Perturbation analysis for the Takagi vector matrix

In this article, we present some perturbation bounds for the Takagi vector matrix when the original matrix undergoes the additive or multiplicative perturbation. Two numerical examples are given to illuminate these bounds.

Improved Privacy Protecting in Distributed Grid Data Resource using Multiplicative Perturbation Based on Frequent Decision Classifier

The enormous amount of data process in distributed grid resource holds sensitive information on centralized access. The common privacy standard needs advancement to protect the sensitive data in various sectors like sharing, legal privacy and policies to access the data. The privacy standards depend the Distributed Data Mining (DDM) approaches like Association Rule Mining algorithms (ARM), clustering, and classification methods to preserve the data from unauthorized access. But the security standards have lacked privacy-preserving rules due to high dimensionality problems of data access leads more time complexity. To overcome the problem, to propose a Multiplicative Perturbation Swapping method based on Frequent Decision Classifier (MPS-FDC). This method is adaptive to data publishing secrecy to hold the privacy standards better than association rule prediction. This optimization resolves the forecasting leakages based on Persuasive Privacy Preserving Data Mining (P2PDM) to secure the data. Which this technique initially does the sanitization to reduce the dimensionality to remove un-variant the outliers. The data perturbation keeps the original data to modify using supportive noise delimiters with state matrix distortion (SMD). So the original data keep safe without effect from the outliers. The frequent rule prediction decides to classify the recurrentdata from unauthorized access to disclosing crypto- privacy policy. The proposed system improves the privacy standard compared to the ARM specification rules.

Designing nanoparticle release systems for drug–vitamin cancer co-therapy with multiplicative perturbation-theory machine learning (PTML) models

Perturbation Theory Machine Learning (PTML) models are presented to predict biological of Nano-systems for cancer co-therapy including vitamins or vitamins derivatives.

Mesoscopic perturbations of large random matrices

We consider the eigenvalues and eigenvectors of small rank perturbations of random [Formula: see text] matrices. We allow the rank of perturbation [Formula: see text] to increase with [Formula: see text], and the only assumption is [Formula: see text]. The spiked population model, proposed by Johnstone [On the distribution of the largest eigenvalue in principal components analysis, Ann. Statist. 29(2) (2001) 295–327], is of this kind, in which all the population eigenvalues are 1’s except for a few fixed eigenvalues. Our model is more general since we allow the number of non-unit population eigenvalues to grow with the population size. In both additive and multiplicative perturbation models, we study the nonasymptotic relation between the extreme eigenvalues of the perturbed random matrix and those of the perturbation. As [Formula: see text] goes to infinity, we derive the empirical distribution of the extreme eigenvalues of the perturbed random matrix. We also compute the appropriate projection of eigenvectors corresponding to the extreme eigenvalues of the perturbed random matrix. We prove that they are approximate eigenvectors of the perturbation. Our results can be regarded as an extension of the finite rank perturbation case to the full generality up to [Formula: see text].