Asymptotic coverage probabilities of bootstrap percentile confidence intervals for constrained parameters

The asymptotic behaviour of the commonly used bootstrap percentile confidence interval is investigated when the parameters are subject to linear inequality constraints. We concentrate on the important one- and two-sample problems with data generated from general parametric distributions in the natural exponential family. The focus of this paper is on quantifying the coverage probabilities of the parametric bootstrap percentile confidence intervals, in particular their limiting behaviour near boundaries. We propose a local asymptotic framework to study this subtle coverage behaviour. Under this framework, we discover that when the true parameters are on, or close to, the restriction boundary, the asymptotic coverage probabilities can always exceed the nominal level in the one-sample case; however, they can be, remarkably, both under and over the nominal level in the two-sample case. Using illustrative examples, we show that the results provide theoretical justification and guidance on applying the bootstrap percentile method to constrained inference problems.Comment: 22 pages, 6 figure

Uniform lower bound for the least common multiple of a polynomial sequence

Let $n$ be a positive integer and $f(x)$ be a polynomial with nonnegative integer coefficients. We prove that ${\rm lcm}_{\lceil n/2\rceil \le i\le n} \{f(i)\}\ge 2^n$ except that $f(x)=x$ and $n=1, 2, 3, 4, 6$ and that $f(x)=x^s$ with $s\ge 2$ being an integer and $n=1$, where $\lceil n/2\rceil$ denotes the smallest integer which is not less than $n/2$. This improves and extends the lower bounds obtained by Nair in 1982, Farhi in 2007 and Oon in 2013.Comment: 6 pages. To appear in Comptes Rendus Mathematiqu

The elementary symmetric functions of a reciprocal polynomial sequence

Erd\"{o}s and Niven proved in 1946 that for any positive integers $m$ and $d$, there are at most finitely many integers $n$ for which at least one of the elementary symmetric functions of $1/m, 1/(m+d), ..., 1/(m+(n-1)d)$ are integers. Recently, Wang and Hong refined this result by showing that if $n\geq 4$, then none of the elementary symmetric functions of $1/m, 1/(m+d), ..., 1/(m+(n-1)d)$ is an integer for any positive integers $m$ and $d$. Let $f$ be a polynomial of degree at least $2$ and of nonnegative integer coefficients. In this paper, we show that none of the elementary symmetric functions of $1/f(1), 1/f(2), ..., 1/f(n)$ is an integer except for $f(x)=x^{m}$ with $m\geq2$ being an integer and $n=1$.Comment: 4 pages. To appear in Comptes Rendus Mathematiqu

A novel fault location method for a cross-bonded hv cable system based on sheath current monitoring

In order to improve the practice in the operation and maintenance of high voltage (HV) cables, this paper proposes a fault location method based on the monitoring of cable sheath currents for use in cross-bonded HV cable systems. This method first analyzes the power–frequency component of the sheath current, which can be acquired at cable terminals and cable link boxes, using a Fast Fourier Transform (FFT). The cable segment where a fault occurs can be localized by the phase difference between the sheath currents at the two ends of the cable segment, because current would flow in the opposite direction towards the two ends of the cable segment with fault. Conversely, in other healthy cable segments of the same circuit, sheath currents would flow in the same direction. The exact fault position can then be located via electromagnetic time reversal (EMTR) analysis of the fault transients of the sheath current. The sheath currents have been simulated and analyzed by assuming a single-phase short-circuit fault to occur in every cable segment of a selected cross-bonded high voltage cable circuit. The sheath current monitoring system has been implemented in a 110 kV cable circuit in China. Results indicate that the proposed method is feasible and effective in location of HV cable short circuit faults

Overexpression of an isoform of AML1 in acute leukemia and its potential role in leukemogenesis

AML1/RUNX1 is a critical transcription factor in hematopoietic cell differentiation and proliferation. From the _AML1_ gene, at least three isoforms, _AML1a_, _AML1b_ and _AML1c_, are produced through alternative splicing. AML1a interferes with the function of AML1b/1c, which are often called AML1. In the current study, we found a higher expression level of _AML1a_ in ALL patients in comparison to the controls. Additionally, AML1a represses transcription from promotor of macrophage-colony simulating factor receptor (M-CSFR) mediated by AML1b, indicating that AML1a antagonized the effect of AML1b. In order to investigate the role of _AML1a_ in hematopoiesis and leukemogenesis _in vivo_, bone marrow mononuclear cells (BMMNCs) from mice were transduced with AML1a and transplanted into lethally irradiated mice, which develop lymphoblastic leukemia after transplantation. Taken together, these results indicate that overexpression of AML1a may be an important contributing factor to leukemogenesis

On compression rate of quantum autoencoders: Control design, numerical and experimental realization

Quantum autoencoders which aim at compressing quantum information in a low-dimensional latent space lie in the heart of automatic data compression in the field of quantum information. In this paper, we establish an upper bound of the compression rate for a given quantum autoencoder and present a learning control approach for training the autoencoder to achieve the maximal compression rate. The upper bound of the compression rate is theoretically proven using eigen-decomposition and matrix differentiation, which is determined by the eigenvalues of the density matrix representation of the input states. Numerical results on 2-qubit and 3-qubit systems are presented to demonstrate how to train the quantum autoencoder to achieve the theoretically maximal compression, and the training performance using different machine learning algorithms is compared. Experimental results of a quantum autoencoder using quantum optical systems are illustrated for compressing two 2-qubit states into two 1-qubit states