Singular Transformation Research Articles

T–S Fuzzy-Affine-Model-Based Reliable Output Feedback Control of Nonlinear Systems with Actuator Faults

This article presents a singular system approach to the reliable $$\mathscr {H}_{\infty }$$ static output feedback (SOF) control for continuous-time nonlinear systems with Markovian jumping actuator faults. The approximation of nonlinear plants is carried out in a Takagi–Sugeno fuzzy-affine (FA) environment, and the Markov chain is adopted to characterize the actuator failure phenomenon. Specifically, by utilizing a singular model transformation strategy, the traditional closed-loop system is converted into a singular FA system. With the construction of a mode-dependent Lyapunov function, and invoking S-procedure and some convexifying techniques, the reliable piecewise SOF controller design is then carried out for the underlying systems via a convex program. An illustrative example is finally given to show the efficacy of the developed method.

A Robust and Efficient Copy-Move Forgery Detection Technique based on SIFT and SVD

Objective: To detect copy-move forgery from a given digital image by reducing false detection thus increasing precision rate and F1 score. It is also invariant to scaling, rotation, noise attack. Methods/Analysis: The paper describes an effective and novel method to detect the copy-move forgery detection using Singular Value Decomposition (SVD) and Scale-Invariant Feature Transform (SIFT) features. It divides the given image into equal sized blocks and applies keypoint detection and feature descriptor for each block of the image. Then again SVD is calculated from128 SIFT descriptor to detect the forgery part of the given image. In this approach, a correlation is calculated for different images under different attacks like scaling, rotation, and noise. Finding: The proposed system is tested using standard image data against various types of image attacks like scaling, rotation, noise, blur etc. From the result, it is found that the proposed system is robust and invariant to most of the image attacks. The proposed system easily detects the copied part of the image more efficiently compared to other block based method since SIFT feature is invariant to scaling, rotation, noise, blur etc. Novelty/Improvement: The proposed methods uses block based technique and apply SIFT and SVD technique for detecting forged region in the given image. False detection is reduced in the proposed system which increases the precision and F1 score.

Design of Non-Singular Two-Dimensional Layered Cloaks Mapped from Small Areas

A singular coordinate transformation leads to extreme materials in a transformation-based cloak. If a non-singular transformation is used, the perfect invisibility is lost. The invisibility is also influenced by the homogenization process. In this paper, we investigate these two influences in 2-D circular cylindrical cloaks, obtained from different non-singular mappings. Considering a further deterministic optimization, we also conclude that it is better to use a non-singular cloak based on a mapping scale up to 20%, since it has lower scattering and simpler materials when compared with cloaks based on other mappings.

Multilevel watermarking technique for securing multibiometric templates using DTCWT and SVD

The proposed multibiometric technique implements finger vein as an additional biometric trait along with fingerprint and iris. Finger vein is non-invasive in nature and increases security. In addition, in order to overcome spoofing attack on system database of multibiometric system template, the existing system further focuses on securing the Biometric template by implementing Digital watermarking technique. Watermarking is carried out by using Singular Value Decomposition (SVD) and Discrete Wavelet Transform (DWT) techniques. The performance metrics such as PSNR, NCC and SSIM is simulated using MATLAB tool. The Existing technique is not robust against JPEG compression, median filtering and noise addition like Gaussian noise, salt & pepper noise etc., and also the Discrete Wavelet Transform has Lack of Shift Invariance problem. To overcome this problem, this project is implemented with Dual Tree Complex Wavelet Transform (DTCWT) in multilevel watermarking technique. The advantage of Dual Tree Complex Wavelet Transform improves denoising performance. The Authentication is implemented to prove the security. The performance metrics such as PSNR, NCC and SSIM is simulated using MATLAB for the Dual Tree Complex Wavelet Transform (DTCWT) and the security measures parameters like FAR, FRR, System Accuracy and the ROC comparison curve of the DWT and DTCWT are obtained.

Mimetic Gravity: A Review of Recent Developments and Applications to Cosmology and Astrophysics

Mimetic gravity is a Weyl-symmetric extension of General Relativity, related to the latter by a singular disformal transformation, wherein the appearance of a dust-like perfect fluid can mimic cold dark matter at a cosmological level. Within this framework, it is possible to provide a unified geometrical explanation for dark matter, the late-time acceleration, and inflation, making it a very attractive theory. In this review, we summarize the main aspects of mimetic gravity, as well as extensions of the minimal formulation of the model. We devote particular focus to the reconstruction technique, which allows the realization of any desired expansionary history of the universe by an accurate choice of potential or other functions defined within the theory (as in the case of mimeticf(R)gravity). We briefly discuss cosmological perturbation theory within mimetic gravity. As a case study within which we apply the concepts previously discussed, we study a mimetic Hořava-like theory, of which we explore solutions and cosmological perturbations in detail. Finally, we conclude the review by discussing static spherically symmetric solutions within mimetic gravity and apply our findings to the problem of galactic rotation curves. Our review provides an introduction to mimetic gravity, as well as a concise but self-contained summary of recent findings, progress, open questions, and outlooks on future research directions.

Idempotency of Left-Sided Identity on Singular Transformation Semigroup

Idempotency of Left-Sided Identity on Singular Transformation Semigroup

A New Augmented Singular Transform and its Partial Newton-Correction Method for Finding More Solutions

With the information provided by previously found solutions, an augmented singular transform is introduced in Xie et al. (JCAM 286:145---157, 2015) to change the local basin structure of the original problem for finding new solutions. However the old formulation in Xie et al. (JCAM 286:145---157, 2015) involves the kernel of an unknown solution to be found or the kernels of all previously found solutions, thus left several theoretical issues unsolved and prevents from further development. In this paper, we derive a new augmented singular transform which changes only the local basin/barrier structure around $$u=0$$u=0 for finding more solutions. Comparing to the old formulation, the new one is much easier to apply and resolves all unsolved theoretical issues left in Xie et al. (JCAM 286:145---157, 2015). A corresponding partial Newton-correction method is then designed to solve the augmented problem on the solution set. Mathematical justification of the new formulation, method and its local convergence are established. The new method is first tested on two very different variational problems and then applied to solve a nonvariational nonlinear convection-diffusion equation for multiple solutions, which are, for the first time, numerically computed and visualized with their profile and contour plots. Several interesting phenomena are observed for the first time and open for mathematical verification. Since the new formulation is general and simple, it can also be modified to treat other problems, e.g., quasilinear PDEs, a large system of PDEs with equality constraints, for finding multiple solutions.

Singular Space-Time Transformations. Towards One Method For Solving the Painlevé Problem

We develop the method of singular space-time transformations for systems with impact and friction. We consider a mathematical model of a Painleve problem concerning impacts of an absolutely rigid bar with a rough surface. Using the method of singular space-time change of variables, we obtain the model of an absolutely rigid body by passing to the limit as the generalized rigidity parameter tends to infinity.

Analysis of the Out-of-Plane Coordinate Transformation to Obtain Anisotropic Layered Cloaks

A possible strategy for avoiding singular material parameters in a transformation-based invisibility cloak involves an out-of-plane stretching, calculated to compensate the in-plane singular transformation. In this paper, we used numerical simulations to analyze the relation among the out-of-plane transformation, the resulting material anisotropy, and the total scattering cross width. Moreover, we show how this information can be used to optimize a cloak with homogeneous anisotropic layers.

Adaptive Integration and Singular Boundary Transformations

We apply and compare results of transformations used to annihilate boundary singularities for multivariate integration over hyper-rectangular and simplicial domains. While classically these transformations are applied with a product trapezoidal rule, we use adaptive methods in the PARINT software package, based on rules of higher polynomial degree for the integration over subdomains. PARINT is layered over the MPI environment (Message Passing Interface) and deploys advanced parallel computation techniques such as load balancing among processes that are distributed over a network of nodes. The message passing is performed in a non-blocking and asynchronous manner, and permits overlapping of computation and communication. Comparisons of computation times using long double vs. double precision confirm that the extended format does not considerably increase the time for long doubles. We further apply the proposed methods to problems arising from self-energy Feynman loop diagrams with massless internal lines, in particular where the corresponding integrand has singularities on the boundaries of the integration domain.

無線LAN信号強度の特異スペクトル変換を利用した屋内環境の状態変化検出

This paper describes a method for detection of change of enviornmental conditions using analysis of series of wireless LAN signals. The method uses the charcteristics that the signal strength of the wireless LAN changes according to the conditions of the indoor environment such as the number of persons surroundings of the wireless LAN access points and clients. The paper discusses the method for validating the change of the conditions using the measurement of the indoor environment using the imaging devices and the change detection result of the series of the signal strength of wireless LAN system using singular spectrum transformation. We show the feasibility of the proposed method through the system integration and experimental results.

The Blow-up of Electromagnetic Fields in 3-Dimensional Invisibility Cloaking for Maxwell's Equations

Transformation optics constructions have allowed the design of cloaking devices that steer electromagnetic, acoustic, and quantum waves around a region without penetrating it, so that this region is hidden from external observations. The proposed material parameters are anisotropic, and singular at the interface between the cloaked region and the cloaking device. The presence of these singularities causes various mathematical problems and physical effects on the interface surface. In this paper, we analyze the 3-dimensional cloaking for Maxwell's equations when there are sources or sinks present inside the cloaked region. In particular, we consider nonsingular approximate invisibility cloaks based on the truncation of the singular transformations. We analyze the limit of solutions when the approximate cloaking approaches the ideal cloaking in the sense of distributions. We show that the solutions in the approximate cloaks converge to a distribution that contains Dirac's delta distribution supported on the interface surface. In particular, this implies that the limit of solutions are not measurable functions, making them outside of those classes of functions that have earlier been used in the models of the ideal invisibility cloaks. Also, we give a rigorous meaning for the “extraordinary surface voltage effect" considered in physical literature of invisibility cloaks.

Seamless integration of global Dirichlet-to-Neumann boundary condition and spectral elements for transformation electromagnetics

In this paper, we present an efficient spectral-element method (SEM) for solving general two-dimensional Helmholtz equations in anisotropic media, with particular applications in accurate simulation of polygonal invisibility cloaks, concentrators and circular rotators arisen from the field of transformation electromagnetics (TE). In practice, we adopt a transparent boundary condition (TBC) characterised by the Dirichlet-to-Neumann (DtN) map to reduce wave propagation in an unbounded domain to a bounded domain. We then introduce a semi-analytic technique to integrate the global TBC with local curvilinear elements seamlessly, which is accomplished by using a novel elemental mapping and analytic formulas for evaluating global Fourier coefficients on spectral-element grids exactly.From the perspective of TE, an invisibility cloak is devised by a singular coordinate transformation of Maxwell’s equations that leads to anisotropic materials coating the cloaked region to render any object inside invisible to observers outside. An important issue resides in the imposition of appropriate conditions at the outer boundary of the cloaked region, i.e., cloaking boundary conditions (CBCs), in order to achieve perfect invisibility. Following the spirit of Yang and Wang (2015), we propose new CBCs for polygonal invisibility cloaks from the essential “pole” conditions related to singular transformations. This allows for the decoupling of the governing equations of inside and outside the cloaked regions. With this efficient spectral-element solver at our disposal, we can study the interesting phenomena when some defects and lossy or dispersive media are placed in the cloaking layer of an ideal polygonal cloak.

Unscented Attitude Estimator Based on Dual Attitude Representations

This paper investigates an unscented attitude estimator based on modified Rodriguez parameter (MRP) and quaternion using a linearized attitude representation transformation. When the singularity transformation conditions do not occur, the developed filter can benefit from the MRP representation in terms of decreased calculation burden and improved filter consistency. When the singularity transformation conditions occur, the developed filter has a comparable performance in terms of accuracy to the well-known unscented quaternion estimator but with better filtering consistency and lower calculation burden. The validation of the developed filter is demonstrated through a high-precision strapdown inertial navigation system/Global Positioning System (SINS/GPS) simulation test and a low-cost SINS/GPS car-mounted experiment.

Derivative-dependent metric transformation and physical degrees of freedom

We study metric transformations which depend on a scalar field $\phi$ and its first derivatives and confirm that the number of physical degrees of freedom does not change under such transformations, as long as they are not singular. We perform a Hamiltonian analysis of a simple model in the gauge $\phi = t$. In addition, we explicitly show that the transformation and the gauge fixing do commute in transforming the action. We then extend the analysis to more general gravitational theories and transformations in general gauges. We verify that the set of all constraints and the constraint algebra are left unchanged by such transformations and conclude that the number of degrees of freedom is not modified by a regular and invertible generic transformation among two metrics. We also discuss the implications on the recently called "hidden" constraints and on the case of a singular transformation, a.k.a. mimetic gravity.

On the (m, r)-potent ranks of certain semigroups of transformations

It is known that the ranks of the semigroups 𝒮ingn and 𝒮𝒫𝒯n (the semigroups of singular self-maps and partial transformations on Xn = {1, 2, …, n}, respectively) are [Formula: see text], respectively. The idempotent ranks, defined as the smallest number of idempotents generating set, of 𝒮ingn and 𝒮𝒫𝒯n are the same value as the ranks, respectively. Idempotent can be seen as a special case (with m = r = 1) of (m, r)-potent. In this paper, we determine the (m, r)-potent ranks, defined as the smallest number of (m, r)-potent generating set, of the semigroups 𝒮ingn and 𝒮𝒫𝒯n.

Positing “not-yet-nationalism”: limits to the impact of nationalism theory on Kurdish historiography

This article examines the impact of nationalism theory, and specifically the theory of national awakening, on Kurdish historiography. Kurdish experts cite several famous nationalism theorists, but seem most impressed by Anthony Smith's model of a singular transformation in which a not-yet-national community becomes a proper nation. Kurdish experts do not always use Smith's terminology, however, and often invoke other scholars in support of the singular transformation model. Kurdish historiography disagrees what the singular transformation entails, and different thresholds of nationalism imply wildly different dates for the birth of Kurdish nationalism. Stage theories of national awakening have had little impact, and ought to be reconsidered.

Multispectral and Panchromatic Image Fusion using Empirical Wavelet Transform

Pan sharpening is the process of fusion of panchromatic and multispectral image to obtain an output image of high spatial and spectral resolution. It is very important for various remote sensing applications such as image segmentation studies, image classification, temporal change detection etc. The present work demonstrates the application of Empirical Wavelet Transform for the fusion of panchromatic image and multispectral image by simple average fusion rule. The Proposed method is experimented on panchromatic and multispectral images captured by high resolution earth observation satellites such as GeoEye-1, QuickBird, WorldView-2 and World View-3. The effectiveness of our proposed method is evaluated by visual perception and quantitative assessment measures. The experimental analysis shows that the proposed method performs comparable to the existing fusion algorithms such as Multi-resolution Singular Value Decomposition and Discrete Wavelet Transform.

A symmetrical presentation for the singular part of the symmetric inverse monoid

We give a presentation for \({\mathcal{I}_n \ \mathcal{S}_n}\), the semigroup of all singular injective partial transformations on an n-element set, in terms of a particularly symmetrical generating set. Our generators are all restrictions of transpositions, and the relations we obtain display all the symmetry possessed by \({\mathcal{I}_n \ \mathcal{S}_n}\).

Immersed surfaces and membranes transformations

Physical and biological observation methods provide a variety of bilayer membranes’ shapes and their transformations. Besides, the topological and geometrical methods allow us to deduce a classification of all possible membrane surfaces. This double-sided approach leads to a deeper insight into membranes properties. Our goal is to apply an appropriate mathematical technique for classifying vesicles (closed surfaces in mathematical terminology) and for their transformation ways. The problem turned out to be an intricate one, and to our knowledge no mathematical techniques have been applied to its solution. We find that all vesicles can be decomposed in a small number of universality classes generated by a few ‘bricks’: a torus, a screwed torus, and the real projective plane. We consider several ways of transforming membrane surfaces, bearing in mind that they possess an additional extremal property. Our method exploits different constructions of minimal surfaces in S3. We estimate energetic barrier for transformation of minimal membrane surfaces using the so-called doubling procedure. This problem is far from being a pure theoretical exercise. For instance, almost all cells’ biological functions, or tumor progression, are accompanied by apparently singular cell membrane transformations.