Network Reduction Method Research Articles

Dimension Reduction of Large Sparse AND-NOT Network Models

In this manuscript we propose and implement a dimension reduction algorithm of AND-NOT networks for the purpose of steady state computation. Our method of network reduction consists in using “steady state approximations” that do not change the number of steady states. The algorithm is designed to work at the wiring diagram level without the need to evaluate or simplify Boolean functions. Also, our implementation of the algorithm takes advantage of the sparsity typical of discrete models of biological systems.The main features of our reduction algorithm are that it works at the wiring diagram level and it preserves the number of steady states. Furthermore, the steady states of the original network can be recovered from the steady states of the reduced network; thus, all steady states are found. Also, heuristic analysis and simulations show that it runs in polynomial time. We used our results to study AND-NOT network models of gene networks and showed that our algorithm greatly simplifies steady state analysis. Furthermore, our algorithm can handle sparse AND-NOT networks with up to 1,000,000 nodes.

Exploiting stoichiometric redundancies for computational efficiency and network reduction.

Analysis of metabolic networks typically begins with construction of the stoichiometry matrix, which characterizes the network topology. This matrix provides, via the balance equation, a description of the potential steady-state flow distribution. This paper begins with the observation that the balance equation depends only on the structure of linear redundancies in the network, and so can be stated in a succinct manner, leading to computational efficiencies in steady-state analysis. This alternative description of steady-state behaviour is then used to provide a novel method for network reduction, which complements existing algorithms for describing intracellular networks in terms of input-output macro-reactions (to facilitate bioprocess optimization and control). Finally, it is demonstrated that this novel reduction method can be used to address elementary mode analysis of large networks: the modes supported by a reduced network can capture the input-output modes of a metabolic module with significantly reduced computational effort.

Synchronization in Quotient Network Based on Symmetry

Symmetry is a universal structural property of networks and many real networks have this characteristic. Pres- ently, reducing an original network to a small-size quotient network by means of network symmetry is a promising method for network reduction. This paper studies the synchronization relationship between an original network and its quotient network and concludes that the network and its quotient network reach frequency synchronization simultane- ously. We analyze the conclusion in theory and validate it with several simulations on synthetic networks.

Reduction of streamflow monitoring networks by a reference point approach

Adoption of an integrated approach to water management strongly forces policy and decision-makers to focus on hydrometric monitoring systems as well. Existing hydrometric networks need to be assessed and revised against the requirements on water quantity data to support integrated management. One of the questions that a network assessment study should resolve is whether a current monitoring system can be consolidated in view of the increased expenditures in time, money and effort imposed on the monitoring activity. Within the last decade, governmental monitoring agencies in Turkey have foreseen an audit on all their basin networks in view of prevailing economic pressures. In particular, they question how they can decide whether monitoring should be continued or terminated at a particular site in a network. The presented study is initiated to address this question by examining the applicability of a method called “reference point approach” (RPA) for network assessment and reduction purposes. The main objective of the study is to develop an easily applicable and flexible network reduction methodology, focusing mainly on the assessment of the “performance” of existing streamflow monitoring networks in view of variable operational purposes. The methodology is applied to 13 hydrometric stations in the Gediz Basin, along the Aegean coast of Turkey. The results have shown that the simplicity of the method, in contrast to more complicated computational techniques, is an asset that facilitates the involvement of decision makers in application of the methodology for a more interactive assessment procedure between the monitoring agency and the network designer. The method permits ranking of hydrometric stations with regard to multiple objectives of monitoring and the desired attributes of the basin network. Another distinctive feature of the approach is that it also assists decision making in cases with limited data and metadata. These features of the RPA approach highlight its advantages over the existing network assessment and reduction methods.

Quantitative Analysis of LIBS Reduces the Matrix Effect Methods

This paper introduced the principle about the technology of Laser-induced Breakdown Spectroscopy (LIBS) of quantitative analysis. It was reviewed about the quantitative analysis of LIBS reduced method of matrix. The reason of cause matrix effect was not clear, but the matrix effect on the LIBS quantitative analysis of the impact can not be ignored. The LIBS quantitative analysis method was divided into two categories: one was based on the calibration curve with the mathematical matrix correction method; the other was combined with neural network reduction method of matrix. This paper was introduced for the two categories of methods, and gives an example to explain.

Equivalent Network for Wind Farm Harmonic Assessments

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> There is a global commitment to tackle climate change which is evidenced by a huge surge in the uptake of renewable generation, mainly wind in the energy supply industries. Against this background, the effects of these vast numbers of connections to transmission and distribution system will have a critical impact on the standard and quality of supply in the network. In the U.K., utilities are required to perform harmonic assessments for large nonlinear loads. From an engineering perspective, it is imperative that these assessments are done accurately, efficiently, and effectively to ensure that all present and future connections can be accommodated without any problems. This paper presents a network reduction method for reducing detailed low-voltage wind farms networks to assess the effects of its connection onto a main interconnected transmission system. The rationale and method for this assessment is presented with a comparison of results against current approaches, such as IEC current aggregation, to demonstrate and prove its validity and effectiveness. </para>

Lead Time Estimation Method for Complex Product Development Process

As the lifecycle of a product gets shorter, the timely introduction of new products becomes an invaluable asset to most manufacturing firms. It is needless to say that the competitive edge is given to a firm with the better knowledge on how to estimate the product development (PD) process because reducing the product development time is a critical issue for manufacturing firms. However, it is difficult to estimate the performance of the PD process because of its complexity. So far, in spite of its strategic importance, only a few studies have been done. To overcome this limitation, in this study, the authors provide a heuristic algorithm that can estimate the lead time of a complex PD process by series–parallel network transformation and network reduction methods with estimates of the makespans of branch–merge types. To show the usefulness of this method, computational experiments have been carried out.

Powerful tools for thermal characterisation of MEMS

Thermal aspects of design and fabrication of sensor structures based on thermally isolated heater filaments [Cs. Dücső, et al., Porous Si bulk micro-machining for thermally isolated membrane formation, Sens. Actuators A 60 (1997) 235–243 [1]] were investigated with special attention to their dynamic properties in order to demonstrate the outstanding possibilities of modelling and characterisation tools in analysis MEMS structures. Thermal engineering was aided by high performance simulation methods, such as finite element modelling (COSMOS) and thermal equivalent circuit simulation using successive network reduction method (SUNRED). The detailed static and dynamic thermal behaviour of the structure was experimentally characterised by applying the high resolution thermography system of the Thermosensorik GmbH and thermal transient tester (T3Ster) of the MicReD Ltd.

An Approach to Network Parameter Estimation in Power System State Estimation

In energy management systems, state estimation is a key function for building a network real-time model. This article describes an approach to network parameter estimation. An appropriate method for network parameter error detection, identification, and correction is developed. The method shown is applicable to single as well as multiple parameter errors. An approximate formula for the perturbed pseudoinverse is developed. To speed up operator's decision-making procedure, a network reduction method and a graphical user interface feature is developed.

A rank correlation-based method for power network reduction

We present a coherency measure and a network reduction algorithm. The rank correlation function was used to determine the mutual couplings of generators. Generators were grouped at two correlation levels. These are grouping tolerances whose values are unique for a given system. The first produces the most strictly coupled generators to be aggregated, and the second identifies the generators to be saved during reduction. The terminals of the generators in each group were extended to include load buses to partition the network. Previously reported techniques were used to reduce generator and load buses.

An arnoldi based thermal network reduction method for electro-thermal analysis

In this paper we consider the problem of approximating the large discretized thermal network that models the heat conduction phenomenon in an electrical system by means of models of reduced state-space dimensions. To this aim we present an efficient and numerically stable Arnoldi type algorithm by which a multi-point moment matching approximant of the discretized thermal network is obtained and we apply it to the electro-thermal analysis of an operational transconductance amplifier.

Reduction of analytical thermal models and their development in the form of networks

The aim of model reduction is to obtain the simplest model while reflecting as far as possible the dynamic behaviour of a system. First, we present the reduction method based on a complex admittance matrix [Y(s)] of the whole initial model. From which we obtain by two inversions, the matrix , which can be interpreted as a reduced network. We give an example of application of the numeric reduction method. The same method is applied with success to analytical expression of impedances kept from the quadrupole representation of heat conduction. In order to simulate easily the transient responses of analytical models, we present the development of analytical impedance in the form of an equivalent network, which is proved to be very efficient during simulations. The first application is done with a heterogeneous system made of two bars of different materials, one is made of copper and the other is made of steel. The second application is done with a more complex thermal system constituting a cooler with 7 branches. This cooler is reduced to 1, 2 and 3 nodes to obtain the simplest model while reflecting as far as possible the dynamic behaviour. This document presents a generalisation of the method of network reduction in the case where the models' impedances have analytical expressions. In this case, we show that contrary to the numerical reduction, which approximates admittances to the first order, we are free to choose the model order, whatever the kept nodes, in such a manner that the model's bandwidth is considered as sufficient. The resulting equivalent networks allow easy simulations of the transient responses thanks to standard electric network softwares. Beyond the dealt examples of analytical reduction, for industrial systems non analytically calculable but governed by an equation of heat diffusion, the structures (topologies) of the reduced models would be the same. That opens prospects to obtain thermal reduced models from an automated networking realised in CAD.

A new computational approach for project management networks

Every project, whether large or small, requires a plan, a schedule, a system of control. One method of accomplishing the required function is with an activity network — most notably PERT networks. Recent research has shown numerical approximation methods to be superior to either deterministic analysis (such as critical paths) or simulation sampling techniques in terms of accuracy and run time on comparable problems. In this paper, a new family of Polygonal Approximation and Reduction Techniques (PART) for the linear polynomial approximation of activity time probability distributions in stochastic project management networks is presented. PART is based on the development of the first new method for network approximation and reduction to be advanced since discretization, which was the basis of all previously developed numerical approximation methods. Polygonal approximation overcomes several shortcomings of the previous methods. It provides the user with a menu of available probability distributions (in addition to the beta distribution which is traditionally used) to represent individual tasks. A much smaller amount of computer storage is required to represent a project network. The central limit theorem is not used as an approximation, since the direct convolution of activity task times is calculated. In this paper, we present a description of the PART concept and the construction of PART-based network approximation and reduction algorithms. We have also constructed, though not reported here, a wide range of project management network models using a random network generator to challenge both the new and existing methods. Analysis of algorithm performance over these models has shown that PART executes an order of magnitude faster while requiring less computer memory than its competitors. This means that for the same investment of time and computer resources, larger networks may be analyzed than were previously possible.

Dealing with missing values in neural network-based diagnostic systems

Backpropagation neural networks have been applied to prediction and classification problems in many real world situations. However, a drawback of this type of neural network is that it requires a full set of input data, and real world data is seldom complete. We have investigated two ways of dealing with incomplete data — network reduction using multiple neural network classifiers, and value substitution using estimated values from predictor networks — and compared their performance with an induction method. On a thyroid disease database collected in a clinical situation, we found that the network reduction method was superior. We conclude that network reduction can be a useful method for dealing with missing values in diagnostic systems based on backpropagation neural networks.

Parametric max flow problems in a class of networks with series-parallel structure

This paper considers a parametric max flow network problem where arc capacities are not fixed but stated as unknown variables to be determined optimally such that the corresponding max flow satisfies flow requirement between source and sink. For the problem, a max flow algorithm may be adapted as a subroutine to be used recursively in an enumerative solution search until finding the optimal solution. However, such an enumerative approach is not practical because it is not guaranteed to solve the problem in a finite number of steps. Therefore, this paper pays attention to the instance defined in a special class of networks, called basically-series-parallel networks, for which all minimal cutsets can easily be enumerated in polynomial time by introducing a set of network reduction methods, called 2-neighbor-node, parallel and source-delta reductions, while such minimal cutset enumeration itself is NP-hard in general. Once all minimal cutsets are found, the associated parametric max flow problem remains simply to solve in a linear programming approach.

Failure probability of strict [formula omitted] systems : IEEE Trans. Reliab.R-36, 551 (1987)

This paper considers a parametric max flow network problem where arc capacities are not fixed but stated as unknown variables to be determined optimally such that the corresponding max flow satisfies flow requirement between source and sink. For the problem, a max flow algorithm may be adapted as a subroutine to be used recursively in an enumerative solution search until finding the optimal solution. However, such an enumerative approach is not practical because it is not guaranteed to solve the problem in a finite number of steps. Therefore, this paper pays attention to the instance defined in a special class of networks, called basically-series-parallel networks, for which all minimal cutsets can easily be enumerated in polynomial time by introducing a set of network reduction methods, called 2-neighbor-node, parallel and source-delta reductions, while such minimal cutset enumeration itself is NP-hard in general. Once all minimal cutsets are found, the associated parametric max flow problem remains simply to solve in a linear programming approach.

Bang‐bang‐type optimal constant current control of parallel AC‐DC power transmission systems

The transient stability of an ac-dc hybrid system can be improved greatly by controlling the power flow of the dc transmission line. In this study the optimal changeover curve of dc current setting value on the phase plane with a quadratic curve are approximated. The coefficients of this curve are calculated in advance taking into account the loading condition of the power system and hence the proposed control scheme can be used for emergency control of the power system. The main conclusions from this study were that: to facilitate transient stability analysis, the dc transmission line is represented by equivalent load admittances, which vary every second with the operating condition of the transmission line; the action of the speed governor increases the damping coefficient of the power system and reduces the control time which means that the admissible range of the dc current setting value can be reduced by increasing the governor gain; and the optimal change-over curve of the dc current setting value is approximated by a quadratic curve, whose coefficients can be calculated in advance taking into account the loading condition of the power system. The suboptimal changeover curve thus obtained makes it possible to change the settingmore » value of dc current without time delay in emergency condition. While the case of three-phase short-circuit fault was specifically discussed, it is possible to extend the results obtained to the case of successful or unsuccessful reclosing. The proposed method could also be applied to multimachine systems by using equivalent network reduction methods.« less