相关论文: Period Lengths for Iterated Functions

We present a simple formula for the expected number of inversions in a permutation of size $n$ obtained by applying $t$ random (not necessarily adjacent) transpositions to the identity permutation. More general, for any finite irreducible…

Let $\{X_n;n\ge 1\}$ be a sequence of independent and identically distributed random variables on a sub-linear expectation space $(\Omega,\mathscr{H},\widehat{\mathbb E})$, $S_n=X_1+\ldots+X_n$. We consider the moments of $\max_{n\ge…

We consider first-order linear systems of ordinary differential equations with periodic coefficients. Supposing that right-hand sides of equations are not known and subjected to some quadratic restrictions, we obtain optimal, in certain…

A novel algorithm for the computation of the quadratic numerical range is presented and exemplified yielding much better results in less time compared to the random vector sampling method. Furthermore, a bound on the probability for the…

The asymmetric switch process is a binary stochastic process that alternates between the values one and minus one, where the distributions of the time in these states may differ. Two versions of the process are considered: a non-stationary…

A general method for estimating the approximation numbers of composition operators on $\Ht$, using finite-dimensional model subspaces, is studied and applied in the case when the symbol of the operator maps the unit disc to a domain whose…

Using kicked differential equations of motion with derivatives of noninteger orders, we obtain generalizations of the dissipative standard map. The main property of these generalized maps, which are called fractional maps, is long-term…

Consider a random graph G in G(n,p) and the graph property: G contains a copy of a specific graph H. (Note: H depends on n; a motivating example: H is a Hamiltonian cycle.) Let q be the minimal value for which the expected number of copies…

We investigate decomposable combinatorial labeled structures more fully, focusing on the exp-log class of type a=1 or 1/2. For instance, the modal length of the second longest cycle in a random n-permutation is (0.2350...)n, whereas the…

The problem of reconstructing a sequence of independent and identically distributed symbols from a set of equal size, consecutive, fragments, as well as a dependent reference sequence, is considered. First, in the regime in which the…

We study fast approximation of integrals with respect to stationary probability measures associated to iterated functions systems on the unit interval. We provide an algorithm for approximating the integrals under certain conditions on the…

Iterative phase retrieval algorithms typically employ projections onto constraint subspaces to recover the unknown phases in the Fourier transform of an image, or, in the case of x-ray crystallography, the electron density of a molecule.…

Permutation entropy measures the complexity of deterministic time series via a data symbolic quantization consisting of rank vectors called ordinal patterns or just permutations. The reasons for the increasing popularity of this entropy in…

Record numbers are basic statistics in random walks, whose deviation principles are not very clear so far. In this paper, the asymptotic probabilities of large and moderate deviations for numbers of weak records in right continuous or left…

Fluctuations of observables as functions of time, or "fluctuation patterns", are studied in a chaotic microscopically reversible system that has irreversibly reached a nonequilibrium stationary state. Supposing that during a certain, long…

We analyze the asymptotic states in the partially ordered phase of a system of globally coupled logistic maps. We confirm that, regardless of initial conditions, these states consist of a few clusters, and they properly belong in the…

Oversubscribed treatments are often allocated using randomized waiting lists. Applicants are ranked randomly, and treatment offers are made following that ranking until all seats are filled. To estimate causal effects, researchers often…

Periods are defined as integrals of semialgebraic functions defined over the rationals. Periods form a countable ring not much is known about. Examples are given by taking the antiderivative of a power series which is algebraic over the…

Based on a review of anecdotal beliefs, we explored patterns of track-sequencing within professional music albums. We found that songs with high levels of valence, energy and loudness are more likely to be positioned at the beginning of…

We construct a time-consistent sublinear expectation in the setting of volatility uncertainty. This mapping extends Peng's G-expectation by allowing the range of the volatility uncertainty to be stochastic. Our construction is purely…