On the Hamming distances of repeated-root constacyclic codes of length 4ps

Let $p$ be an odd prime, $s$, $m$ be positive integers, $\gamma ,\lambda$ be nonzero elements of the finite field ${\mathbb{F}}_{p^m}$ such that ${\gamma }^{p^s}=\lambda$. In this paper, we show that, for any positive integer $\eta$, the Hamming distances of all repeated-root $\lambda$-constacyclic codes of length $\eta p^s$ can be determined by those of certain simple-root $\gamma$-constacyclic codes of length $\eta$. Using this result, Hamming distances of all constacyclic codes of length $4p^s$ are obtained. As an application, we identify all MDS $\lambda$-constacyclic codes of length $4p^s$.     

Spin-Spin Relaxation Process of 23Na-NMR in Na-Loaded NaY

Abstract

Spin-spin relaxation of ²³Na-NMR is observed by the spin echo method at room temperature for Y-type zeolite loaded with Na metal without hydration. For saturated and no levels of loading, the echo decay is well fitted by single exponential function. T ₂ decreases to be 0.25 times smaller by loading. This decrease of T ₂ is explained semiquantitatively with assuming nuclear dipole-dipole interaction between neighboring Na.     

Distance rendering and perception of nearby virtual sound sources with a near-field filter model

Headphone rendering of nearby virtual sound sources represents to date an open issue in 3-D audio, due to a number of technical challenges and temporal requirements involved in the measurement of individual Head-Related Transfer Functions (HRTFs). In order to tackle this problem, we propose a filter model of near-field effects based on the Distance Variation Function (Kan et al., 2009). Thanks to its simple structure and low order, the model can be applied to any far-field virtual auditory display to yield a realistic and computationally efficient near-field compensation of spectral and binaural effects. The model is subjectively evaluated in two psychophysical experiments where the relative distance of pairs of virtually rendered sound sources is judged. Results show that even though sound intensity overshadows subtler near-field effects when it is available as a cue for distance, the model is capable of offering relative distance information of near lateral virtual sources when intensity cues are removed. Furthermore, performances of the model in relative distance rendering are compared to those of alternative near-field rendering methods available in the literature.     

Controllable 1D Patterned Assembly of Colloidal Quantum Dots on PbSO4 Nanoribbons

Control of the 1D self‐assembly pattern of colloidal quantum dots (QDs) on PbSO₄ nanoribbon (NRb) templates is achieved. The internal structure of the NRbs is investigated by X‐ray diffraction, revealing the isotropic packing of the PbSO₄ nanoclusters in the NRbs. Colloidal QDs in a chloroform/hexane mixture are adsorbed onto the region close to the edges of the NRbs and form a 1D assembly of straight single line or double lines by controlling the amount of OAm. This is the first demonstration of a densely packed 1D self‐assembly of colloidal QDs with a straight line pattern without the use of any molecular bridge or adhesive. Atomic force microscopy measurements of the NRbs show depressions in the phase profile along the width of the NRbs, corresponding to the position of the 1D QD chain. The amount of adsorbed QDs on the NRbs in solution decreases as the addition of OAm increases, suggesting that additional OAm prevents interaction between the QDs and NRbs but facilitates the uniform adsorption of the 1D assembly. The low‐dimensional self‐assembly of colloidal QDs in this study opens up the possibility for the creation of anisotropically assembled QD superstructures.     

Linear codes associated to skew-symmetric determinantal varieties

In this article we consider linear codes coming from skew-symmetric determinantal varieties, which are defined by the vanishing of minors of a certain fixed size in the space of skew-symmetric matrices. In odd characteristic, the minimum distances of these codes are determined and a recursive formula for the weight of a general codeword in these codes is given.     

A bound on the Wasserstein-2 distance between linear combinations of independent random variables

We provide a bound on a distance between finitely supported elements and general elements of the unit sphere of ${?}^2\left({\mathbb{N}}^1\right)$. We use this bound to estimate the Wasserstein-2 distance between random variables represented by linear combinations of independent random variables. Our results are expressed in terms of a discrepancy measure related to Nourdin–Peccati’s Malliavin–Stein method. The main application is towards the computation of quantitative rates of convergence to elements of the second Wiener chaos. In particular, we explicit these rates for non-central asymptotic of sequences of quadratic forms and the behavior of the generalized Rosenblatt process at extreme critical exponent.     

MOEPGA: A novel method to detect protein complexes in yeast protein–protein interaction networks based on MultiObjective Evolutionary Programming Genetic Algorithm

The identification of protein complexes in protein–protein interaction (PPI) networks has greatly advanced our understanding of biological organisms. Existing computational methods to detect protein complexes are usually based on specific network topological properties of PPI networks. However, due to the inherent complexity of the network structures, the identification of protein complexes may not be fully addressed by using single network topological property. In this study, we propose a novel MultiObjective Evolutionary Programming Genetic Algorithm (MOEPGA) which integrates multiple network topological features to detect biologically meaningful protein complexes. Our approach first systematically analyzes the multiobjective problem in terms of identifying protein complexes from PPI networks, and then constructs the objective function of the iterative algorithm based on three common topological properties of protein complexes from the benchmark dataset, finally we describe our algorithm, which mainly consists of three steps, population initialization, subgraph mutation and subgraph selection operation. To show the utility of our method, we compared MOEPGA with several state-of-the-art algorithms on two yeast PPI datasets. The experiment results demonstrate that the proposed method can not only find more protein complexes but also achieve higher accuracy in terms of fscore. Moreover, our approach can cover a certain number of proteins in the input PPI network in terms of the normalized clustering score. Taken together, our method can serve as a powerful framework to detect protein complexes in yeast PPI networks, thereby facilitating the identification of the underlying biological functions.