A time-integrated Richardson model

Richardson equations are widely studied models of simplified multi-player arms races. In this paper, we derive a novel and more theoretically-consistent formulation, which implicitly includes a mapping from observed economic data to the model variables. We define new variables which are time-integrated versions of scaled `defense' expenditures, and show that they may be robustly estimated from historical data. We illustrate the model's usefulness with historical examples and a simplified risk analysis of simulated data.     

A computational method for fitting Richardson equations of arms races

Several mathematical models have been developed for describing international arms races, military conflicts, and other interactions between nations. A crucial question is whether or not such equations can be fitted to actual data. If the answer is in the affirmative, then there are tremendous opportunities for prediction and planning. We present a mathematical and computational method for estimating not only parameters in dynamical models of armament races, but also a complete set of unknown initial conditions. Computational results show the comple feasibility of the quasilinearization method, but further investigation is needed to determine capabilities and limitations of this new approach.     

Actuarial model and its application for implicit pension debt in China

Whether the pension system transition is successful is closely related to the accurately accounted IPD amount and rationally solved scheme. China faces the problem of IPD with no exception. This paper uses individual cost method theory, combining Chinese pension system and its operation, builds up the implicit pension debt calculation model, then it measures the Chinese IPD quantity by statistical data. The paper finds out that the average IPD per-year is 39.404 billion Yuan in 2013–2050, the maximum is 185.053 in 2022, the minimum is 0.150 in 2050, and the accumulative IPD will sustain growth with annual growth rate of 7.06% in 2013–2050, from 119.787 billion Yuan to 1497.337 billion Yuan. Finally, this paper proposes the government to raise the legal retirement age, reduce the pension substitution rate, expand the coverage of endowment insurance, improve the investment yield of the pension fund, and so on, to compensate the IPD in China.     

基于XGBoost的上市企业财务违约预测研究

公司年度报告中的管理层讨论与分析部分是企业信息披露的重要组成.构建表面情感语调STONE和隐含违约倾向IPD两个文本特征指标对年报中管理层讨论与分析的定性文本数据进行量化,并提出了一种基于XGBoost的上市公司财务违约预测模型,该方法对上市公司财务违约实现了较好的预测效果.根据特征重要性排序对特征与财务违约之间的关系进行挖掘,进一步利用敏感性分析验证了表面情感语调和隐含违约倾向指标的有效性.     

On Global Stability of the Lotka Reactions with Generalized Mass-Action Kinetics

The three-sphere swimmer by Najafi and Golestanian is composed of three spheres connected by two arms. The case in which the swimmer can control the lengths of the two arms has been studied in detail. Here we study a variation of the model in which the swimmer’s arms are constructed according to Hill’s model of muscular contraction. The swimmer is able to control the tension developed in the active components of the arms. The two shape parameters and the tensions acting on the two arms are then obtained by solving a system of ordinary differential equations. We study the qualitative properties of the solutions, compute analytically their leading order approximation and compare them with numerical simulations. We also formulate and solve some optimisation problems, aimed at finding the actuation strategies maximising performance, for various performance measures. Finally, we discuss the structure of the governing equations of our microswimmers from the point of view of control theory. We show that our systems are control affine systems with drift.     

Contests with productive effort

I consider competitions in which, conditional on winning or losing, the effort exerted by a competitor does not necessarily decrease his payoff. This happens, for example, in competitions for promotions in which workers are intrinsically motivated, and in research and development races in which better performance implies a higher payoff from winning. I characterize players’ equilibrium payoffs in closed form, thereby generalizing Siegel (Econometrica 77(1):71–92, 2009) payoff result to contests in which players’ payoff functions are non-monotonic.     

单兵种对双兵种作战模型

本文讨论了单兵种对双兵种作战的 Lanchester模型 ,分析研究了战斗进程中各方兵力的动态变化 ,给出了单兵种方的最优兵力分配原则 .     

Stochastic optimization of sailing trajectories in an upwind regatta

In a sailboat race, the navigator’s attempts to plot the fastest possible course are hindered by shifty winds. We present mathematical models appropriate for this situation, which use statistical analysis of wind fluctuations and are amenable to stochastic optimization methods. We describe the decision tool that was developed and used in the 2007 America’s Cup race and its impact on the races.     

The effect of bearing cage run-out on the nonlinear dynamics of a rotating shaft

This paper presents an analytical model to investigate the nonlinear dynamic behavior of an unbalanced rotor-bearing system due to cage run-out. Due to run-out of the cage, the rolling elements no longer stay equally spaced. The mathematical model takes into account the sources of nonlinearity such as Hertzian contact forces and cage run-out, and the resulting transition from a state of no contact to contact between the rolling elements and the races. The contact between the rolling elements and races is treated as nonlinear springs and the system is analyzed for varying numbers of balls. The results are presented in the form of fast Fourier transformations and Poincaré maps. The results show that the ball passage frequency is modulated with the rotational frequency. The response falls into three regimes: periodic motion, quasi-periodic oscillations, and chaotic response.     

Periodic Optical Pulses in Nonlinear Optical Fibers

We discuss the problem of transmitting polarized pulses along optical fibers with variable dispersion. The dissipation and mean dispersion are assumed to be zero, which allows using the model of the vector nonlinear Schrödinger equation. We consider an optical fiber consisting of arms of equal length, which is assumed to be large. We propose an asymptotic recursive procedure for calculating the amplitude and the phase of an optical pulse propagating along the optical cable with variable dispersion.     

Dynamic analysis and system identification of an LCD glass-handling robot driven by a PMSM

In this paper, Hamilton’s principle is employed to derive Lagrange’s equations of an liquid crystal display (LCD) glass-handling robot driven by a permanent magnet synchronous motor (PMSM). The robot has three arms driven by two timing belts. The dynamic formulations can be expressed by one and four independent variables, which are named as the rigid and flexible models, respectively. In order to verify the dynamic formulation is correct, we reduce the flexible model to the rigid one under some assumptions. In this paper, we adopt the real-coded genetic algorithm (RGA) to identify all the parameters of the robot and PMSM simultaneously. It is found that the RGA can identify system parameters which are difficult to be measured in practical problems, for examples, the inductance, stator resistance, motor torque constant, damping coefficient of the motor and timing belts. In numerical simulations, vibrations due to flexibility of the timing belts are investigated for the angular displacements, speeds, accelerations of arms, and the horizontal and vertical displacements of the robot. The angular displacements of the robot arm and the translational positions of the robot end are obtained in the numerical simulations and experimental results. From their comparisons, it is demonstrated that identification results of the dynamic model with four independent variables present the better matching with experimental results of the system.     

Planning Formula One race strategies using discrete-event simulation

A discrete-event simulation model that imitates most on-track events, including car failures, passing manoeuvres and pit stops during a Formula One race, is presented. The model is intended for use by a specific team. It will enable decision-makers to plan and evaluate their race strategy, consequently providing them with a possible competitive advantage. The simulation modelling approach presented in this paper captures the mechanical complexities and physical interactions of a race car with its environment through a time-based approach. Model verification and validation are demonstrated using three races from the 2005 season. The application of the model is illustrated by evaluating the race strategies employed by a specific team during these three races.     

Some Optimal Strategies for Bandit Problems with Beta Prior Distributions

A bandit problem with infinitely many Bernoulli arms is considered. The parameters of Bernoulli arms are independent and identically distributed random variables from a common distribution with beta(a, b). We investigate the k-failure strategy which is a modification of Robbins's stay-with-a-winner/switch-on-a-loser strategy and three other strategies proposed recently by Berry et al. (1997, Ann. Statist., 25, 2103–2116). We show that the k-failure strategy performs poorly when b is greater than 1, and the best strategy among the k-failure strategies is the 1-failure strategy when b is less than or equal to 1. Utilizing the formulas derived by Berry et al. (1997), we obtain the asymptotic expected failure rates of these three strategies for beta prior distributions. Numerical estimations and simulations for a variety of beta prior distributions are presented to illustrate the performances of these strategies.     

Multifractal analysis of heartbeat time series in human races

We present a multifractal analysis of heartbeat and heart rate time series in human races. In order to improve the training of athletes, we compare heart rate multifractal behavior in free and constant speed 10,000 m runnings. We analyze also marathon races, free pace 42.195 km running, we compare the first and the second half heartbeat signals to measure the effect of fatigue. We find that freedom for choosing the own pace variation could be the racing condition for keeping good health conditions in an exhausting exercise.     

On the Piano Movers' problem: IV. Various decomposable two-dimensional motion-planning problems

Various special motion-planning problems involving arbitrarily many degrees of freedom are shown to admit relatively simple solutions by techniques based on the connectivity graph approach described by Schwartz and Sharir. The solutions exploit the particularly simple configuration space structure of the robot systems considered. A typical problem is that of planning motions for a 2-dimensional robot system consisting of several arms all jointed at one common endpoint and free to rotate past each other. The algorithm given for solving this problem runs in time O(n^k+4), where k is the number of arms.     

Adapting support vector machine methods for horserace odds prediction

The methodology of Support Vector Machine Methods is adapted in a straightforward manner to enable the analysis of stratified outcomes such as horseracing results. As the strength of the Support Vector Machine approach lies in its apparent ability to produce generalisable models when the dimensionality of the inputs is large relative to the the number of observations, such a methodology would appear to be particularly appropriate in the horseracing context, where often the number of input variables deemed as being potentially relevant can be difficult to reconcile with the scarcity of relevant race results. The methods are applied to a relatively small (200 races in-sample) sample of Australian racing data and tested on 100 races out-of-sample with promising results, especially considering the relatively large number (12) of input variables used.     

A system of grabbing particles related to Galton‐Watson trees

We consider a system of particles with arms that are activated randomly to grab other particles as a toy model for polymerization. We assume that the following two rules are fulfilled: once a particle has been grabbed then it cannot be grabbed again, and an arm cannot grab a particle that belongs to its own cluster. We are interested in the shape of a typical polymer in the situation when the initial number of monomers is large and the numbers of arms of monomers are given by i.i.d. random variables. Our main result is a limit theorem for the empirical distribution of polymers, where limit is expressed in terms of a Galton‐Watson tree. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 2010     

Dynamics of discrete automata

This review deals with the theory and practice of discrete automata, especially with transition processes and hazardous races in such automata.Translated from Itogi Nauki i Tekhniki. Teoriya Veroyatnostei, Matematicheskaya Statistika, Teoreticheskaya Kibernetika, Vol. 14, pp. 81–122, 1977.     

An analysis of combined arms teaming for the Australian defence force

This study presents a quantitative analysis of combined arms teams consisting of three stages. First, an agent-based model of two generic combined arms teams is used to study the relationships between six key attributes of combined arms teams: communication, detection, lethality, mobility, protection and sustainment. Second, a genetic algorithm is applied to evolve strategies for combined arms teams against a static opposing force. Finally, a two-population genetic algorithm is used to coevolve two forces against each other. Games theory is used to analyse the results and to provide advice on the impact of adding, removing and replacing assets or capabilities within the teams. We conclude that diversity and specialization within combined arms teams is essential. Furthermore, no single combined arms team is sufficient to ensure a tactical victory on the battlefield against all potential opponents. A range of different options for constructing combined arms teams is required.     

Parametric shape optimization of biaxial tensile specimen

Common cruciform specimen for biaxial tensile testing of sheet moulding compound, take damage and finally fail in uniaxially loaded areas. When using these specimen, an observation of damage initialization and failure in biaxially loaded areas is, therefore, not possible. In this paper, a parametric shape optimization is described to find a more suitable specimen shape. The parametrization of the specimen is presented. Objective functions are introduced to measure the appropriateness of specimen. A weighted summation transfers the constraint multiobjective optimization problem into a constraint scalar-valued problem. Findings of experiments suggest that a specimen shape with straight, non-tapering arms and slits along the arms is reasonable. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)