Computation of analytical expressions for transfer functions

A new method for computing transfer functions of linear time-invariant multi-variable control systems is presented. This method has the following attractive features: (i) it produces analytical expressions for transfer functions, (ii) computations are inherently parallel and can be implemented, for instance, on parallel processors with a fine-grain architecture, (iii) calculations of transfer functions are reduced to two well-studied computational problems: solution of simultaneous linear equations and the fast Fourier transform (FFT), and (iv) state-variable formulations can be avoided. Theoretical conclusions are demonstrated with numerical examples.     

On the use of I-divergence for generating distribution approximations

The existence of an upper bound for the error probability as a function of I-divergences between an original and an approximating distribution is proved. Such a bound is shown to be a monotonic nondecreasing function of the I-divergences, reaching the Bayes error probability when they vanish. It has been shown that if the closeness between the original and approximating distributions is assessed by the probability of error associated with a particular two-class recognition problem in which those functions are the class conditional distributions, then the best upper bound for such probability is ? regardless of the value of the I-divergences between them. Approaching the approximation problem from a rather different viewpoint, this correspondence considers the problem of a two-class discrete measurement classification where the original distributions are replaced by approximations, and its effects on the probability of error. The corresponding analysis is presented in detail.     

链状分布的神经网络聚类分析

针对以往很多聚类方法不适用于链状分布的样品的情况,运用簇的概念确定新的“重心”点,然后将原始意义上的“距离”改用弧度来表征,再运用神经网络来对样品进行聚类。应用著名的“古斯塔夫森十字”图形进行仿真实验。结果显示：该方法算法简洁,运算迅速,条理清晰,分类准确,适合于处理链状分布的聚类问题。     

A simple analytical framework to analyze search strategies in large-scale peer-to-peer networks

This paper presents an analytical framework to study search strategies in large-scale decentralized unstructured peer-to-peer (P2P) networks. The peers comprising the P2P network and their application-level connections are modeled as generalized random graphs (GRGs) whose simple and efficient analysis is accomplished using the generating function of the graph’s degree distribution. The framework we defined allows the computation of several interesting performance indexes to be used to compare different search strategies: in particular, the average number of messages sent throughout the P2P network and the probability that a query is successful are used as examples. Furthermore, assuming that the cumulative distribution function (CDF) of the time required by a peer to positively reply to a query is known, we show how to derive the CDF of the time it takes for a randomly chosen peer to obtain at least one positive reply from other peers. The approach is validated through simulation showing that the accuracy of the proposed model improves as the size of the P2P network increases making it a suitable tool for the analysis of search strategies in large-scale systems.     

架空配电线路雷电感应电压特性及解析算法性能分析

为了深入理解架空线雷电感应电压特性为配电网雷电防护提供技术参考,本文采用时域有限差分法及Agrawal耦合模型对10 kV架空配电线路雷电感应电压进行了数值计算.以解析计算方法中导线高度、回击电流幅值以及落雷距离3个特征参数为考察对象,分析了三者对架空线雷电感应电压的影响,实现了对解析计算公式计算精度的定量化分析.计算表明,雷电感应电压脉冲幅值随导线高度和回击电流幅值增大均线性提高,随落雷距离减小非线性提高.受水平电场特性及导线相互作用的影响,落雷距离减小和导线数增多均会显著加重雷电感应电压波形的畸变.以数值计算为标准,解析算法误差可高达45%⁵0%,本文研究结果可为配电网运维工作提供理论参考.     

On detecting faults for Boolean expressions

Fault based testing aims at detecting hypothesized faults based on specifications or program source. There are some fault based techniques for testing Boolean expressions which are commonly used to model conditions in specifications as well as logical decisions in program source. The MUMCUT strategy has been proposed to generate test cases from Boolean expressions. Moreover, it detects eight common types of hypothesized faults provided that the original expression is in irredundant disjunctive normal form, IDNF. Software practitioners are more likely to write the conditions and logical decisions in general form rather than IDNF. Hence, it is interesting to investigate the fault detecting capability of the MUMCUT strategy with respect to general form Boolean expressions. In this article, we perform empirical studies to investigate the fault detection capability of the MUMCUT strategy with respect to general form Boolean expressions as well as mutated expressions. A mutated expression can be obtained from the original given Boolean expression by making a syntactic change based on a particular type of fault.

An improved analytical model for static pull-in voltage of a flexured MEMS switch

Microsystem Technologies - This paper presents the design of low-k meander based MEMS shunt capacitive switch with beam perforations. A closed form model to accurately calculate the pull-in voltage...     

On the complexity of simple arithmetic expressions

Let $\text{E}$ be the set of all simple arithmetic expressions of the form E(x) = xT_l…T_k where x is a nonnegative integer variable and each T_i is a multiplication or integer division by a positive integer constant. We investigate the complexity of the inequivalence and the bounded inequivalence problems for expressions in $\text{E}$. (The bounded inequivalence problem is the problem of deciding for arbitrary expressions E₁(x) and E₂(x) and a positive integer l whether or not E₁(x) ≠ E₂(x) for some nonnegative integer x<l. If l = ∞, i.e., there is no upper bound on x, the problem becomes the inequivalence problem.) We show that the inequivalence problem (or equivalently, the equivalence problem) for a large subclass of $\text{E}$ is decidable in polynomial time. Whether or not the problem is decidable in polynomial time for the full class $\text{E}$ remains open. We also show that the bounded inequivalence problem is NP-complete even if the divisors are restricted to be equal to 2. This last result can be used to sharpen some known NP-completeness results in the literature. Note that if division is rational division, all problems are trivially decidable in polynomial time.     

Improvements to the sensitivity of gravitational clustering for multiple neuron recordings

We outline two improvements to the technique of gravitational clustering for detection of neuronal synchrony, which are capable of improving the method's detection of weak synchrony with limited data. The advantages of the enhancements are illustrated using data with known levels of synchrony and different interspike interval distributions. The novel simulation method described can easily generate such test data. An important dependence of the sensitivity of gravitational clustering to the interspike interval distribution of the analysed spike trains is described.     

Design considerations of rectangular electrostatic torsionactuators based on new analytical pull-in expressions

An important design issue of electrostatic torsion actuator is the relative locations of the actuating electrodes, where the bias voltage is applied. These geometrical design parameters affect both the pull-in angle as well as the pull-in voltage. In this paper, a new approximated analytical solution for the pull-in equation of an electrostatic torsion actuator with rectangular plates is derived. The analytical expression is shown to be within 0.1% of the one degree of freedom (1DOF) lumped-element model numerical simulations. Moreover, the analytical expressions are compared with the full coupled-domain finite-elements/boundary-elements (FEM/BEM) simulations provided by MEMCAD4.8 Co-solve tool, showing excellent agreement. The approach presented here provides better physical insight, more rapid simulations and an improved design optimization tool for the actuator     

Enhanced Dickson voltage multiplier rectenna by developing analytical model for radio frequency harvesting applications

Radio frequency (RF) energy harvesting has experienced a rapid development recently because of the increasing number of RF transmitter sources. This article illustrates a novel analytical model for the voltage multiplier rectifier at 900 MHz. The model proposes a method of deriving the output characteristics of the rectifying circuits in terms of two main parameters; voltage and current. The design consists of seven stages of Dickson voltage multiplier rectifier. A Schottky diode HSMS 285C was used in the design. Equations for the model were developed. These equations were used to extract the values of output voltage and current. A simulation was optimized using advanced design systems. The system was correspondingly fabricated and tested for input power range of 1 × 10^?5‐1 × 10^?1 W. Experimental results show that an output voltage of 5.45 V and current of 1.26 × 10^?5 A are achieved at 10 dBm using a 10 kΩ load, achieving an efficiency of 37.82%.     

A straightforward determination of fluid viscosity and density using microcantilevers: From experimental data to analytical expressions

Vibrating microcantilevers are used to measure the density and the viscosity of surrounding fluids. The classical procedure involves experimental acquisition of the deflection spectrum of the beam, but a systematic calibration step is mandatory for obtaining viscosity and density. In the present study, a method is proposed to facilitate these measurements for Newtonian fluids with only one calibration step in air during the cantilever lifetime. Our approach relies on a complete theoretical analysis allowing to approximate semi-analytically the deflection spectrum with a second-order transfer function and to determine an analytical relationship between viscosity, density and the parameters of the transfer function. Fluid parameter determination results are shown for validation and discussed.     

Analysis and analytical modeling of static pull-In with application to MEMS-based voltage reference and process monitoring

The pull-in voltage of one- and two-degrees-of-freedom (DOF) structures has been symbolically and numerically analyzed with respect to drive mode dependence and hysteresis. Moreover, the time and temperature stability has been investigated and tested. Modeling results have been applied in the design of both folded-spring-suspended 1-DOF structures and single-side-clamped 2-DOF beams with a nominal pull-in voltage in the 5-10 V range and fabricated in an epi-poly process. Asymmetrically driven structures reveal pull-in close to the value predicted by the model (V/sub pi/ 1-DOF is 4.65 V analytically simulated and 4.56 V measured; V/sub pi/ 2-DOF is 9.24 V analytically simulated, 9.30 V in FEM and 9.34 V measured). Also the hysteresis is in close agreement (release voltage, V/sub r/, 1-DOF is 1.41 V analytically simulated and 1.45 V measured; V/sub r/ 2-DOF is 9.17 V analytically simulated, 9.15 V in FEM and 9.27 V measured). In symmetrically operated devices the differences between the computed and measured V/sub pi/ and V/sub r/ are much larger and are due to process dependencies, which make these devices very suitable for process monitoring. The 2-DOF asymmetrically operated device is the most suitable for MEMS-based voltage reference. The stability in time is limited by charge build-up and calls for a 100-hour initial burn-in. Temperature dependence is -100 /spl mu/V/K at V/sub pi//spl ap/5 V, however, is calculable and thus can be corrected or compensated.     

On the distribution approach to location problems

While making location decisions, the distribution of travel distances among the service recipients (clients) is an important issue. It is usually tackled with the minimax (center) or the minisum (median) solution concepts. Both concepts minimize only simple scalar characteristics of the distribution: the maximal distance and the average distance, respectively. In this paper, all the distances for the individual clients are considered as a set of multiple uniform criteria to be minimized. This results in a multiple criteria model taking into account the entire distribution of distances. Our analysis of the multiple criteria problem focuses on the symmetrically efficient solutions which comply with minimization of distances as well as with impartial consideration of the clients. Various solution concepts generating symmetrically efficient location patterns are analyzed. Finally, the reference distribution approach is developed as an interactive technique which enables us to identify a satisfactory symmetrically efficient location pattern by evolving a reference (target) distribution of distances.     

On the analytical derivation of the Pareto-optimal set with applications to structural design

The Fritz John conditions for Pareto-optimality have been set in matrix form and used for introducing a procedure for the analytical derivation of the Pareto-optimal set in the design variables domain. Subsequently, the derivation of the Pareto-optimal set in the objective functions domain can be obtained, if possible, by a proper analytical derivation. Both the objective and constraint functions are assumed to be available in analytical form and twice differentiable and convex (or pseudo-convex). The proposed procedure to find the Pareto-optimal set is relatively simple. The computation of the determinant of a matrix is required. A symbolic manipulator can be exploited. If there are two design variables and two objective functions, the Pareto-optimal set can be easily computed by applying a simple formula derived in the paper. If the number of design variables equals the number of objective functions, the Pareto-optimal set in the design variables domain can be found by computing the product of the constraint functions times the determinant of the Jacobian of the objective functions. A number of case studies have been proposed to test the effectiveness of the proposed procedure. The optimal structural design of, respectively, a pair of compressed spheres, a cantilever with rectangular cross section have been faced and solved. Additionally the test problem proposed by Fonseca and Fleming has been addressed and solved analytically. Optimization problems with low dimensionality (2 or 3 design variables and 2 objective functions, 2 or more constraints) have been easily solved. The proposed procedure can be useful in the actual engineering practice at the earliest design stage. In this case the designer can be made aware on the proper design variables setting to obtain the desired tradeoff among conflicting objective functions.     

The use of genetic algorithms for assessment of high voltage fields

There are several numerical methods for calculation of electric fields but they need some sort of experience and trial and error to get the correct solution. A genetic algorithm (GA) based approach is used to eliminate the need for the experience and to save time and effort spent in the trial and error. Two enhancement techniques, namely, Refreshment Method and No-Twins Method, are used with the GA operators to improve the performance of the GA in assessment of high voltage fields. The performance of these two enhancement techniques has been studied for computing the electrostatic field in high voltage applications.     

Construction of an analytical framework for polygon-based land use transition analyses

Polygon representation is important for characterizing land uses and the relationships among them. This study aims to establish an analytical framework for polygon-based land use transitions to understand the processes of change regarding types of land uses and their shapes. The polygon event and polygon state help to reveal continuity both spatially and temporally. A polygon event represents a combination of changes in both the type of land use and its shape through a transition process. A polygon state reflects homogeneity during the transition process. Two indices, the stability index and the compactness, were used to enhance the understanding of the transition process. The stability index evaluates the succession of an attribute, while compactness recognizes the geometrical characteristics of a polygon. A case study on Tsukuba City, Japan, was evaluated to demonstrate the feasibility of the approach that is presented here. The proposed analytical framework supports the clarification of land use transition patterns and is effective in explaining the spatiotemporal land use transition process.     

On analytical design of controllers

A method to design controllers of linear plants under bounded sectionally continuous external disturbances was proposed.     

On optimizing the evaluation of a set of expressions

A branch- and-bound type algorithm is developed to optimize the evaluation of a set of expressions. The algorithm proceeds in a depth-first manner and achieves an optimal solution. The algorithm is applied to optimize the evaluation of sets of relational expressions. Analogies to the heuristic information associated with theA* algorithm are investigated. Examples are presented illustrating the use of the algorithm. Pragmatics associated with the algorithm and its application to Boolean optimization are also discussed.Research supported by the National Science Foundation under grant number NSF MCS 79-19418 and by the National Aeronautics and Space Administration under grant number NGR 21-002-270-9.