Exponential Stabilisation of Continuous-time Periodic Stochastic Systems by Feedback Control Based on Periodic Discrete-time Observations

Since Mao in 2013 discretised the system observations for stabilisation problem of hybrid SDEs (stochastic differential equations with Markovian switching) by feedback control, the study of this topic using a constant observation frequency has been further developed. However, time-varying observation frequencies have not been considered. Particularly, an observational more efficient way is to consider the time-varying property of the system and observe a periodic SDE system at the periodic time-varying frequencies. This study investigates how to stabilise a periodic hybrid SDE by a periodic feedback control, based on periodic discrete-time observations. This study provides sufficient conditions under which the controlled system can achieve pth moment exponential stability for p > 1 and almost sure exponential stability. Lyapunov's method and inequalities are main tools for derivation and analysis. The existence of observation interval sequences is verified and one way of its calculation is provided. Finally, an example is given for illustration. Their new techniques not only reduce observational cost by reducing observation frequency dramatically but also offer flexibility on system observation settings. This study allows readers to set observation frequencies according to their needs to some extent

Coding for interactive communication correcting insertions and deletions

We consider the question of interactive communication, in which two remote parties perform a computation while their communication channel is (adversarially) noisy. We extend here the discussion into a more general and stronger class of noise, namely, we allow the channel to perform insertions and deletions of symbols. These types of errors may bring the parties "out of sync", so that there is no consensus regarding the current round of the protocol. In this more general noise model, we obtain the first interactive coding scheme that has a constant rate and resists noise rates of up to $1/18-\varepsilon$. To this end we develop a novel primitive we name edit distance tree code. The edit distance tree code is designed to replace the Hamming distance constraints in Schulman's tree codes (STOC 93), with a stronger edit distance requirement. However, the straightforward generalization of tree codes to edit distance does not seem to yield a primitive that suffices for communication in the presence of synchronization problems. Giving the "right" definition of edit distance tree codes is a main conceptual contribution of this work

Variable Precision Rough Set Approximations in Concept Lattice

The notions of variable precision rough set and concept lattice are can be shared by a basic notion, which is the definability of a set of objects based on a set of properties. The two theories of rough set and concept lattice can be compared, combined and applied to each other based on definability. Based on introducing the definitions of variable precision rough set and concept lattice, this paper shows that any extension of a concept in concept lattice is an equivalence class of variable precision rough set. After that, we present a definition of lower and upper approximations in concept lattice and generate the lower and upper approximations concept of concept lattice. Afterwards, we discuss the properties of the new lower and upper approximations. Finally, an example is given to show the validity of the properties that the lower and upper approximations have

Assessing the Jeans Anisotropic Multi-Gaussian Expansion method with the Illustris simulation

We assess the effectiveness of the Jeans-Anisotropic-MGE (JAM) technique with a state-of-the-art cosmological hydrodynamic simulation, the Illustris project. We perform JAM modelling on 1413 simulated galaxies with stellar mass M^* > 10^{10}M_{sun}, and construct an axisymmetric dynamical model for each galaxy. Combined with a Markov Chain Monte Carlo (MCMC) simulation, we recover the projected root-mean-square velocity (V_rms) field of the stellar component, and investigate constraints on the stellar mass-to-light ratio, M^*/L, and the fraction of dark matter f_{DM} within 2.5 effective radii (R_e). We find that the enclosed total mass within 2.5 R_e is well constrained to within 10%. However, there is a degeneracy between the dark matter and stellar components with correspondingly larger individual errors. The 1 sigma scatter in the recovered M^*/L is 30-40% of the true value. The accuracy of the recovery of M^*/L depends on the triaxial shape of a galaxy. There is no significant bias for oblate galaxies, while for prolate galaxies the JAM-recovered stellar mass is on average 18% higher than the input values. We also find that higher image resolutions alleviate the dark matter and stellar mass degeneracy and yield systematically better parameter recovery.Comment: 14 pages, 12 figure

Role of Extractable and Residual Organic Matter Fractions on Sorption of Phenanthrene in Sediments

Two sediments were demineralized and sequentially fractionated into extracted fractions [free lipid (FL), bound lipid (BL) and lignin (LG)] and residual fractions [free lipid free (FLF), bound lipid free (BLF) and lignin free (LGF)]. The sorption isotherms of phenanthrene (Phen) were examined to evaluate the importance of various fractions on sorption. A lignin extraction procedure was for the first time applied to separate the lignin or degraded lignin fraction from sediment organic matter (SOM). The extracted LG was similar to model lignin in terms of elemental ratios and sorption behavior. FL and LG fractions were quite important, as their contents were much higher than reported values. Phen sorption for the extracted fractions was almost linear, whereas that for the residual fractions was nonlinear, especially for LGF with n 0.56-0.63. As the different organic fractions were removed sequentially, sorption energy distribution on the residual sediment organic matter (SOM) became more heterogeneous. In addition, increasing sorption capacity for the residual fractions, except for BLF with its high polarity, suggested that more sorption sites on the SOM matrix became accessible to Phen. The sorption capacity for LGF was comparable to that of condensed SOM. The residual fraction LGF generally controlled the overall sorption at low Phen concentration, but the extractable fraction FL surpassed the former fraction at high Phen concentration, demonstrating the importance of condensed SUM in the sorption of hydrophobic organic compounds (HOCs) in sediments. (c) 2012 Elsevier Ltd. All rights reserved

A Randomized Algorithm for Single-Source Shortest Path on Undirected Real-Weighted Graphs

In undirected graphs with real non-negative weights, we give a new randomized algorithm for the single-source shortest path (SSSP) problem with running time $O(m\sqrt{\log n \cdot \log\log n})$ in the comparison-addition model. This is the first algorithm to break the $O(m+n\log n)$ time bound for real-weighted sparse graphs by Dijkstra's algorithm with Fibonacci heaps. Previous undirected non-negative SSSP algorithms give time bound of $O(m\alpha(m,n)+\min\{n\log n, n\log\log r\})$ in comparison-addition model, where $\alpha$ is the inverse-Ackermann function and $r$ is the ratio of the maximum-to-minimum edge weight [Pettie & Ramachandran 2005], and linear time for integer edge weights in RAM model [Thorup 1999]. Note that there is a proposed complexity lower bound of $\Omega(m+\min\{n\log n, n\log\log r\})$ for hierarchy-based algorithms for undirected real-weighted SSSP [Pettie & Ramachandran 2005], but our algorithm does not obey the properties required for that lower bound. As a non-hierarchy-based approach, our algorithm shows great advantage with much simpler structure, and is much easier to implement.Comment: 17 page

9-Ethyl-9H-carbazole-3-carbaldehyde

The title mol­ecule, C15H13NO, approximates a planar conformation except for the alkyl chain (ethyl group) bonded to the N atom with a maximum deviation from the least-squares plane through the 15 planar atoms of 0.120 (2) Å for the O atom. The distance of the formyl O atom from the plane of the carbazole ring is 0.227 (2) Å. The N—C bond lengths in the central ring are significantly different, reflecting the electron-withdrawing properties of the aldehyde group. As a consequence, charge transfer may occur from the carbazole N atom to the substituted benzene ring

Gender differences in outcomes in people with schizophrenia in rural China: 14-year follow-up study

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A multichannel thiacalix[4]arene-based fluorescent chemosensor for Zn²⁺, F⁻ ions and imaging of living cells

The fluorescent sensor (3) based on the 1,3-alternate conformation of the thiacalix[4]arene bearing the coumarin fluorophore, appended via an imino group, has been synthesised. Sensing properties were evaluated in terms of a colorimetric and fluorescence sensor for Zn 2+ and F - . High selectivity and excellent sensitivity were exhibited, and off-on optical behaviour in different media was observed. All changes were visible to the naked eye, whilst the presence of the Zn 2+ and F - induces fluorescence enhancement and the formation of a 1:1 complex with 3. In addition, 3 exhibits low cytotoxicity and good cell permeability and can readily be employed for assessing the change of intracellular levels of Zn 2+ and F -