Parametric Approximation Method Research Articles

A novel strategy for dynamic modeling of genome-scale interaction networks.

The recent availability of omics data allows the construction of holistic maps of interactions between numerous role-playing biomolecules. However, these networks are often static, ignoring the dynamic behavior of biological processes. On the other hand, dynamic models are commonly constructed on small scales. Hence, the construction of large-scale dynamic models that can quantitatively predict the time-course cellular behaviors remains a big challenge. In this study, a pipeline is proposed for the automatic construction of large-scale dynamic models. The pipeline uses a list of biomolecules and their time-course trajectories in a given phenomenon as input. First, the interaction network of the biomolecules is constructed. To state the underlying molecular events of each interaction, it is translated into a map of biochemical reactions. Next, to define the kinetics of the reactions, an ordinary differential equation (ODE) is generated for each involved biomolecule. Finally, the parameters of the ODE system are estimated by a novel large-scale parameter approximation method. The high performance of the pipeline is demonstrated by modeling the response of a colorectal cancer cell line to different chemotherapy regimens. In conclusion, Systematic Protein Association Dynamic ANalyzer constructs genome-scale dynamic models, filling the gap between large-scale static and small-scale dynamic modeling strategies. This simulation approach allows for holistic quantitative predictions which are critical for the simulation of therapeutic interventions in precision medicine. Detailed information about the constructed large-scale model of colorectal cancer is available in supplementary data. The SPADAN toolbox source code is also available on GitHub (https://github.com/PooyaBorzou/SPADAN). Supplementary data are available at Bioinformatics online.

BLF-Based Neuroadaptive Fault-Tolerant Control for Nonlinear Vehicular Platoon With Time-Varying Fault Directions and Distance Restrictions

This paper investigates the neuroadaptive fault-tolerant control of nonlinear vehicular platoon with unmodeled dynamics, external disturbances, time-varying actuator fault directions, and distance restrictions. For the cases of known and unknown fault directions, by combining adaptive terminal sliding mode (TSM) control technique with barrier Lyapunov function (BLF), two neuroadaptive fault-tolerant controllers are designed based on symmetric and asymmetric BLF to ensure reliability and safety of vehicular platoon. BLF approaches are adopted to avoid collisions and to maintain communication connections simultaneously. In addition, it is worth mentioning that the unfavorable symmetry assumptions in the symmetric BLF and prescribed performance methods can be removed by adopting asymmetric BLF. In the proposed scheme, we also combine the Nussbaum function to solve the influence of unknown time-varying fault directions effectively. Furthermore, the nonsingular TSM control technique and the minimum parameter approximation method in radial basis function neural network (RBFNN) are adopted to ensure that the spacing error can converge to an arbitrarily small region in finite-time. Through the Lyapunov stability theory, we prove that all signals in the closed-loop system are bounded in finite time. The proposed control schemes are validated by means of simulation examples.

Performance Analysis and Waveform Optimization of Integrated FD-MIMO Radar-Communication Systems

Multiple-input multiple-output (MIMO) has been used in wireless communications to increase data rates via multiplexing or improve performance via diversity. Additionally, in radar systems, MIMO promises improved parameter identifiability and target resolution. Frequency diverse (FD)-MIMO radar can effectively distinguish targets that are closely spaced in the same angle cell by exploiting its range-angle-dependent transmit beamform. Therefore, in this paper, we first propose an integrated waveform design by embedding weighted, phase-modulated communication signals in the FD-MIMO radar waveform. Then, we derive the Cramer-Rao lower bound (CRLB) of the location estimation and analyze the communication performance achieved when the communication receiver extracts information from the integrated signals. Next, transmit beamforming is optimized to achieve the best tradeoff between the radar and communication performances of the system. Due to the nonconvexity of the optimization problem, we apply sequential parametric convex approximation (SPCA) and semidefinite relaxation (SDR) methods to solve the problem. The simulation results reveal the effects of some parameters, such as the frequency interval, symbol period, and communication symbol sequence, on radar and communication performance and demonstrate the tradeoff between radar and communication obtained by optimizing the transmit beamforming vector.

Joint Beamwidth and Power Optimization in MmWave Hybrid Beamforming-NOMA Systems

The use of directional transmission in millimeter-Wave (mmWave) frequencies results in limited channel coherence time. In this paper, we take the limited channel coherence time into account for non-orthogonal multiple access (NOMA) in mmWave hybrid beamforming systems. Due to the limited coherence time, the beamwidth of the hybrid beamformer affects the beam-training time, which in turn directly impacts the data transmission rate. To investigate this trade-off, we utilize a combined beam-training algorithm. Then, we formulate a sum-rate expression which considers the channel coherence time and beam-training time as well as users' power and other system parameters. Further, a joint power and beamwidth optimization problem is solved by iterating between the power allocation and the beamwidth optimization. When allocating the power, we use the log-exponential reformulation and the sequential parametric convex approximation (SPCA) methods to solve the non-convex problem. Since beamwidth optimization involves too many variables, we propose an algorithm which iterates between clusters of users. Numerical results show that the optimized mmWave hybrid beamforming-NOMA system can achieve much higher sum-rates compared to NOMA with analog beamforming and traditional multiple access techniques.

Hedging crash risk in optimal portfolio selection.

When almost all underlying assets suddenly lose a certain part of their nominal value in a market crash, the diversification effect of portfolios in a normal market condition no longer works. We integrate the crash risk into portfolio management and investigate performance measures, hedging and optimization of portfolio selection involving derivatives. A suitable convex conic programming framework based on parametric approximation method is proposed to make the problem a tractable one. Simulation analysis and empirical study are performed to test the proposed approach.

Finite Element Analysis based on A Parametric Model by Approximating Point Clouds

Simplified models are widely applied in finite element computations regarding mechanical and structural problems. However, the simplified model sometimes causes many deviations in the finite element analysis (FEA) of structures, especially in the non-designed structures which have undergone unknowable deformation features. Hence, a novel FEA methodology based on the parametric model by approximating three-dimensional (3D) feature data is proposed to solve this problem in the present manuscript. Many significant and effective technologies have been developed to detect 3D feature information accurately, e.g., terrestrial laser scanning (TLS), digital photogrammetry, and radar technology. In this manuscript, the parametric FEA model combines 3D point clouds from TLS and the parametric surface approximation method to generate 3D surfaces and models accurately. TLS is a popular measurement method for reliable 3D point clouds acquisition and monitoring deformations of structures with high accuracy and precision. The B-spline method is applied to approximate the measured point clouds data automatically and generate a parametric description of the structure accurately. The final target is to reduce the effects of the model description and deviations of the FEA. Both static and dynamic computations regarding a composite structure are carried out by comparing the parametric and general simplified models. The comparison of the deformation and equivalent stress of future behaviors are reflected by different models. Results indicate that the parametric model based on the TLS data is superior in the finite element computation. Therefore, it is of great significance to apply the parametric model in the FEA to compute and predict the future behavior of the structures with unknowable deformations in engineering accurately.

Multi-Objective Optimal Control Approach for Static Voltage Stability of Power System Considering Interval Uncertainty of the Wind Farm Output

The static voltage stability margin (SVSM) of a power system considering the uncertain fluctuation range of wind farm (WF) output can be described as an interval value called the SVSM interval. A multi-objective optimal control model for SVS of a power system considering the interval uncertainty of WF output is proposed. The objective functions of the model are to increase the central value and reduce the fluctuation range of the SVSM interval, and the decision variables are the active power output and terminal voltage of generators and the switching capacity of shunt capacitors. Thus, it is a multi-layer optimization model. A parametric approximation (PA) method is used to obtain the approximate functional relationship between the optimal objective function values and the decision variables of the inner-layer and mid-layer optimization models and convert the optimization model into a single-layer bi-objective optimization model. A method for obtaining the continuous Pareto frontier of the bi-objective optimization model is proposed based on the normalized normal constraint and PA methods, and the compromise optimal solution calculated from the continuous Pareto frontier is used as the optimal control scheme. Two methods for improving the calculation efficiency of the PA method are also proposed. Finally, results from experimentation on the IEEE 39-bus system and an actual provincial power grid demonstrate the effectiveness of the proposed method.

Application of the sequential parametric convex approximation method to the design of robust trusses

We study an algorithm recently proposed, which is called sequential parametric approximation method, that finds the solution of a differentiable nonconvex optimization problem by solving a sequence of differentiable convex approximations from the original one. We show as well the global convergence of this method under weaker assumptions than those made in the literature. The optimization method is applied to the design of robust truss structures. The optimal structure of the model considered minimizes the total amount of material under mechanical equilibrium, displacements and stress constraints. Finally, Robust designs are found by considering load perturbations.

Fast algorithm for singly linearly constrained quadratic programs with box-like constraints

This paper focuses on a singly linearly constrained class of convex quadratic programs with box-like constraints. We propose a new fast algorithm based on parametric approach and secant approximation method to solve this class of quadratic problems. We design efficient implementations for our proposed algorithm and compare its performance with two state-of-the-art standard solvers called Gurobi and Mosek. Numerical results on a variety of test problems demonstrate that our algorithm is able to efficiently solve the large-scale problems with the dimension up to fifty million and it substantially outperforms Gurobi and Mosek in terms of the running time.

The Vibration Model Establishment and Solution of Bending-Torsion-Axial-Swing Coupled the Helical Gear Transmission System Based on Lumped Parameter Approximation Method

Based on comprehensive considerations the influences of stiffness excitation, deviation excitation, meshing impact excitation, friction of tooth surface, and other kinds of nonlinear factors, it established a nonlinear coupled vibration model of bending-torsion-axial-swing coupled helical gear transmission system by applying the Lumped Mass Method. After transformed the model to dimensionless form, it used Runge-Kutta method to solve the nonlinear vibration model of the system, and then the time domain chart, spectrum chart, phase chart, Poincare chart, and FFT chart were obtained; it discussed the influence of system parameters on its dynamic characteristics.

The Design of Permanent Magnetic Adhesion System for Wall-Climbing Robot

In order to satisfy the requirements on payload ability and maneuverability of the wall-climbing robot, a novel permanent magnetic adhesion system based on the linear Halbach array is designed. The permanent magnetic adhesion system and the wheel locomotion mechanism are employed in the robot system. By static and dynamic force analysis of the robot, design requirements about adhesion system are derived. The optimal dimensions of the mechanism are obtained using numerical modeling and parameter approximation method of first order partial derivative of dependent variables. Finally, the adhesion mechanism has been constructed and the maximum and minimum adhesion forces are measured and compared with numerical simulation and a good agreement is found.

Modeling of large-deflection links for compliant mechanisms

The traditional pseudo-rigid-body model (PRBM) has one degree of freedom (DOF) and performs a good simulation to the tip locus of flexible links for compliant mechanisms on the basis of a parametric approximation method. In this study, a new approach of a two-DOF PRBM is proposed to simulate both the tip locus and tip deflection angle of large-deflection links for compliant mechanisms on the basis of the angular deflection approximation technique. A linear regression for the spring stiffness coefficient of the 2R PRBM using the optimization technique is presented. The advantage of the new model is well illustrated through a numerical comparison between the 1R and the 2R PRBM.

On the nearest parametric approximation of a fuzzy number

Many nearest parametric approximation methods of fuzzy sets are proposed in the literature. It is clear that the specific approximations may lead to the loss of information about fuzziness. To overcome this problem, most of these methods rely on the minimization of the distance between the original fuzzy set and its approximation. But these approximations mostly are not flexible to the decision maker's choice. Hence, in this paper, we offer a parametric fuzzy approximation method based on the decision maker's strategy as an extension of trapezoidal approximation of a fuzzy number. This method comprises the selection of the form of the parametric membership function and its evaluation.

Collision Free Quasi-Minimum-Time Trajectory Planning for Skid-Steer Platforms.

This paper addresses a problem of time-optimal trajectory planning for skid-steer platforms considering obstacle avoidance. Considering both time-optimality and obstacle avoidance for mobile robot is not easy, because the two problems are coupled in the trajectory planning problem. Using an idea of path parameter, the trajectory planning problem is divided into two sub-problems, i.e., (1) time-optimization of trajectory along specified path, (2) optimal path planning considering obstacle avoidance. Then an efficient search method is proposed for each problem, using the idea of path parameter and B-Spline approximation method. The idea of path parameter simplifies the optimization problem for specified path planning problem of mobile robot. Simulation results show the effectiveness of the proposed trajectory planning method.

Aqueous equilibria of pyrazole complexes

Association equilibria of pyrazole with H +, Cu 2+, and Ni 2+ were studied as a function of ionic strength. Glass electrode potentiometry was the principal technique employed. Graphical analyses of the data yielded acid dissociation constants for quaternized pyrazole of 2·69 × 10 −3, 2·49 × 10 −3, and 1·65 × 10 −3 at molar ionic strenghts 0·08, 0·20 and 1·00, respectively. The first stability constants of Ni(II) and Cu(II) pyrazole complexes were accurately determined by a graphical analysis method. The results were K 1 = 213, 221 and 260 for copper and K 1 = 72, 76 and 82 for nickel at ionic strengths 0·08, 0·20 and 1·00. A two parameter approximation method gave approximate higher order stepwise stability constants of K 2 = 77, K 3 = 27, K 4 = 9 for copper-pyrazole at ionic strength 0·2, and K 2 = 25, K 3 = 8, K 4 = 2·7, K 5 = 0·9 and K 6 = 0·3 for the nickel-pyrazole system at ionic strength 0·20.