The author introduces a new class of step functions and defines them in terms of the Rademacher functions. Two complete systems of orthogonal slant step functions are constructed and their characteristics are analyzed...
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The author introduces a new class of step functions and defines them in terms of the Rademacher functions. Two complete systems of orthogonal slant step functions are constructed and their characteristics are analyzed. The relationship between the basis functions of these systems and the system of the Walsh functions is established and their orthonormality is proved. It is shown that the proposed systems of slant step functions can be efficiently used to code video signal.
We establish sufficient conditions under which the harmonic measure distribution functions h(n) of a sequence of domains D-n converge pointwise to the distribution function h of the limiting domain D, at all points of...
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We establish sufficient conditions under which the harmonic measure distribution functions h(n) of a sequence of domains D-n converge pointwise to the distribution function h of the limiting domain D, at all points of continuity of h. In the case of a model example, we establish this convergence of the distribution functions. Here, the value of the function h(r) gives the harmonic measure of the part of the boundary of the domain that lies within distance r of a fixed basepoint in the domain, thus relating the geometry of the domain to the behaviour of Brownian motion in the domain.
An important task in analysing time series of the current passed by a single ion channel is the restoration of the true signal from the noisy recording. Hodgson [1] devised a reversible jump Markov chain Monte Carlo (...
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An important task in analysing time series of the current passed by a single ion channel is the restoration of the true signal from the noisy recording. Hodgson [1] devised a reversible jump Markov chain Monte Carlo (MCMC) algorithm to implement fully Bayesian single channel analysis. Noiseless ion channel signals are typically modelled as step functions with a discrete number of levels. As the number of steps is unknown, the joint posterior distribution under the Bayesian paradigm exhibits variable dimensionality, necessitating the use of reversible jump MCMC (Green [2]). This paper addresses the task of summarising posterior knowledge about the step function representing the noiseless channel signal, using Bayesian decision theory and the ideas of Rue [3]. We compute Bayes estimates of the true step function under a selection of loss functions from the same family.
In a recent work J. Sci. Comput. 16, 479 - 524 (2001), B. Despres and F. Lagoutiere introduced a new approach to derive numerical schemes for hyperbolic conservation laws. Its most important feature is the ability to ...
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In a recent work J. Sci. Comput. 16, 479 - 524 (2001), B. Despres and F. Lagoutiere introduced a new approach to derive numerical schemes for hyperbolic conservation laws. Its most important feature is the ability to perform an exact resolution for a single traveling discontinuity. However their scheme is not entropy satisfying and can keep nonentropic discontinuities. The purpose of our work is, starting from the previous one, to introduce a new class of schemes for monotone scalar conservation laws, that satisfy an entropy inequality, while still resolving exactly the single traveling shocks or contact discontinuities. We show that it is then possible to have an excellent resolution of rarefaction waves, and also to avoid the undesirable staircase effect. In practice, our numerical experiments show second-order accuracy.
SIR—In a recent letter to this journal [1], Drs. Shlaes and Moellering expressed concern regarding the US Food and Drug Administration's (FDA) reassessment of noninferiority limits, also called “deltas,” for cl...
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SIR—In a recent letter to this journal [1], Drs. Shlaes and Moellering expressed concern regarding the US Food and Drug Administration's (FDA) reassessment of noninferiority limits, also called “deltas,” for clinical trials of antimicrobial agents. We would like to clarify some of the issues raised in their letter and emphasize that the FDA has not decided upon recommending a 10% delta for all clinical trials of antimicrobial agents. Prior to initiation of a clinical trial that compares a test drug with a control agent that has known efficacy, an investigator selects an equivalence or noninferiority margin, sometimes called “delta.” This margin is the maximum degree of inferiority of the test drug to the control drug that the clinical trial will attempt to exclude statistically. After completion of a trial, the prespecified delta is compared with the lower bound of the 95% CI around the difference between the point estimates of the efficacies of the agents in the trial. One usually obtains the difference between the point estimates by subtracting the point estimate of the efficacy of the control agent from that of the test drug. For example, if the point estimates of the efficacies of a test drug and a control drug are 82% and 90%, respectively, then the difference between the point estimates is -8%. To assess the variability around this estimate, one can then calculate a 95% CI around this difference. In our example, let us assume that the calculated 95% CI around the difference between the efficacy of the test drug and that of the control drug ranges from –14% to +3%, which contains the -8% point estimate. This means that one has 95% confidence that the true difference in efficacy between the test drug and the control drug may be anywhere from 14% less effective for the test drug to 3% more effective for the test drug, as compared with the control agent. If the prespecified delta for this trial were chosen to be -15%, then the test drug would meet the statistical
It is shown that every cliquish function f mapping a pseudometrizable space X into a separable metric space Y can be expressed as the quasiuniform limit of a sequence of quasicontinuous functions fk.
It is shown that every cliquish function f mapping a pseudometrizable space X into a separable metric space Y can be expressed as the quasiuniform limit of a sequence of quasicontinuous functions fk.
This note concerns the generalized Riemann integrals using free tagged subdivisions, and leading to absolute integration theories. We first establish an approximation theorem by step functions. This result will allow ...
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This note concerns the generalized Riemann integrals using free tagged subdivisions, and leading to absolute integration theories. We first establish an approximation theorem by step functions. This result will allow us to define a natural notion of equi-integrability in Lebesgue space L1. Some applications, as a new caracterization of compact parts of L1, are presented.
We present a Bayesian method of ion channel analysis and apply it to a simulated data set. An alternating renewal process prior is assigned to the signal, and an autoregressive process is fitted to the noise. After ch...
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We present a Bayesian method of ion channel analysis and apply it to a simulated data set. An alternating renewal process prior is assigned to the signal, and an autoregressive process is fitted to the noise. After choosing model hyperconstants to yield 'uninformative' priors on the parameters, the joint posterior distribution is computed by using the reversible jump Markov chain Monte Carte method. A novel form of simulated tempering is used to improve the mixing of the original sampler.
In this paper nearly unstable AR( p) processes (in other words, models with characteristic roots near the unit circle) are studied. Our main aim is to describe the asymptotic behavior of the least-squares estimators o...
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In this paper nearly unstable AR( p) processes (in other words, models with characteristic roots near the unit circle) are studied. Our main aim is to describe the asymptotic behavior of the least-squares estimators of the coefficients. A convergence result is presented for the general complex-valued case, The limit distribution is given by the help of some continuous time AR processes. We apply the results for real-valued nearly unstable AR(p) models. In this case the limit distribution can be identified with the maximum likelihood estimator of the coefficients of the corresponding continuous time AR processes.
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