The paper generalizes the direct method of moving planes to the Logarithmic Laplacian system.Firstly,some key ingredients of the method are discussed,for example,Narrow region principle and Decay at infinity.Then,the ...The paper generalizes the direct method of moving planes to the Logarithmic Laplacian system.Firstly,some key ingredients of the method are discussed,for example,Narrow region principle and Decay at infinity.Then,the radial symmetry of the solution of the Logarithmic Laplacian system is obtained.展开更多
Weak signal reception is a very important and challenging problem for communication systems especially in the presence of non-Gaussian noise,and in which case the performance of optimal linear correlated receiver degr...Weak signal reception is a very important and challenging problem for communication systems especially in the presence of non-Gaussian noise,and in which case the performance of optimal linear correlated receiver degrades dramatically.Aiming at this,a novel uncorrelated reception scheme based on adaptive bistable stochastic resonance(ABSR)for a weak signal in additive Laplacian noise is investigated.By analyzing the key issue that the quantitative cooperative resonance matching relationship between the characteristics of the noisy signal and the nonlinear bistable system,an analytical expression of the bistable system parameters is derived.On this basis,by means of bistable system parameters self-adaptive adjustment,the counterintuitive stochastic resonance(SR)phenomenon can be easily generated at which the random noise is changed into a benefit to assist signal transmission.Finally,it is demonstrated that approximately 8dB bit error ratio(BER)performance improvement for the ABSR-based uncorrelated receiver when compared with the traditional uncorrelated receiver at low signal to noise ratio(SNR)conditions varying from-30dB to-5dB.展开更多
Let 0<α<2,p≥1,m∈ℕ_(+).Consider the positive solution u of the PDE(-△)^(α/2+m)u(x)=u^(p)(x) in R^(n).(0.1) In[1](Transactions of the American Mathematical Society,2021),Cao,Dai and Qin showed that,under the ...Let 0<α<2,p≥1,m∈ℕ_(+).Consider the positive solution u of the PDE(-△)^(α/2+m)u(x)=u^(p)(x) in R^(n).(0.1) In[1](Transactions of the American Mathematical Society,2021),Cao,Dai and Qin showed that,under the condition u∈Lα,(0.1)possesses a super polyharmonic property (-△)^(k+α/2)u≥0 for k=0,1,⋯,m−1.In this paper,we show another kind of super polyharmonic property(−Δ)^(k)u>0 for k=1,⋯,m−1,under the conditions and(−Δ)^(m)u≥0.Both kinds of super polyharmonic properties can lead to an equivalence between(0.1)and the integral equation u(x)=∫_(R^(n))u^(p)(y)/|x-y|^(n-2m-α)dy.One can classify solutions to(0.1)following the work of[2]and[3]by Chen,Li,Ou.展开更多
Decision-making(DM)is a process in which several persons concur-rently engage,examine the problems,evaluate potential alternatives,and select an appropriate option to the problem.Technique for determining order prefer...Decision-making(DM)is a process in which several persons concur-rently engage,examine the problems,evaluate potential alternatives,and select an appropriate option to the problem.Technique for determining order preference by similarity to the ideal solution(TOPSIS)is an established DM process.The objective of this report happens to broaden the approach of TOPSIS to solve the DM issues designed with Hesitancy fuzzy data,in which evaluation evidence given by the experts on possible solutions is presents as Hesitancy fuzzy decision matrices,each of which is defined by Hesitancy fuzzy numbers.Findings:we represent analytical results,such as designing a satellite communication network and assessing reservoir operation methods,to demonstrate that our suggested thoughts may be used in DM.Aim:We studied a new testing method for the arti-ficial communication system to give proof of the future construction of satellite earth stations.We aim to identify the best one from the different testing places.We are alsofinding the best operation schemes in the reservoir.In this article,we present the concepts of Laplacian energy(LE)in Hesitancy fuzzy graphs(HFGs),the weight function of LE of HFGs,and the TOPSIS method technique is used to produce the hesitancy fuzzy weighted-average(HFWA).Also,consider practical examples to illustrate the applicability of thefinest design of satellite communication systems and also evaluation of reservoir schemes.展开更多
The precise diagnosis of Alzheimer’s disease is critical for patient treatment,especially at the early stage,because awareness of the severity and progression risks lets patients take preventative actions before irre...The precise diagnosis of Alzheimer’s disease is critical for patient treatment,especially at the early stage,because awareness of the severity and progression risks lets patients take preventative actions before irreversible brain damage occurs.It is possible to gain a holistic view of Alzheimer’s disease staging by combining multiple data modalities,known as image fusion.In this paper,the study proposes the early detection of Alzheimer’s disease using different modalities of Alzheimer’s disease brain images.First,the preprocessing was performed on the data.Then,the data augmentation techniques are used to handle overfitting.Also,the skull is removed to lead to good classification.In the second phase,two fusion stages are used:pixel level(early fusion)and feature level(late fusion).We fused magnetic resonance imaging and positron emission tomography images using early fusion(Laplacian Re-Decomposition)and late fusion(Canonical Correlation Analysis).The proposed system used magnetic resonance imaging and positron emission tomography to take advantage of each.Magnetic resonance imaging system’s primary benefits are providing images with excellent spatial resolution and structural information for specific organs.Positron emission tomography images can provide functional information and the metabolisms of particular tissues.This characteristic helps clinicians detect diseases and tumor progression at an early stage.Third,the feature extraction of fused images is extracted using a convolutional neural network.In the case of late fusion,the features are extracted first and then fused.Finally,the proposed system performs XGB to classify Alzheimer’s disease.The system’s performance was evaluated using accuracy,specificity,and sensitivity.All medical data were retrieved in the 2D format of 256×256 pixels.The classifiers were optimized to achieve the final results:for the decision tree,the maximum depth of a tree was 2.The best number of trees for the random forest was 60;for the support vector machine,the maximum depth was 4,and the kernel gamma was 0.01.The system achieved an accuracy of 98.06%,specificity of 94.32%,and sensitivity of 97.02%in the case of early fusion.Also,if the system achieved late fusion,accuracy was 99.22%,specificity was 96.54%,and sensitivity was 99.54%.展开更多
基金Supported by Natural Science Foundation of Xinjiang Uygur Autonomous Region(2021D01B35)Natural Science Foundation of colleges and universities in Xinjiang Uygur Au-tonomous Region(XJEDU2021Y048)Doctoral Initiation Fund of Xinjiang Institute of Engineering(2020xgy012302).
基金Natural Science Foundation of Xinjiang Uygur Autonomous Region(2021D01B35)Natural Science Foundation of colleges and universities in Xinjiang Uygur Autonomous Region(XJEDU2021Y048)。
基金Supported by the National Natural Science Foundation of China(11501342,12001344)。
文摘The paper generalizes the direct method of moving planes to the Logarithmic Laplacian system.Firstly,some key ingredients of the method are discussed,for example,Narrow region principle and Decay at infinity.Then,the radial symmetry of the solution of the Logarithmic Laplacian system is obtained.
基金supported in part by the National Natural Science Foundation of China(62001356)in part by the National Natural Science Foundation for Distinguished Young Scholar(61825104)+1 种基金in part by the National Key Research and Development Program of China(2022YFC3301300)in part by the Innovative Research Groups of the National Natural Science Foundation of China(62121001)。
文摘Weak signal reception is a very important and challenging problem for communication systems especially in the presence of non-Gaussian noise,and in which case the performance of optimal linear correlated receiver degrades dramatically.Aiming at this,a novel uncorrelated reception scheme based on adaptive bistable stochastic resonance(ABSR)for a weak signal in additive Laplacian noise is investigated.By analyzing the key issue that the quantitative cooperative resonance matching relationship between the characteristics of the noisy signal and the nonlinear bistable system,an analytical expression of the bistable system parameters is derived.On this basis,by means of bistable system parameters self-adaptive adjustment,the counterintuitive stochastic resonance(SR)phenomenon can be easily generated at which the random noise is changed into a benefit to assist signal transmission.Finally,it is demonstrated that approximately 8dB bit error ratio(BER)performance improvement for the ABSR-based uncorrelated receiver when compared with the traditional uncorrelated receiver at low signal to noise ratio(SNR)conditions varying from-30dB to-5dB.
文摘Let 0<α<2,p≥1,m∈ℕ_(+).Consider the positive solution u of the PDE(-△)^(α/2+m)u(x)=u^(p)(x) in R^(n).(0.1) In[1](Transactions of the American Mathematical Society,2021),Cao,Dai and Qin showed that,under the condition u∈Lα,(0.1)possesses a super polyharmonic property (-△)^(k+α/2)u≥0 for k=0,1,⋯,m−1.In this paper,we show another kind of super polyharmonic property(−Δ)^(k)u>0 for k=1,⋯,m−1,under the conditions and(−Δ)^(m)u≥0.Both kinds of super polyharmonic properties can lead to an equivalence between(0.1)and the integral equation u(x)=∫_(R^(n))u^(p)(y)/|x-y|^(n-2m-α)dy.One can classify solutions to(0.1)following the work of[2]and[3]by Chen,Li,Ou.
文摘Decision-making(DM)is a process in which several persons concur-rently engage,examine the problems,evaluate potential alternatives,and select an appropriate option to the problem.Technique for determining order preference by similarity to the ideal solution(TOPSIS)is an established DM process.The objective of this report happens to broaden the approach of TOPSIS to solve the DM issues designed with Hesitancy fuzzy data,in which evaluation evidence given by the experts on possible solutions is presents as Hesitancy fuzzy decision matrices,each of which is defined by Hesitancy fuzzy numbers.Findings:we represent analytical results,such as designing a satellite communication network and assessing reservoir operation methods,to demonstrate that our suggested thoughts may be used in DM.Aim:We studied a new testing method for the arti-ficial communication system to give proof of the future construction of satellite earth stations.We aim to identify the best one from the different testing places.We are alsofinding the best operation schemes in the reservoir.In this article,we present the concepts of Laplacian energy(LE)in Hesitancy fuzzy graphs(HFGs),the weight function of LE of HFGs,and the TOPSIS method technique is used to produce the hesitancy fuzzy weighted-average(HFWA).Also,consider practical examples to illustrate the applicability of thefinest design of satellite communication systems and also evaluation of reservoir schemes.
基金This research was supported by the MSIT(Ministry of Science and ICT),Korea,under the ICT Creative Consilience Program(IITP-2021-2020-0-01821)supervised by the IITP(Institute for Information&communications Technology Planning&evaluation)the National Research Foundation of Korea(NRF)grant funded by the Korea government(MSIT)(No.2021R1A2C1011198).
文摘The precise diagnosis of Alzheimer’s disease is critical for patient treatment,especially at the early stage,because awareness of the severity and progression risks lets patients take preventative actions before irreversible brain damage occurs.It is possible to gain a holistic view of Alzheimer’s disease staging by combining multiple data modalities,known as image fusion.In this paper,the study proposes the early detection of Alzheimer’s disease using different modalities of Alzheimer’s disease brain images.First,the preprocessing was performed on the data.Then,the data augmentation techniques are used to handle overfitting.Also,the skull is removed to lead to good classification.In the second phase,two fusion stages are used:pixel level(early fusion)and feature level(late fusion).We fused magnetic resonance imaging and positron emission tomography images using early fusion(Laplacian Re-Decomposition)and late fusion(Canonical Correlation Analysis).The proposed system used magnetic resonance imaging and positron emission tomography to take advantage of each.Magnetic resonance imaging system’s primary benefits are providing images with excellent spatial resolution and structural information for specific organs.Positron emission tomography images can provide functional information and the metabolisms of particular tissues.This characteristic helps clinicians detect diseases and tumor progression at an early stage.Third,the feature extraction of fused images is extracted using a convolutional neural network.In the case of late fusion,the features are extracted first and then fused.Finally,the proposed system performs XGB to classify Alzheimer’s disease.The system’s performance was evaluated using accuracy,specificity,and sensitivity.All medical data were retrieved in the 2D format of 256×256 pixels.The classifiers were optimized to achieve the final results:for the decision tree,the maximum depth of a tree was 2.The best number of trees for the random forest was 60;for the support vector machine,the maximum depth was 4,and the kernel gamma was 0.01.The system achieved an accuracy of 98.06%,specificity of 94.32%,and sensitivity of 97.02%in the case of early fusion.Also,if the system achieved late fusion,accuracy was 99.22%,specificity was 96.54%,and sensitivity was 99.54%.
