Recursive grid methods to compute value sets and Horowitz–Sidi bounds

In reverse engineering, the point cloud data processing is the key, it will directly affect the quality and efficiency of the subsequent reconstruction of the surface. However, the amount of data obtained by three-dimensional laser scanning is often larger and redundant, which will increase the difficulty of the surface reconstruction, therefore, the point cloud data is needed to streamline. Depth analysis of the efficiency and accuracy of curvature grid method, a secondary streamlined algorithm is proposed, which take use of non-uniform grid streamline law based on octree to streamline to the point cloud, and re-use curvature streamline method based on B-spline surface fitting to streamline it. This method, whose streamline ratio is relatively high, can effectively retain the feature point cloud data, providing a great convenience for the follow-up of reverse engineering.

Various forms of data such as profile, cross section, volume, height, and surface area can be derived from the digital terrain model (DTM). Although many research studies were carried out on the accuracy of the DTM, especially on grid data-based DTMs and on the effect of the grid size or grid resolution, the accuracy of profile data derived from a scattered data-based DTM and the effect of the gridding (interpolation) method on the accuracy of the profile data derived are still unfamiliar to many DTM producers and users. Therefore, the purpose of this study was to determine the accuracy of DTM profile data based on scattered data points for several gridding methods. Linear interpolation in triangles and interpolations of Sibson (natural neighbor), nearest neighbor, weighted average, polynomial, multiquadric, and minimum curvature were tested on five theoretical test surfaces. After 1-m grid DTMs were generated using the gridding methods mentioned above, nine different profile data in the y direction for each test surface and for each gridding method were derived from the DTMs. The standard deviation of each profile for each gridding method was derived by differences between true and interpolated profile values. As a result of the case study, the author recommends using interpolations of minimum curvature and multiquadric curvature for more accurate DTM profile data.

Recursive prediction error method is one of the main tools for analysis of controlled auto-regressive systems with quantised output. In this study, a recursive identification algorithm is proposed based on the auxiliary model principle by modifying the standard stochastic gradient algorithm. To improve the convergence performance of the algorithm, a particle filtering technique, which approximates the posterior probability density function with a weighted set of discrete random sampling points is utilised to correct the linear output estimates. It can exclude those invalid particles according to their corresponding weights. The performance of the particle filtering technique-based algorithm is much better than that of the auxiliary model-based one. Finally, results are verified by examples from simulation and engineering.

We present an efficient, stable, recursive T-matrix algorithm to calculate the scattered field from a heterogeneous collection of spatially separated objects. The algorithm is based on the use of higher order multipole expansions than those typically employed in recursive T-matrix techniques. The use of these expansions introduces instability in the recursions developed by Chew (1990) and by Wang and Chew (1990), specifically in the case of near-field computations. By modifying the original recursive algorithm to avoid these instabilities, we arrive at a flexible and efficient forward solver appropriate for a variety of scattering calculations. The algorithm can be applied when the objects are dielectric, metallic, or a mixture of both. We verify this method for cases where the scatterers are electrically small (fraction of a wavelength) or relatively large (12/spl lambda/). While developed for near-field calculation, this approach is applicable for far-field problems as well. Finally, we demonstrate that the computational complexity of this approach compares favorably with comparable recursive algorithms.

In order to improve the shortcomings of long calculation time and uneven path in the pathfinding process of A* algorithm, an optimization algorithm is proposed. First, on the basis of the A* algorithm, combined with the jump point search algorithm (JPS), the amount of calculation is reduced by replacing the expansion nodes in the A* algorithm with jump points. Secondly, a pruning algorithm is used to prune the obtained path to further remove unnecessary nodes in the path. Finally, the path is smoothed with a quadratic Bézier curve. At the end of paper, simulations were carried out in grid maps of different sizes, and experiments were carried out in the real environment. It is shorter and realizes the optimization of path length and smoothness.

Spatial data structures form a core ingredient of many geometric algorithms, both in theory and in practice. Many of these data structures, especially the ones used in practice, are based on partitioning the underlying space (examples are binary space partitions and decompositions of polygons) or partitioning the set of objects (examples are bounding-volume hierarchies). The efficiency of such data structures---and, hence, of the algorithms that use them---depends on certain characteristics of the partitioning. For example the performance of many algorithms that use binary space partitions (BSPs) depends on the size of the BSPs. Similarly, the performance of answering range queries using bounding-volume hierarchies (BVHs) depends on the so-called crossing number that can be associated with the partitioning on which the BVH is based. Much research has been done on the problem of computing partitioning whose characteristics are good in the worst case. In this thesis, we studied the problem from a different point of view, namely instance-optimality. In particular, we considered the following question: given a class of geometric partitioning structures---like BSPs, simplicial partitions, polygon triangulations, …---and a cost function---like size or crossing number---can we design an algorithm that computes a structure whose cost is optimal or close to optimal for any input instance (rather than only worst-case optimal). We studied the problem of finding optimal data structures for some of the most important spatial data structures. As an example having a set of n points and an input parameter r, It has been proved that there are input sets for which any simplicial partitions has crossing number ¿(vr). It has also been shown that for any set of n input points and the parameter r one can make a simplicial partition with stabbing number O(vr). However, there are input point sets for which one can make simplicial partition with lower stabbing number. As an example when the points are on a diagonal, one can always make a simplicial partition with stabbing number 1. We started our research by studying BSPs for line segments in the plane, where the cost function is the size of the BSPs. A popular type of BSPs for line segments are the so-called auto-partitions. We proved that finding an optimal auto-partition is NP-hard. In fact, finding out if a set of input segments admits an auto-partition without any cuts is already NP-hard. We also studied the relation between two other types of BSPs, called free and restricted BSPs, and showed that the number of cuts of an optimal restricted BSP for a set of segments in R2 is at most twice the number of cuts of an optimal free BSP for that set. The details are being represented in Chapter 1 of the thesis. Then we turned our attention to so-called rectilinear r-partitions for planar point sets, with the crossing number as cost function. A rectilinear r-partition of a point set P is a partitioning of P into r subsets, each having roughly |P|/r points. The crossing number of the partition is defined using the bounding boxes of the subsets; in particular, it is the maximum number of bounding boxes that can be intersected by any horizontal or vertical line. We performed some theoretical as well as experimental studies on rectilinear r-partitions. On the theoretical side, we proved that computing a rectilinear r-partition with optimal stabbing number for a given set of points and parameter r is NP-hard. We also proposed an exact algorithm for finding optimal rectilinear r-partitions whose running time is polynomial when r is a constant, and a faster 2-approximation algorithm. Our last theoretical result showed that considering only partitions whose bounding boxes are disjoint is not sufficient for finding optimal rectilinear r-partitions. On the experimental side, we performed a comparison between four different heuristics for constructing rectilinear r-partitions. The so-called windmill KD-tree gave the best results. Chapter 2 of the thesis describes all the details of our research on rectilinear r-partitions. We studied another spatial data structure in Chapter 3 of the thesis. Decomposition of the interior of polygons is one of the fundamental problems in computational geometry. In case of a simple polygon one usually wants to make a Steiner triangulation of it, and when we have a rectilinear polygon at hand, one typically wants to make a rectilinear decomposition for it. Due to this reason there are algorithms which make Steiner triangulations and rectangular decompositions with low stabbing number. These algorithms are worst-case optimal. However, similar to the two previous data structures, there are polygons for which one can make decompositions with lower stabbing numbers. In 3 we proposed a 3-approximation for finding an optimal rectangular decomposition of a rectilinear polygon. We also proposed an O(1)-approximation for finding optimal Steiner triangulation of a simple polygon. Finally, in Chapter 4 of the thesis, we considered another optimization problem, namely how to approximate a piecewise-linear function F: R ¿R with another piecewise-linear function with fewer pieces. Here one can distinguish two versions of the problem. The first one is called the min-k problem; the goal is then to approximate the function within a given error e such that the resulting function has the minimum number of links. The second one is called the min-e problem; here the goal is to find an approximation with at most k links (for a given k) such that the error is minimized. These problems have already been studied before. Our contribution is to consider the problem for so-called uncertain functions, where the value of the input function F at its vertices is given as a discrete set of different values, each with an associated probability. We show how to compute an approximation that minimizes the expected error.

The number of social individuals who interact with their friends through social networks is increasing, leading to an undeniable fact that word-of-mouth marketing has become one of the useful ways to promote sale of products. The Constrained Profit Maximization in Attribute network (CPMA) problem, as an extension of the classical influence maximization problem, is the main focus of this paper. We propose the profit maximization in attribute network problem under a cardinality constraint which is closer to the actual situation. The profit spread metric of CPMA calculates the total benefit and cost generated by all the active nodes. Different from the classical Influence Maximization problem, the influence strength should be recalculated according to the emotional tendency and classification label of nodes in attribute networks. The profit spread metric is no longer monotone and submodular in general. Given that the profit spread metric can be expressed as the difference between two submodular functions and admits a DS decomposition, a three-phase algorithm named as Marginal increment and Community-based Prune and Search(MCPS) Algorithm frame is proposed which is based on Louvain algorithm and logistic function. Due to the method of marginal increment, MPCS algorithm can compute profit spread more directly and accurately. Experiments demonstrate the effectiveness of MCPS algorithm.

We consider the Discretizable Molecular Distance Geometry Problem (DMDGP), which consists in a subclass of instances of the distance geometry problem related to molecular conformations for which a combinatorial reformulation can be supplied. We investigate the performances of two different algorithms for solving the DMDGP. The first one is the Branch and Prune (BP) algorithm, an exact algorithm that is strongly based on the structure of the combinatorial problem. The second one is the Monkey Search (MS) algorithm, a meta-heuristic algorithm that is inspired by the behavior of a monkey climbing trees in search for food supplies, and that exploits ideas and strategies from other meta-heuristic searches, such Genetic Algorithms, Differential Evolution, and so on. The comparison between the two algorithms is performed on a set of instances related to protein conformations. The used instances simulate data obtained from the Nuclear Magnetic Resonance (NMR), because the typical distances provided by NMR are considered and a predetermined number of wrong distances are included.

The possibility of using the recursion method in order to calculate the phonon spectra (with special application to the zincblende structure) is discussed. It is shown that in order to obtain a realistic picture, interactions between nearest and next-nearest neighbours are to be taken into account. Numerical calculations are performed for the case of ZnS. The parameters used in the recursion method have been extracted from the experimental data.

An interpolation method based on the criterion to maximize the smoothness is proposed. In contrast to the conventional approach, where the interpolated signal is made smooth by low-pass filtering, in the proposed method, the smoothness is obtained by minimizing a global energy function. With the minimum energy formulation for interpolation, a recursive method is used to derive the solution and named the recursive minimum energy algorithm. Because the smoothness is improved by increasing the calculation iteration but not by increasing the tap length, the controllability of this system is increased. Experiments show that the smoothness and the frequency performance obtained by the proposed algorithm are better than those of the conventional method. Also, the corresponding architecture design for the image interpolation is presented and shown to be suitable for VLSI implementation.

We suggest a simple modification to the Kd-tree search algorithm for nearest neighbor search resulting in an improved performance. The Kd-tree data structure seems to work well in finding nearest neighbors in low dimensions but its performance degrades even if the number of dimensions increases to more than two. Since the exact nearest neighbor search problem suffers from the curse of dimensionality we focus on approximate solutions; a c-approximate nearest neighbor is any neighbor within distance at most c times the distance to the nearest neighbor. We show that for a randomly constructed database of points if the query point is chosen close to one of the points in the data base, the traditional Kd-tree search algorithm has a very low probability of finding an approximate nearest neighbor; the probability of success drops exponentially in the number of dimensions d as e − Ω(d/c). However, a simple change to the search algorithm results in a much higher chance of success. Instead of searching for the query point in the Kd-tree we search for a random set of points in the neighborhood of the query point. It turns out that searching for e Ω(d/c) such points can find the c-approximate nearest neighbor with a much higher chance of success.KeywordsSuccess ProbabilityRandom PointNeighbor SearchComputational GeometryQuery PointThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

A large-scale survey and on-site measurements on space heating systems in Beijing has been carried out since 2005. Detailed analysis shows that the improvement of system regulation to adjust the heating demand and to avoid over-heating in building space is the key to reduce the heating energy consumption. It also indicates that combined heat and power (CHP) based district heating network is the most suitable solution for the space heating in Chinese northern cities. Thus, the priority should be in the research and development of new techniques to improve heating system regulation and control. In China, there are three reasons for poor heating system regulation: • the lack of control devices in space heating system, • the complex and inconvenient operation, and • the insufficient motivation because the charging policy is based on the heating areas. Field test results show that 20% to 30% of thermal energy is wasted because of the poor heating system regulation. In order to solve these problems, a novel “wireless on-off control” system for household heat adjusting and metering has been proposed. This technology works in the following way: 1) a calorimeter is installed at each building to measure the total heat consumption of the whole building; 2) an on-off valve is installed for each household and an indoor temperature controller is provided for the occupants. The operation procedure is as follows. First, the desired indoor temperature is set by the users through the indoor temperature controller and wireless signals are sent to the on-off valve. Then the on-off valve detects the real indoor temperature and determines the difference between the real temperature and the set value. After this, the valve calculates the proportion of on-time to off-time in the next step according to the thermal strategies programmed in the valve’ CPU. Then the valve is controlled according to the proportion to maintain the desired indoor temperature; and 3) the heating cost of each household can be allocated according to its heating area and the accumulative open time of the valve. The proposed technique has been applied in fifteen residential communities with the total areas of 1,200,000 m2. The testing results show that: 1) indoor temperatures were accurately controlled within +/− 0.5 °C around the set point, so that the problem of overheating can be avoided; 2) the difference of temperature in different room is less than 1 °C. Therefore, if radiators in each room are designed reasonably, to control the temperature of one room can meet the requirements of the entire user’s apartment; 3) energy consumption in the controlled household was approximately 30% lower than the uncontrolled household with the same building type.

The problem of finding hidden patterns in nested samples of objects, the measurement of feature values was considered. The objects of each sample were divided into representatives of two non-intersecting classes. Using a recursive method, the feature values were divided into intervals within which representatives of one of the classes dominated. The results of the partitioning were used to calculate the stability of features. The presence of restrictions on the set of admissible stability values is explained through the properties of membership functions to fuzzy sets. The results of the computational experiment were used to predict the survival of patients with chronic lymphocytic leukemia, depending on the stages of their examination.

Indonesia has enormous potential for the Hydroelectric Power Plant (PLTA). Considering that PLTA is an environmentallyfriendly power plant, the components of this plant are worthy of further development. One of them is the development of the hydropower governoor control system. The PID controller is a control system that is often used in the control of theGovernoor System in a hydropower plant because of its simple controller. At present hydro power plants still use theconventional method of PID control trial-error on average. For this method it is difficult to adjust parameters and it takes a long time and the accuracy of controls is not good. Therefore a smart method is needed to overcome this problem.In the past few years, researchers have used many intelligent methods (Artificial Intelligent) to determine the DC PIDparameters. One of them is Cucckoo Search Algorithm (CSA) which is inspired by the behavior of cuckoo birds in placingtheir eggs. By using the CSA method, it is expected to provide a better system response than using the old system PIDcontrol (trial-error). The final goal of the PID control system used in the hydro generator is to regulate the movement ofthe turbine guide vane, which will affect the electrical power produced by the generator. Here the Guide Vane blade settingscan be likened to adjusting the angle of a DC motor. In this study a miniature prototype system governor will be createdthat is controlled by using a PID controller optimized using the Cuckoo Search Algorithm method. In experiments withthe trial error method, the Kp = 3, Ki = 1 and Kd = 10 values with the magnitude of the control parameters obtainedthe average settling time for set point 4 to set point 8 of 24.2 second. Furthermore, the CSA method is used for tuning the PID. After being tuned to the CSA method the values of Kp, Ki and Kd are different for each set point. For set point 4,Kp = 0.99, Ki = 1.00 and Kd = 0.99, while the average settling time is also better than PID trial error, which is 18.8 second.

This paper is concerned with a recursive algorithm as a preprocessing step to find the convex hull of [Formula: see text] random points uniformly distributed in the plane. For such a set of points, it is shown that eliminating all but [Formula: see text] of points can derive the same convex hull as the input set. Finally it will be shown that the running time of the algorithm is [Formula: see text].