基于双曲正切函数约束的时间序列建模表示

针对传统的时间序列分段算法往往忽略时间序列的时间特性,导致分段结果不够精确,对此,提出基于双曲正切函数约束的时间序列建模表示算法。该算法在分段聚合近似的基础上引入双曲正切函数并且提出了移动增强因子的概念,在考虑时间影响的基础上抽取出各个子序列所含信息量的差异完成最终的时间序列分段。实验表明该算法有较小的拟合误差,能够更好地利用分段后的序列,完成宏观的相似性查找等工作,并且满足时间序列动态增长的特点,算法的通用性、普适性、准确性均有所提高。     

Rotating brane-world black hole lensing in the strong deflection limit

We consider the metric describing a rotating black hole with tidal charge in the Randall-Sundrum brane world. We study strong field gravitational lensing by this black hole in the quasi-equatorial plane. We compute the angular position of the relativistic caustic points, magnification of the relativistic images and also the critical curves as functions of the metric parameters including the tidal charge. Certain interesting comparisons of the lensing quantities are found with their corresponding properties for the Kerr black hole.     

Backstepping control of flexible joint manipulator based on hyperbolic tangent function with control input and rate constraints

In this paper, we investigate the trajectory tracking problems of the link angle and angle speed of the flexible joint manipulator model based on external disturbance, the control input and rate constraints. The controller of the flexible joint manipulator model is designed using the backstepping control scheme. To achieve this objective, the smooth hyperbolic tangent function is used to solve the problems of control input and rate constraints, and the stability is proved using Lyapunov function in the design procedure of the backstepping control scheme. Finally, the effectiveness of the proposed backstepping controller is verified by numerical simulation.     

Identifying redundancy in multi-dimensional knapsack constraints based on surrogate constraints

Redundancy identification techniques play an important role in improving the solvability of a linear program. In this paper, we address the redundancy in multi-dimensional knapsack constraints by proposing a new redundancy identification method. The proposed method is based on the constraint intercepts of Paulraj, Chellappan, and Natesan [A heuristic approach for identification of redundant constraints in linear programming models, Int. J. Comput. Math. 83 (2006), pp. 675–683] and surrogate constraints. In it, feasibility problems are constructed in order to determine the redundancy of the constraints, and are solved by a heuristic algorithm, which is developed to check the redundancy fast. The results of computational experiments show that the proposed method may be used in a preprocessing stage in order to reduce the number of knapsack constraints.     

Dark energy and inflation in a gravitational wave dominated universe

The empty space (with no matter fields) is not really empty because of natural metric fluctuations, quantum (gravitons) and classical (gravitational waves). We show that gravitons as well as classical gravitational waves of super-horizon wavelengths are able to form a de Sitter state of the empty homogeneous isotropic Universe. This state is an exact solution to the self-consistent equations of finite one-loop quantum gravity for gravitons in the empty FLRW space. It is also an exact solution to the selfconsistent equations of back-reaction for classical gravitational waves in the same space. Technically, to get this de Sitter solution in both quantum and classical cases, it is necessary to carry out a transition to imaginary time and then to return to real time, which is possible because this de Sitter state is invariant with respect to Wick rotation. Such a procedure means that time was used as a complex variable, and this fact has a deep but still not understood significance. The de Sitter accelerated expansion of the empty Universe naturally explains the origin of dark energy and inflation because the Universe is empty at the start (inflation) and by the end (dark energy) of its evolution. This theory is consistent with the existing observational data. The CMB anisotropy of the order of 10^?5 is produced by fluctuations in the number of gravitons. The existence of a threshold and a unique coincidence of topologically impenetrable barriers for tunneling takes place for the matter-dominated epoch and de Sitter State only. These facts provide a solution to the coincidence problem. The theoretical prediction that the equation-of-state parameter should be w > ?1 for inflation and w < ?1 for dark energy is consistentwith the observational data. To provide the reader with a complete picture, this paper gather together new and some published results of the graviton theory of the origin of inflation and dark energy.     

Solving geometric constraints in a parallel network

The paper describes a network implementation of the SUP-INF method for solving sets of inequalities, giving several advantages over previous implementations. The cost of symbolic manipulation is transferred to compile time allowing an increase in speed at run time due to parallel evaluation. Further, allowing iteration in the network improves the competence of the method when working with nonlinear expressions. The network is used to implement a geometric reasoner for a computer vision program and this is shown to meet the general requirements for such a system.     

Control reconstruction in hyperbolic systems

We consider an inverse dynamics problem which is to reconstruct a priori unknown distributed controls in a hyperbolic system given the results of approximate observations of the movements of this system. To solve this ill-posed problem, we propose to use the Tikhonov’s method with a regularizer containing the sum of mean squared norm and the total variation over the time of an admissible control. Using such a regularizer lets one get, in a number of cases, better results than just approximating the control in question in Lebesgue spaces. In particular, along these lines we can establish pointwise and piecewise uniform convergence for regularized approximations, which opens up new opportunities for numerical reconstruction of the fine structure of the control. We give numerical modeling results.     

Path planning for a manipulator with constraints on orientation

This paper discusses the work undertaken at the U.K. National Advanced Robotics Research Centre in the area of path planning. Experiments have been undertaken with the Best First Planner (BFP) and Random Path Planner (RPP) algorithms developed at Stanford University by Barraquand and Latombe. These look particularly suitable for solving a wide range of motion planning problems and for providing the basic mechanism for path planning in an advanced robotic architecture. From this basic mechanism higher level functional primitives have been developed to enable paths to be planned with a pre-defined orientation of the end effector at the goal location or maintaining an orientation throughout the whole path. These functions are achieved through placing additional constraints on the search through configuration space and modifying the workspace potential.     

Negotiation based on constraints in cooperation

This paper presents some aspects of cooperation in organizations. In the first part, we present the importance to coordination processes within an organization. Indeed, the information perceived by the company no longer pertains to the realm of the repetitive, predictable and programmable. In this context of limited rationality, how can one define an efficient and acceptable decision coordination and distribution structure? We argue that the intervention of man in the decisional process remains inescapable on account of the limitations of the coordination process, and define several forms of cooperation between decision centers on an industrial site. In the second part, the assumption retained is that for the management of a production system the decision is made through a network of decision centers. The approach presented puts forward the development of decision and cooperation aid tools only exploiting the information contained in the constraints linking together the decision variables so as to highlight the degrees of freedom effectively available to the decision maker. Finally, we discuss about cooperation and power, where the power issue cannot be disregarded.     

Layer-stripping and parameter reconstruction for a hyperbolic equation in a three-dimensional inhomogeneous half-space

A time domain wave-splitting approach to the inverse problem for a hyperbolic differential equation in an inhomogeneous half-space is considered (the wave velocity is assumed to be constant). A layer stripping method is used to reconstruct the parameter in a non-iterative way, using the reflected field which is produced by an exterior step-function point source. Local continuation formulas of the field are used, and in particular the continuation formulas for the field in the vicinity of a discontinuous wavefront are derived. Numerical results for data continuation and the reconstruction of the dissipation coefficient are presented.     

Time optimal control of a linear hyperbolic system†

The time optimal control of transmission lines with amplitude constraints on the control is considered as a typical problem involving systems governed by hyperbolic partial differential equations. Using a Laplace transformation formulation to yield a time ‘optimal’ solution, it is shown how this sub-optimal control which is bang-bang develops into an optimal control which is not always at its limiting values—demonstrating the effect which the nature of the differential equation has on the form of the optimal control. A simple physical interpretation of the results is given.     

Multiview constraints on homographies

The image motion of a planar surface between two camera views is captured by a homography (a 2D projective transformation). The homography depends on the intrinsic and extrinsic camera parameters, as well as on the 3D plane parameters. While camera parameters vary across different views, the plane geometry remains the same. Based on this fact, we derive linear subspace constraints on the relative homographies of multiple (⩾ 2) planes across multiple views. The paper has three main contributions: 1) We show that the collection of all relative homographies (homologies) of a pair of planes across multiple views, spans a 4-dimensional linear subspace. 2) We show how this constraint can be extended to the case of multiple planes across multiple views. 3) We show that, for some restricted cases of camera motion, linear subspace constraints apply also to the set of homographies of a single plane across multiple views. All the results derived are true for uncalibrated cameras. The possible utility of these multiview constraints for improving homography estimation and for detecting nonrigid motions are also discussed     

On the numerical approximation of a degenerated hyperbolic system

The heat exchanger in a heat pump system may be conveniently described by a degenerated hyperbolic system, namely the zero Mach-number limit of the Euler equations. This leads to a mixed hyperbolic/parabolic system with coupled time-dependent boundary conditions. We propose a method-of-lines discretisation by using an upwinding scheme. We derive stability estimates for the linearisation with frozen coefficients. The resulting differential–algebraic equation has a perturbation index of 2 and a weak instability with respect to the space step size. The latter property is validated experimentally even for the nonlinear system. In contrast, the perturbation index did not exceed one in the numerical experiments.     

A numerical study of a particular non-conservative hyperbolic problem

We study the ability of several numerical schemes to solve a non-conservative hyperbolic system arising from a flow simulation of solid-liquid-gas slurries with the so-called virtual mass effect. Two classes of numerical schemes are used: some Roe-type finite volume schemes, which are based on the resolution of linearized Riemann problems, and some (centered or upwind) schemes with an additional artificial diffusion, such as the classical Rusanov scheme. For flow regimes of interest (steady as well as unsteady flows), the computational process breaks down for some schemes. Indeed, for such flows, the system has at least one eigenvalue having a small magnitude in the interior of the computational domain and this is a possible reason for the failure of some upwind schemes using the resolution of a linearized Riemann problem. Such a failure does not appear with, for instance, the Rusanov scheme which is well known for its robustness. Furthermore, since the system is non-conservative, it is not clear what a weak solution is, when the solution is discontinuous (at least, one needs to have the non-conservative equivalent of the Rankine-Hugoniot jump conditions) and we show that the approximate solution given by different numerical schemes converges towards different “weak solutions”.     

Physical constraints on hypercomputation

Many attempts to transcend the fundamental limitations to computability implied by the Halting Problem for Turing Machines depend on the use of forms of hypercomputation that draw on notions of infinite or continuous, as opposed to bounded or discrete, computation. Thus, such schemes may include the deployment of actualised rather than potential infinities of physical resources, or of physical representations of real numbers to arbitrary precision. Here, we argue that such bases for hypercomputation are not materially realisable and so cannot constitute new forms of effective calculability.     

Stability analysis of a degenerate hyperbolic system modelling a heat exchanger

Mathematical modelling of a heat exchanger in a carbon dioxide heat pump, an evaporator, is considered. A reduced model, called the the zero Mach-number limit, is derived from the Euler equations of compressible liquid flow through elimination of time scales associated with sound waves. The well-posedness of the resulting partial differential-algebraic equation (PDAE) is investigated by analysis of a frozen coefficient linearisation as well as by numerical experiments.