Asynchronous federated learning(AsynFL)can effectivelymitigate the impact of heterogeneity of edge nodes on joint training while satisfying participant user privacy protection and data security.However,the frequent ex...Asynchronous federated learning(AsynFL)can effectivelymitigate the impact of heterogeneity of edge nodes on joint training while satisfying participant user privacy protection and data security.However,the frequent exchange of massive data can lead to excess communication overhead between edge and central nodes regardless of whether the federated learning(FL)algorithm uses synchronous or asynchronous aggregation.Therefore,there is an urgent need for a method that can simultaneously take into account device heterogeneity and edge node energy consumption reduction.This paper proposes a novel Fixed-point Asynchronous Federated Learning(FixedAsynFL)algorithm,which could mitigate the resource consumption caused by frequent data communication while alleviating the effect of device heterogeneity.FixedAsynFL uses fixed-point quantization to compress the local and global models in AsynFL.In order to balance energy consumption and learning accuracy,this paper proposed a quantization scale selection mechanism.This paper examines the mathematical relationship between the quantization scale and energy consumption of the computation/communication process in the FixedAsynFL.Based on considering the upper bound of quantization noise,this paper optimizes the quantization scale by minimizing communication and computation consumption.This paper performs pertinent experiments on the MNIST dataset with several edge nodes of different computing efficiency.The results show that the FixedAsynFL algorithm with an 8-bit quantization can significantly reduce the communication data size by 81.3%and save the computation energy in the training phase by 74.9%without significant loss of accuracy.According to the experimental results,we can see that the proposed AsynFixedFL algorithm can effectively solve the problem of device heterogeneity and energy consumption limitation of edge nodes.展开更多
Discrete Tomography(DT)is a technology that uses image projection to reconstruct images.Its reconstruction problem,especially the binary image(0–1matrix)has attracted strong attention.In this study,a fixed point iter...Discrete Tomography(DT)is a technology that uses image projection to reconstruct images.Its reconstruction problem,especially the binary image(0–1matrix)has attracted strong attention.In this study,a fixed point iterative method of integer programming based on intelligent optimization is proposed to optimize the reconstructedmodel.The solution process can be divided into two procedures.First,the DT problem is reformulated into a polyhedron judgment problembased on lattice basis reduction.Second,the fixed-point iterativemethod of Dang and Ye is used to judge whether an integer point exists in the polyhedron of the previous program.All the programs involved in this study are written in MATLAB.The final experimental data show that this method is obviously better than the branch and bound method in terms of computational efficiency,especially in the case of high dimension.The branch and bound method requires more branch operations and takes a long time.It also needs to store a large number of leaf node boundaries and the corresponding consumptionmatrix,which occupies a largememory space.展开更多
Fixed-point fast sweeping WENO methods are a class of efficient high-order numerical methods to solve steady-state solutions of hyperbolic partial differential equations(PDEs).The Gauss-Seidel iterations and alternati...Fixed-point fast sweeping WENO methods are a class of efficient high-order numerical methods to solve steady-state solutions of hyperbolic partial differential equations(PDEs).The Gauss-Seidel iterations and alternating sweeping strategy are used to cover characteristics of hyperbolic PDEs in each sweeping order to achieve fast convergence rate to steady-state solutions.A nice property of fixed-point fast sweeping WENO methods which distinguishes them from other fast sweeping methods is that they are explicit and do not require inverse operation of nonlinear local systems.Hence,they are easy to be applied to a general hyperbolic system.To deal with the difficulties associated with numerical boundary treatment when high-order finite difference methods on a Cartesian mesh are used to solve hyperbolic PDEs on complex domains,inverse Lax-Wendroff(ILW)procedures were developed as a very effective approach in the literature.In this paper,we combine a fifthorder fixed-point fast sweeping WENO method with an ILW procedure to solve steadystate solution of hyperbolic conservation laws on complex computing regions.Numerical experiments are performed to test the method in solving various problems including the cases with the physical boundary not aligned with the grids.Numerical results show highorder accuracy and good performance of the method.Furthermore,the method is compared with the popular third-order total variation diminishing Runge-Kutta(TVD-RK3)time-marching method for steady-state computations.Numerical examples show that for most of examples,the fixed-point fast sweeping method saves more than half CPU time costs than TVD-RK3 to converge to steady-state solutions.展开更多
The present paper is devoted to a novel smoothing function method for convex quadratic programming problem with mixed constrains, which has important application in mechanics and engineering science. The problem is re...The present paper is devoted to a novel smoothing function method for convex quadratic programming problem with mixed constrains, which has important application in mechanics and engineering science. The problem is reformulated as a system of non-smooth equations, and then a smoothing function for the system of non-smooth equations is proposed. The condition of convergences of this iteration algorithm is given. Theory analysis and primary numerical results illustrate that this method is feasible and effective.展开更多
For the unsorted database quantum search with the unknown fraction λ of target items, there are mainly two kinds of methods, i.e., fixed-point and trail-and-error.(i) In terms of the fixed-point method, Yoder et al. ...For the unsorted database quantum search with the unknown fraction λ of target items, there are mainly two kinds of methods, i.e., fixed-point and trail-and-error.(i) In terms of the fixed-point method, Yoder et al. [Phys. Rev. Lett.113 210501(2014)] claimed that the quadratic speedup over classical algorithms has been achieved. However, in this paper, we point out that this is not the case, because the query complexity of Yoder’s algorithm is actually in O(1/λ01/2)rather than O(1/λ1/2), where λ0 is a known lower bound of λ.(ii) In terms of the trail-and-error method, currently the algorithm without randomness has to take more than 1 times queries or iterations than the algorithm with randomly selected parameters. For the above problems, we provide the first hybrid quantum search algorithm based on the fixed-point and trail-and-error methods, where the matched multiphase Grover operations are trialed multiple times and the number of iterations increases exponentially along with the number of trials. The upper bound of expected queries as well as the optimal parameters are derived. Compared with Yoder’s algorithm, the query complexity of our algorithm indeed achieves the optimal scaling in λ for quantum search, which reconfirms the practicality of the fixed-point method. In addition, our algorithm also does not contain randomness, and compared with the existing deterministic algorithm, the query complexity can be reduced by about 1/3. Our work provides a new idea for the research on fixed-point and trial-and-error quantum search.展开更多
The aim of this paper is to gain insight into the nonlinear vibration feature of a dynamic model of a gas turbine.First,a rod fastening rotor-bearing coupling model with fixed-point rubbing is proposed,where the fract...The aim of this paper is to gain insight into the nonlinear vibration feature of a dynamic model of a gas turbine.First,a rod fastening rotor-bearing coupling model with fixed-point rubbing is proposed,where the fractal theory and the finite element method are utilized.For contact analysis,a novel contact force model is introduced in this paper.Meanwhile,the Coulomb model is adopted to expound the friction characteristics.Second,the governing equations of motion of the rotor system are numerically solved,and the nonlinear dynamic characteristics are analyzed in terms of the bifurcation diagram,Poincarémap,and time history.Third,the potential effects provided by contact degree of joint interface,distribution position,and amount of contact layer are discussed in detail.Finally,the contrast analysis between the integral rotor and the rod fastening rotor is conducted under the condition of fixed-point rubbing.展开更多
Using the hypothesis that data transmitted by different users are statistically independent of each other,this paper proposes a fixed-point blind adaptive multiuser detection algorithm for Time-Hopping (TH) Impulse Ra...Using the hypothesis that data transmitted by different users are statistically independent of each other,this paper proposes a fixed-point blind adaptive multiuser detection algorithm for Time-Hopping (TH) Impulse Radio (IR) Ultra Wide Band (UWB) systems in multipath channel,which is based on Independent Component Analysis (ICA) idea. The proposed algorithm employs maximizing negentropy criterion to separate the data packets of different users. Then the user characteristic se-quences are utilized to identify the data packet order of the desired user. This algorithm only needs the desired user’s characteristic sequence instead of channel information,power information and time-hoping code of any user. Due to using hypothesis of statistical independence among users,the proposed algorithm has the outstanding Bit Error Rate (BER) performance and the excellent ability of near-far resistance. Simulation results demonstrate that this algorithm has the performance close to that of Maximum-Likelihood (ML) algorithm and is a suboptimum blind adaptive multiuser detection algorithm of excellent near-far resistance and low complexity.展开更多
The Brouwer fixed-point theorem in topology states that for any continuous mapping <em>f</em> on a compact convex set into itself admits a fixed point, <em>i.e.</em>, a point <em>x</em...The Brouwer fixed-point theorem in topology states that for any continuous mapping <em>f</em> on a compact convex set into itself admits a fixed point, <em>i.e.</em>, a point <em>x</em><sub>0</sub> such that<em> f</em>(<em>x</em><sub>0</sub>) = <em>x</em><sub>0</sub>. Under suitable conditions, this fixed point corresponds to the throat of a traversable wormhole, <em>i.e.</em>, <em>b</em>(<em>r</em><sub>0</sub>) = <em>r</em><sub>0</sub> for the shape function <em>b</em> = <em>b</em>(<em>r</em>). The possible existence of wormholes can therefore be deduced from purely mathematical considerations without going beyond the existing physical requirements.展开更多
The development of IoT(Internet of Things)calls for circuit designs with energy and area efficiency for edge devices.Approximate computing which trades unnecessary computation precision for hardware cost savings is a ...The development of IoT(Internet of Things)calls for circuit designs with energy and area efficiency for edge devices.Approximate computing which trades unnecessary computation precision for hardware cost savings is a promising direction for error-tolerant applications.Multipliers,as frequently invoked basic modules which consume non-trivial hardware costs,have been introduced approximation to achieve distinct energy and area savings for data-intensive applications.In this paper,we propose a fixed-point approximate multiplier that employs a linear mapping technique,which enables the configurability of approximation levels and the unbiasedness of computation errors.We then introduce a dynamic truncation method into the proposed multiplier design to cover a wider and more fine-grained configuration range of approximation for more flexible hardware cost savings.In addition,a novel normalization module is proposed for the required shifting operations,which balances the occupied area and the critical path delay compared with normal shifters.The introduced errors of our proposed design are analyzed and expressed by formulas which are validated by experimental results.Experimental evaluations show that compared with accurate multipliers,our proposed approximate multiplier design provides maximum area and power savings up to 49.70%and 66.39%respectively with acceptable computation errors.展开更多
Our Solar System contains eight planets and their respective natural satellites excepting the inner two planets Mercury and Venus. A satellite hosted by a given Planet is well protected by the gravitational pertubatio...Our Solar System contains eight planets and their respective natural satellites excepting the inner two planets Mercury and Venus. A satellite hosted by a given Planet is well protected by the gravitational pertubation of much heavier planets such as Jupiter and Saturn if the natural satellite lies deep inside the respective host Planet Hill sphere. Each planet has a Hill radius a<sub>H</sub> and planet mean radius R<sub>P </sub>and the ratio R<sub>1</sub>=R<sub>P</sub>/a<sub>H</sub>. Under very low R<sub>1 </sub>(less than 0.006) the approximation of CRTBP (centrally restricted three-body problem) to two-body problem is valid and planet has spacious Hill lobe to capture a satellite and retain it. This ensures a high probability of capture of natural satellite by the given planet and Sun’s perturbation on Planet-Satellite binary can be neglected. This is the case with Earth, Mars, Jupiter, Saturn, Neptune and Uranus. But Mercury and Venus has R<sub>1</sub>=R<sub>P</sub>/a<sub>H</sub> =0.01 and 5.9862 × 10<sup>-3</sup> respectively hence they have no satellites. There is a limit to the dimension of the captured body. It must be a much smaller body both dimensionally as well masswise. The qantitative limit is a subject of an independent study.展开更多
Here a fixed-point duality quantum search algorithm is proposed.This algorithm uses iteratively non-unitary operations and measurements to search an unsorted database.Once the marked item is found,the algorithm stops ...Here a fixed-point duality quantum search algorithm is proposed.This algorithm uses iteratively non-unitary operations and measurements to search an unsorted database.Once the marked item is found,the algorithm stops automatically.This algorithm uses a constant non-unitary operator,and requires N/4 steps on average(N is the number of data from the database) to locate the marked state.The implementation of this algorithm in a usual quantum computer is also demonstrated.展开更多
Shor in 1994 proposed a quantum polynomial-time algorithm for finding the order r of an element a in the multiplicative group Z_(n)^(*),which can be used to factor the integer n by computing gcd(a^(r/2)±1,n),and ...Shor in 1994 proposed a quantum polynomial-time algorithm for finding the order r of an element a in the multiplicative group Z_(n)^(*),which can be used to factor the integer n by computing gcd(a^(r/2)±1,n),and hence break the famous RSA cryptosystem.However,the order r must be even.This restriction can be removed.So in this paper,we propose a quantum polynomial-time fixed-point attack for directly recovering the RSA plaintext M from the ciphertext C,without explicitly factoring the modulus n.Compared to Shor’s algorithm,the order r of the fixed-point C for RSA(e,n)satisfying C^(er)≡C(mod n)does not need to be even.Moreover,the success probability of the new algorithm is at least 4φ(r)/π^(2)r and higher than that of Shor’s algorithm,though the time complexity for both algorithms is about the same.展开更多
This paper introduces the fixed-point learning algorithm based on independent component analysis(ICA);the model and process of this algorithm and simulation results are presented.Kurtosis was adopted as the estimation...This paper introduces the fixed-point learning algorithm based on independent component analysis(ICA);the model and process of this algorithm and simulation results are presented.Kurtosis was adopted as the estimation rule of independence.The results of the experiment show that compared with the traditional ICA algorithm based on random grads,this algorithm has advantages such as fast convergence and no necessity for any dynamic parameter,etc.The algorithm is a highly efficient and reliable method in blind signal separation.展开更多
In this paper,we focus on the following coupled system of k-Hessian equations:{S_(k)(λ(D^(2)u))=f_(1)(|x|,-v)in B,S_(k)(λ(D^(2)v))=f2(|x|,-u)in B,u=v=0 on■B.Here B is a unit ball with center 0 and fi(i=1,2)are cont...In this paper,we focus on the following coupled system of k-Hessian equations:{S_(k)(λ(D^(2)u))=f_(1)(|x|,-v)in B,S_(k)(λ(D^(2)v))=f2(|x|,-u)in B,u=v=0 on■B.Here B is a unit ball with center 0 and fi(i=1,2)are continuous and nonnegative functions.By introducing some new growth conditions on the nonlinearities f_(1) and f_(2),which are more flexible than the existing conditions for the k-Hessian systems(equations),several new existence and multiplicity results for k-convex solutions for this kind of problem are obtained.展开更多
This paper tackles the maximum correntropy Kalman filtering problem for discrete time-varying non-Gaussian systems subject to state saturations and stochastic nonlinearities. The stochastic nonlinearities, which take ...This paper tackles the maximum correntropy Kalman filtering problem for discrete time-varying non-Gaussian systems subject to state saturations and stochastic nonlinearities. The stochastic nonlinearities, which take the form of statemultiplicative noises, are introduced in systems to describe the phenomenon of nonlinear disturbances. To resist non-Gaussian noises, we consider a new performance index called maximum correntropy criterion(MCC) which describes the similarity between two stochastic variables. To enhance the “robustness” of the kernel parameter selection on the resultant filtering performance, the Cauchy kernel function is adopted to calculate the corresponding correntropy. The goal of this paper is to design a Kalman-type filter for the underlying systems via maximizing the correntropy between the system state and its estimate. By taking advantage of an upper bound on the one-step prediction error covariance, a modified MCC-based performance index is constructed. Subsequently, with the assistance of a fixed-point theorem, the filter gain is obtained by maximizing the proposed cost function. In addition, a sufficient condition is deduced to ensure the uniqueness of the fixed point. Finally, the validity of the filtering method is tested by simulating a numerical example.展开更多
This paper proposes a passive methodology for detecting a class of stealthy intermittent integrity attacks in cyberphysical systems subject to process disturbances and measurement noise.A stealthy intermittent integri...This paper proposes a passive methodology for detecting a class of stealthy intermittent integrity attacks in cyberphysical systems subject to process disturbances and measurement noise.A stealthy intermittent integrity attack strategy is first proposed by modifying a zero-dynamics attack model.The stealthiness of the generated attacks is rigorously investigated under the condition that the adversary does not know precisely the system state values.In order to help detect such attacks,a backward-in-time detection residual is proposed based on an equivalent quantity of the system state change,due to the attack,at a time prior to the attack occurrence time.A key characteristic of this residual is that its magnitude increases every time a new attack occurs.To estimate this unknown residual,an optimal fixed-point smoother is proposed by minimizing a piece-wise linear quadratic cost function with a set of specifically designed weighting matrices.The smoother design guarantees robustness with respect to process disturbances and measurement noise,and is also able to maintain sensitivity as time progresses to intermittent integrity attack by resetting the covariance matrix based on the weighting matrices.The adaptive threshold is designed based on the estimated backward-in-time residual,and the attack detectability analysis is rigorously investigated to characterize quantitatively the class of attacks that can be detected by the proposed methodology.Finally,a simulation example is used to demonstrate the effectiveness of the developed methodology.展开更多
The Sun has solar rotation;nevertheless, many evidences have suggested that different latitude of the Sun rotates in different speed, which is now known as differential rotation. This work calculates the solar rotatio...The Sun has solar rotation;nevertheless, many evidences have suggested that different latitude of the Sun rotates in different speed, which is now known as differential rotation. This work calculates the solar rotation speeds near the equator and 30? in the northern hemisphere using Fixed-Point Arithmetic method. The calculated results show a greater speed at the equator than the speed at 30?, indicating that the speed decreases as the latitude becomes higher. .展开更多
基金This work was funded by National Key R&D Program of China(Grant No.2020YFB0906003).
文摘Asynchronous federated learning(AsynFL)can effectivelymitigate the impact of heterogeneity of edge nodes on joint training while satisfying participant user privacy protection and data security.However,the frequent exchange of massive data can lead to excess communication overhead between edge and central nodes regardless of whether the federated learning(FL)algorithm uses synchronous or asynchronous aggregation.Therefore,there is an urgent need for a method that can simultaneously take into account device heterogeneity and edge node energy consumption reduction.This paper proposes a novel Fixed-point Asynchronous Federated Learning(FixedAsynFL)algorithm,which could mitigate the resource consumption caused by frequent data communication while alleviating the effect of device heterogeneity.FixedAsynFL uses fixed-point quantization to compress the local and global models in AsynFL.In order to balance energy consumption and learning accuracy,this paper proposed a quantization scale selection mechanism.This paper examines the mathematical relationship between the quantization scale and energy consumption of the computation/communication process in the FixedAsynFL.Based on considering the upper bound of quantization noise,this paper optimizes the quantization scale by minimizing communication and computation consumption.This paper performs pertinent experiments on the MNIST dataset with several edge nodes of different computing efficiency.The results show that the FixedAsynFL algorithm with an 8-bit quantization can significantly reduce the communication data size by 81.3%and save the computation energy in the training phase by 74.9%without significant loss of accuracy.According to the experimental results,we can see that the proposed AsynFixedFL algorithm can effectively solve the problem of device heterogeneity and energy consumption limitation of edge nodes.
基金funded by the NSFC under Grant Nos.61803279,71471091,62003231 and 51874205in part by the Qing Lan Project of Jiangsu,in part by the China Postdoctoral Science Foundation under Grant Nos.2020M671596 and 2021M692369+2 种基金in part by the Suzhou Science and Technology Development Plan Project(Key Industry Technology Innovation)under Grant No.SYG202114in part by the Natural Science Foundation of Jiangsu Province under Grant No.BK20200989Postdoctoral Research Funding Program of Jiangsu Province.
文摘Discrete Tomography(DT)is a technology that uses image projection to reconstruct images.Its reconstruction problem,especially the binary image(0–1matrix)has attracted strong attention.In this study,a fixed point iterative method of integer programming based on intelligent optimization is proposed to optimize the reconstructedmodel.The solution process can be divided into two procedures.First,the DT problem is reformulated into a polyhedron judgment problembased on lattice basis reduction.Second,the fixed-point iterativemethod of Dang and Ye is used to judge whether an integer point exists in the polyhedron of the previous program.All the programs involved in this study are written in MATLAB.The final experimental data show that this method is obviously better than the branch and bound method in terms of computational efficiency,especially in the case of high dimension.The branch and bound method requires more branch operations and takes a long time.It also needs to store a large number of leaf node boundaries and the corresponding consumptionmatrix,which occupies a largememory space.
基金Research was supported by the NSFC Grant 11872210Research was supported by the NSFC Grant 11872210 and Grant No.MCMS-I-0120G01+1 种基金Research supported in part by the AFOSR Grant FA9550-20-1-0055NSF Grant DMS-2010107.
文摘Fixed-point fast sweeping WENO methods are a class of efficient high-order numerical methods to solve steady-state solutions of hyperbolic partial differential equations(PDEs).The Gauss-Seidel iterations and alternating sweeping strategy are used to cover characteristics of hyperbolic PDEs in each sweeping order to achieve fast convergence rate to steady-state solutions.A nice property of fixed-point fast sweeping WENO methods which distinguishes them from other fast sweeping methods is that they are explicit and do not require inverse operation of nonlinear local systems.Hence,they are easy to be applied to a general hyperbolic system.To deal with the difficulties associated with numerical boundary treatment when high-order finite difference methods on a Cartesian mesh are used to solve hyperbolic PDEs on complex domains,inverse Lax-Wendroff(ILW)procedures were developed as a very effective approach in the literature.In this paper,we combine a fifthorder fixed-point fast sweeping WENO method with an ILW procedure to solve steadystate solution of hyperbolic conservation laws on complex computing regions.Numerical experiments are performed to test the method in solving various problems including the cases with the physical boundary not aligned with the grids.Numerical results show highorder accuracy and good performance of the method.Furthermore,the method is compared with the popular third-order total variation diminishing Runge-Kutta(TVD-RK3)time-marching method for steady-state computations.Numerical examples show that for most of examples,the fixed-point fast sweeping method saves more than half CPU time costs than TVD-RK3 to converge to steady-state solutions.
文摘The present paper is devoted to a novel smoothing function method for convex quadratic programming problem with mixed constrains, which has important application in mechanics and engineering science. The problem is reformulated as a system of non-smooth equations, and then a smoothing function for the system of non-smooth equations is proposed. The condition of convergences of this iteration algorithm is given. Theory analysis and primary numerical results illustrate that this method is feasible and effective.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11504430 and 61502526)the National Basic Research Program of China(Grant No.2013CB338002)
文摘For the unsorted database quantum search with the unknown fraction λ of target items, there are mainly two kinds of methods, i.e., fixed-point and trail-and-error.(i) In terms of the fixed-point method, Yoder et al. [Phys. Rev. Lett.113 210501(2014)] claimed that the quadratic speedup over classical algorithms has been achieved. However, in this paper, we point out that this is not the case, because the query complexity of Yoder’s algorithm is actually in O(1/λ01/2)rather than O(1/λ1/2), where λ0 is a known lower bound of λ.(ii) In terms of the trail-and-error method, currently the algorithm without randomness has to take more than 1 times queries or iterations than the algorithm with randomly selected parameters. For the above problems, we provide the first hybrid quantum search algorithm based on the fixed-point and trail-and-error methods, where the matched multiphase Grover operations are trialed multiple times and the number of iterations increases exponentially along with the number of trials. The upper bound of expected queries as well as the optimal parameters are derived. Compared with Yoder’s algorithm, the query complexity of our algorithm indeed achieves the optimal scaling in λ for quantum search, which reconfirms the practicality of the fixed-point method. In addition, our algorithm also does not contain randomness, and compared with the existing deterministic algorithm, the query complexity can be reduced by about 1/3. Our work provides a new idea for the research on fixed-point and trial-and-error quantum search.
基金the National Natural Science Foundation of China(No.12172307)the Key Laboratory of Vibration and Control of Aero-Propulsion System,Ministry of Education,Northeastern University of China(No.VCAME202103)the Fundamental Research Funds for the Central Universities in Southwest Jiaotong University of China(No.2682021ZTPY036)。
文摘The aim of this paper is to gain insight into the nonlinear vibration feature of a dynamic model of a gas turbine.First,a rod fastening rotor-bearing coupling model with fixed-point rubbing is proposed,where the fractal theory and the finite element method are utilized.For contact analysis,a novel contact force model is introduced in this paper.Meanwhile,the Coulomb model is adopted to expound the friction characteristics.Second,the governing equations of motion of the rotor system are numerically solved,and the nonlinear dynamic characteristics are analyzed in terms of the bifurcation diagram,Poincarémap,and time history.Third,the potential effects provided by contact degree of joint interface,distribution position,and amount of contact layer are discussed in detail.Finally,the contrast analysis between the integral rotor and the rod fastening rotor is conducted under the condition of fixed-point rubbing.
文摘Using the hypothesis that data transmitted by different users are statistically independent of each other,this paper proposes a fixed-point blind adaptive multiuser detection algorithm for Time-Hopping (TH) Impulse Radio (IR) Ultra Wide Band (UWB) systems in multipath channel,which is based on Independent Component Analysis (ICA) idea. The proposed algorithm employs maximizing negentropy criterion to separate the data packets of different users. Then the user characteristic se-quences are utilized to identify the data packet order of the desired user. This algorithm only needs the desired user’s characteristic sequence instead of channel information,power information and time-hoping code of any user. Due to using hypothesis of statistical independence among users,the proposed algorithm has the outstanding Bit Error Rate (BER) performance and the excellent ability of near-far resistance. Simulation results demonstrate that this algorithm has the performance close to that of Maximum-Likelihood (ML) algorithm and is a suboptimum blind adaptive multiuser detection algorithm of excellent near-far resistance and low complexity.
文摘The Brouwer fixed-point theorem in topology states that for any continuous mapping <em>f</em> on a compact convex set into itself admits a fixed point, <em>i.e.</em>, a point <em>x</em><sub>0</sub> such that<em> f</em>(<em>x</em><sub>0</sub>) = <em>x</em><sub>0</sub>. Under suitable conditions, this fixed point corresponds to the throat of a traversable wormhole, <em>i.e.</em>, <em>b</em>(<em>r</em><sub>0</sub>) = <em>r</em><sub>0</sub> for the shape function <em>b</em> = <em>b</em>(<em>r</em>). The possible existence of wormholes can therefore be deduced from purely mathematical considerations without going beyond the existing physical requirements.
基金supported by the National Key Research and Development Program of China under Grant No.2018YFE0126300the National Natural Science Foundation of China under Grant Nos.62034007,62141404.
文摘The development of IoT(Internet of Things)calls for circuit designs with energy and area efficiency for edge devices.Approximate computing which trades unnecessary computation precision for hardware cost savings is a promising direction for error-tolerant applications.Multipliers,as frequently invoked basic modules which consume non-trivial hardware costs,have been introduced approximation to achieve distinct energy and area savings for data-intensive applications.In this paper,we propose a fixed-point approximate multiplier that employs a linear mapping technique,which enables the configurability of approximation levels and the unbiasedness of computation errors.We then introduce a dynamic truncation method into the proposed multiplier design to cover a wider and more fine-grained configuration range of approximation for more flexible hardware cost savings.In addition,a novel normalization module is proposed for the required shifting operations,which balances the occupied area and the critical path delay compared with normal shifters.The introduced errors of our proposed design are analyzed and expressed by formulas which are validated by experimental results.Experimental evaluations show that compared with accurate multipliers,our proposed approximate multiplier design provides maximum area and power savings up to 49.70%and 66.39%respectively with acceptable computation errors.
文摘Our Solar System contains eight planets and their respective natural satellites excepting the inner two planets Mercury and Venus. A satellite hosted by a given Planet is well protected by the gravitational pertubation of much heavier planets such as Jupiter and Saturn if the natural satellite lies deep inside the respective host Planet Hill sphere. Each planet has a Hill radius a<sub>H</sub> and planet mean radius R<sub>P </sub>and the ratio R<sub>1</sub>=R<sub>P</sub>/a<sub>H</sub>. Under very low R<sub>1 </sub>(less than 0.006) the approximation of CRTBP (centrally restricted three-body problem) to two-body problem is valid and planet has spacious Hill lobe to capture a satellite and retain it. This ensures a high probability of capture of natural satellite by the given planet and Sun’s perturbation on Planet-Satellite binary can be neglected. This is the case with Earth, Mars, Jupiter, Saturn, Neptune and Uranus. But Mercury and Venus has R<sub>1</sub>=R<sub>P</sub>/a<sub>H</sub> =0.01 and 5.9862 × 10<sup>-3</sup> respectively hence they have no satellites. There is a limit to the dimension of the captured body. It must be a much smaller body both dimensionally as well masswise. The qantitative limit is a subject of an independent study.
基金supported by the National Natural Science Foundation of China (Grant Nos 10775076 and 10874098)the SRFPD Program in the Ministry of Education of China (Grant No 20060003048)+1 种基金the National Basic Research Program of China (Grant No 2006CB921106)Educational Commission of Liaoning Province of China (Grant No 2008130)
文摘Here a fixed-point duality quantum search algorithm is proposed.This algorithm uses iteratively non-unitary operations and measurements to search an unsorted database.Once the marked item is found,the algorithm stops automatically.This algorithm uses a constant non-unitary operator,and requires N/4 steps on average(N is the number of data from the database) to locate the marked state.The implementation of this algorithm in a usual quantum computer is also demonstrated.
基金Supported by Nanhu Scholars Program for Young Scholars of Xinyang Normal University。
文摘Shor in 1994 proposed a quantum polynomial-time algorithm for finding the order r of an element a in the multiplicative group Z_(n)^(*),which can be used to factor the integer n by computing gcd(a^(r/2)±1,n),and hence break the famous RSA cryptosystem.However,the order r must be even.This restriction can be removed.So in this paper,we propose a quantum polynomial-time fixed-point attack for directly recovering the RSA plaintext M from the ciphertext C,without explicitly factoring the modulus n.Compared to Shor’s algorithm,the order r of the fixed-point C for RSA(e,n)satisfying C^(er)≡C(mod n)does not need to be even.Moreover,the success probability of the new algorithm is at least 4φ(r)/π^(2)r and higher than that of Shor’s algorithm,though the time complexity for both algorithms is about the same.
基金supported by the Shanxi Young Science Fund (No.2008021022).
文摘This paper introduces the fixed-point learning algorithm based on independent component analysis(ICA);the model and process of this algorithm and simulation results are presented.Kurtosis was adopted as the estimation rule of independence.The results of the experiment show that compared with the traditional ICA algorithm based on random grads,this algorithm has advantages such as fast convergence and no necessity for any dynamic parameter,etc.The algorithm is a highly efficient and reliable method in blind signal separation.
基金supported by the National Natural Science Foundation of China (11961060)the Graduate Research Support of Northwest Normal University (2021KYZZ01032)。
文摘In this paper,we focus on the following coupled system of k-Hessian equations:{S_(k)(λ(D^(2)u))=f_(1)(|x|,-v)in B,S_(k)(λ(D^(2)v))=f2(|x|,-u)in B,u=v=0 on■B.Here B is a unit ball with center 0 and fi(i=1,2)are continuous and nonnegative functions.By introducing some new growth conditions on the nonlinearities f_(1) and f_(2),which are more flexible than the existing conditions for the k-Hessian systems(equations),several new existence and multiplicity results for k-convex solutions for this kind of problem are obtained.
基金supported in part by the National Natural Science Foundation of China (62273088, 62273087)the Shanghai Pujiang Program of China (22PJ1400400)the Program of Shanghai Academic/Technology Research Leader (20XD1420100)。
文摘This paper tackles the maximum correntropy Kalman filtering problem for discrete time-varying non-Gaussian systems subject to state saturations and stochastic nonlinearities. The stochastic nonlinearities, which take the form of statemultiplicative noises, are introduced in systems to describe the phenomenon of nonlinear disturbances. To resist non-Gaussian noises, we consider a new performance index called maximum correntropy criterion(MCC) which describes the similarity between two stochastic variables. To enhance the “robustness” of the kernel parameter selection on the resultant filtering performance, the Cauchy kernel function is adopted to calculate the corresponding correntropy. The goal of this paper is to design a Kalman-type filter for the underlying systems via maximizing the correntropy between the system state and its estimate. By taking advantage of an upper bound on the one-step prediction error covariance, a modified MCC-based performance index is constructed. Subsequently, with the assistance of a fixed-point theorem, the filter gain is obtained by maximizing the proposed cost function. In addition, a sufficient condition is deduced to ensure the uniqueness of the fixed point. Finally, the validity of the filtering method is tested by simulating a numerical example.
基金This work was supported by the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Skodowska-Curie(101027980(CSPCPS-A-ICA),739551(KIOS CoE-TEAMING))the Italian Ministry for Research in the Framework of the 2017 Program for Research Projects of National Interest(PRIN)(2017YKXYXJ)+3 种基金the National Natural Science Foundation of China(61903188,62073165,62020106003)the Natural Science Foundation of Jiangsu Province(BK20190403)the 111 Project(B20007)the Priority Academic Program Development of Jiangsu Higher Education Institutions.
文摘This paper proposes a passive methodology for detecting a class of stealthy intermittent integrity attacks in cyberphysical systems subject to process disturbances and measurement noise.A stealthy intermittent integrity attack strategy is first proposed by modifying a zero-dynamics attack model.The stealthiness of the generated attacks is rigorously investigated under the condition that the adversary does not know precisely the system state values.In order to help detect such attacks,a backward-in-time detection residual is proposed based on an equivalent quantity of the system state change,due to the attack,at a time prior to the attack occurrence time.A key characteristic of this residual is that its magnitude increases every time a new attack occurs.To estimate this unknown residual,an optimal fixed-point smoother is proposed by minimizing a piece-wise linear quadratic cost function with a set of specifically designed weighting matrices.The smoother design guarantees robustness with respect to process disturbances and measurement noise,and is also able to maintain sensitivity as time progresses to intermittent integrity attack by resetting the covariance matrix based on the weighting matrices.The adaptive threshold is designed based on the estimated backward-in-time residual,and the attack detectability analysis is rigorously investigated to characterize quantitatively the class of attacks that can be detected by the proposed methodology.Finally,a simulation example is used to demonstrate the effectiveness of the developed methodology.
文摘The Sun has solar rotation;nevertheless, many evidences have suggested that different latitude of the Sun rotates in different speed, which is now known as differential rotation. This work calculates the solar rotation speeds near the equator and 30? in the northern hemisphere using Fixed-Point Arithmetic method. The calculated results show a greater speed at the equator than the speed at 30?, indicating that the speed decreases as the latitude becomes higher. .
