A convergence rate for approximate solutions of Fredholm integral equations of the first kind

We study the convergence rate for solving Fredholm integral equations of the first kind by using the well known collocation method. By constructing an approximate interpolation neural network, we deduce the convergence rate of the approximate solution by only using continuous functions as basis functions for the Fredholm integral equations of the first kind. This convergence rate is bounded in terms of a modulus of smoothness.     

Interest rate futures: estimation of volatility parameters in an arbitrage-free framework

Hedging interest rate exposures using interest rate futures contracts requires some knowledge of the volatility function of the interest rates. Use of historical data as well as interest rate options like caps and swaptions to estimate this volatility function have been proposed in the literature. In this paper the interest rate futures price is modelled within an arbitrage-free framework for a volatility function which includes a stochastic variable, the instantaneous spot interest rate. The resulting system is expressed in a state space form which is solved using an extended Kalman filter. The residual diagnostics indicate suitability of the model and the bootstrap resampling technique is used to obtain small sample properties of the parameters of the volatility function.     

Determining an adequate probe separation for estimating the arrival rate in an M/D/1 queue using single-packet probing

We present a technique to estimate the arrival rate from delay measurements, acquired using single-packet probing. With practical applications in mind, we investigate a lower bound on the value of probe separation, to obtain a satisfactory estimate in a fixed amount of time. This leads to a problem: how long does it take for an M/D/1 queue to converge to its steady state as a function of the load? We examine this problem using three independent approaches: the time until the autocovariance of the transient workload process becomes negligible; the time it takes for the first transient moment of the workload process to get close to its stationary limit; and the convergence rate of the transient workload distribution to stationarity. These approaches yield different, yet strikingly similar results. We conclude with a recommendation for the probe separation threshold, and a practical approach to obtaining an arrival rate estimate using single-packet probing.     

直接资本化法中自有资本收益率的算法探讨

在分析我国房地产自有资本收益率操作中所存在问题的基础上,论述了自有资本收益率的实质是自有资金直接资本化率,并在房地产持有期小于抵押贷款期以及房地产持有期和土地批租年限相同的两种情况下,推导出了与土地有限期使用制度相适应的房地产资本化率和自有资本收益率的计算方法,提出了利用债务保障比率的取值范围检验资本化率合理性的基本公式.     

An application of braid group theory to the finite time dead-core rate

We consider the dead-core problem for the semilinear heat equation with strong absorption and with positive boundary values in a ball. We investigate the dead-core rate, i.e. the rate at which the solution reaches its first zero. We first show, as in the one-dimensional case, that the dead-core rate is always faster than the self-similar rate. By using some special solutions and the braid group theory, we then derive the exact dead-core rates for a large class of initial data.     

Plastic flow in very low temperature regime within annular micropores

The rate of deformation for glassy (amorphous) matter confined in microscopic domain at very low temperature regime was investigated using a rate-state-dependent model considering the shear thinning behavior which means, once material being subjected to high shear rates, the viscosity diminishes with increasing shear rate. The preliminary results show that there might be the enhanced rate of deformation and (shear) yield stress due to the almost vanishing viscosity in micropores subjected to some surface conditions: The relatively larger roughness (compared to the macroscopic domain) inside micropores and the slip. As the pore size decreases, the surface-to-volume ratio increases and therefore, surface roughness will greatly affect the (plastic) flow in micropores. By using the boundary perturbation method, we obtained a class of microscopic fields for the rate of deformation and yield stress at low temperature regime with the presumed small wavy roughness distributed along the walls of an annular micropore.     

Large deviations and the generalized processor sharing scheduling for a multiple-queue system

We establish asymptotic upper and lower bounds on the asymptotic decay rate of per-session queue length tail distributions for a multiple-queue system where a single constant rate server services the queues using the generalized processor sharing (GPS) scheduling discipline. In the special case where there are only two queues, the upper and lower bounds match, yielding the optimal bound proved in [15]. The dynamics of bandwidth sharing of a multiple-queue GPS system is captured using the notion of partial feasible sets, and the bounds are obtained using the sample-path large deviation principle. The results have implications in call admission control for high-speed communication networks. This revised version was published online in June 2006 with corrections to the Cover Date.     

Plastic flow in very low temperature regime within annular micropores

The rate of deformation for glassy (amorphous) matter confined in microscopic domain at very low temperature regime was investigated using a rate-state-dependent model considering the shear thinning behavior which means, once material being subjected to high shear rates, the viscosity diminishes with increasing shear rate. The preliminary results show that there might be the enhanced rate of deformation and (shear) yield stress due to the almost vanishing viscosity in micropores subjected to some surface conditions: The relatively larger roughness (compared to the macroscopic domain) inside micropores and the slip. As the pore size decreases, the surface-to-volume ratio increases and therefore, surface roughness will greatly affect the (plastic) flow in micropores. By using the boundary perturbation method, we obtained a class of microscopic fields for the rate of deformation and yield stress at low temperature regime with the presumed small wavy roughness distributed along the walls of an annular micropore.     

Energy decay rate for a coupled hyperbolic system with nonlinear damping

In this paper we investigate the energy decay rate for the solution of a coupled hyperbolic system. The explicit energy decay rate is established by using multiplier techniques and constructing a suitable energy functional.     

带时变增长率、迁移率、波动率的种群变动模型与生物防治最小成本的确定方法

用回归方法确定种群数量增长率、迁移率与波动率的最优拟合曲线,求解带时变漂移串与波动串的It(?)随机微分方程,建立有迁移行为的害虫种群的数量变动模型,进而给出确定生物防治最小成本的计算方法,指出了确定模型中参数的统计方法。     

Nonlinear,finite deformation,finite element analysis

The roles of the consistent Jacobian matrix and the material tangent moduli, which are used in nonlinear incremental finite deformation mechanics problems solved using the finite element method, are emphasized in this paper, and demonstrated using the commercial software ABAQUS standard. In doing so, the necessity for correctly employing user material subroutines to solve nonlinear problems involving large deformation and/or large rotation is clarified. Starting with the rate form of the principle of virtual work, the derivations of the material tangent moduli, the consistent Jacobian matrix, the stress/strain measures, and the objective stress rates are discussed and clarified. The difference between the consistent Jacobian matrix (which, in the ABAQUS UMAT user material subroutine is referred to as DDSDDE) and the material tangent moduli (C^e) needed for the stress update is pointed out and emphasized in this paper. While the former is derived based on the Jaumann rate of the Kirchhoff stress, the latter is derived using the Jaumann rate of the Cauchy stress. Understanding the difference between these two objective stress rates is crucial for correctly implementing a constitutive model, especially a rate form constitutive relation, and for ensuring fast convergence. Specifically, the implementation requires the stresses to be updated correctly. For this, the strains must be computed directly from the deformation gradient and corresponding strain measure (for a total form model). Alternatively, the material tangent moduli derived from the corresponding Jaumann rate of the Cauchy stress of the constitutive relation (for a rate form model) should be used. Given that this requirement is satisfied, the consistent Jacobian matrix only influences the rate of convergence. Its derivation should be based on the Jaumann rate of the Kirchhoff stress to ensure fast convergence; however, the use of a different objective stress rate may also be possible. The error associated with energy conservation and work-conjugacy due to the use of the Jaumann objective stress rate in ABAQUS nonlinear incremental analysis is viewed as a consequence of the implementation of a constitutive model that violates these requirements.     

失访和迄今存活病人的生存率

癌症临床工作的关键指标是生存率，尤其是那些失访和迄今存活病人即终检（也称删失）病例的生存率。后者尚无估计方法。本文提出生存率终检模型，利用该模型从整个样本生存率分离出终检病例生存率，并按二项分布理论构造其方差和置信限。其统计学意义是它揭示出生存率的终检成份和非终检成份，临床意义是它实现了对失访和迄今存活病人生存率的估计。与以往的笼统生存率估计相比，这显然提高了一步。附有工作实例描述其临床应用     

用单位变化率定义和认识费雪效应公式

通过分析利用连续复利解释费雪效应公式中存在的问题,利用单位变化率概念给出了费雪效应关系新的表达式,并证明了所给公式与通常教材中的费雪效应公式等价.     

A cyclical square-root model for the term structure of interest rates

This paper presents a cyclical square-root model for the term structure of interest rates assuming that the spot rate converges to a certain time-dependent long-term level. This model incorporates the fact that the interest rate volatility depends on the interest rate level and specifies the mean reversion level and the interest rate volatility using harmonic oscillators. In this way, we incorporate a good deal of flexibility and provide a high analytical tractability. Under these assumptions, we compute closed-form expressions for the values of different fixed income and interest rate derivatives. Finally, we analyze the empirical performance of the cyclical model versus that proposed in Cox et al. (1985) and show that it outperforms this benchmark, providing a better fitting to market data.     

Managing uncertainty in call centres using Poisson mixtures

We model a call centre as a queueing model with Poisson arrivals having an unknown varying arrival rate. We show how to compute prediction intervals for the arrival rate, and use the Erlang formula for the waiting time to compute the consequences for the occupancy level of the call centre. We compare it to the current practice of using a point estimate of the arrival rate (assumed constant) as forecast. Copyright © 2001 John Wiley & Sons, Ltd.     

Nonparametric Estimation of Hazard Rate Under the Constraint of Monotonicity

This article shows how to smoothly “monotonize” standard kernel estimators of hazard rate, using bootstrap weights. Our method takes a variety of forms, depending on choice of kernel estimator and on the distance function used to define a certain constrained optimization problem. We confine attention to a particularly simple kernel approach and explore a range of distance functions. It is straightforward to reduce “quadratic” inequality constraints to “linear” equality constraints, and so our method may be implemented using little more than conventional Newton–Raphson iteration. Thus, the necessary computational techniques are very familiar to statisticians. We show both numerically and theoretically that monotonicity, in either direction, can generally be imposed on a kernel hazard rate estimator regardless of the monotonicity or otherwise of the true hazard rate. The case of censored data is easily accommodated. Our methods have straightforward extension to the problem of testing for monotonicity of hazard rate, where the distance function plays the role of a test statistic.     

含有非线性梯度项的退化抛物方程解的爆破率估计

利用尺度变换方法和抛物方程的正则性估计,证明了一类含有非线性梯度项的退化多孔介质方程解的爆破率,它是由扩散项和边界流相互作用决定的．与以前有关的结论比较,有趣的发现是,次数不超过2的梯度项不会影响解的爆破率．     

Oberbeck convection through vertical porous stratum

Natural convection through a vertical porous stratum is investigated both analytically and numerically. Analytical solutions are obtained using a perturbation method valid for small values of buoyancy parameterN and the numerical solutions are obtained using Runge-Kutta-Gill method. It is shown that analytical solutions are valid forN < 1 and several features of the effect of large values ofN are reported. The combined effects of increase in the values of temperature difference between the plates and the permeability parameter on velocity, temperature, mass flow rate and the rate of heat transfer are reported. It is shown that higher temperature difference is required to achieve the mass flow rate in a porous medium equivalent to that of viscous flow.     

Efficient algorithms for buffer space allocation

This paper describes efficient algorithms for determining how buffer space should be allocated in a flow line. We analyze two problems: a primal problem, which minimizes total buffer space subject to a production rate constraint; and a dual problem, which maximizes production rate subject to a total buffer space constraint. The dual problem is solved by means of a gradient method, and the primal problem is solved using the dual solution. Numerical results are presented. Profit optimization problems are natural generalizations of the primal and dual problems, and we show how they can be solved using essentially the same algorithms.     

Accelerating autonomous learning by using heuristic selection of actions

This paper investigates how to make improved action selection for online policy learning in robotic scenarios using reinforcement learning (RL) algorithms. Since finding control policies using any RL algorithm can be very time consuming, we propose to combine RL algorithms with heuristic functions for selecting promising actions during the learning process. With this aim, we investigate the use of heuristics for increasing the rate of convergence of RL algorithms and contribute with a new learning algorithm, Heuristically Accelerated Q-learning (HAQL), which incorporates heuristics for action selection to the Q-Learning algorithm. Experimental results on robot navigation show that the use of even very simple heuristic functions results in significant performance enhancement of the learning rate.