Modelling of Energy Storage Photonic Medium by Wavelength-Based Multivariable Second-Order Differential Equation

Wavelength-dependent mathematical modelling of the differential energy change of a photon has been performed inside a proposed hypothetical optical medium.The existence of this medium demands certain mathematical constraints,which have been derived in detail.Using reverse modelling,a medium satisfying the derived conditions is proven to store energy as the photon propagates from the entry to exit point.A single photon with a given intensity is considered in the analysis and hypothesized to possess a definite non-zero probability of maintaining its energy and velocity functions analytic inside the proposed optical medium,despite scattering,absorption,fluorescence,heat generation,and other nonlinear mechanisms.The energy and velocity functions are thus singly and doubly differentiable with respect to wavelength.The solution of the resulting second-order differential equation in two variables proves that energy storage or energy flotation occurs inside a medium with a refractive index satisfying the described mathematical constraints.The minimum-value-normalized refractive index profiles of the modelled optical medium for transformed wavelengths both inside the medium and for vacuum have been derived.Mathematical proofs,design equations,and detailed numerical analyses are presented in the paper.

Solving sparse non-negative tensor equations： algorithms and applications

We study iterative methods for solving a set of sparse non-negative tensor equations （multivariate polynomial systems） arising from data mining applications such as information retrieval by query search and community discovery in multi-dimensional networks. By making use of sparse and non-negative tensor structure, we develop Jacobi and Gauss-Seidel methods for solving tensor equations. The multiplication of tensors with vectors are required at each iteration of these iterative methods, the cost per iteration depends on the number of non-zeros in the sparse tensors. We show linear convergence of the Jacobi and Gauss-Seidel methods under suitable conditions, and therefore, the set of sparse non-negative tensor equations can be solved very efficiently. Experimental results on information retrieval by query search and community discovery in multi-dimensional networks are presented to illustrate the application of tensor equations and the effectiveness of the proposed methods.

Probability method for cryptanalysis of general multivariate modular linear equation

Finding the solution to a general multivariate modular linear equation plays an important role in cryptanalysis field. Earlier results show that obtaining a relatively short solution is possible in polynomial time. However, one problem arises here that if the equation has a short solution in given bounded range, the results outputted by earlier algorithms are often not the ones we are interested in. In this paper, we present a probability method based on lattice basis reduction to solve the problem. For a general multivariate modular linear equation with short solution in the given bounded range, the new method outputs this short solution in polynomial time, with a high probability. When the number of unknowns is not too large （smaller than 68）, the probability is approximating 1. Experimental results show that Knapsack systems and Lu-Lee type systems are easily broken in polynomial time with this new method.

HIOC:a hybrid imputation method to predict missing values in medical datasets

Purpose-Decision support systems developed using machine learning classifiers have become a valuable tool in predicting various diseases.However,the performance of these systems is adversely affected by the missing values in medical datasets.Imputation methods are used to predict these missing values.In this paper,a new imputation method called hybrid imputation optimized by the classifier(HIOC)is proposed to predict missing values efficiently.Design/methodology/approach-The proposed HIOC is developed by using a classifier to combine multivariate imputation by chained equations(MICE),K nearest neighbor(KNN),mean and mode imputation methods in an optimum way.Performance of HIOC has been compared to MICE,KNN,and mean and mode methods.Four classifiers support vector machine(SVM),naive Bayes(NB),random forest(RF)and decision tree(DT)have been used to evaluate the performance of imputation methods.Findings-The results show that HIOC performed efficiently even with a high rate of missing values.It had reduced root mean square error(RMSE)up to 17.32%in the heart disease dataset and 34.73%in the breast cancer dataset.Correct prediction of missing values improved the accuracy of the classifiers in predicting diseases.It increased classification accuracy up to 18.61%in the heart disease dataset and 6.20%in the breast cancer dataset.Originality/value-The proposed HIOC is a new hybrid imputation method that can efficiently predict missing values in any medical dataset.