Error Reduction for Visible Watermarking in Still Images

Different digital watermarking techniques and their applications are brieflyreviewed. Solution to a practical problem with visible image marking is presented, together withexperimental results and discussion. Main focus is on reduction of error caused by the mark additionand subtraction. Image classification based on its mean gray level and adjustment of out-of-rangegray levels are implemented.

ERROR REDUCTION, CONVERGENCE AND OPTIMALITY FOR ADAPTIVE MIXED FINITE ELEMENT METHODS FOR DIFFUSION EQUATIONS

Error reduction, convergence and optimality are analyzed for adaptive mixed finite element methods （AMFEM） for diffusion equations without marking the oscillation of data. Firstly, the quasi-error, i.e. the sum of the stress variable error and the scaled error estimator, is shown to reduce with a fixed factor between two successive adaptive loops, up to an oscillation. Secondly, the convergence of AMFEM is obtained with respect to the quasi-error plus the divergence of the flux error. Finally, the quasi-optimal convergence rate is established for the total error, i.e. the stress variable error plus the data oscillation.

A New Approach for Error Reduction in the Volume Penalization Method

A new approach for reducing error of the volume penalization method is proposed.The mask function is modified by shifting the interface between solid and fluid by√νηtoward the fluid region,whereνandηare the viscosity and the permeability,respectively.The shift length√νηis derived from the analytical solution of the one-dimensional diffusion equation with a penalization term.The effect of the error reduction is verified numerically for the one-dimensional diffusion equation,Burgers’equation,and the two-dimensional Navier-Stokes equations.The results show that the numerical error is reduced except in the vicinity of the interface showing overall second-order accuracy,while it converges to a non-zero constant value as the number of grid points increases for the original mask function.However,the new approach is effective when the grid resolution is sufficiently high so that the boundary layer,whose width is proportional to√νη,is resolved.Hence,the approach should be used when an appropriate combination ofνandηis chosen with a given numerical grid.

A-posteriori error estimation for second order mechanical systems

One important issue for the simulation of flexible multibody systems is the reduction of the flexible bodies de- grees of freedom. As far as safety questions are concerned knowledge about the error introduced by the reduction of the flexible degrees of freedom is helpful and very important. In this work, an a-posteriori error estimator for linear first order systems is extended for error estimation of me- chanical second order systems. Due to the special second order structure of mechanical systems, an improvement of the a-posteriori error estimator is achieved. A major advan- tage of the a-posteriori error estimator is that the estimator is independent of the used reduction technique. Therefore, it can be used for moment-matching based, Gramian matrices based or modal based model reduction techniques. The capability of the proposed technique is demon- strated by the a-posteriori error estimation of a mechanical system, and a sensitivity analysis of the parameters involved in the error estimation process is conducted.

Not Relying on the Newton Gravitational Constant Gives More Accurate Gravitational Predictions

The Newton gravitational constant is considered a cornerstone of modern gravity theory. Newton did not invent or use the gravity constant;it was invented in 1873, about the same time as it became standard to use the kilogram mass definition. We will claim that G is just a term needed to correct the incomplete kilogram definition so to be able to make gravity predictions. But there is another way;namely, to directly use a more complete mass definition, something that in recent years has been introduced as collision-time and a corresponding energy called collision-length. The collision-length is quantum gravitational energy. We will clearly demonstrate that by working with mass and energy based on these new concepts, rather than kilogram and the gravitational constant, one can significantly reduce the uncertainty in most gravity predictions.

Current strategies for the treatment of inborn errors of metabolism

Inborn errors of metabolism（IEMs） are a large group of inherited disorders characterized by disruption of metabolic pathways due to deficient enzymes, cofactors, or transporters. The rapid advances in the understanding of the molecular pathophysiology of many IEMs, have led to significant progress in the development of many new treatments. The institution and continued expansion of newborn screening provide the opportunity for early treatment, leading to reduced morbidity and mortality. This review provides an overview of the diverse therapeutic approaches and recent advances in the treatment of IEMs that focus on the basic principles of reducing substrate accumulation, replacing or enhancing absent or reduced enzyme or cofactor, and supplementing product deficiency. In addition, the challenges and obstacles of current treatment modalities and future treatment perspectives are reviewed and discussed.

Identification and Structure Selection for Nonlinear Stochastic Systems

A nonlinear model is proposed for effective adaptive control design. The model represents a natural way to describe input output nonlinear systems. A combined parameter off line estimation and structure detection algorithm is developed that can use an initial set of data. Then, an efficient model is obtained using orthogonal estimation with an error reduction test and other monitoring modifications. A recursive on line identification scheme is established based on the ELS algorithm to account for future time variations in the process of the parsimonious model.

CONVERGENCE OF ADAPTIVE EDGE ELEMENT METHODS FOR THE 3D EDDY CURRENTS EQUATIONS

We consider an Adaptive Edge Finite Element Method （AEFEM） for the 3D eddy currents equations with variable coefficients using a residual-type a posteriori error estimator. Both the components of the estimator and certain oscillation terms, due to the occurrence of the variable coefficients, have to be controlled properly within the adaptive loop which is taken care of by appropriate bulk criteria. Convergence of the AEFEM in terms of reductions of the energy norm of the discretization error and of the oscillations is shown. Numerical results are given to illustrate the performance of the AEFEM.