Showing papers on "Constant (mathematics) published in 1995"

Sample mean based index policies by O(log n) regret for the multi-armed bandit problem

Abstract: We consider a non-Bayesian infinite horizon version of the multi-armed bandit problem with the objective of designing simple policies whose regret increases sldwly with time. In their seminal work on this problem, Lai and Robbins had obtained a O(logn) lower bound on the regret with a constant that depends on the KullbackLeibler number. They also constructed policies for some specific families of probability distributions (including exponential families) that achieved the lower bound. In this paper we construct index policies that depend on the rewards from each arm only through their sample mean. These policies are computationally much simpler and are also applicable much more generally. They achieve a O(logn) regret with a constant that is also based on the Kullback-Leibler number. This constant turns out to be optimal for one-parameter exponential families; however, in general it is derived from the optimal one via a 'contraction' principle. Our results rely entirely on a few key lemmas from the theory of large deviations.

Computer simulation of liquid/liquid interfaces. I. Theory and application to octane/water

Abstract: Statistical ensembles for simulating liquid interfaces at constant pressure and/or surface tension are examined, and equations of motion for molecular dynamics are obtained by various extensions of the Andersen extended system approach. Valid ensembles include: constant normal pressure and surface area; constant tangential pressure and length normal to the interface; constant volume and surface tension; and constant normal pressure and surface tension. Simulations at 293 K and 1 atm normal pressure show consistent results with each other and with a simulation carried out at constant volume and energy. Calculated surface tensions for octane/water (61.5 dyn/cm), octane/vacuum (20.4 dyn/cm) and water/vacuum (70.2 dyn/cm) are in very good agreement with experiment (51.6, 21.7, and 72.8 dyn/cm, respectively). The practical consequences of simulating with two other approaches commonly used for isotropic systems are demonstrated on octane/water: applying equal normal and tangential pressures leads to an instabil...

Modeling of a constant Q; methodology and algorithm for an efficient and optimally inexpensive viscoelastic technique

Abstract: Linear anelastic phenomena in wave propagation problems can be well modeled through a viscoelastic mechanical model consisting of standard linear solids. In this paper we present a method for modeling of constant Q as a function of frequency based on an explicit closed formula for calculation of the parameter fields. Several standard linear solids connected in parallel can be tuned through a single parameter to yield an excellent constant Q approximation. The proposed method enables substantial savings in computations and memory requirements. Experiments show that the new method also yields higher accuracy in the modeling of Q than, e.g., the Pade approximant method.

Uniqueness of complete spacelike hypersurfaces of constant mean curvature in generalized Robertson-Walker spacetimes

Abstract: A new technique is introduced in order to solve the following question:When is a complete spacelike hypersurface of constant mean curvature in a generalized Robertson-Walker spacetime totally umbilical and a slice? (Generalized Robertson-Walker spacetimes extend classical Robertson-Walker ones to include the cases in which the fiber has not constant sectional curvature.) First, we determine when this hypersurface must be compact. Then, all these compact hypersurfaces in (necessarily spatially closed) spacetimes are shown to be totally umbilical and, except in very exceptional cases, slices. This leads to proof of a new Bernstein-type result. The power of the introduced tools is also shown by reproving and extending several known results.

Ruin estimates under interest force

Abstract: In the present paper we discuss infinite time ruin probabilities in continuous time in a compound Poisson process with a constant premium rate and a constant interest rate. We discuss equations for the ruin probability as well as approximations and upper and lower bounds. Two special cases are treated in more detail: the case with zero initial reserve, and the case with exponential claim sizes.

Influence of Temperature Variations on Rate of Development in Insects: Analysis of Case Studies from Entomological Literature

Abstract: Case studies on development-time data collected at constant and varying temperatures in a number of insects have been analyzed in a comparative manner to investigate the effects of temperature variations on rate of development. Sources of experimental errors are many and are not always adequately controlled. For statistical analysis, the more common problems include the assumption of a linear relationship between temperature and development rate over the whole temperature range and extrapolation or subjective vertical cutoff of the rate function in rate summation for varying temperatures. Development-time data of 26 species were selected for the analysis. For each species, the expected development time under each varying temperature regime was estimated by integrating constant temperature development rates over the 24-h varying temperature cycle. These estimates were then compared with the development times observed under the corresponding varying temperature regimes, and the significance of the differences was evaluated. The results as a whole suggest that the differences in development times between constant and varying temperatures could usually be accounted for by the effect of rate summation based on the curvilinear relationship between temperature and rate of development. The possible physiological mechanisms that act in addition to the rate-summation effect are briefly discussed. Finally, the need for more extensive and detailed investigations in this area of study is indicated.

Modelling Inflation in Australia

Abstract: This paper develops an empirically constant, data-coherent, error correction model for inflation in Australia. The level of consumer prices is a mark-up over domestic and import costs, with adjustments for dynamics and relative aggregate demand. We address issues of cointegration, general to specific modelling, dynamic specification, model evaluation and testing, parameter constancy, and exogeneity. We also test this model against existing models of Australian prices: this model encompasses (but is not encompassed by) the existing models.

Polynomial bounds on the number of resonances for some complete spaces of constant negative curvature near infinity

Abstract: Guillope,L. and M. Zworski, Polynomial bounds on the number of resonances for some complete spaces of constant negative curvature near infinity, Asymptotic Analysis 11 (1995) 1-22. Let X be a conforrnally compact n-dimensional manifold with constant negative curvature -1 near infinity. The resolvent (ilsCn 1 s»-I, Re s > n 1, of the Laplacian on X extends to a meromorphic family of operators on C and its poles are called resonances or scattering poles. If NxCr) is the number of resonances in a disc of radius r we prove the following upper bound: NxCr) :( Crn+! + C.

Defective units in a continuous review (s, Q) system

Abstract: This paper considers the number of defective items in a lot to be a random variable and derives a modified (s, Q) model with stochastic demand and constant lead time. The paper develops explicit results for the case of exponential and uniform demand during lead time when the number of defective items in a lot follows a binomial process. It also investigates the effect of lower setup costs on the operating characteristics of the model. A numerical example is given and sensitivity analysis is performed.

Some Formulae for a New Type of Path-Dependent Option

Abstract: In this paper we present an explicit form of the distribution function of the occupation time of a Brownian motion with a constant drift (if there is no drift, this is the well-known arc-sine law). We also define the $\alpha$-percentile of the stock price and give an explicit form of the distribution function of this random variable. Using this explicit distribution, we calculate the price of a new type of path-dependent option, called the $\alpha$-percentile option. This option was first introduced by Miura and is based on order statistics.

Self-adjusting pressure relief support system and methodology

Abstract: A pressure relief support system (10) utilizes a self-adjusting approach to maintaining generally constant pressure in fluid support bladders (70-76). A constant force, such as from a constant force linear spring (106, 108) or from a counterweight system (238), is applied directed to a fluid support bladder (182) or to a reservoir in fluid communication with such bladder. Plural self-adjusting arrangements may be provided in a single device for fabricating a support body with sectionalized support. Such arrangements may be incorporated into mattress support systems (68) or into seating arrangements (538) or other alternative uses. By appropriately selecting system components, such as the amount of the constant force applied, the original volume of fluid to which the force is applied, and the reservoir size, pressure dispersion for a patient or supported object of any type may be controlled at a predetermined generally constant point.

Constant-magnetic-field effect in Néel relaxation of single-domain ferromagnetic particles.

Abstract: The relaxation behavior of an assembly of noninteracting single-domain ferromagnetic particles in the presence of a constant magnetic field is studied by solving the corresponding Fokker-Planck equation. The analysis is performed by first converting that equation into a hierarchy of differential-recurrence relations by expanding the solution in Legendre polynomials. The spectrum of eigenvalues and their associated amplitudes is then determined by matrix methods where all the desired physical quantities such as the magnetization correlation time and complex magnetic susceptibility may be computed numerically. In order to ensure the accuracy of the results obtained this solution is compared with an exact solution derived in terms of matrix continued fractions. It is shown that the conventional assumption in the theory of superparamagnetism, that except in the very early stages of relaxation to equilibrium the only appreciable time constant is the one associated with the smallest nonvanishing eigenvalue, is no longer true when an applied constant magnetic field exceeds a certain critical value. The breakdown of this assumption manifests itself in (a) a dramatically large deviation of the magnetization correlation time (area under the curve of the decay of the magnetization) from the inverse of the lowest eigenvalue, and (b) in the presence of relatively strong high-frequency modes superimposed on the N\'eel one usually assigned to the lowest eigenvalue. The results are compared with available experimental data.

On convergence of posterior distributions

Abstract: Z.A general (asymptotic) theory of estimation was developed by Ibragimov and Has’minskii under certain conditions on the normalized likelihood ratios. In an earlier work, the present authors studied the limiting behaviour of the posterior distributions under the general setup of Ibragimov and Has’minskii. In particular, they obtained a necessary condition for the convergence of a suitably centered (and normalized) posterior to a constant limit in terms of the limiting likelihood ratio process. In this paper, it is shown that this condition is also sufficient to imply the posterior convergence. Some related results are also presented.

Averaging correlated data

Abstract: The problem of averaging strongly correlated data is addressed for the case that the exact correlation pattern is unknown. A procedure is proposed to estimate the effective size of the correlations from the data themselves and to take them properly into account when forming the average. The properties of the procedure are illustrated by using it for averaging measurements of the strong coupling constant and QCD colour-factor ratios.

Curves of Constant Precession

Abstract: 1. INTRODUCTION. Given initial position and direction, the flight-path of a ship in Euclidean space is completely determined by how much it turns and how much it twists at each odometer reading. This is an intuitive interpretation of the Fundamental Theorem for Space Curves, which states that curvature K and torsion , as functions of arclength s, determine a space curve uniquely up to rigid motion. This statement of the Fundamental Theorem ([14], §1-8) should be tempered with the reservations expressed by Nomizu [12] and Wong & Lai [15]. Given a parametric space curve, there are well-known formulae for the arclength, curvature, and torsion (as functions of the parameter). Given two functions of one parameter (potentially curvature and torsion parametrized by arc-length) one might like to find a parametrized space curve for which the two functions are the curvature and torsion. This activity, called "solving natural equations" ([14], §1-10), is generally achieved by solving Riccati equations like dw/ds = -iz/2 iKW + i7W /2. Although the solution generally exists, it usually cannot be obtained explicitly. Euler [6] found explicit integral formulae for plane curves (where z - O) through direct geometric analysis. Hoppe [9] developed a general method for solving the natural equations for space curves by solving Riccati equations through a complicated sequence of integral transformations. He digressed to obtain formulae for the tangent, normal, and binormal indicatrices for general helices and essentially for curves of constant precession. Enneper [5] obtained explicit closed-form solutions for helices on revolved conic sections through direct geometric analysis. A curve of constant precession is defined by the property that as the curve is traversed with unit speed, its centrode revolves about a fixed axis with constant angle and constant speed. In this paper we obtain an arclength-parametrized closed-form solution of the natural equations for curves of constant precession through direct geometric analysis. As part of this analysis, we obtain a new theorem for curves of constant precession analogous with Lancret's Theorem for general helices. We provide the first rendering of a curve of constant precession. We also note for the first time that curves of constant precession lie on circular hyperboloids of one sheet and have closure conditions that are simply related to their arclength, curvature, and torsion. These are 3-type curves, except one family of closed 2-type curves (when Z = 4,u; see [2], [3], and [1]). Given a closed C3 curve in space, it is rather obvious that the curvature and torsion functions will be periodic functions of the arclength, with period equal the total arclength. This is a necessary condition but, as the circular helices (K and z both constant) show, not a sufficient condition that integral curves be closed. Efimov [4] and Fenchel [7] independently formulated The Closed Curve Problem. Find (explicit) necessary and sufficient conditions that determine when, given two periodic functions K(S) and z(s) with the same period L, the integral curve is closed.

Evaluation of boundary element methods for the EEG forward problem: effect of linear interpolation

Abstract: The authors implement the approach for solving the boundary integral equation for the electroencephalography (EEG) forward problem proposed by de Munck (1992), in which the electric potential varies linearly across each plane triangle of the mesh. Previous solutions have assumed the potential is constant across an element. The authors calculate the electric potential and systematically investigate the effect of different mesh choices and dipole locations by using a three concentric sphere head model for which there is an analytic solution. Implementing the linear interpolation approximation results in errors that are approximately half those of the same mesh when the potential is assumed to be constant, and provides a reliable method for solving the problem. >

Analytical Models for One‐Dimensional Virus Transport in Saturated Porous Media

Abstract: Analytical solutions to two mathematical models for virus transport in one-dimensional homogeneous, saturated porous media are presented, for constant flux as well as constant concentration boundary conditions, accounting for first-order inactivation of suspended and adsorbed (or filtered) viruses with different inactivation constants. Two processes for virus attachment onto the solid matrix are considered. The first process is the nonequilibrium reversible adsorption, which is applicable to viruses behaving as solutes; whereas, the second is the filtration process, which is suitable for viruses behaving as colloids. Since the governing transport equations corresponding to each physical process have identical mathematical forms, only one generalized closed-form analytical solution is developed by Laplace transform techniques. The impact of the model parameters on virus transport is examined. An empirical relation between inactivation rate and subsurface temperature is employed to investigate the effect of temperature on virus transport. It is shown that the differences between the two boundary conditions are minimized at advection-dominated transport conditions.

Analysis of Event Histories

Abstract: Event histories are generated by so-called failure-time processes and take the following form. The dependent variable—for example, some social state—is discrete or continuous. Over time it evolves as follows. For finite periods of time (from one calendar date to another) it stays constant at a given value. At a later date, which is a random variable, the dependent variable jumps to a new value. The process evolves in this manner from the calendar date, when one change occurs, to a later date, when another change occurs. Between the dates of the changes, the dependent variable stays constant.

Variable steps for reversible integration methods

Abstract: Conventional variable-step implementation of symplectic or reversible integration methods destroy the symplectic or reversible structure of the system. We show that to preserve the symplectic structure of a method the step size has to be kept almost constant. For reversible methods variable steps are possible but the step size has to be equal for “reflected” steps. We demonstrate possible ways to construct reversible variable step size methods. Numerical experiments show that for the Kepler problem the new methods perform better than conventional variable step size methods or symplectic constant step size methods. In particular they exhibit linear growth of the global error (as symplectic methods with constant step size).

Connected sum constructions for constant scalar curvature metrics

Abstract: We give a general procedure for gluing together possibly noncompact manifolds of constant scalar curvature which satisfy an extra nondegeneracy hypothesis. Our aim is to provide a simple paradigm for making "analytic" connected sums. In particular, we can easily construct complete metrics of constant positive scalar curvature on the complement of certain configurations of an even number of points on the sphere, which is a special case of Schoen's [S1] well-known, difficult construction. Applications of this construction produces metrics with prescribed asymptotics. In particular, we produce metrics with cylindrical ends, the simplest type of asymptotic behaviour. Solutions on the complement of an infinite number of points are also constructed by an iteration of our construction.

Controlling chaos in unidimensional maps using constant feedback.

Abstract: We demonstrate that a constant feedback can control chaotic oscillations in one-dimensional discrete maps. This is a simple method of controlling chaos as the feedback signal does not require a priori knowledge of the dynamics of the system and it generates the desired behavior by simply varying the strength of the feedback. We illustrate this method with an application to the quadratic and exponential logistic maps.