AN IMPROVED RECURSIVE DOUBLING ALGORITHM FOR THE PARALLEL SOLUTION OF LINEAR RECURRENCE R

An improved recursive doubling algorithm for solving linear recurrence R <n,1>is given,whose parallel time complexity is (τ++τ.) logn when n processors are available,achieving the lower bound in array processor type computation.

PARTIAL ELIMINTATION ALGORITHM FOR A LINEAR RECURRENCE SYSTEM R(n, m) OF ORDER m

This paper presents an algorithm for computing a linear recurrence system R(n, m) of order m for n equations on MIMD parallel system. This algorithm is not only easy to be programmed on a parallel computer system, but also reduces the data-waiting time due to compute-ahead strategy. The paper analyses how to achieve maximal load balancing when the algorithm is implemented on MIMD parallel system. By the end of the paper, an analysis on the speedup and parallel efficiency are given. The results indicate that the new parallel elimination algorithm has great improvement compared with the old ones.

Sums of Primes and Quadratic Linear Recurrence Sequences

Let u be a sequence of positive integers which grows essentially as a geometric progression. We give a criterion on u in terms of its distribution modulo d, d = 1, 2,..., under which the set of positive integers expressible by the sum of a prime number and an element of u has a positive lower density. This criterion is then checked for some second order linear recurrence sequences. It follows, for instance, that the set of positive integers of the form p ＋ [（2 ＋ √3）n], where p is a prime number and n is a positive integer, has a positive lower density. This generalizes a recent result of Enoch Lee. In passing, we show that the periods of linear recurrence sequences of order m modulo a prime number p cannot be ＂too small＂ for most prime numbers p.

A COLUMN RECURRENCE ALGORITHM FOR SOLVING LINEAR LEAST SQUARES PROBLEM

A new column recurrence algorithm based on the classical Greville method and modified Huang update is proposed for computing generalized inverse matrix and least squares solution. The numerical results have shown the high efficiency and stability of the algorithm.

Global stability of interval recurrent neural networks

The robust global exponential stability of a class of interval recurrent neural networks（RNNs） is studied,and a new robust stability criterion is obtained in the form of linear matrix inequality.The problem of robust stability of interval RNNs is transformed into a problem of solving a class of linear matrix inequalities.Thus,the robust stability of interval RNNs can be analyzed by directly using the linear matrix inequalities（LMI） toolbox of MATLAB.Numerical example is given to show the effectiveness of the obtained results.

An IoT Based Secure Patient Health Monitoring System

Internet of things(IoT)field has emerged due to the rapid growth of artificial intelligence and communication technologies.The use of IoT technology in modern healthcare environments is convenient for doctors and patients as it can be used in real-time monitoring of patients,proper administration of patient information,and healthcare management.However,the usage of IoT in the healthcare domain will become a nightmare if patient information is not securely maintainedwhile transferring over an insecure network or storing at the administrator end.In this manuscript,the authors have developed a secure IoT healthcare monitoring system using the Blockchainbased XOR Elliptic Curve Cryptography(BC-XORECC)technique to avoid various vulnerable attacks.Initially,thework has established an authentication process for patient details by generating tokens,keys,and tags using Length Ceaser Cipher-based PearsonHashingAlgorithm(LCC-PHA),EllipticCurve Cryptography(ECC),and Fishers Yates Shuffled Based Adelson-Velskii and Landis(FYS-AVL)tree.The authentications prevent unauthorized users from accessing or misuse the data.After that,a secure data transfer is performed using BC-XORECC,which acts faster by maintaining high data privacy and blocking the path for the attackers.Finally,the Linear Spline Kernel-Based Recurrent Neural Network(LSK-RNN)classification monitors the patient’s health status.The whole developed framework brings out a secure data transfer without data loss or data breaches and remains efficient for health care monitoring via IoT.Experimental analysis shows that the proposed framework achieves a faster encryption and decryption time,classifies the patient’s health status with an accuracy of 89%,and remains robust comparedwith the existing state-of-the-art method.

K-Dimensional Optimal Parallel Algorithm for the Solution of a General Class of Recurrence Equations

This paper proposes a parallel algorithm, called KDOP (K-DimensionalOptimal Parallel algorithm), to solve a general class of recurrence equations efficiently. The KDOP algorithm partitions the computation into a series of sub-computations, each of which is executed in the fashion that all the processors work simultaneously with each one executing an optimal sequential algorithm to solve a subcomputation task. The algorithm solves the equations in O(N/p)steps in EREW PRAM model (Exclusive Read Exclusive Write Parallel Ran-dom Access Machine model) using p<N1-e processors, where N is the size of the problem, and e is a given constant. This is an optimal algorithm (itsspeedup is O(p)) in the case of p<N1-e. Such an optimal speedup for this problem was previously achieved only in the case of p<N0.5. The algorithm can be implemented on machines with multiple processing elements or pipelined vector machines with parallel memory systems.

Further research on public-key cryptosystems based on third-order recurrence sequence

Properties of third-order recurrence sequences were investigated and a new variant of the GH public-key cryptosystem,which was further improved to be a probabil-istic public-key cryptosystem,was proposed.Then security analysis of the proposed scheme was provided and it was proved that the one-wayness of the proposed scheme is equivalent to partial discrete logarithm and its semantic se-curity is equivalent to decisional Diffie-Hellman problem in ring extension.Finally,efficiency analysis of the proposed scheme was provided,and that these two encryption schemes need to transfer 2log N and 4log N bits data re-spectively.

Intelligent non-linear modelling of an industrial winding process using recurrent local linear neuro-fuzzy networks

This study deals with the neuro-fuzzy (NF) modelling of a real industrial winding process in which the acquired NF model can be exploited to improve control performance and achieve a robust fault-tolerant system. A new simulator model is proposed for a winding process using non-linear identification based on a recurrent local linear neuro-fuzzy (RLLNF) network trained by local linear model tree (LOLIMOT), which is an incremental tree-based learning algorithm. The proposed NF models are compared with other known intelligent identifiers, namely multilayer perceptron (MLP) and radial basis function (RBF). Comparison of our proposed non-linear models and associated models obtained through the least square error (LSE) technique (the optimal modelling method for linear systems) confirms that the winding process is a non-linear system. Experimental results show the effectiveness of our proposed NF modelling approach.