A fast algorithm for constructing balanced binary search trees

We suggest a new non-recursive algorithm for constructing a binary search tree given an array of numbers. The algorithm has $O(N)$ time and $O(1)$ memory complexity if the given array of $N$ numbers is sorted. The resulting tree is of minimal height and can be transformed to a complete binary search tree (retaining minimal height) with $O(\log N)$ time and $O(1)$ memory. The algorithm allows simple and effective parallelization

On the rate of Poisson approximation to partial sum processes

We investigate approximation of a Bernoulli partial sum process to the accompanying Poisson process in the non-i.i.d. case. The rate of closeness is studied in terms of the minimal distance in probability

A Pulse Wave Velocity Based Method to Assess the Mean Arterial Blood Pressure Limits of Autoregulation in Peripheral Arteries

Background: Constant blood flow despite changes in blood pressure, a phenomenon called autoregulation, has been demonstrated for various organ systems. We hypothesized that by changing hydrostatic pressures in peripheral arteries, we can establish these limits of autoregulation in peripheral arteries based on local pulse wave velocity (PWV).Methods: Electrocardiogram and plethysmograph waveforms were recorded at the left and right index fingers in 18 healthy volunteers. Each subject changed their left arm position, keeping the right arm stationary. Pulse arrival times (PAT) at both fingers were measured and used to calculate PWV. We calculated ΔPAT (ΔPWV), the differences between the left and right PATs (PWVs), and compared them to the respective calculated blood pressure at the left index fingertip to derive the limits of autoregulation.Results: ΔPAT decreased and ΔPWV increased exponentially at low blood pressures in the fingertip up to a blood pressure of 70 mmHg, after which changes in ΔPAT and ΔPWV were minimal. The empirically chosen 20 mmHg window (75–95 mmHg) was confirmed to be within the autoregulatory limit (slope = 0.097, p = 0.56). ΔPAT and ΔPWV within a 20 mmHg moving window were not significantly different from the respective data points within the control 75–95 mmHg window when the pressure at the fingertip was between 56 and 110 mmHg for ΔPAT and between 57 and 112 mmHg for ΔPWV.Conclusions: Changes in hydrostatic pressure due to changes in arm position significantly affect peripheral arterial stiffness as assessed by ΔPAT and ΔPWV, allowing us to estimate peripheral autoregulation limits based on PWV

Universal Local Linear Kernel Estimators in Nonparametric Regression

New local linear estimators are proposed for a wide class of nonparametric regression models. The estimators are uniformly consistent regardless of satisfying traditional conditions of dependence of design elements. The estimators are the solutions of a specially weighted least-squares method. The design can be fixed or random and does not need to meet classical regularity or independence conditions. As an application, several estimators are constructed for the mean of dense functional data. The theoretical results of the study are illustrated by simulations. An example of processing real medical data from the epidemiological cross-sectional study ESSE-RF is included. We compare the new estimators with the estimators best known for such studies