Optimal precision in the presence of uncertainty

We consider the problem of achieving coordinated actions in a real-time distributed system. In particular, we consider how closely (in terms of real time) processors can be guaranteed to perform a particular action, in a system where message transmission is guaranteed, but there is some uncertainty in message transmission time. We present an algorithm to achieve optimal precision in arbitrary networks. In networks where clocks run at the rate of real time, the optimal precision achievable in a network is exactly how tightly clocks can be guaranteed to be synchronized.     

Localized sampling in the presence of noise

When the sampled values are corrupted by noise, error estimates for the localized sampling series for approximating a band-limited function are obtained. The result provides error bounds for practical cases including error caused by average sampling, jitter error and amplitude error.     

Non-analytic hypoellipticity in the presence of symplecticity

Here we construct non-analytic solutions to a class of hypoelliptic operators with symplectic characteristic set and in the form of a sum of squares of real analytic vector fields.

     

Advancing in the presence of a demon

We study a parameter that contains approximate counting, i.e., the level reached after n random increments, driven by geometric probabilities, and insertion costs for tries as special cases. We are able to compute all moments of this parameter in a semi-automatic fashion. This is another showcase of the machinery developed in an earlier paper of these authors. Roughly speaking, it works when the underlying distributions are distributed according to the Gumbel distribution, or something similar. G. Louchard visited this center in June 2006 and thanks for its hospitality.     

Super-efficiency DEA in the presence of infeasibility

It is well known that super-efficiency data envelopment analysis (DEA) approach can be infeasible under the condition of variable returns to scale (VRS). By extending of the work of Chen (2005), the current study develops a two-stage process for calculating super-efficiency scores regardless whether the standard VRS super-efficiency mode is feasible or not. The proposed approach examines whether the standard VRS super-efficiency DEA model is infeasible. When the model is feasible, our approach yields super-efficiency scores that are identical to those arising from the original model. For efficient DMUs that are infeasible under the super-efficiency model, our approach yields super-efficiency scores that characterize input savings and/or output surpluses. The current study also shows that infeasibility may imply that an efficient DMU does not exhibit super-efficiency in inputs or outputs. When infeasibility occurs, it can be necessary that (i) both inputs and outputs be decreased to reach the frontier formed by the remaining DMUs under the input-orientation and (ii) both inputs and outputs be increased to reach the frontier formed by the remaining DMUs under the output-orientation. The newly developed approach is illustrated with numerical examples.     

Simulated annealing in the presence of noise

In many practical optimization problems, evaluation of a solution is subject to noise, e.g., due to stochastic simulations or measuring errors. Therefore, heuristics are needed that are capable of handling such noise. This paper first reviews the state-of-the-art in applying simulated annealing to noisy optimization problems. Then, two new algorithmic variants are proposed: an improved version of stochastic annealing that allows for arbitrary annealing schedules, and a new approach called simulated annealing in noisy environments (SANE). The latter integrates ideas from statistical sequential selection in order to reduce the number of samples required for making an acceptance decision with sufficient statistical confidence. Finally, SANE is shown to significantly outperform other state-of-the-art simulated annealing techniques on a stochastic travelling salesperson problem.     

Factorial orthogonality in the presence of covariates

Summary The present paper obtains necessary and sufficient conditions for factorial orthogonality in the presence of covariates. In particular, when interactions are absent, combinatorial characterizations of the conditions, as natural generalizations of the well-known equal and proportional frequency criteria, have been derived.     

水星近日点进动的建模与摄动解

本文针对水星近日点进动现象 ,结合广义相对论建立了奇摄动微分方程模型 ,并运用多重尺度法 ,求出了一般行星进动问题的摄动解 ,从而很好的解释了水星进动之谜和一般行星的进动问题 .     

Composition methods in the presence of small parameters

We derive numerical methods for arbitrary small perturbations of exactly solvable differential equations. The methods, based in one instance on Gaussian quadrature, are symplectic if the system is Hamiltonian and are asymptotically more accurate than previously known methods.     

Ruin probability in the presence of risky investments

We consider an insurance company in the case when the premium rate is a bounded non-negative random function _ct$c_t$ and the capital of the insurance company is invested in a risky asset whose price follows a geometric Brownian motion with mean return a   and volatility σ>0$\sigma >0$. If β?2a/σ²-1>0$\beta ?2a/{\sigma }^2-1>0$ we find exact the asymptotic upper and lower bounds for the ruin probability Ψ(u)$\Psi (u)$ as the initial endowment u   tends to infinity, i.e. we show that _C*u^-β?Ψ(u)?C^*u^-β$C_{*}{u}^{-\beta }?\Psi (u)?C^{*}{u}^{-\beta }$ for sufficiently large u  . Moreover if _ct=c^*e^γt$c_t=c^{*}{\mathrm{e}}^{\gamma t}$ with γ?0$\gamma ?0$ we find the exact asymptotics of the ruin probability, namely Ψ(u)∼u^-β$\Psi (u)\sim u^{-\beta }$. If β?0$\beta ?0$, we show that Ψ(u)=1$\Psi (u)=1$ for any u?0$u?0$.     

Bayes factors in the presence of population stratification

Hidden population stratification (PS) is a main concern in the analysis of case-control genetic association studies. All methods to correct for hidden PS have been focused on classical hypothesis testing, and cannot be directly applied to Bayesian analysis. In this paper, to study the impact and the correction of hidden PS on Bayes factor (BF), we use a simple approximation of BF in terms of the maximum likelihood estimates of the odds ratio (OR) and its asymptotic variance. One advantage is that the commonly used principal components analysis method with a large panel of null markers scanned from existing genome-wide association studies can be directly employed to correct for hidden PS in estimating the OR and its asymptotic variance, through which a correction to BF for hidden PS can be achieved. Using simulations, we examine the impact of ignoring hidden PS on BF and show that the proposed method yields an appropriate correction in Bayesian analysis.     

Mean estimation in the presence of change points

In this study we address the problem of the mean estimation of the IBEX-35 index stock quotes in the presence of change points. We rely on nonparametric regression methods for detecting and estimating changes points, and for estimating the discontinuous regression function. Model-assisted and model-based estimators and their jump-preserving counterparts are used for mean estimation and an empirical comparison between the methods is performed.     

On equilibrium in the presence of friction I

A known equilibrium rule that refers to rigid bodies possibly subject to some external constraintsK _(e), and that is essential in many cases where friction is present, is shown to give unacceptable results in some cases that can be carried out experimentally. Then the same rule is replaced by a new one which is more complex. When the bearings that carry outK _(e) are kinematically independent in a suitable sense, the new rule is proved to simplify into the old one. The afore-mentioned cases can be treated satisfactorily by means of another simple rule. However this rule is shown to be too weak to treat other (simple) cases.     

Optimum design in the presence of parametric uncertainty

A new class of optimal design problems that incorporates environmental uncertainty is formulated and related to worst-case design, minimax objective design, and game theory. A numerical solution technique is developed and applied to a weapon allocation problem, a structural design problem with an infinite family of load conditions, and a vibration isolator design problem with a band of excitation frequencies.     

Nonlinear programming methods in the presence of noise

The problem of minimizing a nonlinear function with nonlinear constraints when the values of the objective, the constraints and their gradients have errors, is studied. This noise may be due to the stochastic nature of the problem or to numerical error.Various previously proposed methods are reviewed. Generally, the minimization algorithms involve methods of subgradient optimization, with the constraints introduced through penalty, Lagrange, or extended Lagrange functions. Probabilistic convergence theorems are obtained. Finally, an algorithm to solve the general convex (nondifferentiable) programming problem with noise is proposed.Originally written for presentation at the 1976 Budapest Symposium on Mathematical Programming.     

Optimal take-off trajectories in the presence of windshear

This paper is concerned with optimal flight trajectories in the presence of windshear. With particular reference to take-off, eight fundamental optimization problems [Problems (P1)–(P8)] are formulated under the assumptions that the power setting is held at the maximum value and that the airplane is controlled through the angle of attack.Problems (P1)–(P3) are least-square problems of the Bolza type. Problems (P4)–(P8) are minimax problems of the Chebyshev type, which can be converted into Bolza problems through suitable transformations. These problems are solved employing the dual sequential gradient-restoration algorithm (DSGRA) for optimal control problems.Numerical results are obtained for a large number of combinations of performance indexes, boundary conditions, windshear models, and windshear intensities. However, for the sake of brevity, the presentation of this paper is restricted to Problem (P6), minimax h, and Problem (P7), minimax . Inequality constraints are imposed on the angle of attack and the time derivative of the angle of attack.The following conclusions are reached: (i) optimal trajectories are considerably superior to constant-angle-of-attack trajectories; (ii) optimal trajectories achieve minimum velocity at about the time when the windshear ends; (iii) optimal trajectories can be found which transfer an aircraft from a quasi-steady condition to a quasi-steady condition through a windshear; (iv) as the boundary conditions are relaxed, a higher final altitude can be achieved, albeit at the expense of a considerable velocity loss; (v) among the optimal trajectories investigated, those solving Problem (P7) are to be preferred, because the altitude distribution exhibits a monotonic behavior; in addition, for boundary conditions BC2 and BC3, the peak angle of attack is below the maximum permissible value; (vi) moderate windshears and relatively severe windshears are survivable employing an optimized flight strategy; however, extremely severe windshears are not survivable, even employing an optimized flight strategy; and (vii) the sequential gradient-restoration algorithm (SGRA), employed in its dual form (DSGRA), has proven to be a powerful algorithm for solving the problem of the optimal flight trajectories in a windshear.Portions of this paper were presented at the AIAA Atmospheric Flight Mechanics Conference, Snowmass, Colorado, August 19–21, 1985. The authors are indebted to Boeing Commercial Aircraft Company, Seattle, Washington and to Pratt and Whitney Aircraft, East Hartford, Connecticut for supplying some of the technical data pertaining to this study.This research was supported by NASA-Langley Research Center, Grant No. NAG-1-516. The authors are indebted to Dr. R. L. Bowles, NASA-Langley Research Center, Hampton, Virginia, for helpful discussions.This paper is based in part on Refs. 1–5.