatial information of width and direction of narrow and thin river channels with width less than 500 m and sandstone thickness less than 35 m is accurately identified,providing bases for well deployment and horizontal well fracturing section selection.展开更多
The Boltzmann equilibrium distribution is an important rigorous tool for determining entropy, since this function cannot be measured, but only calculated in accordance with Boltzmann＇s law. On the basis of the commen...The Boltzmann equilibrium distribution is an important rigorous tool for determining entropy, since this function cannot be measured, but only calculated in accordance with Boltzmann＇s law. On the basis of the commensuration coefficient of discrete and continuous similarly-named distributions developed by the authors, the article analyses the statistical sum in the Boltzmann distribution to the commensuration with the improper integral of the similarly-named function in the full range of the term of series of the statistical sum at the different combination of the temperature and the step of variation （quantum） of the particle energy. The convergence of series based on the Cauchy, Maclaurin criteria and the equal commensuration of series and improper integral of the similarly-named function in each unit interval of variation of series and similarly-named function were estab- lished. The obtained formulas for the commensuration coefficient and statistical sum were analyzed, and a general expres- sion for the total and residual statistical sums, which can be calculated with any given accuracy, is found. Given a direct calculation formula for the Boltzmann distribution, taking into account the values of the improper integral and commensuration coefficient. To determine the entropy from the new expression for the Boltzmann distribution in the form of a series, the conver- gence of the similarly-named improper integral is established. However, the commensuration coefficient of integral and series in each unit interval turns out to be dependent on the number of the term of series and therefore cannot be used to determine the sum of series through the improper integral. In this case, the entropy can be calculated with a given accuracy with a corresponding quantity of the term of series n at a fixed value of the statistical sum. The given accuracy of the statistical sum turns out to be mathematically identical to the fraction of particles with an energy exceeding a given level of the energy barrier equal to the activation energy in the Arrhenius equation. The prospect of development of the proposed method for expressing the Boltzmann distribution and entropy is to establish the relationship between the magnitude of the energy quantum Ae and the properties of the system-forming particles.展开更多
文摘Based on the maximum entropy principle, a probability density function (PDF) is derived for the distribution of wave heights in a random wave field, without any more hypothesis. The present PDF, being a non-Rayleigh form, involves two parameters: the average wave height H— and the state parameter γ. The role of γ in the distribution of wave heights is examined. It is found that γ may be a certain measure of sea state. A least square method for determining γ from measured data is proposed. In virtue of the method, the values of γ are determined for three sea states from the data measured in the East China Sea. The present PDF is compared with the well known Rayleigh PDF of wave height and it is shown that it much better fits the data than the Rayleigh PDF. It is expected that the present PDF would fit some other wave variables, since its derivation is not restricted only to the wave height.
基金This research was financially supported by the National Natural Science Foundation of China(Grant Nos.52071306 and 51379195)the Natural Science Foundation of Shandong Province(Grant No.ZR2019MEE050).
文摘Marine environmental design parameter extrapolation has important applications in marine engineering and coastal disaster prevention.The distribution models used for environmental design parameter usually pass the hypothesis tests in statistical analysis,but the calculation results of different distribution models often vary largely.In this paper,based on the information entropy,the overall uncertainty test criteria were studied for commonly used distributions including Gumbel,Weibull,and Pearson-III distribution.An improved method for parameter estimation of the maximum entropy distribution model is proposed on the basis of moment estimation.The study in this paper shows that the number of sample data and the degree of dispersion are proportional to the information entropy,and the overall uncertainty of the maximum entropy distribution model is minimal compared with other models.
基金supported by the Open Fund of the Key Laboratory of Research on Marine Hazards Forecasting (Grant No.LOMF1101)the Shanghai Typhoon Research Fund (Grant No. 2009ST05)the National Natural Science Foundation of China(Grant No. 40776006)
文摘A new compound distribution model for extreme wave heights of typhoon-affected sea areas is proposed on the basis of the maximum-entropy principle. The new model is formed by nesting a discrete distribution in a continuous one, having eight parameters which can be determined in terms of observed data of typhoon occurrence-frequency and extreme wave heights by numerically solving two sets of equations derived in this paper. The model is examined by using it to predict the N-year return-period wave height at two hydrology stations in the Yellow Sea, and the predicted results are compared with those predicted by use of some other compound distribution models. Examinations and comparisons show that the model has some advantages for predicting the N-year return-period wave height in typhoon-affected sea areas.
基金Under the auspices of National Basic Research Program of China (No.2010CB951704)Institutional Consolidation for Coordinated and Integrated Monitoring of Natural Resources towards Sustainable Development and Environmental Conservation in the Hindu Kush-Karakoram-Himalaya Mountain Complex (No.76444-000)External Cooperation Program of Chinese Academy of Sciences (No.GJHZ0954)
文摘Tibetan spruce (Picea smithiana) is an endemic species of the Himalayas,and it distributes only in a re-stricted area with very low number.To address the lack of detailed distributional information,we used maximum en-tropy (Maxent) niche-based model to predict the species' potential distribution from limited occurrence-only records.The location data of P.smithiana,relative bioclimatic variables,vegetation data,digital elevation model (DEM),and the derived data were analyzed in Maxent.The receiver operating characteristic (ROC) curve was applied to assess the prediction accuracy.The Maxent jackknife test was performed to quantify the training gains from data layers and the response of P.smithiana distribution to four typical environmental variables was analyzed.Results show that the model performs well at the regional scale.There is a potential for continued expansion of P.smithiana population numbers and distribution in China.P.smithiana potentially distributes in the lower reaches of Gyirong Zangbo and Poiqu rivers in Gyirong and Nyalam counties in Qomolangma (Mount Everest) National Nature Preserve (QNNP),China.The species prefers warm temperate climate in mountain area and mainly distributes in needle-leaved evergreen closed to open forest and mixed forest along the river valley at relatively low altitudes of about 2000-3000 m.Model simulations suggest that distribution patterns of rare species with few species numbers can be well predicted by Max-ent.
基金the National Natural Science Foundation of China(No.11975091)the Program for Innovative Research Team(in Science and Technology)in the University of Henan Province,China(No.21IRTSTHN011).
文摘Configurational information entropy(CIE)analysis has been shown to be applicable for determining the neutron skin thickness(δnp)of neutron-rich nuclei from fragment production in projectile fragmentation reactions.The BNN+FRACS machine learning model was adopted to predict the fragment mass cross-sections(σ_(A))of the projectile fragmentation reactions induced by calcium isotopes from ^(36)Ca to ^(56)Ca on a ^(9)Be target at 140MeV/u.The fast Fourier transform was adopted to decompose the possible information compositions inσA distributions and determine the quantity of CIE(S_(A)[f]).It was found that the range of fragments significantly influences the quantity of S_(A)[f],which results in different trends of S_(A)[f]~δnp correlation.The linear S_(A)[f]~δnp correlation in a previous study[Nucl.Sci.Tech.33,6(2022)]could be reproduced using fragments with relatively large mass fragments,which verifies that S_(A)[f]determined from fragmentσAis sensitive to the neutron skin thickness of neutron-rich isotopes.
基金This work was financially supported by the National Natural Science Foundation of China (Grant No50479028)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No20060423009)
文摘The new distributions of the statistics of wave groups based on the maximum entropy principle are presented. The maximum entropy distributions appear to be superior to conventional distributions when applied to a limited amount of information. Its applications to the wave group properties show the effectiveness of the maximum entropy distribution. FFF filtering method is employed to obtain the wave envelope fast and efficiently. Comparisons of both the maximum entropy distribution and the distribution of Longuet-Higgins （1984） with the laboratory wind-wave data show that the former gives a better fit.
文摘This paper concerns an application of a popular existing law, the maximum entropy principle, to the study of statistical distribution of the ocean wave heights. Under two proper premisses. a conclusion that the wave heights obey the Weibull distribution is drawn by making use of the maximum entropy principle. From this result, we hold that the intnnsic departures using the Rayleigh distribution to describe The realistic wave height must exist, and the Weibull distribution usually used as an empirical one has profound origin in physics. The Gluhovskli's empirical wave heights distribution relying on water depth is also discussed briefly, and a possible physical explanation associated with the maximum entropy principle is carried out.
基金supported by the National Natural Science Foundation of China (Nos. 51279186, 51479183, 51509227)the Shandong Province Natural Science Foundation, China (No. ZR2014EEQ030)the Fundamental Research Funds for the Central Universities (No. 201413003)
文摘The maximum entropy distribution, which consists of various recognized theoretical distributions, is a better curve to estimate the design thickness of sea ice. Method of moment and empirical curve fitting method are common-used parameter estimation methods for maximum entropy distribution. In this study, we propose to use the particle swarm optimization method as a new parameter estimation method for the maximum entropy distribution, which has the advantage to avoid deviation introduced by simplifications made in other methods. We conducted a case study to fit the hindcasted thickness of the sea ice in the Liaodong Bay of Bohai Sea using these three parameter-estimation methods for the maximum entropy distribution. All methods implemented in this study pass the K-S tests at 0.05 significant level. In terms of the average sum of deviation squares, the empirical curve fitting method provides the best fit for the original data, while the method of moment provides the worst. Among all three methods, the particle swarm optimization method predicts the largest thickness of the sea ice for a same return period. As a result, we recommend using the particle swarm optimization method for the maximum entropy distribution for offshore structures mainly influenced by the sea ice in winter, but using the empirical curve fitting method to reduce the cost in the design of temporary and economic buildings.
基金A.R.A.Alanzi would like to thank the Deanship of Scientific Research at Majmaah University for financial support and encouragement.
文摘This paper deals with the Bayesian estimation of Shannon entropy for the generalized inverse exponential distribution.Assuming that the observed samples are taken from the upper record ranked set sampling(URRSS)and upper record values(URV)schemes.Formulas of Bayesian estimators are derived depending on a gamma prior distribution considering the squared error,linear exponential and precautionary loss functions,in addition,we obtain Bayesian credible intervals.The random-walk Metropolis-Hastings algorithm is handled to generate Markov chain Monte Carlo samples from the posterior distribution.Then,the behavior of the estimates is examined at various record values.The output of the study shows that the entropy Bayesian estimates under URRSS are more convenient than the other estimates under URV in the majority of the situations.Also,the entropy Bayesian estimates perform well as the number of records increases.The obtained results validate the usefulness and efficiency of the URV method.Real data is analyzed for more clarifying purposes which validate the theoretical results.
文摘The maximum entropy principle(MEP) is one of the first methods which have been used to predict droplet size and velocity distributions of liquid sprays. This method needs a mean droplets diameter as an input to predict the droplet size distribution. This paper presents a new sub-model based on the deterministic aspects of liquid atomization process independent of the experimental data to provide the mean droplets diameter for using in the maximum entropy formulation(MEF). For this purpose, a theoretical model based on the approach of energy conservation law entitled energy-based model(EBM) is presented. Based on this approach, atomization occurs due to the kinetic energy loss. Prediction of the combined model(MEF/EBM) is in good agreement with the available experimental data. The energy-based model can be used as a fast and reliable enough model to obtain a good estimation of the mean droplets diameter of a spray and the combined model(MEF/EBM) can be used to well predict the droplet size distribution at the primary breakup.
基金Supported by the Natural Science Foundation of Shanghai(No.23ZR1427100)the National Key R&D Program of China(No.2023YFD2401303)the Shanghai Talent Development Funding for the Project(No.2021078)。
文摘The Argentine shortfin squid Illex argentinus is an economically important short-lived species widely distributed in the southwest Atlantic Ocean.The abundance and distribution of I.argentinus are associated with climate change and environmental fluctuations.The potential distribution of I.argentinus was modeled with various environmental variables including sea surface temperature(SST),sea surface height(SSH),chlorophyll a,sea surface salinity(SSS),net primary productivity(NPP),mixed layer depth(MLD),eddy kinetic energy(EKE),and photosynthetically active radiation(PAR)using the maximum entropy(MaxEnt)approach during the peak fishing seasons(January–April).The habitat suitability index(HSI)was defined as the probability of species emergence from the MaxEnt model and the area of HSI≥0.6 was regarded as suitable.Results indicate that the predicted habitat correlated with the actual fishing position,with similar trends in the percentages of suitable habitats and catch per unit effort(CPUE)of I.argentinus from January to April.Moreover,SST,SSH,PAR,and MLD were identified critical environmental variables for the distribution of I.argentinus.In addition,the median of preferred ranges of the critical environmental variables were concentrated within the suitable habitats of I.argentinus.The Area under the Receiver Operating Characteristic Curve(AUC)was greater than 0.96 for all four months.Variations in latitudinal and longitudinal gravity centers(LATG and LONG)of fishing effort were consistent with latitudinal and longitudinal gravity centers(LATG_H and LONG_H)of the HSI.Our findings suggest that the MaxEnt model is an effective tool to predict the potential distribution of I.argentinus.Meanwhile,SST,SSH,PAR,and MLD should be given with more extensive attention in predicting the potential distribution of I.argentinus,as they are important environmental indicators that can help decision-makers search for the fishing ground of I.argentinus in the Southwest Atlantic.
基金Supported by the National Natural Science Foundation of China (No. 20236050)
文摘It is generally recognized that the optimal distribution of catalyst activity in a spherical catalyst is a Dirac d-function. However, catalyst with other alternative distribution may accomplish the same reaction task without necessarily concentrating the catalyst activity in an inside thin layer. Moreover, the alternative with activity on catalyst surface may offer higher reaction rate and better utilization of reaction heat (higher exergy output). Simple cases of first-order exothermal reactions, in particular when the catalyst is limited by the maximum working temperature, are presented to demonstrate the above advantages and to show the importance of studying the optimal activity distribution with the consideration on exergy maximization and entropy production minimization.
基金Key Projects in the National Science & Technology Pillar Program during the Eleventh Five-Year Plan Period(2007BAC29B05)Jiangsu Key Laboratory of Meteorological Disaster(KLME05005)
文摘With temperatures increasing as a result of global warming,extreme high temperatures are becoming more intense and more frequent on larger scale during summer in China.In recent years,a variety of researches have examined the high temperature distribution in China.However,it hardly considers the variation of temperature data and systems when defining the threshold of extreme high temperature.In order to discern the spatio-temporal distribution of extreme heat in China,we examined the daily maximum temperature data of 83 observation stations in China from 1950 to 2008.The objective of this study was to understand the distribution characteristics of extreme high temperature events defined by Detrended Fluctuation Analysis(DFA).The statistical methods of Permutation Entropy(PE)were also used in this study to analyze the temporal distribution.The results showed that the frequency of extreme high temperature events in China presented 3 periods of 7,10—13 and 16—20 years,respectively.The abrupt changes generally happened in the 1960s,the end of 1970s and early 1980s.It was also found that the maximum frequency occurred in the early 1950s,and the frequency decreased sharply until the late 1980s when an evidently increasing trend emerged.Furthermore,the annual averaged frequency of extreme high temperature events reveals a decreasing-increasing-decreasing trend from southwest to northeast China,but an increasing-decreasing trend from southeast to northwest China.And the frequency was higher in southern region than that in northern region.Besides,the maximum and minimum of frequencies were relatively concentrated spatially.Our results also shed light on the reasons for the periods and abrupt changes of the frequency of extreme high temperature events in China.
基金This project was financially supported by the National Natural Science Foundation of China(Grant No.49876012,49976003)
文摘A probability density function of surface elevation is obtained through improvement of the method introduced by Cieslikiewicz who employed the maximum entropy principle to investigate the surface elevation distribution. The density function can be easily extended to higher order according to demand and is non-negative everywhere, satisfying the basic behavior of the probability, Moreover because the distribution is derived without any assumption about sea waves, it is found from comparison with several accepted distributions that the new form of distribution can be applied in a wider range of wave conditions, In addition, the density function can be used to fit some observed distributions of surface vertical acceleration although something remains unsolved.
文摘In this paper, we recall for physicists how it is possible using the principle of maximization of the Boltzmann-Shannon entropy to derive the Burr-Singh-Maddala (BurrXII) double power law probability distribution function and its approximations (Pareto, loglogistic.) and extension (GB2…) first used in econometrics. This is possible using a deformation of the power function, as this has been done in complex systems for the exponential function. We give to that distribution a deep stochastic interpretation using the theory of Weron et al. Applied to thermodynamics, the entropy nonextensivity can be accounted for by assuming that the asymptotic exponents are scale dependent. Therefore functions which describe phenomena presenting power-law asymptotic behaviour can be obtained without introducing exotic forms of the entropy.
文摘The two statistical principles of maximum entropy and maximum likelihood are investigated for the three-parameter kappa distribution. These two methods become equivalent in the discrete case with x, β>0 where 0<α=1/(2k+1)≤1, k=0,1,2…or the maximum entropy method.
基金funding support from the China Scholarship Council(CSC).
文摘Spatial variability of soil properties imposes a challenge for practical analysis and design in geotechnical engineering.The latter is particularly true for slope stability assessment,where the effects of uncertainty are synthesized in the so-called probability of failure.This probability quantifies the reliability of a slope and its numerical calculation is usually quite involved from a numerical viewpoint.In view of this issue,this paper proposes an approach for failure probability assessment based on Latinized partially stratified sampling and maximum entropy distribution with fractional moments.The spatial variability of geotechnical properties is represented by means of random fields and the Karhunen-Loève expansion.Then,failure probabilities are estimated employing maximum entropy distribution with fractional moments.The application of the proposed approach is examined with two examples:a case study of an undrained slope and a case study of a slope with cross-correlated random fields of strength parameters under a drained slope.The results show that the proposed approach has excellent accuracy and high efficiency,and it can be applied straightforwardly to similar geotechnical engineering problems.
基金funded by National Key R&D Program of China(No. 2021YFC2600400)National Natural Science Foundation of China(No. 32171794)Forestry Science and Technology Innovation Special of Jiangxi Forestry Department (No. 201912)
文摘Background: Hylurgus ligniperda(Fabricius) is native to Europe but has established populations in many countries and regions. H. ligniperda mainly infests Pinus species, and can cause severe weakness and even death of the host through its boring activity;it can also be a vector of various pathogenic fungi. This study was conducted to investigate the environmental variables limiting the distribution of H. ligniperda and the change trend of its suitable areas under climate change.Results: We used a maximum entropy model to predict the potential geographical distribution of H. ligniperda on a global scale under near current and future climatic scenarios using its occurrence data and environmental variables. The result shows that the areas surrounding the Mediterranean region, the eastern coastal areas of Asia, and the southeastern part of Oceania are highly suitable for H. ligniperda. The environmental variables with the greatest effect on the distribution of H. ligniperda were determined using the jackknife method and Pearson’s correlation analysis and included the monthly average maximum temperature in April, precipitation of driest quarter, the monthly average minimum temperature in December, precipitation of coldest quarter, mean temperature of driest quarter and mean diurnal range.Conclusions: Excessive precipitation in winter and low temperatures in spring had a great effect on the distribution of H. ligniperda. The potential geographical distribution of H. ligniperda was predicted to change under future climatic conditions compared with near current climate conditions. Highly suitable areas, moderately suitable areas and low suitable areas were predicted to increase by 59.99%, 44.43% and 22.92%, respectively, under the2081–2100 ssp245 scenario.
基金Supported by the General Project of National Natural Science Foundation(4207416041574099)the Sichuan Science and Tech-nology Plan Project(2020JDRC0013)。
文摘In view of the problem of fine characterization of narrow and thin channels,the maximum entropy criterion is used to enhance the focusing characteristics of Wigner-Ville Distribution.On the basis of effectively improving the time-frequency resolution of seismic signal,a new method of microscopic ancient river channel identification is established.Based on the principle of the equivalence between the maximum entropy power spectrum and the AR model power spectrum,the prediction error and the autoregression coefficient of AR model are obtained using the Burg algorithm and Levinson-Durbin recurrence rule.Under the condition of the first derivative of autocorrelation function being 0,the Wigner-Ville Distribution of seismic signal is calculated,and the Wigner-Ville Distribution time-frequency power spectrum(MEWVD)is obtained under the maxi-mum entropy criterion of the microscopic ancient river channel.Through analysis of emulational seismic signal and forward numerical simulation signal of narrow thin model,it is found that MEWVD can effectively avoid the interference of cross term of Wigner-Ville Distribution,and obtain more accurate spectral characteristics than STFT and CWT signal analysis methods.It is also proved that the narrow and thin river channels of different scales can be identified effectively by MEWVD of different frequencies.The method is applied to the third member of Jurassic Shaximiao Formation(J2s33-2)gas reservoir of the Zhongji-ang gas field in Sichuan Basin.The spatial information of width and direction of narrow and thin river channels with width less than 500 m and sandstone thickness less than 35 m is accurately identified,providing bases for well deployment and horizontal well fracturing section selection.
文摘The Boltzmann equilibrium distribution is an important rigorous tool for determining entropy, since this function cannot be measured, but only calculated in accordance with Boltzmann＇s law. On the basis of the commensuration coefficient of discrete and continuous similarly-named distributions developed by the authors, the article analyses the statistical sum in the Boltzmann distribution to the commensuration with the improper integral of the similarly-named function in the full range of the term of series of the statistical sum at the different combination of the temperature and the step of variation （quantum） of the particle energy. The convergence of series based on the Cauchy, Maclaurin criteria and the equal commensuration of series and improper integral of the similarly-named function in each unit interval of variation of series and similarly-named function were estab- lished. The obtained formulas for the commensuration coefficient and statistical sum were analyzed, and a general expres- sion for the total and residual statistical sums, which can be calculated with any given accuracy, is found. Given a direct calculation formula for the Boltzmann distribution, taking into account the values of the improper integral and commensuration coefficient. To determine the entropy from the new expression for the Boltzmann distribution in the form of a series, the conver- gence of the similarly-named improper integral is established. However, the commensuration coefficient of integral and series in each unit interval turns out to be dependent on the number of the term of series and therefore cannot be used to determine the sum of series through the improper integral. In this case, the entropy can be calculated with a given accuracy with a corresponding quantity of the term of series n at a fixed value of the statistical sum. The given accuracy of the statistical sum turns out to be mathematically identical to the fraction of particles with an energy exceeding a given level of the energy barrier equal to the activation energy in the Arrhenius equation. The prospect of development of the proposed method for expressing the Boltzmann distribution and entropy is to establish the relationship between the magnitude of the energy quantum Ae and the properties of the system-forming particles.
