Straight-line compliant mechanisms are important building blocks to design a linear-motion stage, which is very useful in precision applications. However, only a few configurations of straight-line compliant mechanism...Straight-line compliant mechanisms are important building blocks to design a linear-motion stage, which is very useful in precision applications. However, only a few configurations of straight-line compliant mechanisms are applicable. To construct more kinds of them, an approach to design large-displacement straight-line flexural mechanisms with rotational flexural joints is proposed, which is based on a viewpoint that the straight-line motion is regarded as a compromise of rigid and compliant parasitic motion of a rotational flexural joint. An analytical design method based on the Taylor series expansion is proposed to quickly obtain an approximate solution. To illustrate and verify the proposed method, two kinds of flexural joints, cross-axis hinge and leaf-type isosceles-trapezoidal flexural(LITF) pivot are used to reconstruct straight-line flexural mechanisms. Their performances are obtained by analytic and FEA method respectively. The comparisons of the results show the accuracy of the approach. Both examples show that the proposed approach can convert a large-deflection flexural joint into approximate straight-line mechanism with a high linearity that is higher than 5 000 within 5 man displacement. This can lead to a new way to design, analyze or optimize straight-line flexure mechanisms.展开更多
In order to solve four-bar straight-line guidance mechanism synthesis problem for the arbitrarily given straight-line’s"angle requirement"and"point-position requirement",a numerical comparison syn...In order to solve four-bar straight-line guidance mechanism synthesis problem for the arbitrarily given straight-line’s"angle requirement"and"point-position requirement",a numerical comparison synthesis method for single and double straight-line guidance mechanism is presented,which is convenient to realize by computer program.The basic idea of this method is:to select a four-bar linkage whose relative bar length of crank is 1 as a basic four-bar linkage.Then the other three relative bars’length is changed,and a lot of basic four-bar linkage can be obtained.There are many single and double ball-points of each basic four-bar linkage.With the motion of a basic four-bar linkage,there is straight-line segment of each Ball-point’s path.The data of these basic four-bar linkages is saved to a database.When designing a four-bar straight-line guidance mechanism,the design data is compared with the data in database and a satisfactory four-bar linkage can be obtained.The method effectively solves the straight-line guidance mechanism synthesis problem.展开更多
The straight-line method in computing for depreciation expense is the prevailing method used in the Philippines. This paper aims to determine the rationale behind the use of this method. The objective of the study is ...The straight-line method in computing for depreciation expense is the prevailing method used in the Philippines. This paper aims to determine the rationale behind the use of this method. The objective of the study is to determine the length of time within which the depreciation method is used, reasons in using the method, the rate of depreciation used by the companies, and the effects of the depreciation expense on their operating expenses. It also determines if the companies' decisions to use the straight-line method are influenced by the factors mentioned by Reynolds (196 I)----expected amount of services over the life of assets, the amount and timing of operating costs, the decline in the physical efficiency of the assets, and the rate of return--and if they considered capital investments and tax reduction in using this method. The study shows that companies and educational institutions use the straight-line method of computing depreciation expenses, because it is easy to use in computing the depreciation expenses, in comparing with previous years' computations, and in keeping track of the expenses. It is also convenient for tax administration and financial reporting. The rate of depreciation used varies, because the companies and educational institutions use their past experiences in determining the life of fixed assets. The percentage of depreciation to the operating expenses also varies. The companies and educational institutions adhered to the factors mentioned by Reynolds (1961) in choosing the straight-line method of depreciation. The companies did not consider reduction of tax in using the straight-line method.展开更多
Traditional clustering algorithms often struggle to produce satisfactory results when dealing with datasets withuneven density. Additionally, they incur substantial computational costs when applied to high-dimensional...Traditional clustering algorithms often struggle to produce satisfactory results when dealing with datasets withuneven density. Additionally, they incur substantial computational costs when applied to high-dimensional datadue to calculating similarity matrices. To alleviate these issues, we employ the KD-Tree to partition the dataset andcompute the K-nearest neighbors (KNN) density for each point, thereby avoiding the computation of similaritymatrices. Moreover, we apply the rules of voting elections, treating each data point as a voter and casting a votefor the point with the highest density among its KNN. By utilizing the vote counts of each point, we develop thestrategy for classifying noise points and potential cluster centers, allowing the algorithm to identify clusters withuneven density and complex shapes. Additionally, we define the concept of “adhesive points” between two clustersto merge adjacent clusters that have similar densities. This process helps us identify the optimal number of clustersautomatically. Experimental results indicate that our algorithm not only improves the efficiency of clustering butalso increases its accuracy.展开更多
To improve the performance of multiple classifier system, a knowledge discovery based dynamic weighted voting (KD-DWV) is proposed based on knowledge discovery. In the method, all base classifiers may be allowed to ...To improve the performance of multiple classifier system, a knowledge discovery based dynamic weighted voting (KD-DWV) is proposed based on knowledge discovery. In the method, all base classifiers may be allowed to operate in different measurement/feature spaces to make the most of diverse classification information. The weights assigned to each output of a base classifier are estimated by the separability of training sample sets in relevant feature space. For this purpose, some decision tables (DTs) are established in terms of the diverse feature sets. And then the uncertainty measures of the separability are induced, in the form of mass functions in Dempster-Shafer theory (DST), from each DTs based on generalized rough set model. From the mass functions, all the weights are calculated by a modified heuristic fusion function and assigned dynamically to each classifier varying with its output. The comparison experiment is performed on the hyperspectral remote sensing images. And the experimental results show that the performance of the classification can be improved by using the proposed method compared with the plurality voting (PV).展开更多
Electronic voting has partially solved the problems of poor anonymity and low efficiency associated with traditional voting.However,the difficulties it introduces into the supervision of the vote counting,as well as i...Electronic voting has partially solved the problems of poor anonymity and low efficiency associated with traditional voting.However,the difficulties it introduces into the supervision of the vote counting,as well as its need for a concurrent guaranteed trusted third party,should not be overlooked.With the advent of blockchain technology in recent years,its features such as decentralization,anonymity,and non-tampering have made it a good candidate in solving the problems that electronic voting faces.In this study,we propose a multi-candidate voting model based on the blockchain technology.With the introduction of an asymmetric encryption and an anonymity-preserving voting algorithm,votes can be counted without relying on a third party,and the voting results can be displayed in real time in a manner that satisfies various levels of voting security and privacy requirements.Experimental results show that the proposed model solves the aforementioned problems of electronic voting without significant negative impact from an increasing number of voters or candidates.展开更多
We investigate the design of anonymous voting protocols,CV-based binary-valued ballot and CV-based multi-valued ballot with continuous variables(CV) in a multi-dimensional quantum cryptosystem to ensure the security...We investigate the design of anonymous voting protocols,CV-based binary-valued ballot and CV-based multi-valued ballot with continuous variables(CV) in a multi-dimensional quantum cryptosystem to ensure the security of voting procedure and data privacy.The quantum entangled states are employed in the continuous variable quantum system to carry the voting information and assist information transmission,which takes the advantage of the GHZ-like states in terms of improving the utilization of quantum states by decreasing the number of required quantum states.It provides a potential approach to achieve the efficient quantum anonymous voting with high transmission security,especially in large-scale votes.展开更多
In this paper, we use the polynomial function and Chaum's RSA (Rivest, Shamir, Adleman) blind signature scheme to construct a secure anonymous internet electronic voting scheme. In our scheme, each vote does not ne...In this paper, we use the polynomial function and Chaum's RSA (Rivest, Shamir, Adleman) blind signature scheme to construct a secure anonymous internet electronic voting scheme. In our scheme, each vote does not need to be revealed in the tallying phase. The ballot number of each candidate gets is counted by computing the degrees of two polynomials' greatest common divisor. Our scheme does not require a special voting channel and communication can occur entirely over the current internet.展开更多
Extreme learning machine(ELM)has been proved to be an effective pattern classification and regression learning mechanism by researchers.However,its good performance is based on a large number of hidden layer nodes.Wit...Extreme learning machine(ELM)has been proved to be an effective pattern classification and regression learning mechanism by researchers.However,its good performance is based on a large number of hidden layer nodes.With the increase of the nodes in the hidden layers,the computation cost is greatly increased.In this paper,we propose a novel algorithm,named constrained voting extreme learning machine(CV-ELM).Compared with the traditional ELM,the CV-ELM determines the input weight and bias based on the differences of between-class samples.At the same time,to improve the accuracy of the proposed method,the voting selection is introduced.The proposed method is evaluated on public benchmark datasets.The experimental results show that the proposed algorithm is superior to the original ELM algorithm.Further,we apply the CV-ELM to the classification of superheat degree(SD)state in the aluminum electrolysis industry,and the recognition accuracy rate reaches87.4%,and the experimental results demonstrate that the proposed method is more robust than the existing state-of-the-art identification methods.展开更多
The random forest model is universal and easy to understand, which is often used for classification and prediction. However, it uses non-selective integration and the majority rule to judge the final result, thus the ...The random forest model is universal and easy to understand, which is often used for classification and prediction. However, it uses non-selective integration and the majority rule to judge the final result, thus the difference between the decision trees in the model is ignored and the prediction accuracy of the model is reduced. Taking into consideration these defects, an improved random forest model based on confusion matrix (CM-RF)is proposed. The decision tree cluster is selectively constructed by the similarity measure in the process of constructing the model, and the result is output by using the dynamic weighted voting fusion method in the final voting session. Experiments show that the proposed CM-RF can reduce the impact of low-performance decision trees on the output result, thus improving the accuracy and generalization ability of random forest model.展开更多
The communication complexity of the practical byzantine fault tolerance(PBFT)protocol is reduced with the threshold signature technique applied to the consensus process by phase voting PBFT(PV-PBFT).As most communicat...The communication complexity of the practical byzantine fault tolerance(PBFT)protocol is reduced with the threshold signature technique applied to the consensus process by phase voting PBFT(PV-PBFT).As most communication occurs between the primary node and replica nodes in PV-PVFT,consistency verification is accomplished through threshold signatures,multi-PV,and multiple consensus.The view replacement protocol introduces node weights to influence the election of a primary node,reducing the probability of the same node being elected primary multiple times.The experimental results of consensus algorithms show that compared to PBFT,the communication overhead of PV-PBFT decreases by approximately 90% with nearly one-time improvement in the throughput relative and approximately 2/3 consensus latency,lower than that of the scalable hierarchical byzantine fault tolerance.The communication complexity of the PBFT is O(N^(2)),whereas that of PV-PBFT is only O(N),which implies the significant improvement of the operational efficiency of the blockchain system.展开更多
Advanced Metering Infrastructure(AMI)is the metering network of the smart grid that enables bidirectional communications between each consumer’s premises and the provider’s control center.The massive amount of data ...Advanced Metering Infrastructure(AMI)is the metering network of the smart grid that enables bidirectional communications between each consumer’s premises and the provider’s control center.The massive amount of data collected supports the real-time decision-making required for diverse applications.The communication infrastructure relies on different network types,including the Internet.This makes the infrastructure vulnerable to various attacks,which could compromise security or have devastating effects.However,traditional machine learning solutions cannot adapt to the increasing complexity and diversity of attacks.The objective of this paper is to develop an Anomaly Detection System(ADS)based on deep learning using the CIC-IDS2017 dataset.However,this dataset is highly imbalanced;thus,a two-step sampling technique:random under-sampling and the Synthetic Minority Oversampling Technique(SMOTE),is proposed to balance the dataset.The proposed system utilizes a multiple hidden layer Auto-encoder(AE)for feature extraction and dimensional reduction.In addition,an ensemble voting based on both Random Forest(RF)and Convolu-tional Neural Network(CNN)is developed to classify the multiclass attack cate-gories.The proposed system is evaluated and compared with six different state-of-the-art machine learning and deep learning algorithms:Random Forest(RF),Light Gradient Boosting Machine(LightGBM),eXtreme Gradient Boosting(XGboost),Convolutional Neural Network(CNN),Long Short-Term Memory(LSTM),and bidirectional LSTM(biLSTM).Experimental results show that the proposed model enhances the detection for each attack class compared with the other machine learning and deep learning models with overall accuracy(98.29%),precision(99%),recall(98%),F_(1) score(98%),and the UNDetection rate(UND)(8%).展开更多
Oscillatory failure cases(OFC)detection in the fly-by-wire(FBW)flight control system for civil aircraft is addressed in this paper.First,OFC is ranked four levels:Handling quality,static load,global structure fatigue ...Oscillatory failure cases(OFC)detection in the fly-by-wire(FBW)flight control system for civil aircraft is addressed in this paper.First,OFC is ranked four levels:Handling quality,static load,global structure fatigue and local fatigue,according to their respect impact on aircraft.Second,we present voting and comparing monitors based on un-similarity redundancy commands to detect OFC.Third,the associated performances,the thresholds and the counters of the monitors are calculated by the high fidelity nonlinear aircraft models.Finally,the monitors of OFC are verified by the Iron Bird Platform with real parameters of the flight control system.The results show that our approach can detect OFC rapidly.展开更多
基金supported by National Natural Science Foundation of China(Grant No.51275552)Foundation for the Author of National Excellent Doctoral Dissertation of China(Grant No.201234)
文摘Straight-line compliant mechanisms are important building blocks to design a linear-motion stage, which is very useful in precision applications. However, only a few configurations of straight-line compliant mechanisms are applicable. To construct more kinds of them, an approach to design large-displacement straight-line flexural mechanisms with rotational flexural joints is proposed, which is based on a viewpoint that the straight-line motion is regarded as a compromise of rigid and compliant parasitic motion of a rotational flexural joint. An analytical design method based on the Taylor series expansion is proposed to quickly obtain an approximate solution. To illustrate and verify the proposed method, two kinds of flexural joints, cross-axis hinge and leaf-type isosceles-trapezoidal flexural(LITF) pivot are used to reconstruct straight-line flexural mechanisms. Their performances are obtained by analytic and FEA method respectively. The comparisons of the results show the accuracy of the approach. Both examples show that the proposed approach can convert a large-deflection flexural joint into approximate straight-line mechanism with a high linearity that is higher than 5 000 within 5 man displacement. This can lead to a new way to design, analyze or optimize straight-line flexure mechanisms.
文摘In order to solve four-bar straight-line guidance mechanism synthesis problem for the arbitrarily given straight-line’s"angle requirement"and"point-position requirement",a numerical comparison synthesis method for single and double straight-line guidance mechanism is presented,which is convenient to realize by computer program.The basic idea of this method is:to select a four-bar linkage whose relative bar length of crank is 1 as a basic four-bar linkage.Then the other three relative bars’length is changed,and a lot of basic four-bar linkage can be obtained.There are many single and double ball-points of each basic four-bar linkage.With the motion of a basic four-bar linkage,there is straight-line segment of each Ball-point’s path.The data of these basic four-bar linkages is saved to a database.When designing a four-bar straight-line guidance mechanism,the design data is compared with the data in database and a satisfactory four-bar linkage can be obtained.The method effectively solves the straight-line guidance mechanism synthesis problem.
文摘The straight-line method in computing for depreciation expense is the prevailing method used in the Philippines. This paper aims to determine the rationale behind the use of this method. The objective of the study is to determine the length of time within which the depreciation method is used, reasons in using the method, the rate of depreciation used by the companies, and the effects of the depreciation expense on their operating expenses. It also determines if the companies' decisions to use the straight-line method are influenced by the factors mentioned by Reynolds (196 I)----expected amount of services over the life of assets, the amount and timing of operating costs, the decline in the physical efficiency of the assets, and the rate of return--and if they considered capital investments and tax reduction in using this method. The study shows that companies and educational institutions use the straight-line method of computing depreciation expenses, because it is easy to use in computing the depreciation expenses, in comparing with previous years' computations, and in keeping track of the expenses. It is also convenient for tax administration and financial reporting. The rate of depreciation used varies, because the companies and educational institutions use their past experiences in determining the life of fixed assets. The percentage of depreciation to the operating expenses also varies. The companies and educational institutions adhered to the factors mentioned by Reynolds (1961) in choosing the straight-line method of depreciation. The companies did not consider reduction of tax in using the straight-line method.
基金National Natural Science Foundation of China Nos.61962054 and 62372353.
文摘Traditional clustering algorithms often struggle to produce satisfactory results when dealing with datasets withuneven density. Additionally, they incur substantial computational costs when applied to high-dimensional datadue to calculating similarity matrices. To alleviate these issues, we employ the KD-Tree to partition the dataset andcompute the K-nearest neighbors (KNN) density for each point, thereby avoiding the computation of similaritymatrices. Moreover, we apply the rules of voting elections, treating each data point as a voter and casting a votefor the point with the highest density among its KNN. By utilizing the vote counts of each point, we develop thestrategy for classifying noise points and potential cluster centers, allowing the algorithm to identify clusters withuneven density and complex shapes. Additionally, we define the concept of “adhesive points” between two clustersto merge adjacent clusters that have similar densities. This process helps us identify the optimal number of clustersautomatically. Experimental results indicate that our algorithm not only improves the efficiency of clustering butalso increases its accuracy.
基金This project was supported by the National Basic Research Programof China (2001CB309403)
文摘To improve the performance of multiple classifier system, a knowledge discovery based dynamic weighted voting (KD-DWV) is proposed based on knowledge discovery. In the method, all base classifiers may be allowed to operate in different measurement/feature spaces to make the most of diverse classification information. The weights assigned to each output of a base classifier are estimated by the separability of training sample sets in relevant feature space. For this purpose, some decision tables (DTs) are established in terms of the diverse feature sets. And then the uncertainty measures of the separability are induced, in the form of mass functions in Dempster-Shafer theory (DST), from each DTs based on generalized rough set model. From the mass functions, all the weights are calculated by a modified heuristic fusion function and assigned dynamically to each classifier varying with its output. The comparison experiment is performed on the hyperspectral remote sensing images. And the experimental results show that the performance of the classification can be improved by using the proposed method compared with the plurality voting (PV).
基金This work was supported in part by Shandong Provincial Natural Science Foundation(ZR2019PF007)the National Key Research and Development Plan of China(2018YFB0803504)+2 种基金Basic Scientific Research Operating Expenses of Shandong University(2018ZQXM004)Guangdong Province Key Research and Development Plan(2019B010137004)the National Natural Science Foundation of China(U20B2046).
文摘Electronic voting has partially solved the problems of poor anonymity and low efficiency associated with traditional voting.However,the difficulties it introduces into the supervision of the vote counting,as well as its need for a concurrent guaranteed trusted third party,should not be overlooked.With the advent of blockchain technology in recent years,its features such as decentralization,anonymity,and non-tampering have made it a good candidate in solving the problems that electronic voting faces.In this study,we propose a multi-candidate voting model based on the blockchain technology.With the introduction of an asymmetric encryption and an anonymity-preserving voting algorithm,votes can be counted without relying on a third party,and the voting results can be displayed in real time in a manner that satisfies various levels of voting security and privacy requirements.Experimental results show that the proposed model solves the aforementioned problems of electronic voting without significant negative impact from an increasing number of voters or candidates.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61272495,61379153,and 61401519)the Research Fund for the Doctoral Program of Higher Education of China(Grant No.20130162110012)the MEST-NRF of Korea(Grant No.2012-002521)
文摘We investigate the design of anonymous voting protocols,CV-based binary-valued ballot and CV-based multi-valued ballot with continuous variables(CV) in a multi-dimensional quantum cryptosystem to ensure the security of voting procedure and data privacy.The quantum entangled states are employed in the continuous variable quantum system to carry the voting information and assist information transmission,which takes the advantage of the GHZ-like states in terms of improving the utilization of quantum states by decreasing the number of required quantum states.It provides a potential approach to achieve the efficient quantum anonymous voting with high transmission security,especially in large-scale votes.
基金Supported by the National Natural Science Foun-dation of China (60572155) the National Nature Science Founda-tion of China for Distinguished Young Scholars (60225007)
文摘In this paper, we use the polynomial function and Chaum's RSA (Rivest, Shamir, Adleman) blind signature scheme to construct a secure anonymous internet electronic voting scheme. In our scheme, each vote does not need to be revealed in the tallying phase. The ballot number of each candidate gets is counted by computing the degrees of two polynomials' greatest common divisor. Our scheme does not require a special voting channel and communication can occur entirely over the current internet.
基金supported by the National Natural Science Foundation of China(6177340561751312)the Major Scientific and Technological Innovation Projects of Shandong Province(2019JZZY020123)。
文摘Extreme learning machine(ELM)has been proved to be an effective pattern classification and regression learning mechanism by researchers.However,its good performance is based on a large number of hidden layer nodes.With the increase of the nodes in the hidden layers,the computation cost is greatly increased.In this paper,we propose a novel algorithm,named constrained voting extreme learning machine(CV-ELM).Compared with the traditional ELM,the CV-ELM determines the input weight and bias based on the differences of between-class samples.At the same time,to improve the accuracy of the proposed method,the voting selection is introduced.The proposed method is evaluated on public benchmark datasets.The experimental results show that the proposed algorithm is superior to the original ELM algorithm.Further,we apply the CV-ELM to the classification of superheat degree(SD)state in the aluminum electrolysis industry,and the recognition accuracy rate reaches87.4%,and the experimental results demonstrate that the proposed method is more robust than the existing state-of-the-art identification methods.
基金Science Research Project of Gansu Provincial Transportation Department(No.2017-012)
文摘The random forest model is universal and easy to understand, which is often used for classification and prediction. However, it uses non-selective integration and the majority rule to judge the final result, thus the difference between the decision trees in the model is ignored and the prediction accuracy of the model is reduced. Taking into consideration these defects, an improved random forest model based on confusion matrix (CM-RF)is proposed. The decision tree cluster is selectively constructed by the similarity measure in the process of constructing the model, and the result is output by using the dynamic weighted voting fusion method in the final voting session. Experiments show that the proposed CM-RF can reduce the impact of low-performance decision trees on the output result, thus improving the accuracy and generalization ability of random forest model.
基金The National Key R&D Program of China(No.2020YFE0200600)。
文摘The communication complexity of the practical byzantine fault tolerance(PBFT)protocol is reduced with the threshold signature technique applied to the consensus process by phase voting PBFT(PV-PBFT).As most communication occurs between the primary node and replica nodes in PV-PVFT,consistency verification is accomplished through threshold signatures,multi-PV,and multiple consensus.The view replacement protocol introduces node weights to influence the election of a primary node,reducing the probability of the same node being elected primary multiple times.The experimental results of consensus algorithms show that compared to PBFT,the communication overhead of PV-PBFT decreases by approximately 90% with nearly one-time improvement in the throughput relative and approximately 2/3 consensus latency,lower than that of the scalable hierarchical byzantine fault tolerance.The communication complexity of the PBFT is O(N^(2)),whereas that of PV-PBFT is only O(N),which implies the significant improvement of the operational efficiency of the blockchain system.
文摘Advanced Metering Infrastructure(AMI)is the metering network of the smart grid that enables bidirectional communications between each consumer’s premises and the provider’s control center.The massive amount of data collected supports the real-time decision-making required for diverse applications.The communication infrastructure relies on different network types,including the Internet.This makes the infrastructure vulnerable to various attacks,which could compromise security or have devastating effects.However,traditional machine learning solutions cannot adapt to the increasing complexity and diversity of attacks.The objective of this paper is to develop an Anomaly Detection System(ADS)based on deep learning using the CIC-IDS2017 dataset.However,this dataset is highly imbalanced;thus,a two-step sampling technique:random under-sampling and the Synthetic Minority Oversampling Technique(SMOTE),is proposed to balance the dataset.The proposed system utilizes a multiple hidden layer Auto-encoder(AE)for feature extraction and dimensional reduction.In addition,an ensemble voting based on both Random Forest(RF)and Convolu-tional Neural Network(CNN)is developed to classify the multiclass attack cate-gories.The proposed system is evaluated and compared with six different state-of-the-art machine learning and deep learning algorithms:Random Forest(RF),Light Gradient Boosting Machine(LightGBM),eXtreme Gradient Boosting(XGboost),Convolutional Neural Network(CNN),Long Short-Term Memory(LSTM),and bidirectional LSTM(biLSTM).Experimental results show that the proposed model enhances the detection for each attack class compared with the other machine learning and deep learning models with overall accuracy(98.29%),precision(99%),recall(98%),F_(1) score(98%),and the UNDetection rate(UND)(8%).
文摘Oscillatory failure cases(OFC)detection in the fly-by-wire(FBW)flight control system for civil aircraft is addressed in this paper.First,OFC is ranked four levels:Handling quality,static load,global structure fatigue and local fatigue,according to their respect impact on aircraft.Second,we present voting and comparing monitors based on un-similarity redundancy commands to detect OFC.Third,the associated performances,the thresholds and the counters of the monitors are calculated by the high fidelity nonlinear aircraft models.Finally,the monitors of OFC are verified by the Iron Bird Platform with real parameters of the flight control system.The results show that our approach can detect OFC rapidly.