Measuring dynamic efficiency: Theories and an integrated methodology

Almost all dynamic production systems are subject to lagged productive effects, which are an often-ignored latent source of interference in the efficiency measuring process. Existing data envelopment analysis (DEA) approaches rely on a static production environment. They can easily lead to biased evaluation results due to the erroneous assumption. To tackle this issue, this paper develops a dynamic DEA model that allows intertemporal effects in efficiency measuring. Specifically, the dynamic DEA model incorporates dynamic factors via a linear parametric formulation. Our model can be applied in place of static DEA models to a wide range of applications, such as analyzing longitudinal firm performance and productivity changes. As for the empirical efficiencies, we demonstrate how the lag parameters in the dynamic model can be estimated by the panel vector autoregressive model (PVAR). We use our methodology to evaluate advertising efficiencies of several major automobile and pharmaceutical firms in North America. The result shows that using static DEA in dynamic production can lead to both rank reversals and changes in efficiency scores.     

Modeling secrecy and deception in a multiple-period attacker–defender signaling game

In this paper, we apply game theory to model strategies of secrecy and deception in a multiple-period attacker–defender resource-allocation and signaling game with incomplete information. At each period, we allow one of the three possible types of defender signals—truthful disclosure, secrecy, and deception. We also allow two types of information updating—the attacker updates his knowledge about the defender type after observing the defender’s signals, and also after observing the result of a contest (if one occurs in any given time period). Our multiple-period model provides insights into the balance between capital and expense for defensive investments (and the effects of defender private information, such as defense effectiveness, target valuations, and costs), and also shows that defenders can achieve more cost-effective security through secrecy and deception (possibly lasting more than one period), in a multiple-period game.     

A single-shot game of multi-period inspection

This paper deals with an inspection game of Customs and a smuggler during some days. Customs has two options of patrolling or not. The smuggler can take two strategies of shipping its cargo of contraband or not. Two players have several opportunities to take an action during a limited number of days but they may discard some of the opportunities. When the smuggling coincides with the patrol, there occurs one of three events: the capture of the smuggler by Customs, a success of the smuggling and nothing new. If the smuggler is captured or no time remains to complete the game, the game ends. There have been many studies on the inspection game so far by the multi-stage game model, where both players at a stage know players’ strategies taken at the previous stage. In this paper, we consider a two-person zero-sum single-shot game, where the game proceeds through multiple periods but both players do not know any strategies taken by their opponents on the process of the game. We apply dynamic programming to the game to exhaust all equilibrium points on a strategy space of player. We also clarify the characteristics of optimal strategies of players by some numerical examples.     

A unified analysis of linear quaternion dynamic equations on time scales

Over the last years, considerable attention has been paid to the role of the quaternion differential equations (QDEs) which extend the ordinary differential equations. The theory of QDEs was recently well established and has wide applications in physics and life science. This paper establishes a systematic frame work for the theory of linear quaternion dynamic equations on time scales (QDETS), which can be applied to wave phenomena modeling, fluid dynamics and filter design. The algebraic structure of the solutions to the QDETS is actually a left- or right- module, not a linear vector space. On the non-commutativity of the quaternion algebra, many concepts and properties of the classical dynamic equations on time scales (DETS) can not be applied. They should be redefined accordingly. Using $q$-determinant, a novel definition of Wronskian is introduced under the framework of quaternions which is different from the standard one in DETS. Liouville formula for QDETS is also analyzed. Upon these, the solutions to the linear QDETS are established. The Putzer''s algorithms to evaluate the fundamental solution matrix for homogeneous QDETS are presented. Furthermore, the variation of constants formula to solve the nonhomogeneous QDETs is given. Some concrete examples are provided to illustrate the feasibility of the proposed algorithms.     

Reversible aqueous metathesis reactions for potential application in dynamic combinatorial chemistry

Solutions of heterocycles having an allyl sulfide unit and simple alkenes in 50% t-BuOH/H₂O undergo reversible olefin metathesis reactions with the second generation Hoveyda-Grubbs catalyst. The choice of functional groups is limited by competitive chelation of some heterocycles with the catalyst, and other stereoelectronic effects.     

Separation of triphenyl atropisomers of a pharmaceutical compound on a novel mixed mode stationary phase: a case study involving dynamic chromatography, dynamic NMR and molecular modeling

Analysis of atropisomers is of considerable interest in the pharmaceutical industry. For complex chiral molecules with several chiral centers hindered axial rotation can lead to formation of interconverting diastereomers that should be separable on achiral stationary phases. However, achieving the actual separation may be difficult as the on-column separation speed must match or be faster then the rate of isomer interconversion. Often, this requirement can be satisfied by using low-temperature conditions and by improving selectivity via use of chiral stationary phases. In the current study, we present an alternative approach utilizing an Obelisc R column, a novel mixed mode stationary phase that provided acceptable separation of triphenyl atropisomers inside a conventional HPLC temperature range. The separation was investigated under various chromatographic conditions. The interconversion chromatograms exhibited classic peak-plateau-peak behavior indicating the simultaneous atropisomer separation and interconversion. The elution profiles were integrated in order to deconvolute the peak areas of the "pure" (non-exchanged) and interconverted species; these data were used to obtain kinetic information. Analysis of retention data rendered thermodynamic information on the mechanism of retention and selectivity. Chromatographic kinetic data were complemented with variable-temperature NMR and molecular modeling studies, which provided additional support and insights into the energetics of the interconversion process.     

Synthesis, conformation and dynamics of 4,4,5,5,6,6,7,7,8,8-decamethyl-1-oxa-spiro[2.5]octane and 1,2,3,3,4,4,5,5,6,6-decamethyl-cyclohexene

The fragmentation of a suitable methylated 1-oxa-spiro[2.5]octane yields permethyl-cyclohexene. The activation parameters for the chair to chair interconversion of the 1-oxa-spiro[2.5]octane and the half-chair to half-chair interconversion of permethyl-cyclohexene were determined via bandshape analyses of exchange-broadened ¹H and ¹³C NMR spectra, respectively.     

非天然相互作用对均聚多肽链螺旋形成动力学过程的影响的计算机模拟研究

以螺旋结构的形成过程为研究对象,基于粗粒化的格子模型和动态蒙特卡罗模拟方法,初步探讨了非天然氢键相互作用对均聚多肽链螺旋折叠动力学过程的影响.研究发现,非天然氢键的引入虽然延缓了其热力学转变的发生,但也从整体上降低了折叠动力学过程的能垒,在某一特定温度之下,反而可以提高折叠速率.对其折叠路径分布的分析表明,非天然氢键可以减少慢速折叠路径的发生,而后者是导致折叠时间增加的主要因素.另一方面,比较特定温度下多肽链链构象及螺旋片断随时间的演化进程,发现非天然氢键在一定程度上影响了天然氢键的形成以及天然态构象的稳定存在,同时也加快了其部分解折叠过程.这说明,非天然相互作用的存在有利于蛋白质构象的快速动态调整,从而行使其相应的生物功能.     

An RNA folding algorithm including pseudoknots based on dynamic weighted matching

On the basis of maximum weighted matching (MWM) algorithm, we introduced a dynamic weight related with stem length and used a recursive algorithm to predict RNA secondary structures by searching the stem structure with maximum weight summation step-by-step. This algorithm not only avoids the complicated free energy calculation, but also it could attain higher prediction accuracy. Moreover, our algorithm can predict most types of potential pseudoknots in the RNA structure.     

Optimally ending an epidemic

A stochastic and controlled version of the classic three-dimensional Kermack–McKendrick model for the spread of epidemics is considered. The aim is to end the epidemic as soon as possible, taking the quadratic control costs into account. An exact and explicit solution is found in a particular case by making use of the method of similarity solutions to solve the partial differential equation satisfied by the value function, subject to the appropriate conditions.