Waveforms of seismic events,extracted from January 2019 to December 2021 were used to construct a test dataset to investigate the generalizability of PhaseNet in the Shandong region.The results show that errors in the...Waveforms of seismic events,extracted from January 2019 to December 2021 were used to construct a test dataset to investigate the generalizability of PhaseNet in the Shandong region.The results show that errors in the picking of seismic phases(P-and Swaves)had a broadly normal distribution,mainly concentrated in the ranges of−0.4–0.3 s and−0.4–0.8 s,respectively.These results were compared with those published in the original PhaseNet article and were found to be approximately 0.2–0.4 s larger.PhaseNet had a strong generalizability for P-and S-wave picking for epicentral distances of less than 120 km and 110 km,respectively.However,the phase recall rate decreased rapidly when these distances were exceeded.Furthermore,the generalizability of PhaseNet was essentially unaffected by magnitude.The M4.1 earthquake sequence in Changqing,Shandong province,China,that occurred on February 18,2020,was adopted as a case study.PhaseNet detected more than twice the number of earthquakes in the manually obtained catalog.This further verified that PhaseNet has strong generalizability in the Shandong region,and a high-precision earthquake catalog was constructed.According to these precise positioning results,two earthquake sequences occurred in the study area,and the southern cluster may have been triggered by the northern cluster.The focal mechanism solution,regional stress field,and the location results of the northern earthquake sequence indicated that the seismic force of the earthquake was consistent with the regional stress field.展开更多
Wireless communication involving unmanned aerial vehicles(UAVs)is expected to play an important role in future wireless networks.However,different from conventional terrestrial communication systems,UAVs typically hav...Wireless communication involving unmanned aerial vehicles(UAVs)is expected to play an important role in future wireless networks.However,different from conventional terrestrial communication systems,UAVs typically have rather limited onboard energy on one hand,and require additional flying energy consumption on the other hand.This renders energy-efficient UAV communication with smart energy expenditure of paramount importance.In this paper,via extensive flight experiments,we aim to firstly validate the recently derived theoretical energy model for rotary-wing UAVs,and then develop a general model for those complicated flight scenarios where rigorous theoretical model derivation is quite challenging,if not impossible.Specifically,we first investigate how UAV power consumption varies with its flying speed for the simplest straight-and-level flight.With about 12,000 valid power-speed data points collected,we first apply the model-based curve fitting to obtain the modelling parameters based on the theoretical closed-form energy model in the existing literature.In addition,in order to exclude the potential bias caused by the theoretical energy model,the obtained measurement data is also trained using a model-free deep neural network.It is found that the obtained curve from both methods can match quite well with the theoretical energy model.Next,we further extend the study to arbitrary 2-dimensional(2-D)flight,where,to our best knowledge,no rigorous theoretical derivation is available for the closed-form energy model as a function of its flying speed,direction,and acceleration.To fill the gap,we first propose a heuristic energy model for these more complicated cases,and then provide experimental validation based on the measurement results for circular level flight.展开更多
Complicated changes occur inside the steel parts during quenching process. A three dimensional nonlinear mathematical model for quenching process has been established and the numerical simulation on temperature field,...Complicated changes occur inside the steel parts during quenching process. A three dimensional nonlinear mathematical model for quenching process has been established and the numerical simulation on temperature field, microstructure and stress field has been realized. The alternative technique for the formation of high-strength materials has been developed on the basis of intensification of heat transfer at phase transformations. The technology for the achievement of maximum compressive residual stresses on the hard surface is introduced. It has been shown that there is an optimal depth of hard layer providing the maximum compression stresses on the surface. It has also been established that in the surface hard layer additional strengthening (superstrengthening) of the material is observed. The generalized formula for the determination of the time of reaching maximum compressive stresses on the surface has been proposed.展开更多
The constraints and the operations play an important role in database generalization.They guide and govern database generalization.The constraints are translation of the required conditions that should take into accou...The constraints and the operations play an important role in database generalization.They guide and govern database generalization.The constraints are translation of the required conditions that should take into account not only the objects and relationships among objects but also spatial data schema (classification and aggregation hierarchy) associated with the final existing database.The operations perform the actions of generalization in support of data reduction in the database.The constraints in database generalization are still lack of research.There is still the lack of frameworks to express the constraints and the operations on the basis of object_oriented data structure in database generalization.This paper focuses on the frameworks for generalization operations and constraints on the basis of object_oriented data structure in database generalization.The constraints as the attributes of the object and the operations as the methods of the object can be encapsulated in classes.They have the inheritance and polymorphism property.So the framework of the constraints and the operations which are based on object_oriented data structure can be easily understood and implemented.The constraint and the operations based on object_oriented database are proposed based on object_oriented database.The frameworks for generalization operations,constraints and relations among objects based on object_oriented data structure in database generalization are designed.The categorical database generalization is concentrated on in this paper.展开更多
This article presents very original and relatively brief or very brief proofs about of two famous problems: 1) Are there any odd perfect numbers? and 2) “Fermat’s last theorem: A new proof of theorem and its general...This article presents very original and relatively brief or very brief proofs about of two famous problems: 1) Are there any odd perfect numbers? and 2) “Fermat’s last theorem: A new proof of theorem and its generalization”. They are achieved with elementary mathematics. This is why these proofs can be easily understood by any mathematician or anyone who knows basic mathematics. Note that, in both problems, proof by contradiction was used as a method of proof. The first of the two problems to date has not been resolved. Its proof is completely original and was not based on the work of other researchers. On the contrary, it was based on a simple observation that all natural divisors of a positive integer appear in pairs. The aim of the first work is to solve one of the unsolved, for many years, problems of the mathematics which belong to the field of number theory. I believe that if the present proof is recognized by the mathematical community, it may signal a different way of solving unsolved problems. For the second problem, it is very important the fact that it is generalized to an arbitrarily large number of variables. This generalization is essentially a new theorem in the field of the number theory. To the classical problem, two solutions are given, which are presented in the chronological order in which they were achieved. <em>Note that the second solution is very short and does not exceed one and a half pages</em>. This leads me to believe that Fermat, as a great mathematician was not lying and that he had probably solved the problem, as he stated in his historic its letter, with a correspondingly brief solution. <em>To win the bet on the question of whether Fermat was telling truth or lying, go immediately to the end of this article before the General Conclusions.</em>展开更多
A natural generalization of random choice finite difference scheme of Harten and Lax for Courant number larger than 1 is obtained. We handle interactions between neighboring Riemann solvers by linear superposition of ...A natural generalization of random choice finite difference scheme of Harten and Lax for Courant number larger than 1 is obtained. We handle interactions between neighboring Riemann solvers by linear superposition of their conserved quantities. We show consistency of the scheme for arbitrarily large Courant numbers. For scalar problems the scheme is total variation diminishing.A brief discussion is given for entropy condition.展开更多
Explores the generalization error of fuzzy neural network, analyzes the reason for occurrence and presents the equation of calculating error by the confidence interval approach. In addition, a generalization error tra...Explores the generalization error of fuzzy neural network, analyzes the reason for occurrence and presents the equation of calculating error by the confidence interval approach. In addition, a generalization error transfering(GET) method of improving the generalization error is proposed. The simulation experimental results of heating furnance show that the GET scheme is efficient.展开更多
The analysis of an overlaid map with different attributes has a very important function in GIS. In an overlaid map, approximately half of the constructed polygons are tiny and only account for less than 5% of the tota...The analysis of an overlaid map with different attributes has a very important function in GIS. In an overlaid map, approximately half of the constructed polygons are tiny and only account for less than 5% of the total area. In subsequent analysis of an overlaid map, a tiny polygon may require the same amount of computing time and memory space as any large one. In addition, in most cases it is meaningless to treat such polygons as distinct analysis units. So eliminating the tiny polygons is useful to improve efficiency. Now we often use the methods of “boundary comparison” and “fuzzy discriminance” to merge tiny polygons. But in the boundary comparison method, a polygon may be merged into a neighbor of quite different attribute values. In the second method, when the fuzzy grades of two boundary lines are almost the same and their lengths are different, this can lead to large error. In this paper, the partition principle of fuzzy Voronoi (F V) is proposed based on the characteristic of fuzzy boundary and the contiguity of Voronoi diagram. The bigger tiny polygons are divided by Voronoi diagram, and then are merged to neighbor polygon according to contiguity. The F V principle and arithmetic are presented in detail. In the end, an experiment is given; the result has proved that error in the F V method, compared with the two other methods, is only about 30%.展开更多
There may be several internal defects in railway track work that have different shapes and distribution rules,and these defects affect the safety of high-speed trains.Establishing reliable detection models and methods...There may be several internal defects in railway track work that have different shapes and distribution rules,and these defects affect the safety of high-speed trains.Establishing reliable detection models and methods for these internal defects remains a challenging task.To address this challenge,in this study,an intelligent detection method based on a generalization feature cluster is proposed for internal defects of railway tracks.First,the defects are classified and counted according to their shape and location features.Then,generalized features of the internal defects are extracted and formulated based on the maximum difference between different types of defects and the maximum tolerance among same defects’types.Finally,the extracted generalized features are expressed by function constraints,and formulated as generalization feature clusters to classify and identify internal defects in the railway track.Furthermore,to improve the detection reliability and speed,a reduced-dimension method of the generalization feature clusters is presented in this paper.Based on this reduced-dimension feature and strongly constrained generalized features,the K-means clustering algorithm is developed for defect clustering,and good clustering results are achieved.Regarding the defects in the rail head region,the clustering accuracy is over 95%,and the Davies-Bouldin index(DBI)index is negligible,which indicates the validation of the proposed generalization features with strong constraints.Experimental results prove that the accuracy of the proposed method based on generalization feature clusters is up to 97.55%,and the average detection time is 0.12 s/frame,which indicates that it performs well in adaptability,high accuracy,and detection speed under complex working environments.The proposed algorithm can effectively detect internal defects in railway tracks using an established generalization feature cluster model.展开更多
Let TA（f）=integral form n= to 1/2（P<sub><</sub>sup>n</sup>（x） + P<sub>b</sub><sup>n</sup>（x））dx and let TM（f）=integral form n= to P<sub>（+b）/2</sub...Let TA（f）=integral form n= to 1/2（P<sub><</sub>sup>n</sup>（x） + P<sub>b</sub><sup>n</sup>（x））dx and let TM（f）=integral form n= to P<sub>（+b）/2</sub><sup>n+1</sup>（x）dx, where P<sub>c</sub><sup>n</sup> denotes theTaylor polynomial to f at c of order n, where n is even. TA and TM are reach generalizations of theTrapezoidal rule and the midpoint rule, respectively. and are each exact for all polynomial of degree ≤n+1.We let L（f） = αTM（f） + （1-α）TA（f）, where α =(2<sup>n+1</sup>（n+1）)/(2<sup>n+1</sup>（n+1）+1), to obtain a numerical integrationrule L which is exact for all polynomials of degree≤n+3 （see Theorem l）. The case n = 0 is just the classicolSimpson’s rule. We analyze in some detail the case n=2, where our formulae appear to be new. By replacingP<sub>+b</sub>/2)<sup>n+1</sup>（x） by the Hermite cabic interpolant at a and b. we obtain some known formulae by a different ap-proach （see [1] and [2]）. Finally we discuss some nonlinear numerical integration rules obtained by takingpiecewise polynomials of odd degree, each piece being the Taylor polynomial off at a and b. respectively. Ofcourse all of our formulae can be compounded over subintervals of [a, b].展开更多
Three-dimensional (3D) human pose tracking has recently attracted more and more attention in the computer vision field. Real-time pose tracking is highly useful in various domains such as video surveillance, somatosen...Three-dimensional (3D) human pose tracking has recently attracted more and more attention in the computer vision field. Real-time pose tracking is highly useful in various domains such as video surveillance, somatosensory games, and human-computer interaction. However, vision-based pose tracking techniques usually raise privacy concerns, making human pose tracking without vision data usage an important problem. Thus, we propose using Radio Frequency Identification (RFID) as a pose tracking technique via a low-cost wearable sensing device. Although our prior work illustrated how deep learning could transfer RFID data into real-time human poses, generalization for different subjects remains challenging. This paper proposes a subject-adaptive technique to address this generalization problem. In the proposed system, termed Cycle-Pose, we leverage a cross-skeleton learning structure to improve the adaptability of the deep learning model to different human skeletons. Moreover, our novel cycle kinematic network is proposed for unpaired RFID and labeled pose data from different subjects. The Cycle-Pose system is implemented and evaluated by comparing its prototype with a traditional RFID pose tracking system. The experimental results demonstrate that Cycle-Pose can achieve lower estimation error and better subject generalization than the traditional system.展开更多
In order to simplify the three-dimensional building group model, this paper proposes a clustering generalization method based on visual cognitive theory. The method uses road elements to roughly divide scenes, and the...In order to simplify the three-dimensional building group model, this paper proposes a clustering generalization method based on visual cognitive theory. The method uses road elements to roughly divide scenes, and then uses spatial cognitive elements such as direction, area, height and their topological constraints to classify them precisely, so as to make them conform to the urban morphological characteristics. Delaunay triangulation network and boundary tracking synthesis algorithm are used to merge and summarize the models, and the models are stored hierarchically. The proposed algorithm should be verified experimentally with a typical urban complex model. The experimental results show that the efficiency of the method used in this paper is at least 20% higher than that of previous one, and with the growth of test data, the higher efficiency is improved. The classification results conform to human cognitive habits, and the generalization levels of different models can be relatively unified by adaptive control of each threshold in the clustering generalization process.展开更多
Generalization is widely accepted as adaptive behavioral conditions that allow individuals to quickly respond to similar circumstances.But once overgeneralization occurs,e.g.due to the inability to suppress generalize...Generalization is widely accepted as adaptive behavioral conditions that allow individuals to quickly respond to similar circumstances.But once overgeneralization occurs,e.g.due to the inability to suppress generalized fear,it could result in anxiety,depression and related mental disorders.Endocannabinoids(eCB)are important endogenous substance,known to play a role in contextual fear memory generalization.However,less is known in terms of the precise neural mechanism and the regulation of overgeneralization,in particular,for the eCB/CB1R signaling.Using fear memory generalization task,we show that type 1 cannabinoid receptors(CB1R)in hippocampal GABAergic neurons are necessary and sufficient for avoiding overgeneralization.Suppression or deletion of CB1R in hippocampal GABAergic neurons produces overgeneralized contextual fear memory.展开更多
A new two-parameter count distribution is derived starting with probabilistic arguments around the gamma function and the digamma function. This model is a generalization of the Poisson model with a noteworthy assortm...A new two-parameter count distribution is derived starting with probabilistic arguments around the gamma function and the digamma function. This model is a generalization of the Poisson model with a noteworthy assortment of qualities. For example, the mean is the main model parameter;any possible non-trivial variance or zero probability can be attained by changing the other model parameter;and all distributions are visually natural-shaped. Thus, exact modeling to any degree of over/under-dispersion or zero-inflation/deflation is possible.展开更多
This article presents a brief and new solution to the problem known as the “Fermat’s Last Theorem”. It is achieved without the use of abstract algebra elements or elements from other fields of modern mathematics of...This article presents a brief and new solution to the problem known as the “Fermat’s Last Theorem”. It is achieved without the use of abstract algebra elements or elements from other fields of modern mathematics of the twentieth century. For this reason it can be easily understood by any mathematician or by anyone who knows basic mathematics. The important thing is that the above “theorem” is generalized. Thus, this generalization is essentially a new theorem in the field of number theory.展开更多
Privacy preserving data mining (PPDM) has become more and more important because it allows sharing of privacy sensitive data for analytical purposes. A big number of privacy techniques were developed most of which use...Privacy preserving data mining (PPDM) has become more and more important because it allows sharing of privacy sensitive data for analytical purposes. A big number of privacy techniques were developed most of which used the k-anonymity property which have many shortcomings, so other privacy techniques were introduced (l-diversity, p-sensitive k-anonymity, (α, k)-anonymity, t-closeness, etc.). While they are different in their methods and quality of their results, they all focus first on masking the data, and then protecting the quality of the data. This paper is concerned with providing an enhanced privacy technique that combines some anonymity techniques to maintain both privacy and data utility by considering the sensitivity values of attributes in queries using sensitivity weights which determine taking in account utility-based anonymization and then only queries having sensitive attributes whose values exceed threshold are to be changed using generalization boundaries. The threshold value is calculated depending on the different weights assigned to individual attributes which take into account the utility of each attribute and those particular attributes whose total weights exceed the threshold values is changed using generalization boundaries and the other queries can be directly published. Experiment results using UT dallas anonymization toolbox on real data set adult database from the UC machine learning repository show that although the proposed technique preserves privacy, it also can maintain the utility of the publishing data.展开更多
Multiscalar topography influence on soil distribution has a complex pattern that is related to overlay of pedological processes which occurred at different times, and these driving forces are correlated with many geom...Multiscalar topography influence on soil distribution has a complex pattern that is related to overlay of pedological processes which occurred at different times, and these driving forces are correlated with many geomorphologic scales. In this sense, the present study tested the hypothesis whether multiscale geomorphometric generalized covariables can improve pedometric modeling. To achieve this goal, this case study applied the Random Forest algorithm to a multiscale geomorphometric database to predict soil surface attributes. The study area is in phanerozoic sedimentary basins, in the Alter do Ch<span style="white-space:nowrap;">ã</span>o geological formation, Eastern Amazon, Brazil. The multiscale geomorphometric generalization was applied at general and specific geomorphometric covariables, producing groups for each scale combination. The modeling was run using Random Forest for A-horizon thickness, pH, silt and sand content. For model evaluation, visual analysis of digital maps, metrics of forest structures and effect of variables on prediction were used. For evaluation of soil textural classifications, the confusion matrix with a Kappa index, and the user’s and producer’s accuracies were employed. The geomorphometry generalization tends to smooth curvatures and produces identifiable geomorphic representations at sub-watershed and watershed levels. The forest structures and effect of variables on prediction are in agreement with pedological knowledge. The multiscale geomorphometric generalized covariables improved accuracy metrics of soil surface texture classification, with the Kappa Index going from 43% to 62%. Therefore, it can be argued that topography influences soil distribution at combined coarser spatial scales and is able to predict soil particle size contents in the studied watershed. Future development of the multiscale geomorphometric generalization framework could include generalization methods concerning preservation of features, landform classification adaptable at multiple scales.展开更多
By introducing the notions of L-spaces and L_r-spaces, a complete generalization of Kalton’s closed graph theorem is obtained. It points out the class of L_r-spaces is the maximal class of range spaces for the closed...By introducing the notions of L-spaces and L_r-spaces, a complete generalization of Kalton’s closed graph theorem is obtained. It points out the class of L_r-spaces is the maximal class of range spaces for the closed graph theorem when the class of domain spaces is the class of Mackey spaces with weakly * sequentially complete dual.Some examples are constructed showing that the class of L_r-spaces is strictly larger than the class of separable B_r-complete spaces.Some properties of L-spaces and L_r-spaces are discussed and the relations between B-complete (resp. B_r-complete) spaces and L-spaces (resp. L_r-spaces) are given.展开更多
基金funded by the General Scientific Research Project of the Shandong Earthquake Agency(No.YB2202)the National Key Research and Development Program Project(No.2021YFC3000700)a Key Project under the Natural Science Foundation of Shandong Province(No.ZR2020KF003).
文摘Waveforms of seismic events,extracted from January 2019 to December 2021 were used to construct a test dataset to investigate the generalizability of PhaseNet in the Shandong region.The results show that errors in the picking of seismic phases(P-and Swaves)had a broadly normal distribution,mainly concentrated in the ranges of−0.4–0.3 s and−0.4–0.8 s,respectively.These results were compared with those published in the original PhaseNet article and were found to be approximately 0.2–0.4 s larger.PhaseNet had a strong generalizability for P-and S-wave picking for epicentral distances of less than 120 km and 110 km,respectively.However,the phase recall rate decreased rapidly when these distances were exceeded.Furthermore,the generalizability of PhaseNet was essentially unaffected by magnitude.The M4.1 earthquake sequence in Changqing,Shandong province,China,that occurred on February 18,2020,was adopted as a case study.PhaseNet detected more than twice the number of earthquakes in the manually obtained catalog.This further verified that PhaseNet has strong generalizability in the Shandong region,and a high-precision earthquake catalog was constructed.According to these precise positioning results,two earthquake sequences occurred in the study area,and the southern cluster may have been triggered by the northern cluster.The focal mechanism solution,regional stress field,and the location results of the northern earthquake sequence indicated that the seismic force of the earthquake was consistent with the regional stress field.
基金This work was supported in part by the Program for Innovative Talents and Entrepreneur in Jiangsu Province under Grant 1104000402in part by the Research Fund by Nanjing Government under Grant 1104000396+4 种基金in part by the National Science Foundation of China under Grants 62001109&61921004in part by the China Postdoctoral Science Foundation under Grants BX20200083&2020M681456in part by the Fundamental Research Funds for the Central Universities of China under Grants 3204002004A2&2242020R20011in part by the open research fund of the National and Local Joint Engineering Laboratory of RF Integration and Micro-Assembly Technology under Grant No.KFJJ20180205in part by the NUPTSF Grants No.NY218113&No.NY219077.
文摘Wireless communication involving unmanned aerial vehicles(UAVs)is expected to play an important role in future wireless networks.However,different from conventional terrestrial communication systems,UAVs typically have rather limited onboard energy on one hand,and require additional flying energy consumption on the other hand.This renders energy-efficient UAV communication with smart energy expenditure of paramount importance.In this paper,via extensive flight experiments,we aim to firstly validate the recently derived theoretical energy model for rotary-wing UAVs,and then develop a general model for those complicated flight scenarios where rigorous theoretical model derivation is quite challenging,if not impossible.Specifically,we first investigate how UAV power consumption varies with its flying speed for the simplest straight-and-level flight.With about 12,000 valid power-speed data points collected,we first apply the model-based curve fitting to obtain the modelling parameters based on the theoretical closed-form energy model in the existing literature.In addition,in order to exclude the potential bias caused by the theoretical energy model,the obtained measurement data is also trained using a model-free deep neural network.It is found that the obtained curve from both methods can match quite well with the theoretical energy model.Next,we further extend the study to arbitrary 2-dimensional(2-D)flight,where,to our best knowledge,no rigorous theoretical derivation is available for the closed-form energy model as a function of its flying speed,direction,and acceleration.To fill the gap,we first propose a heuristic energy model for these more complicated cases,and then provide experimental validation based on the measurement results for circular level flight.
文摘Complicated changes occur inside the steel parts during quenching process. A three dimensional nonlinear mathematical model for quenching process has been established and the numerical simulation on temperature field, microstructure and stress field has been realized. The alternative technique for the formation of high-strength materials has been developed on the basis of intensification of heat transfer at phase transformations. The technology for the achievement of maximum compressive residual stresses on the hard surface is introduced. It has been shown that there is an optimal depth of hard layer providing the maximum compression stresses on the surface. It has also been established that in the surface hard layer additional strengthening (superstrengthening) of the material is observed. The generalized formula for the determination of the time of reaching maximum compressive stresses on the surface has been proposed.
文摘The constraints and the operations play an important role in database generalization.They guide and govern database generalization.The constraints are translation of the required conditions that should take into account not only the objects and relationships among objects but also spatial data schema (classification and aggregation hierarchy) associated with the final existing database.The operations perform the actions of generalization in support of data reduction in the database.The constraints in database generalization are still lack of research.There is still the lack of frameworks to express the constraints and the operations on the basis of object_oriented data structure in database generalization.This paper focuses on the frameworks for generalization operations and constraints on the basis of object_oriented data structure in database generalization.The constraints as the attributes of the object and the operations as the methods of the object can be encapsulated in classes.They have the inheritance and polymorphism property.So the framework of the constraints and the operations which are based on object_oriented data structure can be easily understood and implemented.The constraint and the operations based on object_oriented database are proposed based on object_oriented database.The frameworks for generalization operations,constraints and relations among objects based on object_oriented data structure in database generalization are designed.The categorical database generalization is concentrated on in this paper.
文摘This article presents very original and relatively brief or very brief proofs about of two famous problems: 1) Are there any odd perfect numbers? and 2) “Fermat’s last theorem: A new proof of theorem and its generalization”. They are achieved with elementary mathematics. This is why these proofs can be easily understood by any mathematician or anyone who knows basic mathematics. Note that, in both problems, proof by contradiction was used as a method of proof. The first of the two problems to date has not been resolved. Its proof is completely original and was not based on the work of other researchers. On the contrary, it was based on a simple observation that all natural divisors of a positive integer appear in pairs. The aim of the first work is to solve one of the unsolved, for many years, problems of the mathematics which belong to the field of number theory. I believe that if the present proof is recognized by the mathematical community, it may signal a different way of solving unsolved problems. For the second problem, it is very important the fact that it is generalized to an arbitrarily large number of variables. This generalization is essentially a new theorem in the field of the number theory. To the classical problem, two solutions are given, which are presented in the chronological order in which they were achieved. <em>Note that the second solution is very short and does not exceed one and a half pages</em>. This leads me to believe that Fermat, as a great mathematician was not lying and that he had probably solved the problem, as he stated in his historic its letter, with a correspondingly brief solution. <em>To win the bet on the question of whether Fermat was telling truth or lying, go immediately to the end of this article before the General Conclusions.</em>
基金The Project Supported by National Natural Science Foundation of China.
文摘A natural generalization of random choice finite difference scheme of Harten and Lax for Courant number larger than 1 is obtained. We handle interactions between neighboring Riemann solvers by linear superposition of their conserved quantities. We show consistency of the scheme for arbitrarily large Courant numbers. For scalar problems the scheme is total variation diminishing.A brief discussion is given for entropy condition.
文摘Explores the generalization error of fuzzy neural network, analyzes the reason for occurrence and presents the equation of calculating error by the confidence interval approach. In addition, a generalization error transfering(GET) method of improving the generalization error is proposed. The simulation experimental results of heating furnance show that the GET scheme is efficient.
基金Supported by the National Natural Science Foundation of China(No.6983 3 0 10 )
文摘The analysis of an overlaid map with different attributes has a very important function in GIS. In an overlaid map, approximately half of the constructed polygons are tiny and only account for less than 5% of the total area. In subsequent analysis of an overlaid map, a tiny polygon may require the same amount of computing time and memory space as any large one. In addition, in most cases it is meaningless to treat such polygons as distinct analysis units. So eliminating the tiny polygons is useful to improve efficiency. Now we often use the methods of “boundary comparison” and “fuzzy discriminance” to merge tiny polygons. But in the boundary comparison method, a polygon may be merged into a neighbor of quite different attribute values. In the second method, when the fuzzy grades of two boundary lines are almost the same and their lengths are different, this can lead to large error. In this paper, the partition principle of fuzzy Voronoi (F V) is proposed based on the characteristic of fuzzy boundary and the contiguity of Voronoi diagram. The bigger tiny polygons are divided by Voronoi diagram, and then are merged to neighbor polygon according to contiguity. The F V principle and arithmetic are presented in detail. In the end, an experiment is given; the result has proved that error in the F V method, compared with the two other methods, is only about 30%.
基金National Natural Science Foundation of China(Grant No.61573233)Guangdong Provincial Natural Science Foundation of China(Grant No.2018A0303130188)+1 种基金Guangdong Provincial Science and Technology Special Funds Project of China(Grant No.190805145540361)Special Projects in Key Fields of Colleges and Universities in Guangdong Province of China(Grant No.2020ZDZX2005).
文摘There may be several internal defects in railway track work that have different shapes and distribution rules,and these defects affect the safety of high-speed trains.Establishing reliable detection models and methods for these internal defects remains a challenging task.To address this challenge,in this study,an intelligent detection method based on a generalization feature cluster is proposed for internal defects of railway tracks.First,the defects are classified and counted according to their shape and location features.Then,generalized features of the internal defects are extracted and formulated based on the maximum difference between different types of defects and the maximum tolerance among same defects’types.Finally,the extracted generalized features are expressed by function constraints,and formulated as generalization feature clusters to classify and identify internal defects in the railway track.Furthermore,to improve the detection reliability and speed,a reduced-dimension method of the generalization feature clusters is presented in this paper.Based on this reduced-dimension feature and strongly constrained generalized features,the K-means clustering algorithm is developed for defect clustering,and good clustering results are achieved.Regarding the defects in the rail head region,the clustering accuracy is over 95%,and the Davies-Bouldin index(DBI)index is negligible,which indicates the validation of the proposed generalization features with strong constraints.Experimental results prove that the accuracy of the proposed method based on generalization feature clusters is up to 97.55%,and the average detection time is 0.12 s/frame,which indicates that it performs well in adaptability,high accuracy,and detection speed under complex working environments.The proposed algorithm can effectively detect internal defects in railway tracks using an established generalization feature cluster model.
文摘Let TA（f）=integral form n= to 1/2（P<sub><</sub>sup>n</sup>（x） + P<sub>b</sub><sup>n</sup>（x））dx and let TM（f）=integral form n= to P<sub>（+b）/2</sub><sup>n+1</sup>（x）dx, where P<sub>c</sub><sup>n</sup> denotes theTaylor polynomial to f at c of order n, where n is even. TA and TM are reach generalizations of theTrapezoidal rule and the midpoint rule, respectively. and are each exact for all polynomial of degree ≤n+1.We let L（f） = αTM（f） + （1-α）TA（f）, where α =(2<sup>n+1</sup>（n+1）)/(2<sup>n+1</sup>（n+1）+1), to obtain a numerical integrationrule L which is exact for all polynomials of degree≤n+3 （see Theorem l）. The case n = 0 is just the classicolSimpson’s rule. We analyze in some detail the case n=2, where our formulae appear to be new. By replacingP<sub>+b</sub>/2)<sup>n+1</sup>（x） by the Hermite cabic interpolant at a and b. we obtain some known formulae by a different ap-proach （see [1] and [2]）. Finally we discuss some nonlinear numerical integration rules obtained by takingpiecewise polynomials of odd degree, each piece being the Taylor polynomial off at a and b. respectively. Ofcourse all of our formulae can be compounded over subintervals of [a, b].
基金supported in part by the US National Science Foundation(NSF)under Grants ECCS-1923163 and CNS-2107190through the Wireless Engineering Research and Education Center at Auburn University.
文摘Three-dimensional (3D) human pose tracking has recently attracted more and more attention in the computer vision field. Real-time pose tracking is highly useful in various domains such as video surveillance, somatosensory games, and human-computer interaction. However, vision-based pose tracking techniques usually raise privacy concerns, making human pose tracking without vision data usage an important problem. Thus, we propose using Radio Frequency Identification (RFID) as a pose tracking technique via a low-cost wearable sensing device. Although our prior work illustrated how deep learning could transfer RFID data into real-time human poses, generalization for different subjects remains challenging. This paper proposes a subject-adaptive technique to address this generalization problem. In the proposed system, termed Cycle-Pose, we leverage a cross-skeleton learning structure to improve the adaptability of the deep learning model to different human skeletons. Moreover, our novel cycle kinematic network is proposed for unpaired RFID and labeled pose data from different subjects. The Cycle-Pose system is implemented and evaluated by comparing its prototype with a traditional RFID pose tracking system. The experimental results demonstrate that Cycle-Pose can achieve lower estimation error and better subject generalization than the traditional system.
文摘In order to simplify the three-dimensional building group model, this paper proposes a clustering generalization method based on visual cognitive theory. The method uses road elements to roughly divide scenes, and then uses spatial cognitive elements such as direction, area, height and their topological constraints to classify them precisely, so as to make them conform to the urban morphological characteristics. Delaunay triangulation network and boundary tracking synthesis algorithm are used to merge and summarize the models, and the models are stored hierarchically. The proposed algorithm should be verified experimentally with a typical urban complex model. The experimental results show that the efficiency of the method used in this paper is at least 20% higher than that of previous one, and with the growth of test data, the higher efficiency is improved. The classification results conform to human cognitive habits, and the generalization levels of different models can be relatively unified by adaptive control of each threshold in the clustering generalization process.
文摘Generalization is widely accepted as adaptive behavioral conditions that allow individuals to quickly respond to similar circumstances.But once overgeneralization occurs,e.g.due to the inability to suppress generalized fear,it could result in anxiety,depression and related mental disorders.Endocannabinoids(eCB)are important endogenous substance,known to play a role in contextual fear memory generalization.However,less is known in terms of the precise neural mechanism and the regulation of overgeneralization,in particular,for the eCB/CB1R signaling.Using fear memory generalization task,we show that type 1 cannabinoid receptors(CB1R)in hippocampal GABAergic neurons are necessary and sufficient for avoiding overgeneralization.Suppression or deletion of CB1R in hippocampal GABAergic neurons produces overgeneralized contextual fear memory.
文摘A new two-parameter count distribution is derived starting with probabilistic arguments around the gamma function and the digamma function. This model is a generalization of the Poisson model with a noteworthy assortment of qualities. For example, the mean is the main model parameter;any possible non-trivial variance or zero probability can be attained by changing the other model parameter;and all distributions are visually natural-shaped. Thus, exact modeling to any degree of over/under-dispersion or zero-inflation/deflation is possible.
文摘This article presents a brief and new solution to the problem known as the “Fermat’s Last Theorem”. It is achieved without the use of abstract algebra elements or elements from other fields of modern mathematics of the twentieth century. For this reason it can be easily understood by any mathematician or by anyone who knows basic mathematics. The important thing is that the above “theorem” is generalized. Thus, this generalization is essentially a new theorem in the field of number theory.
文摘Privacy preserving data mining (PPDM) has become more and more important because it allows sharing of privacy sensitive data for analytical purposes. A big number of privacy techniques were developed most of which used the k-anonymity property which have many shortcomings, so other privacy techniques were introduced (l-diversity, p-sensitive k-anonymity, (α, k)-anonymity, t-closeness, etc.). While they are different in their methods and quality of their results, they all focus first on masking the data, and then protecting the quality of the data. This paper is concerned with providing an enhanced privacy technique that combines some anonymity techniques to maintain both privacy and data utility by considering the sensitivity values of attributes in queries using sensitivity weights which determine taking in account utility-based anonymization and then only queries having sensitive attributes whose values exceed threshold are to be changed using generalization boundaries. The threshold value is calculated depending on the different weights assigned to individual attributes which take into account the utility of each attribute and those particular attributes whose total weights exceed the threshold values is changed using generalization boundaries and the other queries can be directly published. Experiment results using UT dallas anonymization toolbox on real data set adult database from the UC machine learning repository show that although the proposed technique preserves privacy, it also can maintain the utility of the publishing data.
文摘Multiscalar topography influence on soil distribution has a complex pattern that is related to overlay of pedological processes which occurred at different times, and these driving forces are correlated with many geomorphologic scales. In this sense, the present study tested the hypothesis whether multiscale geomorphometric generalized covariables can improve pedometric modeling. To achieve this goal, this case study applied the Random Forest algorithm to a multiscale geomorphometric database to predict soil surface attributes. The study area is in phanerozoic sedimentary basins, in the Alter do Ch<span style="white-space:nowrap;">ã</span>o geological formation, Eastern Amazon, Brazil. The multiscale geomorphometric generalization was applied at general and specific geomorphometric covariables, producing groups for each scale combination. The modeling was run using Random Forest for A-horizon thickness, pH, silt and sand content. For model evaluation, visual analysis of digital maps, metrics of forest structures and effect of variables on prediction were used. For evaluation of soil textural classifications, the confusion matrix with a Kappa index, and the user’s and producer’s accuracies were employed. The geomorphometry generalization tends to smooth curvatures and produces identifiable geomorphic representations at sub-watershed and watershed levels. The forest structures and effect of variables on prediction are in agreement with pedological knowledge. The multiscale geomorphometric generalized covariables improved accuracy metrics of soil surface texture classification, with the Kappa Index going from 43% to 62%. Therefore, it can be argued that topography influences soil distribution at combined coarser spatial scales and is able to predict soil particle size contents in the studied watershed. Future development of the multiscale geomorphometric generalization framework could include generalization methods concerning preservation of features, landform classification adaptable at multiple scales.
文摘By introducing the notions of L-spaces and L_r-spaces, a complete generalization of Kalton’s closed graph theorem is obtained. It points out the class of L_r-spaces is the maximal class of range spaces for the closed graph theorem when the class of domain spaces is the class of Mackey spaces with weakly * sequentially complete dual.Some examples are constructed showing that the class of L_r-spaces is strictly larger than the class of separable B_r-complete spaces.Some properties of L-spaces and L_r-spaces are discussed and the relations between B-complete (resp. B_r-complete) spaces and L-spaces (resp. L_r-spaces) are given.
