Showing papers on "Constant (mathematics) published in 1998"

Blind equalization using the constant modulus criterion: a review

Abstract: This paper provides a tutorial introduction to the constant modulus (CM) criterion for blind fractionally spaced equalizer (FSE) design via a (stochastic) gradient descent algorithm such as the constant modulus algorithm (CMA). The topical decisions utilized in this tutorial can be used to help catalog the emerging literature on the CM criterion and on the behavior of (stochastic) gradient descent algorithms used to minimize it.

Studies in Astronomical Time Series Analysis. V. Bayesian Blocks, a New Method to Analyze Structure in Photon Counting Data*

Abstract: I describe a new time-domain algorithm for detecting localized structures (bursts), revealing pulse shapes, and generally characterizing intensity variations. The input is raw counting data, in any of three forms: time-tagged photon events (TTE), binned counts, or time-to-spill (TTS) data. The output is the most probable segmentation of the observation into time intervals during which the photon arrival rate is perceptibly constant, i.e., has no statistically significant variations. The idea is not that the source is deemed to have this discontinuous, piecewise constant form, rather that such an approximate and generic model is often useful. Since the analysis is based on Bayesian statistics, I call the resulting structures Bayesian blocks. Unlike most, this method does not stipulate time bins—instead the data determine a piecewise constant representation. Therefore the analysis procedure itself does not impose a lower limit to the timescale on which variability can be detected. Locations, amplitudes, and rise and decay times of pulses within a time series can be estimated independent of any pulse-shape model—but only if they do not overlap too much, as deconvolution is not incorporated. The Bayesian blocks method is demonstrated by analyzing pulse structure in BATSE γ-ray data.

The running gravitational couplings

Abstract: We compute the running of the cosmological constant and Newton's constant at sub-Planckian energies, taking into account the effect of quantum fields with any spin between 0 and 2. We find that Newton's constant does not vary appreciably but the cosmological constant can change by many orders of magnitude when one goes from cosmological scales to typical elementary particle scales. In the extreme infrared, zero modes drive a positive cosmological constant to zero.

Boolean Functions With Low Average Sensitivity Depend On Few Coordinates

Abstract: The sensitivity of a point is dist , ie the number of neighbors of the point in the discrete cube on which the value of differs The average sensitivity of is the average of the sensitivity of all points in (This can also be interpreted as the sum of the influences of the variables on , or as a measure of the edge boundary of the set which is the characteristic function of) We show here that if the average sensitivity of is then can be approximated by a function depending on coordinates where is a constant depending only on the accuracy of the approximation but not on We also present a more general version of this theorem, where the sensitivity is measured with respect to a product measure which is not the uniform measure on the cube

Determination of the equilibrium melting temperature of polymer crystals : Linear and nonlinear Hoffman-Weeks extrapolations

Abstract: The applicability of the Hoffman−Weeks (HW) linear extrapolation for the determination of equilibrium melting temperatures of polymers is critically reviewed. In the first paper of this series, it is shown that the linear extrapolation of observed melting temperatures cannot, in general, provide a reliable estimate of the equilibrium melting temperature. A combination of the experimentally observed undercooling dependence of the initial lamellar thickness, l* = C1/ΔT + C2, and the finite lamellar thickness dependent melting temperature depression, as described by the Gibbs−Thomson treatment, provides a venue to the general relationship between the crystallization and observed melting temperatures. It is further shown that, for a constant thickening coefficient, the observed melting temperature must vary nonlinearly with the crystallization temperature. The origin of this nonlinearity lies in the term C2, which is neglected in the classical HW treatment. The principal implications of this study in the cont...

Sequential prediction of individual sequences under general loss functions

Abstract: We consider adaptive sequential prediction of arbitrary binary sequences when the performance is evaluated using a general loss function. The goal is to predict on each individual sequence nearly as well as the best prediction strategy in a given comparison class of (possibly adaptive) prediction strategies, called experts. By using a general loss function, we generalize previous work on universal prediction, forecasting, and data compression. However, here we restrict ourselves to the case when the comparison class is finite. For a given sequence, we define the regret as the total loss on the entire sequence suffered by the adaptive sequential predictor, minus the total loss suffered by the predictor in the comparison class that performs best on that particular sequence. We show that for a large class of loss functions, the minimax regret is either /spl theta/(log N) or /spl Omega/(/spl radic//spl Lscr/log N), depending on the loss function, where N is the number of predictors in the comparison class and/spl Lscr/ is the length of the sequence to be predicted. The former case was shown previously by Vovk (1990); we give a simplified analysis with an explicit closed form for the constant in the minimax regret formula, and give a probabilistic argument that shows this constant is the best possible. Some weak regularity conditions are imposed on the loss function in obtaining these results. We also extend our analysis to the case of predicting arbitrary sequences that take real values in the interval [0,1].

Restricted diffusion and exchange of intracellular water: theoretical modelling and diffusion time dependence of 1H NMR measurements on perfused glial cells.

Abstract: Intracellular diffusion properties of water in F98 glioma cells immobilized in basement membrane gel threads, are investigated with a pulsed-field-gradient spin-echo NMR technique at diffusion times from 6 to 2000 ms and at different temperatures. In extended model calculations the concept of 'restricted intracellular diffusion at permeable boundaries' is described by a combined Tanner-Karger formula. Signal components in a series of ct experiments (constant diffusion time) are separated due to different diffusion properties (Gaussian and restricted diffusion), and physiological as well as morphological cell parameters are extracted from the experimental data. The intracellular apparent diffusion coefficients strongly depend on the diffusion time and are up to two orders of magnitude smaller than the self diffusion constant of water. Propagation lengths are found to be in the range of 4-7 microns. Hereby intracellular signals of compartments with a characteristic diameter could be selected by an appropriate gradient strength. With cg experiments (constant gradient) a mean intracellular residence time for water is determined to be about 50 ms, and the intrinsic intracellular diffusion constant is estimated to 1 x 10(-3)mm2/s. Studying the water diffusion in glial cells provides basic understanding of the intracellular situation in brain tissue and may elucidate possible influences on the changes in the diffusion contrast during ischemic conditions.

On Pricing Barrier Options

Abstract: Pricing and hedging barrier options using a binomial lattice can be quite delicate. If the barrier is not constant, or if there are multiple barriers, then in all likelihood binomial lattices will produce erroneous answers even when a large number of time steps are used. While in some cases the time partitions of the binomial method can be carefully chosen so as to reduce the bias, for many barrier contracts more efficient procedures exist. This article explains how a very simple and extremely efficient trinomial lattice procedure can be used to price and hedge most types of exotic barriers.

Uniqueness of ground states for quasilinear elliptic equations in the exponential case

Abstract: where β is an appropriate positive constant, see [1, 2, 4, 6, 7]. The question of uniqueness of ground states for (1.1) when f(u) has such exponential behavior has not previously been treated; the purpose of this paper is to make a beginning on this problem. Appropriate assumptions on the operator A will be given in the next section. On the other hand, for the nonlinearity f we consider the specific family of functions

Constraints on the effects of locally biased galaxy formation

Abstract: While it is well known that "" biased galaxy formation II can increase the strength of galaxy clustering, it is less clear whether straightforward biasing schemes can change the shape of the galaxy correlation function on large scales. Here we consider "" local II biasing models, in which the galaxy density -eld at d g a point x is a function of the matter-density -eld d at that point: We consider both determin- d g \ f (d). istic biasing, where f is simply a function, and stochastic biasing, in which the galaxy-density is a d g random variable whose distribution depends on the matter density: We show that even when d g \ X(d). this mapping is performed on a highly nonlinear density -eld with a hierarchical correlation structure, the correlation function m is simply scaled up by a constant, as long as m > 1. In stochastic biasing models, the galaxy autocorrelation function behaves exactly as in deterministic models, with (the X(d) mean value of X for a given value of d) taking the role of the deterministic bias function. We extend our results to the power spectrum P(k), showing that for sufficiently small k the e†ect of local biasing is equivalent to the multiplication of P(k) by a constant, with the addition of a constant term. If a cosmo- logical model predicts a large-scale mass correlation function in conNict with the shape of the observed galaxy correlation function, then the model cannot be rescued by appealing to a complicated but local relation between galaxies and mass. Subject headings: galaxies: clusters: general E galaxies: formation E large-scale structure of universe

Variable-feedrate CNC interpolators for constant material removal rates along Pythagorean-hodograph curves

Abstract: An NC system that machines a curved shape at fixed depth of cut experiences time-varying cutting forces due to the ‘curvature effect’—the material removal rate is higher than nominal in concave regions, and lower in convex regions. A curvature-dependent feedrate function that automatically compensates for this effect is formulated, and it is shown that, for Pythagorean-hodograph (PH) curves, the periodic real time computation of reference points in accordance with this function can be analytically reduced to a sequence of root-finding problems for simple monotone functions. Empirical results from an implementation of this variable-feedrate interpolators on an open-architecture CNC milling machine are presented and compared with results from fixed-feedrate interpolators. The curvature-compensated feedrate scheme has important potential applications in ensuring part accuracy and in optimizing part programs consistent with a prescribed accuracy.

Families of K3 surfaces

Abstract: We use automorphic forms to prove that a compact family of Kaehler K3 surfaces with constant Picard number is isotrivial.

Multidimensional analogues of Bohr's theorem on power series

Abstract: Generalizing the classical result of Bohr, we show that if an n-variable power series converges in an n-circular bounded complete domain D and its sum has modulus less than 1, then the sum of the maximum of the moduli of the terms is less than 1 in the homothetic domain r*D, where r = 1 - (2/3)^(1/n). This constant is near to the best one for the domain D = {z: |z_1| + ... + |z_n| < 1}.

Active Implicit Surface for Animation

Abstract: This paper introduces a new model of deformable surfaces designed for animation, which we call active implicit surfaces. The underlying idea is to animate a potential field defined by discrete values stored in a grid, rather than directly animating a surface. This surface, defined as an iso-potential of the field, has the ability to follow a given object using a snake-like strategy. Surface tension and other characteristics such as constant surface area or constant volume may be added to this model. The implicit formulation allows the surface to easily experience topology changes during simulation. We present an optimized implementation: computations are restricted to a close neighborhood around the surface. Applications range from the coating of deformablematerials simulated by particle systems (the surface hides the granularity of the underlying model) to the generation of metamorphosis between shapes that may not have the same topology.

A causal model of radiating stellar collapse

Abstract: We find a simple exact model of radiating stellar collapse, with a shear-free and non-accelerating interior matched to a Vaidya exterior. The heat flux is subject to causal thermodynamics, leading to self-consistent determination of the temperature T. We solve for T exactly when the mean collision time is constant, and perturbatively in a more realistic case of variable . Causal thermodynamics predicts temperature behaviour that can differ significantly from the predictions of non-causal theory. In particular, the causal theory gives a higher central temperature and greater temperature gradient.

A linearly constrained constant modulus approach to blind adaptive multiuser interference suppression

Abstract: This article presents a linearly constrained constant modulus approach for the blind suppression of multiuser interferences in direct-sequence code division multiple access systems. The method performs the same as minimum mean square error receivers and outperforms existing blind approaches because it only requires a rough estimate of the desired user code and timing.

Comments on "The Cramer-Rao lower bounds for signals with constant amplitude and polynomial phase

Abstract: For original paper see IEEE Trans. Signal Processing, vol.39, p.749-52 (March 1991). Different expressions for the Cramer-Rao lower bounds (CRLBs) of constant amplitude polynomial phase signals embedded in white Gaussian noise appear in the literature. The present paper revisits the derivation of the bounds reported by Peleg and Porat (1991) and indicates that the resulting expressions depend on the interval over which the signal is defined. The proper choice of the interval is the one that centers the signal around zero and results in the minimum lower bounds.

New concepts for linear beam theory with arbitrary geometry and loading

Abstract: A new approach is introduced for the analysis and calculation of straight prismatic beams of piecewise constant cross-section under arbitrary loads. This theory can be called “exact” because it determines exact static and kinematic generalized quantities. Moreover, contrary to classical theories, it is not limited to high-aspect ratio (i.e. relatively slender) beams.

Leptonic contribution to the effective electromagnetic coupling constant up to three loops

Abstract: In this note the leptonic contribution to the running of the electromagnetic coupling constant is discussed up to the three-loop level. Special emphasize is put on the evaluation of the double-bubble diagrams.

The inverse approach with simple triangular shell elements for large strain predictions of sheet metal forming parts

Abstract: An efficient algorithm to estimate the large elasto‐plastic strains encountered in thin sheet metal forming parts has been continuously developed by the authors since 1987. The algorithm is based on a finite element discretization of the known final shape. In this paper a new simple triangular shell element with constant membrane and bending strains is presented using discrete Kirchhoff constraints. The expressions of the internal force vector and logarithmic strains through the thickness are derived. Two applications are considered to discuss the validity and efficiency of the numerical procedure.

A sharp bound for an eigenvalue moment of the one-dimensional Schrödinger operator

Abstract: We give a proof of the Lieb-Thirring inequality in the critical case d=1, γ = 1/2, which yields the best possible constant.

Henry's Law Constant for Trichloroethylene between 10 and 95 °C

Abstract: Experimental data on air−water partitioning of organic contaminants at temperatures above 40 °C is extremely scarce. We present Henry's law constants for trichloroethylene (TCE) in water between 10...

Best constants in Sobolev inequalities

Abstract: Let ( M, g ) be a smooth compact Riemannian N -manifold, with N ≥ 2, and let p (1, N ) be real, and H 1 P ( M ) be the standard Sobolev space of order p . By the Sobolev embedding theorem, we have the inclusion H 1 p ( M ) ⊂ L p ⋆ )( M ), where p ⋆ = Np/(N - p ). Classically, this leads to some Sobolev inequality (I p 1 ), and then to some Sobolev inequality (I p p ), where each term in (I p 1 ) is elevated to the power p . Long standing questions were to know if the optimal versions with respect to the first constant of (I p 1 ) and (I p p ) do hold. Such questions received an affirmative answer by Hebey-Vaugon for p = 2. We prove here that, for p > 2 with p 2 N , the optimal version of (I p p ) is false if the scalar curvature of g is positive somewhere. In particular, there exist manifolds for which the optimal versions of (I p 1 ) is true, while the optimal version of (I p p ) is false. Among other results, we prove also that the assumption on the sign of the scalar curvature is minimal by showing that for any p (1, N ), the optimal version of (I p p ) holds on flat tori.

Global one-dimensional optimization using smooth auxiliary functions

Abstract: In this paper new global optimization algorithms are proposed for solving problems where the objective function is univariate and has Lipschitzean first derivatives. To solve this problem, smooth auxiliary functions, which are adaptively improved during the course of the search, are constructed. Three new algorithms are introduced: the first used the exact a priori known Lipschitz constant for derivatives; the second, when this constant is unknown, estimates it during the course of the search and finally, the last method uses neither the exact global Lipschitz constant nor its estimate but instead adaptively estimates the local Lipschitz constants in different sectors of the search region during the course of optimization. Convergence conditions of the methods are investigated from a general viewpoint and some numerical results are also given. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.

Varying-$\alpha $ Theories and Solutions to the Cosmological Problems

Abstract: If the fine structure constant $\alpha =e^2/(\hbar c)$ were to change, then a number of interpretations would be possible, attributing this change either to variations in the electron charge, the dielectric constant of the vacuum, the speed of light, or Planck's constant. All these variations should be operationally equivalent and can be related by changes of standard units. We show how the varying speed of light cosmology recently proposed can be rephrased as a dielectric vacuum theory, similar to the one proposed by Bekenstein. The cosmological problems will therefore also be solved in such a theory.