Linear Operators Preserving Symplectic Group over a Field Consisting of at Least Four Elements

Suppose F is a field consisting of at least four elements. Let Mn（F） and SP2n（F） be the linear space of all n × n matrices and the group of all 2n × 2n symplectic matrices over F, respectively. A linear operator L ： M2n（F） → M2n（F） is said to preserve the symplectic group if L（SP2n（F）） = SP2n（F）. It is shown that L is an invertible preserver of the symplectic group if and only if L takes the form （i） L（X） = QPXP^-1 for any X ∈ M2n（F） or （ii） L（X） = QPX^TP^-1 for any X ∈M2n（F）, where Q ∈ SP2n（F） and P is a generalized symplectic matrix. This generalizes the result derived by Pierce in Canad J. Math., 3（1975）, 715-724.

Copy Move Forgery Detection Using Novel Quadsort Moth Flame Light Gradient Boosting Machine

A severe problem in modern information systems is Digital media tampering along with fake information.Even though there is an enhancement in image development,image forgery,either by the photographer or via image manipulations,is also done in parallel.Numerous researches have been concentrated on how to identify such manipulated media or information manually along with automatically;thus conquering the complicated forgery methodologies with effortlessly obtainable technologically enhanced instruments.However,high complexity affects the developed methods.Presently,it is complicated to resolve the issue of the speed-accuracy trade-off.For tackling these challenges,this article put forward a quick and effective Copy-Move Forgery Detection(CMFD)system utilizing a novel Quad-sort Moth Flame(QMF)Light Gradient Boosting Machine(QMF-Light GBM).Utilizing Borel Transform(BT)-based Wiener Filter(BWF)and resizing,the input images are initially pre-processed by eliminating the noise in the proposed system.After that,by utilizing the Orientation Preserving Simple Linear Iterative Clustering(OPSLIC),the pre-processed images,partitioned into a number of grids,are segmented.Next,as of the segmented images,the significant features are extracted along with the feature’s distance is calculated and matched with the input images.Next,utilizing the Union Topological Measure of Pattern Diversity(UTMOPD)method,the false positive matches that took place throughout the matching process are eliminated.After that,utilizing the QMF-Light GBM visualization,the visualization of forged in conjunction with non-forged images is performed.The extensive experiments revealed that concerning detection accuracy,the proposed system could be extremely precise when contrasted to some top-notch approaches.

Preservation of local linearity by neighborhood subspace scaling for solving the pre-image problem

An important issue involved in kernel methods is the pre-image problem. However, it is an ill-posed problem, as the solution is usually nonexistent or not unique. In contrast to direct methods aimed at minimizing the distance in feature space, indirect methods aimed at constructing approximate equivalent models have shown outstanding performance. In this paper, an indirect method for solving the pre-image problem is proposed. In the proposed algorithm, an inverse mapping process is constructed based on a novel framework that preserves local linearity. In this framework, a local nonlinear transformation is implicitly conducted by neighborhood subspace scaling transformation to preserve the local linearity between feature space and input space. By extending the inverse mapping process to test samples, we can obtain pre-images in input space. The proposed method is non-iterative,and can be used for any kernel functions. Experimental results based on image denoising using kernel principal component analysis(PCA) show that the proposed method outperforms the state-of-the-art methods for solving the pre-image problem.

Linear Maps Preserving Invertibility or Related Spectral Properties

We survey some recent results on linear maps on operator algebras that preserve invertibility. We also consider related problems such as the problem of the characterization of linear maps preserving spectrum, various parts of spectrum, spectral radius, quasinilpotents, etc. We present some results on elementary operators and additive operators preserving invertibility or related properties. In particular, we give a negative answer to a problem posed by Gao and Hou on characterizing spectrum-preserving elementary operators. Several open problems are also mentioned.

Additive Preservers of Drazin Invertible Operators with Bounded Index

Let B（X） be the algebra of all bounded linear operators on an infinite-dimensional complex or real Banach space X. Given an integer n 〉 1, we show that an additive surjective map Ф on B（X） preserves Drazin invertible operators of index non-greater than n in both directions if and only if Ф is either of the form Ф（T） = aATA-1 or of the form Ф（T） = aBT＊B-1 where a is a non-zero scalar, A ： X → X and B ： X＊ → X are two bounded invertible linear or conjugate linear operators.