Related papers: Phase relations and pyramids
We establish a general framework to study the rate of convergence of a Euler type approximation scheme with decreasing time steps to the invariant measure, for a general class of stochastic systems. The error is measured in general…
If two signals are phase synchronous then the respective Fourier component at each spectral band should exhibit certain properties. In a pair of artificially generated phase synchronous signals the phase difference at each frequency band…
The optimum interval method for finding an upper limit of a one-dimensionally distributed signal in the presence of an unknown background is extended to the case of high statistics. There is also some discussion of how the method can be…
Let $(X_n)_{n\in \mathbb{N}}$ be a sequence of i.i.d. random variables with distribution $\mathbb P(X_1=1)=\mathbb P(X_1=-1)=1/2$. Let $F(\sigma)=\sum_{n=1}^\infty X_nn^{-\sigma}$. We prove that the following holds almost surely…
We investigate the averages of Dedekind sums over rational numbers in the set $$\mathscr{F}_\alpha(Q):=\{\, {v}/{w}\in \mathbb{Q}: 0<w\leq Q\,\}\cap [0, \alpha)$$ for fixed $\alpha\leq 1/2$. In previous work, we obtained asymptotics for…
One of the most commonly used methods for forming confidence intervals for statistical inference is the empirical bootstrap, which is especially expedient when the limiting distribution of the estimator is unknown. However, despite its…
We \emph{propose} a new \emph{invariant} for a \emph{cycle} of an \emph{interval map} $f:[0,1] \to [0,1]$, called its \emph{unfolding number}.
We use the notion of universal extension in a linear abelian category to study extensions of variations of mixed Hodge structure and convergent and overconvergent isocrystals. The results we obtain apply, for example, to prove the exactness…
We address the problem of uncertainty propagation in the discrete Fourier transform by modeling the fast Fourier transform as a factor graph. Building on this representation, we propose an efficient framework for approximate Bayesian…
The averaging theory has been extensively employed for studying periodic solutions of smooth and nonsmooth differential systems. Here, we extend the averaging theory for studying periodic solutions a class of regularly perturbed…
Oscillators are ubiquitous in nature, and usually associated with the existence of an asymptotic phase that governs the long-term dynamics of the oscillator. % We show that asymptotic phase can be estimated using a carefully chosen series…
The study of finite approximations of probability measures has a long history. In (Xu and Berger, 2017), the authors focus on constrained finite approximations and, in particular, uniform ones in dimension $d=1$. The present paper gives an…
Unitary Fourier transform lies at the core of the multitudinous computational and metrological algorithms. Here we show experimentally how the unitary Fourier transform-based phase estimation protocol, used namely in quantum metrology, can…
We develop a method for calculating Riemann sums using Fourier analysis.
We prove essentially optimal $L^p(\mathbb{R})$-estimates for variational variants of the maximal Fourier multiplier operators considered by Bourgain in his work on pointwise convergence of polynomial ergodic averages. As a corollary of our…
Triangular distributions are a well-known class of distributions that are often used as an elementary example of a probability model. Maximum likelihood estimation of the mode parameter of the triangular distribution over the unit interval…
We introduced a new continued fraction expansions in our previous paper. For these expansions, we show formulae of probability about incomplete quotients. Furthermore, we prove the existence of invariant measures with respect to the…
We study orthogonality relations for Fourier frequencies and complex exponentials in Hilbert spaces $L^2(\mu)$ with measures $\mu$ arising from iterated function systems (IFS). This includes equilibrium measures in complex dynamics.…
In this paper, we consider the problem of constructing confidence interval for the correlation coefficient in a bivariate normal distribution. For this problem, we found fifteen approaches in literatures. Also, we have proposed a…
This is a sequel to the paper "Frobenius amplitude and strong vanishing theorems for vector bundles" (math.AG/0202129). We introduce a more elementary variant of the notion of F-amplitude from the earlier paper which we call amplitude. This…