Influence of the topology of a cellular automaton on its dynamical properties

Notwithstanding the numerous scientific efforts that have been spent to unravel the dynamics of cellular automata (CA), there is still only fragmented and incomplete knowledge of the interference that possibly exists between a CA’s dynamical properties in general and its stability in particular, on the one hand, and the whole of its spatial entities and their interconnection, referred to as a CA’s topology, on the other hand. Since a clear understanding of this interference is unbearable to fully comprehend the dynamics of CA, this paper is devoted to a quantitative assessment of this interference. More precisely, after pinning down the so-called representative tessellation size (RTS), it is verified to what extent the input sensitivity of 2-state CA and their stability depends on the characteristics of their topology. Therefore, 12 random graphs having six different vertex degree distributions (VDDs) are used to embody the CA’s topology and to verify how their dynamics is affected by the specificities of these graphs. It is found that the RTS is 400. Further, the interference is strongest with regard to the CA’s stability to the extent that the classification of CA into behavioral classes can be seriously affected by the choice of the VDD.     

Scale elasticity and returns to scale in the presence of alternative solutions

Scale elasticity (SE) and returns to scale (RTS) are important topics in performance analysis, which help managers to make decisions about the expansion or contraction of the operation of decision making units under assessment. In this paper, some new results about these topics in the presence of alternative solutions, regarding the concept of multifunction, are provided.At first, some properties of some multifunctions (functions), defined with respect to the optimal solutions of DEA models, are established which help us in what follows. In turn, the relationships between the considered multifunctions and the concept of RTS and SE are studied. Finally an approach for the estimation of the RTS classification of units is obtained, which leads to an important corollary as an interesting result which introduces a connection between two concepts, RTS and SE. This is important from an applied point of view. Also, from a technical point of view, the proofs of theorems which give this corollary use a main lemma of convex analysis literature and give a constructive proof about RTS.     

One-sided elasticities and technical efficiency in multi-output production: A theoretical framework

One of the concepts that have sparked considerable interest in the theory of production and efficiency is that of returns to scale (RTS). Economics researchers typically define RTS using the notion of elasticity. Considerable research activity on RTS has also been observed by management science researchers, who utilize the methodology of Data Envelopment Analysis (DEA) to gain insights on RTS. In this paper, we present a theoretical framework that integrates existing economics and management science literature on RTS, and provides a solid foundation for research work in this area. Our framework defines, discusses, and proposes an approach to measure input- and output-oriented elasticities, and one-sided RTS. We demonstrate how the work done in DEA is a special case of our framework, and discuss the conditions under which the resulting two left-hand, and the two right-hand elasticities can be equal. Future research directions are also discussed.     

Implementation strategies of a contract-based MRI examination reservation process for stroke patients

Timely imaging examinations are critical for stroke patients due to the potential life threat. We have proposed a contract-based Magnetic Resonance Imaging (MRI) reservation process [1] in order to reduce their waiting time for MRI examinations. Contracted time slots (CTS) are especially reserved for Neural Vascular Department (NVD) treating stroke patients. Patients either wait in a CTS queue for such time slots or are directed to Regular Time Slot (RTS) reservation. This strategy creates “unlucky” patients having to wait for lengthy RTS reservation. This paper proposes and analyzes other contract implementation strategies called RTS reservation strategies. These strategies reserve RTS for NVD but do not direct patients to regular reservations. Patients all wait in the same queue and are served by either CTS or RTS on a FIFO (First In First Out) basis. We prove that RTS reservation strategies are able to reduce the unused time slots and patient waiting time. Extensive numerical results are presented to show the benefits of RTS reservation and to compare various RTS reservation strategies.     

Measurement of returns to scale using a non-radial DEA model: A range-adjusted measure approach

This research theoretically explores the measurement of returns to scale (RTS), using a non-radial DEA (data envelopment analysis) model. A range-adjusted measure (RAM) is used as a representative of such non-radial models. Historically, a type of RTS has been discussed within an analytical framework of radial models. The radial-based RTS measurement is replaced by the non-radial RAM/RTS measurement in this study. When discussing the non-radial RAM/RTS measurement, this study finds a problem of multiple projections that cannot be found in the radial measurement. In this research, a new linear programming approach is proposed to identify all efficient DMUs (decision making units) on a reference set. The important feature of the proposed approach is that it can deal with a simultaneous occurrence of (a) multiple reference sets, (b) multiple supporting hyperplanes and (c) multiple projections. All of the three difficulties are handled by the proposed RAM/RTS measurement. In particular, we discuss both when the three different types of multiple solutions occur on the RAM/RTS measurement and how to deal with such difficulties. Our research results make it possible to measure not only the type of RTS but also the magnitude of RTS in the RAM measurement.     

Global sub-increasing and global sub-decreasing returns to scale in free disposal hull technologies: Definition,characterization and calculation

Global Returns to Scale (GRS) is an important notion in performance analysis under Free Disposal Hull (FDH) technologies. Ray Average Productivity (RAP) function has a crucial role in interpreting the GRS. We define two new notions, called Global Sub-Increasing RTS (G-SIRS) and Global Sub-Decreasing RTS (G-SDRS), invoking the behaviour of the RAP function at its maximizers. These notions are useful from a managerial standpoint, because they help the decision maker to decide about contracting or expanding the operation of the units under consideration. After presenting a motivating example and defining G-SIRS and G-SDRS, some theorems are proved to characterize these new notions. A polynomial-time algorithm is sketched which is able to determine the GRS of the Decision Making Units (DMUs) under evaluation. The second part of the paper is devoted to calculating a stability interval for GRS. It is done through some theorems and a polynomial-time algorithm. The results of the paper are illustrated by numerical examples as well as empirical studies with real-world data. Computational experiments are reported as well.     

Efficiency and returns-to-scale of local governments

Local governments of advanced countries often have financial problems. Most central governments promote re-organization of local governments into larger local governments in order to reduce operating costs. Although cost reductions have been discussed by governments, political parties, economic institutes, etc, changes in industrial efficiency in regions governed by local governments have been overlooked. In this paper, we evaluate the industrial efficiency and the corresponding returns to scale (RTS). We present input–output tables that provide data of regional economies, network data envelopment analysis algorithms to measure the industrial efficiency, and an algorithm to measure the RTS. The Japanese government has proposed plans to merge prefectures, which are equivalent to counties in Britain, into larger states. The results obtained by applying the proposed algorithm to these plans demonstrate that a number of the new states will suffer from decreased RTS and will experience reduced efficiency.     

On the stability of resonant rotation of a symmetric satellite in an elliptical orbit

We deal with the stability problem of resonant rotation of a symmetric rigid body about its center of mass in an elliptical orbit. The resonant rotation is a planar motion such that the body completes one rotation in absolute space during two orbital revolutions of its center of mass. In [1–3] the stability analysis of the above resonant rotation with respect to planar perturbations has been performed in detail.In this paper we study the stability of the resonant rotation in an extended formulation taking into account both planar and spatial perturbations. By analyzing linearized equations of perturbed motion, we found eccentricity intervals, where the resonant rotation is unstable. Outside of these intervals a nonlinear stability study has been performed and subintervals of formal stability and stability for most initial data have been found. In addition, the instability of the resonant rotation was established at several eccentricity values corresponding to the third and fourth order resonances.Our study has also shown that in linear approximation the spatial perturbations have no effect on the stability of the resonant rotation, whereas in a nonlinear system they can lead to its instability at some resonant values of the eccentricity.     

Dynamic concept of returns to scales and its characteristics on production frontier in intersection form

This paper gives a dynamic concept and a new non-parametric method for evaluating returns to scale(RTS) of economic units with multiple inputs and outputs.It is frequently noticed that when we increase the input of a decision making unit(DMU) with a certain status of RTS,different status of RTS is observed.For example,when we increase the input of a DMU with constant RTS under the traditional method,a decreasing RTS is often observed instead of the expected constant RTS.We thus define the RTS of each DMU in both input expansion and contraction regions respectively.The research starts from transferring the production possibility set into the intersection form,by giving the explicit linear inequality representation of production frontiers.The RTS structural characteristics of DMUs’ on the production frontier are described.Status of RTS of those DMUs on the production frontier include increasing RTS,constant RTS,decreasing RTS,saturated RTS and evidence of congestion.Necessary and suficient conditions for RTS evaluation are provided.The definition and evaluation method given here provide more detailed economic characteristics of DMU for policy makers.     

Estimating returns to scale of Chinese airport airside activities using the CCR-0-objective RTS method

The returns to scale (RTS) nature of 41 Chinese airport airsides is investigated in this paper. We introduce take-off distance available and landing distance available into RTS estimation. To deal with the existence of multiple optimal solutions when estimating RTS using the CCR (Charnes, Cooper and Rhodes) RTS method in Data Envelopment Analysis, we introduce the CCR-0-objective RTS method. The empirical study shows that all those airsides with two runway operate under decreasing RTS. Those airsides with only one runway either show constant RTS or show increasing RTS.     

Evaluating returns to scale and congestion by production possibility set in intersection form

This research proposes a new method to estimate returns to scale(RTS) of decision making units(DM Us) with multiple inputs and outputs.The state of return to scale includes increasing RTS,constant RTS,decreasing RTS and evidence of congestion.The method is based on the production possibility set in the intersection form given by a set of linear inequalities.We propose and prove the necessary and sufficient conditions for the RTS estimation.With the new procedure,to estimate the RTS of a DM U is simply to ch...     

Measurement of Returns to Scale and Damages to Scale for DEA-based operational and environmental assessment: How to manage desirable (good) and undesirable (bad) outputs?

Environmental assessment is increasingly important in preventing various types of pollutions. Data Envelopment Analysis (DEA) has been long used as an operational performance measure, but we have insufficiently explored the use of DEA for environmental assessment. This study explores a new use of DEA for the environmental assessment in which outputs are classified into desirable (good) and undesirable (bad) outputs. Such an output separation is important in the DEA-based environmental assessment. This study extends the use of DEA to the measurement of both Returns to Scale (RTS) for desirable outputs and Damages to Scale (DTS) for undesirable outputs. A Range-Adjusted Measure (RAM) is used as a DEA model for this study because the non-radial model can easily combine the two types of outputs in a unified treatment. All the mathematical features regarding the RAM-based RTS/DTS measurement are first discussed from the operational and environmental performance in a separate treatment. Then, this study combines the two performance measures as a unified measure. The RAM-based RTS/DTS is mathematically explored from the unified measure for operational and environmental performance.     

Maximum entropy probability method applied to assess voltage sag frequency due to transmission line fault in the electric power system

Voltage sag caused by faults on an electric power transmission line is one of the most intractable power quality issues for both utility companies and customers. The fault in power system randomly exists along transmission lines due to the combination of many uncertain factors. To predict and assess the annual expected sag frequency (ESF) deriving from the faults along lines, a stochastic‐based method that employs maximum entropy principle, namely the maximum entropy probability method (MEPM), has been introduced in this paper. Moreover, various types of faults have been considered systematically. With the fault line intervals and the sample moments taken into account, the discrete values of distribution probability of fault locations along the transmission lines have been estimated by means of the MEPM. For a given voltage sag magnitude corresponding to the voltage tolerant level of sensitive equipment at the tested bus, the ESF has been calculated in view of the statistical fault rates of interrelated transmission lines. The implementation and application to a classical five‐bus system and IEEE RTS‐30 test system have been presented consequently. The simulations have revealed that compared with the four existing methods, the MEPM is accurate, flexible, and immune of round‐off errors, and therefore it can be widely applied to the various aspects of power systems. Copyright © 2009 John Wiley & Sons, Ltd.     

Local and global returns to scale in performance measurement

In data envelopment analysis, the type of local returns to scale (RTS) exhibited by a technically efficient unit indicates whether an increase or reduction of the scale of operations could improve the productivity of the unit. One of the approaches to testing RTS is based on the comparison of the efficiency of the unit in specially constructed reference technologies. It has been suggested that this approach is equally suitable for convex and non-convex, including the free disposal hull, technologies. In this paper, we construct examples that show that this suggestion in the case of non-convex technologies is not correct. We show that the type of RTS obtained by this approach is not a local, but global, characteristic of the technology, as it indicates the direction to the most productive scale size of the unit. In non-convex technologies, the local and global classifications of RTS are generally different.     

Stability by Lyapunov like functions of nonlinear differential equations with non-instantaneous impulses

The stability of the solutions of a nonlinear differential equation with noninstantaneous impulses is studied using Lyapunov like functions. In these differential equation we have impulses, which start abruptly at some points and their action continue on given finite intervals. Sufficient conditions for stability, uniform stability and asymptotic uniform stability of the solutions are established. Examples are given to illustrate the results. Also, some of the results are applied to study a dynamical model in Pharmacokinetics.     

The measurement of returns to scale under a simultaneous occurrence of multiple solutions in a reference set and a supporting hyperplane

This research theoretically explores the measurement of RTS (Returns to Scale) under a possible occurrence of multiple solutions in DEA (Data Envelopment Analysis). In this study, the occurrence of multiple solutions is classified into Type I and Type II. Type I is an occurrence of multiple solutions in a reference set. Type II is an occurrence of multiple solutions on a supporting hyperplane passing on the reference set. Both Types I and II are very well known among DEA researchers, but previous research has not sufficiently explored a simultaneous occurrence of Type I and Type II in the RTS measurement. The two types of multiple solutions influence a degree of RTS in the DEA measurement. Such a quantitative issue on RTS is examined from the perspective of the Type I and Type II problems. To deal with such difficulties, a new linear programming approach is proposed to identify all efficient DMUs (Decision Making Units) that consist of a reference set, even if multiple solutions occur on the reference set. Based upon the research result, we can identify when multiple solutions of Type I and/or Type II occur on the RTS measurement and how to deal with such difficulties. Our research result makes it possible to measure a degree of scale economies (RTS) under the simultaneous occurrence of Type I and Type II.     

On a basic definition of returns to scale

A concept that has sparked considerable interest in DEA is that of returns to scale (RTS). One of the basic and useful definitions of RTS in DEA models is based upon the PPS. In this work, a discussion about the PPS-based definition of RTS is given, leading to a modified definition of RTS which is suitable in the presence of multiple supporting hyperplanes passing through the unit under assessment. The definition provided is a simplification of a definition given by Tone.     

考虑非期望规模收益的创新型企业并购决策

根据创新型企业持续创新发展的需要, 针对创新型企业并购决策问题, 提出一种考虑到非期望产出的规模收益的并购决策方法.首先, 基于仅限于期望产出的企业规模收益判断方法, 建立包含非期望产出的GDEA模型与WY-DEA模型; 其次, 利用GDEA模型判断弱WY-DEA有效并购方案的规模收益不变、递增、递减或拥挤四种状态; 然后, 在剔除规模收益拥挤的并购方案基础上, 利用交叉效率模型为被收购企业选择最优的收购方; 最后, 以算例说明方法的可行性与优势.