When discovering the potential of canards flying in 4-dimensional slow-fast system with a bifurcation parameter, the key notion “symmetry” plays an important role. It is of one parameter on slow vector field. Then, it should be determined to introduce parameters to all slow/fast vectors. It is, however, there might be no way to explore for another potential in this system, because the geometrical structure is quite different from the system with one parameter. Even in this system, the “symmetry” is also useful to obtain the potentials classified by R. Thom. In this paper, via the coordinates changing, the possible way to explore for the potential will be shown. As it is analyzed on “hyper finite time line”, or done by using “non-standard analysis”, it is called “Hyper Catastrophe”. In the slow-fast system which includes a very small parameter , it is difficult to do precise analysis. Thus, it is useful to get the orbits as a singular limit. When trying to do simulations, it is also faced with difficulty due to singularity. Using very small time intervals corresponding small , we shall overcome the difficulty, because the difference equation on the small time interval adopts the standard differential equation. These small intervals are defined on hyper finite number N, which is nonstandard. As and the intervals are linked to use 1/N, the simulation should be done exactly.
Regularized system identification has become the research frontier of system identification in the past decade.One related core subject is to study the convergence properties of various hyper-parameter estimators as the sample size goes to infinity.In this paper,we consider one commonly used hyper-parameter estimator,the empirical Bayes(EB).Its convergence in distribution has been studied,and the explicit expression of the covariance matrix of its limiting distribution has been given.However,what we are truly interested in are factors contained in the covariance matrix of the EB hyper-parameter estimator,and then,the convergence of its covariance matrix to that of its limiting distribution is required.In general,the convergence in distribution of a sequence of random variables does not necessarily guarantee the convergence of its covariance matrix.Thus,the derivation of such convergence is a necessary complement to our theoretical analysis about factors that influence the convergence properties of the EB hyper-parameter estimator.In this paper,we consider the regularized finite impulse response(FIR)model estimation with deterministic inputs,and show that the covariance matrix of the EB hyper-parameter estimator converges to that of its limiting distribution.Moreover,we run numerical simulations to demonstrate the efficacy of ourtheoretical results.
As the extensive use of cloud computing raises questions about the security of any personal data stored there,cryptography is being used more frequently as a security tool to protect data confidentiality and privacy in the cloud environment.A hypervisor is a virtualization software used in cloud hosting to divide and allocate resources on various pieces of hardware.The choice of hypervisor can significantly impact the performance of cryptographic operations in the cloud environment.An important issue that must be carefully examined is that no hypervisor is completely superior in terms of performance;Each hypervisor should be examined to meet specific needs.The main objective of this study is to provide accurate results to compare the performance of Hyper-V and Kernel-based Virtual Machine(KVM)while implementing different cryptographic algorithms to guide cloud service providers and end users in choosing the most suitable hypervisor for their cryptographic needs.This study evaluated the efficiency of two hypervisors,Hyper-V and KVM,in implementing six cryptographic algorithms:Rivest,Shamir,Adleman(RSA),Advanced Encryption Standard(AES),Triple Data Encryption Standard(TripleDES),Carlisle Adams and Stafford Tavares(CAST-128),BLOWFISH,and TwoFish.The study’s findings show that KVM outperforms Hyper-V,with 12.2%less Central Processing Unit(CPU)use and 12.95%less time overall for encryption and decryption operations with various file sizes.The study’s findings emphasize how crucial it is to pick a hypervisor that is appropriate for cryptographic needs in a cloud environment,which could assist both cloud service providers and end users.Future research may focus more on how various hypervisors perform while handling cryptographic workloads.
Quantum secure direct communication(QSDC)can directly transmit secret messages through quantum channel without keys.Device-independent(DI)QSDC guarantees the message security relying only on the observation of the Bell-inequality violation,but not on any detailed description or trust of the devices'inner workings.Compared with conventional QSDC,DI-QSDC has relatively low secret message capacity.To increase DI-QSDC's secret messages capacity,we propose a high-capacity DI-QSDC protocol based on the hyper-encoding technique.The total message leakage rate of our DI-QSDC protocol only relies on the most robust degree of freedom.We provide the numerical simulation of its secret message capacity altered with the communication distance.Our work serves as an important step toward thefurther development of DI-QSDC systems.
