Set Of Initial Points Research Articles

Affine realizations with affine state processes for stochastic partial differential equations

The goal of this paper is to clarify when a stochastic partial differential equation with an affine realization admits affine state processes. This includes a characterization of the set of initial points of the realization. Several examples, as the HJMM equation from mathematical finance, illustrate our results.

Electric-field-induced weakly chaotic transients in ferroelectric liquid crystals.

Nonlinear dynamics induced in surface stabilized ferroelectric liquid crystals by strong alternating external electric fields is studied both theoretically and experimentally. As has already been shown, molecular reorientations induced by sufficiently strong fields of high-enough frequencies can reveal a long transient behavior that has a weakly chaotic character. The resulting complex dynamics of ferroelectric liquid crystals can be considered not only as a consequence of irregular motions of particular molecules but also as a repercussion of a surface-enforced partial decorrelation of nonlinear molecular motions within smectic layers. To achieve more insight into the nature of this phenomenon and to show that the underlying complex field-induced behavior of smectic liquid crystals is not exceptional, ranges of system parameters for which the chaotic behavior occurs are determined. It is proved that there exists a large enough set of initial phase trajectory points, for which weakly chaotic long-time transitory phenomena occur, and, thereby, it is demonstrated that such a chaotic behavior can be regarded as being typical for strongly field-driven thin liquid crystal systems. Additionally, the influence of low-amplitude random noise on the duration of the transient processes is numerically studied. The strongly nonlinear contribution to the electro-optic response, experimentally determined for liquid crystal samples at frequencies lower than the actual field frequency, is also analyzed for long-time signal sequences. Using a statistical approach to distinguish numerically response signals of samples from noise generated by measuring devices, it is shown that the distribution of sample signals distinctly differs from the device noise. This evidently corroborates the occurrence of the nonlinear low-frequency effect, found earlier for different surface stabilized liquid crystal samples.

A new gradient based step size controlled inverse eigen sensitivity algorithm for identification of material and boundary parameters of plates

The dynamic performance of any structure is function of existing material properties and boundary stiffness parameters which may deteriorate or become more flexible due to prolonged use. These parameters are estimated inversely through optimization of a suitable objective function. The gradient based optimization methods are preferred due to their faster convergence from a set of initial guess points, but suffers mostly from lack of reliable methodology to select appropriate step sizes. Arbitrary selection of step sizes may sometimes work well, depending upon the judgment of the user, but is case specific. The present work describes the estimation of existing material properties and boundary stiffness of isotropic and orthotropic plates from measured frequencies and mode shapes using a new gradient based step size controlled inverse eigensensitivity algorithm. The method takes a strategy that the step sizes automatically become smaller when the change in gradient of objective function is having a high value and similarly, takes larger steps when the gradient is remaining fairly constants in subsequent iterations. The results obtained from the investigations are encouraging, as some convergences could be achieved by this new adaptive step size control only, whereas methods adopting arbitrary or no step size control diverged.

A novel approach to determination of wheel position and orientation for five-axis CNC flute grinding of end mills

In practice, the flutes of end mills are ground using CNC grinding machines via controlling the grinding wheel’s position and orientation to guarantee the designed flute parameters including rake angle, flute angle, helix angle, and core radius. However, for the previous researches, the designed flute profile was ground via building a specific grinding wheel with a free-form profile using two-axis CNC grinder. And, the free-form grinding wheel will greatly increase the manufacturing cost, which is too complicated to implement in practice. In this research, the flute-grinding processes were developed with a standard grinding wheel via five-axis CNC grinding operations. The mathematical representation of machined flute parameters was deduced in terms of the grinding wheel’s position and orientation. The geometrical constraints to avoid interference and abnormal flute profile for the five-axis CNC fluting were first developed in this work. Finally, the difference between the designed flute parameters and the machined flute parameters were formulated as a constrained optimization problem so as to determine the wheel’s position and orientation. The set of effective initial points for this optimization model was found mainly distributed the first quadrant of the contact area. The fminsearch function in Matlab toolbox was recommended to solve the optimization model due to its capability of handling discontinuity problem. The solution obtained in optimization model and the corresponding machined flute parameter were verified and compared with Boolean simulation in CATIA to confirm the validity and efficiency of the proposed approach. The results showed that the accuracy of machined flute parameters could achieve 1e-3 mm and 1e-2°, which satisfied the machining tolerance. This study provides a general solution for the CNC fluting operations and could be extended to grind complex surface of end mills in the future study.

The minimal SUSY B − L model: from the unification scale to the LHC

This paper introduces a random statistical scan over the high-energy initial parameter space of the minimal SUSY B − L model — denoted as the B − L MSSM. Each initial set of points is renormalization group evolved to the electroweak scale — being subjected, sequentially, to the requirement of radiative B − L and electroweak symmetry breaking, the present experimental lower bounds on the B − L vector boson and sparticle masses, as well as the lightest neutral Higgs mass of ∼125 GeV. The subspace of initial parameters that satisfies all such constraints is presented, shown to be robust and to contain a wide range of different configurations of soft supersymmetry breaking masses. The low-energy predictions of each such “valid” point — such as the sparticle mass spectrum and, in particular, the LSP — are computed and then statistically analyzed over the full subspace of valid points. Finally, the amount of fine-tuning required is quantified and compared to the MSSM computed using an identical random scan. The B − L MSSM is shown to generically require less fine-tuninng.

Research on Iris Localization Algorithm based on the Active Contour Model

An automatic and robust iris segmentation algorithm will be employed when iris recognition is used to identify human efficiently. Many studies have shown that iris localization is one of the most important parts of the iris recognition system. Most current studies are based on the assumption that iris edge is round, and the gray information of eye image is used for iris segmentation, which requires very high quality of image. Based on the active contour model, an algorithm for iris location was proposed. First, a plurality of pupil edge points was located as the initial contour point set. Then, the real contour evolution of pupil was approximated by the approximation of energy function. Finally, the accurate iris edge was located by daugman’s circular gradient operator. Based on CASIA (V2.0) iris database, experiment results show that the location effect of the proposed algorithm is more superior than that of the classical calculus method and hough transform method.

Image Registration Technique Based on a Fast CPD Algorithm

The Coherent Point Drift (CPD) algorithm which based on Gauss Mixture Model is a robust point set registration algorithm. However, the selection of robustness weight which used to describe the noise may directly affect the point set registration efficiency. For resolving the problem, this paper presents a CPD registration algorithm which based on distance threshold constraint. Before the point set registration, the inaccurate template point set by resampling become the initial point set of point set matching, in order to eliminate some points that the distance to target point set is too close and too far in the inaccurate template point set, and set the weights of robustness as . In the simulation experiments, we make two group experiments: the first group is the registration of the inaccurate template point set and the accurate target point set, while the second group is the registration of the accurate template point set and the accurate target point set. The results of comparison show that our method can solve the problem of selection for the weight. And it improves the speed and precision of the original CPD registration.

Parameter Optimization for the Extraction of Matching Points Between High-Resolution Multisensor Images in Urban Areas

The objective of this paper is to extract a suitable number of evenly distributed matched points, given the characteristics of the site and the sensors involved. The intent is to increase the accuracy of automatic image-to-image registration for high-resolution multisensor data. The initial set of matching points is extracted using a scale-invariant feature transform (SIFT)-based method, which is further used to evaluate the initial geometric relationship between the features of the reference and sensed images. The precise matching points are extracted considering location differences and local properties of features. The values of the parameters used in the precise matching are optimized using an objective function that considers both the distribution of the matching points and the reliability of the transformation model. In case studies, the proposed algorithm extracts an appropriate number of well-distributed matching points and achieves a higher correct-match rate than the SIFT method. The registration results for all sensors are acceptably accurate, with a root-mean-square error of less than 1.5 m.

A heuristic algorithm for solving the minimum sum-of-squares clustering problems

Clustering is an important task in data mining. It can be formulated as a global optimization problem which is challenging for existing global optimization techniques even in medium size data sets. Various heuristics were developed to solve the clustering problem. The global $$k$$ k -means and modified global $$k$$ k -means are among most efficient heuristics for solving the minimum sum-of-squares clustering problem. However, these algorithms are not always accurate in finding global or near global solutions to the clustering problem. In this paper, we introduce a new algorithm to improve the accuracy of the modified global $$k$$ k -means algorithm in finding global solutions. We use an auxiliary cluster problem to generate a set of initial points and apply the $$k$$ k -means algorithm starting from these points to find the global solution to the clustering problems. Numerical results on 16 real-world data sets clearly demonstrate the superiority of the proposed algorithm over the global and modified global $$k$$ k -means algorithms in finding global solutions to clustering problems.

Algorithm for Locating All Local Minima of Multidimensional Function

为求出具有箱式约束的非线性全局优化问题所有的局部极小点,提出了一种基于Multistart 方法的新算法.结合目标函数在可行域内的总变差、下降率和凹凸性等信息,构造了一个刻划局部极小点分布的G-度量.将可行域剖分为若干个小区域,把初始点按G-度量值的比例分配在每块区域上,使得局部极小点密集的区域能够被分配较多的初始点进行搜索;给出了有效初始点的判断条件为了进一步减少局部优化算法的运行次数.针对G-度量计算量较大的问题,设计了相应的近似计算方法,降低了计算量.选择了4 个2 维~10 维具有大量局部极小点的测试函数进行求解,与Multisatart 和Minfinder 算法的实验结果进行对比,表明了该方法在收敛速度和搜索全部局部极小点上都有了较大的改进和提高.;This paper focuses on locating all local minima of box-constrained, non-linear optimization problems. A new algorithm based on Multistart method is proposed. A quality measure called G-measure is constructed to measure the local minima of a multidimensional continuous and differentiable function distribution inside bounded domain. This paper measures the distribution of local minima in three facets: Gradient, convexity and concavity, and rate of decline. Feasible region is divided into several small regions, and each is assigned a set of initial points in proportion to its G-measures. More initial points can be allocated in the region which includes more local minima. A condition judging whether an initial point is effective is aimed to decrease the run times of local optimal technique. The approximate computing method is constructed to reduce computational complexity of G-measure. Several benchmarks with large quantities of local minima are chosen. The performance of this new method is compared with that of Multistart and Minfinder on benchmark problems. Experimental results show that the proposed method performs better in search efficiency.

Equilibrium measures for uniformly quasiregular dynamics

We establish the existence and fundamental properties of the equilibrium measure in uniformly quasiregular dynamics. We show that a uniformly quasiregular endomorphism $f$ of degree at least 2 on a closed Riemannian manifold admits an equilibrium measure $\mu_f$, which is balanced and invariant under $f$ and non-atomic, and whose support agrees with the Julia set of $f$. Furthermore we show that $f$ is strongly mixing with respect to the measure $\mu_f$. We also characterize the measure $\mu_f$ using an approximation property by iterated pullbacks of points under $f$ up to a set of exceptional initial points of Hausdorff dimension at most $n-1$. These dynamical mixing and approximation results are reminiscent of the Mattila-Rickman equidistribution theorem for quasiregular mappings. Our methods are based on the existence of an invariant measurable conformal structure due to Iwaniec and Martin and the $\cA$-harmonic potential theory.

On resolving singularities of piecewise-smooth discontinuous vector fields via small perturbations

A two-fold singularity is a point on a discontinuity surface of a piecewise-smooth vector field at which the vector field is tangent to the surface on both sides. Due to the double tangency, forward evolution from a two-fold is typically ambiguous. This is an especially serious issue for two-folds that are reached by the forward orbits of a non-zero measure set of initial points. However, arbitrarily small perturbations of the vector field can make forward evolution well-defined, and from an applied perspective, such perturbations may represent additional model features that enhance the realism of a piecewise-smooth mathematical model. Three physically motivated forms of perturbation: hysteresis, time-delay, and noise, are analysed individually. The purpose of this paper is to characterise the perturbed dynamics in the limit that the size of the perturbation tends to zero. This concept is applied to a two-fold in two dimensions. In each case the limit leads to a novel probabilistic notion of forward evolution from the two-fold.

Feature-Preserving Surface Reconstruction and Simplification from Defect-Laden Point Sets

We introduce a robust and feature-capturing surface reconstruction and simplification method that turns an input point set into a low triangle-count simplicial complex. Our approach starts with a (possibly non-manifold) simplicial complex filtered from a 3D Delaunay triangulation of the input points. This initial approximation is iteratively simplified based on an error metric that measures, through optimal transport, the distance between the input points and the current simplicial complex--both seen as mass distributions. Our approach is shown to exhibit both robustness to noise and outliers, as well as preservation of sharp features and boundaries. Our new feature-sensitive metric between point sets and triangle meshes can also be used as a post-processing tool that, from the smooth output of a reconstruction method, recovers sharp features and boundaries present in the initial point set.

A Fully Eulerian formulation for fluid–structure-interaction problems

In this work, we present a Fully Eulerian framework for fluid–structure interaction (fsi) problems coupling the incompressible Navier–Stokes equations with a hyperelastic solid.The Fully Eulerian framework is a monolithic implicit variational formulation for the coupled problem. In contrast to the well-established Arbitrary Lagrangian Eulerian (ALE) coordinates, the Fully Eulerian framework formulates both subproblems, fluid and solid, in Eulerian coordinates. This concept circumvents various difficulties connected to ALE coordinates since no artificial domain mapping is used. The formulation is an interface-capturing method and uses an extension of the solid’s deformation, the Initial Point Set, to detect the interface location.By construction, very large deformation as well as topology changes like contact of the solid to the domain boundary or other solid parts are possible.

Branching points for transition pathways: assessing responses of actors to challenges on pathways to a low carbon future

This paper describes initial analysis of branching points on a set of transition pathways to a UK low carbon electricity future by 2050. As described in other papers in this special issue, we are exploring and analysing a set of core transition pathways, based on alternative governance patterns in which the ‘logics’ of market actors, government actors and civil society actors, respectively dominate. This core pathway analysis is enhanced by analyses of branching points within and across the pathways, which informs how competition between different logics plays out at key decision points. Branching points are defined as key decision points at which choices made by actors, in response to internal or external stresses or triggers, determine whether and in what ways the pathway is followed. A set of initial branching points for our three core transition pathways is identified through project and stakeholder workshops, and drawing on analysis of actors’ choices and responses at past branching points in energy system transitions. The potential responses of the actors are identified at these branching points, and risk mitigation strategies are formulated for the dominant actors to reinforce that pathway, as well as opportunities for actors to move away from the pathway.

A SAR Image Registration Algorithm Using Edge Information Combined with Gray-Level Information

Synthetic Aperture Radar(SAR) images of same scene may have obvious difference in gray\|level characteristic because of correlation noise and different imaging conditions. Method based only on edge feature or gray\|level information doesn't adapt to SAR image registration. This paper describes a new feature\|based approach using edge information of typical objects combined with local gray\|level statistical information to image\|to\|image registration. First, local area with typical object is selected instead of the whole image registration to reduce computation time. In each area, edge feature of the typical object is extracted and initial feature point set is decided according as shape information of the points on edges. Then, a principle combined with edge shape and gray\|level information is used on feature point matching to reduce the effect which the accuracy of edge extraction may add on the accuracy of registration. At last, a root mean square error is computed. Experimental results with pixel level accuracy on Radarsat imagery proves the validity of this approach.

The coexistence of quasi-periodic and blow-up solutions in a class of Hamiltonian systems

The coexistence of quasi-periodic solutions and blow-up phenomena in a class of higher dimensional Duffing-type equations is proved in this paper. Moreover, we show that the initial point sets for both kinds of solutions are of infinite Lebesgue measure in the phase space. For the part of quasi-periodic solutions, the tool we used is the small twist theorem for higher dimensional cases.

EXPONENTIAL GROWTH RATE FOR DERIVATIVES OF STOCHASTIC FLOWS

We show that for a large class of stochastic flows the spatial derivative grows at most exponentially fast even if one takes the supremum over a bounded set of initial points. We derive explicit bounds on the growth rates that depend on the local characteristics of the flow and the box dimension of the set.

Construction of space-filling designs using WSP algorithm for high dimensional spaces

In the computer experiments setting, if the relationship between the response and the inputs is unknown, then the purpose is to use designs that spread the points at which the response is observed evenly throughout the region. These designs are called space-filling designs (SFD) and the most known are Latin Hypercubes (random, orthogonal, optimized) and low discrepancy sequences. But, simulation codes becoming more and more complex, high dimensional optimal designs are needed to study a high number of parameters (more than 20 parameters) and the construction proves difficult. The aim of this study is to explore a construction method of new space-filling designs for high dimensional spaces. After a short presentation of the criteria considered to quantify the intrinsic quality of the designs, the generation of these designs using WSP algorithm is presented. As the first step consists in generating candidate points, the influence of the initial set of points is investigated in dimension 20 and the final designs are compared with others space-filling designs. Then, designs are proposed in dimension 20, 30, 40 and 50 and the study of the intrinsic quality of these new space-filling designs highlights the robustness of this generation method in high dimensional spaces.

Lattice actions on the plane revisited

We study the action of a lattice Γ in the group G = SL(2, R) on the plane. We obtain a formula which simultaneously describes visits of an orbit Γu to either a fixed ball, or an expanding or contracting family of annuli. We also discuss the ‘shrinking target problem’. Our results are valid for an explicitly described set of initial points: all $${{\bf u} \in {\bf R}^2}$$ in the case of a cocompact lattice, and all u satisfying certain diophantine conditions in case $${\Gamma = {\rm SL}(2, \mathbb {Z})}$$ . The proofs combine the method of Ledrappier with effective equidistribution results for the horocycle flow on $${\Gamma {\backslash} G}$$ due to Burger, Strömbergsson, Forni and Flaminio.