Objective Vector Research Articles

On the angular velocity of a rigid body: Matrix and vector representations

Abstract The angular velocity is an important property associated with the velocity state of moving rigid bodies. Unlike the velocity vector of a point, angular velocity vector is not in general equal to the time derivative of any single vector. Hence a unified, simple and comprehensible treatment of the subject may benefit the velocity analysis of complex multibody systems. This paper contributes with a new point of view of matrix and vector representations of angular velocity from the very foundations of classical kinematics of rigid bodies. This contribution was given a systematic, integrated and unified treatment, thus allowing the derivations to be based upon quantities which are expressed in terms of geometric objects (vectors) and geometric operations (vector addition, dot, and cross product). As a result, the approach leads naturally to simple and particularly useful expressions for the angular velocity vector, which allow a readily extension to three important representations involving the position and velocity of three noncollinear points pertaining to a moving rigid body.

Accurate Shadow Modeling Algorithm for Simulation of Fringe Projection System

We present some new idea to implement shadow modeling which is an important process for simulation of fringe projection system: The dot product between normal vector of object’s surface and vector that connecting projector lens centre and point on object’s surface, and the dot product between normal vector of object’s surface and vector that connecting camera lens centre and point on object’s surface are used to model the shadow on object’s surface. Our algorithm do not need to implement the calculation of the silhouettes of the occluders. Simulation result validates that the accuracy of our shadow modeling algorithm is same as shadow volumes algorithm, but our algorithm runs faster than shadow volumes algorithm.

A novel compressed sensing ultra‐wideband channel estimation method based on non‐convex optimization

SummaryDue to the low power spectral density and complicated transfer propagation of ultra‐wideband (UWB) signal, it is important to estimate UWB channel accurately. But it is difficult to sample UWB signals directly due to their wider band width. However, compressed sensing (CS) theory provides a feasible way through lower sampling speed. Common CS‐UWB channel estimation methods adopt convex optimization, non‐sparse or non‐restricted form. In order to strengthen the restriction on sparsity of the reconstructed channel vector, a non‐convex optimization method is proposed in this paper to estimate UWB channel. Proposed method sets the objective function as a non‐convex optimization model using lp–norm. This model is combined as a convex function to approximate the objective function and reconstruct the UWB channel vector iteratively. Because lp–norm is closer to l0–norm than l1 and l2–norm, its restriction on sparsity of objective vector is stricter. The simulation results show that this method can enhance reconstruction performance compared with existing CS‐UWB channel estimation methods. Copyright © 2013 John Wiley & Sons, Ltd.

QoS routing algorithm with multi-dimensions for overlay networks

Overlay networks have emerged as a useful approach to providing a general framework for new applications and services that are to be implemented without significantly changing the IP-layer network infrastructure. Overlay routing has been used as an alternative to the default best effort Internet routing for the absence of end-to-end Quality of Service (QoS). While the former has recently been investigated, the conflict of QoS restraints and resource optimization remains unsolved. Recent studies have shown that overlay paths can give better latency, loss rate and TCP throughput. In this paper, a multi-dimensional QoS objective model based on the analysis of multiple QoS constraints has been presented, and a routing algorithm to optimise the overlay resource of its nodes and links is then proposed. In fact, the algorithm obtained multiple QoS values using probability theory to achieve the routing according to the multi-dimensional QoS objective vector of the QoS objective model. Simulation results reveals that the algorithm works better than other existing algorithms in balancing the network resources, and applications with stringent QoS requirements could be run.

Multi-Objective Integer Programming: An Improved Recursive Algorithm

This paper introduces an improved recursive algorithm to generate the set of all nondominated objective vectors for the Multi-Objective Integer Programming (MOIP) problem. We significantly improve the earlier recursive algorithm of Özlen and Azizoğlu by using the set of already solved subproblems and their solutions to avoid solving a large number of IPs. A numerical example is presented to explain the workings of the algorithm, and we conduct a series of computational experiments to show the savings that can be obtained. As our experiments show, the improvement becomes more significant as the problems grow larger in terms of the number of objectives.

Identifying the redundant, and ranking the critical, constraints in practical optimization problems

This article presents a procedure for identification of the redundant constraints and ranking of the critical constraints by order of their importance, in single- and multi-objective optimization problems. The revelation of the redundant constraints throws light on the physics of the problem which may otherwise not be obvious to the engineers. Furthermore, the ranking of critical constraints allows for an exploration of the potential gain in objective value(s) through a logical elimination of certain constraints. Given a constrained optimization problem, the proposed procedure transforms the constraints into additional objectives (constraint objectives) and obtains a set of non-dominated solutions for the transformed problem by using a multi-objective evolutionary algorithm. Then, operating on the objective vectors of the obtained solutions, the procedure identifies the redundant, and ranks the critical constraints, based on the range of the constraint objectives and their correlations. The utility of the proposed procedure is demonstrated on four practical optimization problems.

Cone contraction and reference point methods for multi-criteria mixed integer optimization

Interactive approaches employing cone contraction for multi-criteria mixed integer optimization are introduced. In each iteration, the decision maker (DM) is asked to give a reference point (new aspiration levels). The subsequent Pareto optimal point is the reference point projected on the set of admissible objective vectors using a suitable scalarizing function. Thereby, the procedures solve a sequence of optimization problems with integer variables. In such a process, the DM provides additional preference information via pair-wise comparisons of Pareto optimal points identified. Using such preference information and assuming a quasiconcave and non-decreasing value function of the DM we restrict the set of admissible objective vectors by excluding subsets, which cannot improve over the solutions already found. The procedures terminate if all Pareto optimal solutions have been either generated or excluded. In this case, the best Pareto point found is an optimal solution. Such convergence is expected in the special case of pure integer optimization; indeed, numerical simulation tests with multi-criteria facility location models and knapsack problems indicate reasonably fast convergence, in particular, under a linear value function. We also propose a procedure to test whether or not a solution is a supported Pareto point (optimal under some linear value function).

Penrose Transform on Induced <i>D<sub>G/H</sub></i>-Modules and Their Moduli Stacks in the Field Theory

We consider generalizations of the Radon-Schmid transform on coherent DG/H-Modules, with the intention of obtaining the equivalence between geometric objects (vector bundles) and algebraic objects (D-Modules) characterizing conformal classes in the space-time that determine a space moduli [1] on coherent sheaves for the securing solutions in field theory [2]. In a major context, elements of derived categories like D-branes and heterotic strings are considered, and using the geometric Langlands program, a moduli space is obtained of equivalence between certain geometrical pictures (non-conformal world sheets [3]) and physical stacks (derived sheaves), that establishes equivalence between certain theories of super symmetries of field of a Penrose transform that generalizes the implications given by the Langlands program. With it we obtain extensions of a cohomology of integrals for a major class of field equations to corresponding Hecke category.

Motion Analysis Using 3D High-Resolution Frequency Analysis

The spatiotemporal spectra of a video that contains a moving object form a plane in the 3D frequency domain. This plane, which is described as the theoretical motion plane, reflects the velocity of the moving objects, which is calculated from the slope. However, if the resolution of the frequency analysis method is not high enough to obtain actual spectra from the object signal, the spatiotemporal spectra disperse away from the theoretical motion plane. In this paper, we propose a high-resolution frequency analysis method, described as 3D nonharmonic analysis (NHA), which is only weakly influenced by the analysis window. In addition, we estimate the motion vectors of objects in a video using the plane-clustering method, in conjunction with the least-squares method, for 3D NHA spatiotemporal spectra. We experimentally verify the accuracy of the 3D NHA and its usefulness for a sequence containing complex motions, such as cross-over motion, through comparison with 3D fast Fourier transform. The experimental results show that increasing the frequency resolution contributes to high-accuracy estimation of a motion plane.

Stability of multiobjective predictive control: A utopia-tracking approach

We propose a utopia-tracking strategy to handle multiple conflicting objectives in model predictive control. The controller minimizes the distance of its vector of objectives to that of the compromise solution: the point along the steady-state Pareto front closest to the utopia point, where all the objectives are independently minimized. We establish conditions for asymptotic stability and propose numerical implementation variants. One of the key advantages of the approach is that it avoids the computation of Pareto fronts in real-time environments. In addition, the approach can handle general objectives of different nature such as economic and regularization.

OBJECT-LEVEL CHANGE DETECTION BASED ON HIGH-RESOLUTION REMOTE-SENSING IMAGES AND ITS APPLICATION IN JAPANESE EARTHQUAKE ON MARCH 11, 2011

Abstract. In accordance with the characteristics of change detection based on high-resolution remote-sensing images, this paper has put forward an object-level change detection method that is based on multi-feature integration and can take into account the properties of different types of object. This method classifies the most essential change information in applications into artificial objects related change information, water-related change information and vegetation-related change information. Direct association of object types and radiation, texture and geometric features is established by analyzing the characteristics of the three types of objects. During the application of object-level change detection method, first, feature vectors of objects are constructed by controlling the weight of radiation, texture and geometric features in different ways; then feature vectors of objects in multi-temporal images are analyzed with the method of object change vector analysis to obtain the change information of object types that are sensitive to a certain feature. In order to verify the validity of this method, this paper uses the high-resolution remote-sensing images from the Internet captured before and after the Japanese earthquake on March 11, 2011 to conduct some change detection experiments based on multifeature integration. Damage information is extracted and by controlling the weight of features, building damage, damage caused by submergence of seawater and vegetation damage are detected respectively. Experiments show that the method and processing put forward in this paper, flexible, practical and adaptable, are effective in such applications as the extraction of information about damage caused by earthquake and tsunami, and investigation of land use change.

A Multiobjective Evolutionary Algorithm That Diversifies Population by Its Density

Most existing multiobjective evolutionary algorithms (MOEAs) assume the existence of Pareto-optimal solutions/Pareto-optimal objective vectors in a neighborhood of an obtained Pareto-optimal set (PS)/Pareto-optimal front (PF). Obviously, this assumption does not work well on the multiobjective problem (MOP) whose true PF and true PS are in the form of multiple segments-truly disconnected MOP (TYD-MOP). Moreover, these MOEAs commonly involve more than three control parameters; and some of them even involve nine control parameters. The stabilities of their performance against parameter settings are generally unknown. In this paper, we propose a MOEA, namely multiobjective density driven evolutionary algorithm (MODdEA), which can handle TYD-MOP. MODdEA stores all evaluated solutions by a binary space partitioning (BSP) tree. Benefiting from the BSP scheme, a fast solution density estimation by the archive is naturally obtained. MODdEA uses this estimated density together with the nondominated rank to probabilistically select mating individuals, which relaxes the neighborhood assumption on PF in a parameter-less manner. Moreover, two genetic operators, extended arithmetic crossover and diversified mutation, are proposed to enhance the explorative search ability of the algorithm. MODdEA is examined on two test problem sets. The first test set consists of six TYD-MOPs; the second test set consists of 17 benchmark MOPs which are commonly examined by the existing MOEAs. Comparing to 14 test MOEAs, MODdEA has superior performance on TYD-MOP and is competitive on MOP whose true PF and PS are one single connected segment.

다수의 경쟁이 존재하는 환경에서 적시 스케줄링에 관한 연구

We consider a multi-agent scheduling problem such that each agent tries to maximize the weighted number of just-in-time jobs. Two objectives are considered : the first is to find the optimal solution for one agent with constraints on the other agents' weight functions, and the second is to find the largest set of efficient schedules of which corresponding objective vectors are different for the case with identical weights. We show that when the number of agents is fixed, the single machine case with the first objective is NP-hard in the ordinary sense, and present the polynomial- time algorithm for the two-machine flow shop case with the second objective and identical weights.

Penrose Transform on <i>D</i>-Modules, Moduli Spaces and Field Theory

We consider a generalization of the Radon-Schmid transform on coherent D-modules of sheaves of holomorphic complex bundles inside a moduli space, with the purpose of establishing the equivalences among geometric objects (vector bundles) and algebraic objects as they are the coherent D-modules, these last with the goal of obtaining conformal classes of connections of the holomorphic complex bundles. The class of these equivalences conforms a moduli space on coherent sheaves that define solutions in field theory. Also by this way, and using one generalization of the Penrose transform in the context of coherent D-modules we find conformal classes of the space-time that include the heterotic strings and branes geometry.

An Improvement on STEM Method in Multi-Criteria Analysis

Multi-criteria decision making (MCDM) refers to making decision in the presence of multiple and conflicting criteria. Multiob- jective programming method such as multiple objective linear program- ming (MOLP) are techniques used to solve such multiple criteria deci- sion making (MCDM) problems. One of the first interactive procedures to solve MOLP is step method (STEM). In this paper we try to improve STEM method by introducing the weight vector of objectives which emphasize that more important objectives be more closer to ideal one. Therefore the presented method try to increase the rate of satisfactoriness of the obtained solution. Finally, a numerical example for illustration of the new method is given to clarify the main results developed in this paper.

Pareto Optimal Solutions for Smoothed Analysts

Consider an optimization problem with $n$ binary variables and $d+1$ linear objective functions. Each valid solution $x \in \{0,1\}^n$ gives rise to an objective vector in $\R^{d+1}$, and one often wants to enumerate the Pareto optima among them. In the worst case there may be exponentially many Pareto optima; however, it was recently shown that in (a generalization of) the smoothed analysis framework, the expected number is polynomial in $n$. Unfortunately, the bound obtained had a rather bad dependence on $d$, roughly $n^{d!}$. We show a significantly improved bound of $n^{2d}$. Our proof is based on defining an algorithm, which we call the $\mathtt{Witness}$ mapping. This algorithm runs on the data and produces an event, in the form of a testimony, that serves as a concise description of what caused a Pareto optimum. We prove that given any testimony, we can check the values of a strict subset of the random variables in the input and deduce some information about the remaining random variables. Hence the $\mathtt{Witness}$ mapping is predictable because, given the output and just some of the input random variables, we can deduce information about the remaining inputs. This immediately implies that any particular testimony is unlikely to occur. We can in fact regard prior work on this problem as being based on a similar principle. Here we are able to prove much stronger bounds because we minimize the description complexity of the output of $\mathtt{Witness}$.

A debris image tracking using optical flow algorithm

This study proposes a motion detection and object tracking technique for GEO debris in a sequence of images. A couple of techniques (called the “stacking method” and “line-identifying technique”) were recently proposed to address the same problem. Although these techniques are effective at detecting the debris position and motion in the image sequences, there are some issues concerned with computational load and assumed debris motion. This study derives a method to estimate motion vectors of objects in image sequence and finally detect the debris locations by using a computer vision technique called an optical flow algorithm. The new method detects these parameters in low computational time in a serial manner, which implies that it has an advantage to track not only linear but also nonlinear motion of GEO debris more easily than the previous methods. The feasibility of the proposed methods is validated using real and synthesized image sequences which contain some typical debris motions.

Evaluating the applicability domain in the case of classification predictive models for carcinogenicity based on the counter propagation artificial neural network

The applicability domain (AD) of models developed for regulatory use has attached great attention recently. The AD of quantitative structure-activity relationship (QSAR) models is the response and chemical structure space in which the model makes predictions with a given reliability. The evaluation of AD of regressions QSAR models for congeneric sets of chemicals can be find in many papers and books while the issue about metrics for the evaluation of an AD for the non-linear models (like neural networks) for the diverse set of chemicals represents the new field of investigations in QSAR studies. The scientific society is standing before the challenge to find out reliable way for the evaluation of an AD of non linear models. The new metrics for the evaluation of the AD of the counter propagation artificial neural network (CP ANN) models are discussed in the article: the Euclidean distances between an object (molecule) and the corresponding excited neuron of the neural network and between an object (molecule) and the representative object (vector of average values of descriptors). The investigation of the training and test sets chemicals coverage in the descriptors space was made with the respect to false predicted chemicals. The leverage approach was used to compare non linear (CP ANN) models with linear ones.

Sampling and processing for compressive holography [Invited

Compressive holography applies sparsity priors to data acquired by digital holography to infer a small number of object features or basis vectors from a slightly larger number of discrete measurements. Compressive holography may be applied to reconstruct three-dimensional (3D) images from two-dimensional (2D) measurements or to reconstruct 2D images from sparse apertures. This paper is a tutorial covering practical compressive holography procedures, including field propagation, reference filtering, and inverse problems in compressive holography. We present as examples 3D tomography from a 2D hologram, 2D image reconstruction from a sparse aperture, and diffuse object estimation from diverse speckle realizations.

Fault diagnosis for sensors in air handling unit based on neural network pre-processed by wavelet and fractal

This paper presents a new fault diagnosis method for sensors in an air-handling unit based on neural network pre-processed by wavelet and fractal (NNPWF). Three-level wavelet analysis is applied to decompose the measurement data, and then fractal dimensions of each frequency band are extracted and used to depict the failure characteristics of the sensors. With these procedures, a signal is extracted into an eigenvector which consists of several fractal dimensions. Following, the eigenvector is introduced into a neural network developed and trained to diagnose the sensor faults. When new measurement data are obtained, similar way is applied to get the eigenvector and the prediction. By comparing the prediction with the objective vectors, the sensor faults can be diagnosed. The fault diagnosis method has been validated and the results show that the proposed method can diagnose different kinds of fault conditions efficiently. Moreover, comparing to the previous work, there is an increase in diagnosis efficiency as large as 15% for the same type of fault.