Weighted Shift Matrices: Unitary Equivalence, Reducibility and Numerical Ranges

An $n$-by-$n$ ($n\ge 3$) weighted shift matrix $A$ is one of the form [{array}{cccc}0 & a_1 & & & 0 & \ddots & & & \ddots & a_{n-1} a_n & & & 0{array}], where the $a_j$'s, called the weights of $A$, are complex numbers. Assume that all $a_j$'s are nonzero and $B$ is an $n$-by-$n$ weighted shift matrix with weights $b_1,..., b_n$. We show that $B$ is unitarily equivalent to $A$ if and only if $b_1... b_n=a_1...a_n$ and, for some fixed $k$, $1\le k \le n$, $|b_j| = |a_{k+j}|$ ($a_{n+j}\equiv a_j$) for all $j$. Next, we show that $A$ is reducible if and only if $A$ has periodic weights, that is, for some fixed $k$, $1\le k \le \lfloor n/2\rfloor$, $n$ is divisible by $k$, and $|a_j|=|a_{k+j}|$ for all $1\le j\le n-k$. Finally, we prove that $A$ and $B$ have the same numerical range if and only if $a_1...a_n=b_1...b_n$ and $S_r(|a_1|^2,..., |a_n|^2)=S_r(|b_1|^2,..., |b_n|^2)$ for all $1\le r\le \lfloor n/2\rfloor$, where $S_r$'s are the circularly symmetric functions.Comment: 27 page

Unifying AoI Minimization and Remote Estimation — Optimal Sensor/Controller Coordination with Random Two-way Delay

The ubiquitous usage of communication networks in modern sensing and control applications has kindled new interests on the timing coordination between sensors and controllers, i.e., how to use the waiting time\u27\u27 judicially to improve the system performance. Contrary to the common belief that a zero-wait policy is optimal, Sun et al. showed that a controller can strictly improve the data freshness, the so-called Age-of-Information (AoI), by postponing transmission in order to lengthen the duration of staying in a good state. The optimal waiting policy for the sensor side was later characterized in the context of remote estimation. Instead of focusing on the sensor and controller sides separately, this work develops the jointly optimal sensor/controller waiting policy in a Wiener-process system. This work generalizes the above two important results in the sense that not only do we consider joint sensor/controller designs (as opposed to sensor-only or controller-only schemes), but we also assume random delay in both the forward and feedback directions (as opposed to random delay in only one direction). In addition to provable optimality, extensive simulation is used to verify the performance of the proposed scheme

Distribution-oblivious Online Algorithms for Age-of-Information Penalty Minimization

The ever-increasing needs of supporting real-time applications have spurred new studies on minimizing Age-of-Information (AoI), a novel metric characterizing the data freshness of the system. This work studies the single-queue information update system and strengthens the seminal results of Sun et al. on the following fronts: (i) When designing the optimal offline schemes with full knowledge of the delay distributions, a new fixed-point-based method is proposed with quadratic convergence rate, an order-of-magnitude improvement over the state-of-the-art; (ii) When the distributional knowledge is unavailable (which is the norm in practice), two new low-complexity online algorithms are proposed, which provably attain the optimal average AoI penalty; and (iii) the online schemes also admit a modular architecture, which allows the designer to upgrade certain components to handle additional practical challenges. Two such upgrades are proposed for the situations: (iii.1) The AoI penalty function is also unknown and must be estimated on the fly, and (iii.2) the unknown delay distribution is Markovian instead of i.i.d. The performance of our schemes is either provably optimal or within 3% of the omniscient optimal offline solutions in all simulation scenarios

Comparisons of housing price risks between first-time buyer and former owner-occupier markets in England

This study employs housing data from the nine main regions of England and from overall England to compare the volatility risks of housing prices for the first-time buyer (FTB) and former owneroccupier (FOO) markets. This study collects data from February 2012 to March 2020 to assess the volatility characteristics of housing prices in these two markets in each region of England. Additionally, the effect of interest rate shocks and the wealth effect of the stock market on these two markets are observed. The results reveal that for most regions, the FTB market has higher housing price volatility risks compared with the FOO market. Additionally, the FTB market is more easily affected by interest rate shocks and the wealth effect. In contrast to FOOs, FTBs are generally younger and less wealthy. If FTBs are facing a market with higher housing price risk, especially when the overall economy is affected by a shock (such as the European Debt Crisis or the COVID-19 pandemic), the response of the FTB housing market is greater; then the government must pay special attention when implementing policies that interfere with the market since these policies would particularly affect the welfare of FTBs

Rule-based Korean Grapheme to Phoneme Conversion Using Sound Patterns

PACLIC 23 / City University of Hong Kong / 3-5 December 200

catena-Poly[[bis­(nitrato-κO)copper(II)]-μ-1,4-bis­(4,5-dihydro-1,3-oxazol-2-yl)­benzene-κ2 N:N′]

In the title coordination polymer, [Cu(NO3)2(C12H12N2O2)]n, the CuII ion, situated on an inversion center, is coordinated by two O atoms from two nitrate anions and two N atoms from two 1,4-bis­(4,5-dihydro-1,3-oxazol-2-yl)benzene (L) ligands in a distorted square-planar geometry. Each L ligand also lies across an inversion center and bridges two CuII ions, forming a polymeric chain running along the [101] direction. The three O atoms of the nitrate group are disordered over two positions in a 3:2 ratio

Employing RFID for an Equipment Management System via Wireless Sensor Network

This paper is mainly in combination with RFID to construct a set of power system equipment remote control, used first on the reader tags received after the use of Visual Basic in order to determine the signal and then transmits the signal via the RS232 cable to control circuit 8051 to control the instrument power switch. The topic is written in the Visual Basic RFID and uses features, such as personnel control systems, and access control systems, which are derived from the time of access control systems, several instrument control systems, and uses records stored in the form of functions, where the other circuit transmits signals to Visual Basic 8051, and then, by 8051, controls the instrument power switch

Driving Assistance System with Lane Change Detection

In this study, a simple technology for a self-driving system called “driver assistance system” is developed based on embedded image identification. The system consists of a camera, a Raspberry Pi board, and OpenCV. The camera is used to capture lane images, and the image noise is overcome through color space conversion, grayscale, Otsu thresholding, binarization, erosion, and dilation. Subsequently, two horizontal lines parallel to the X-axis with a fixed range and interval are used to detect left and right lane lines. The intersection points between the left and right lane lines and the two horizontal lines can be obtained, and can be used to calculate the slopes of the left and right lanes. Finally, the slope change of the left and right lanes and the offset of the lane intersection are determined to detect the deviation. When the angle of lanes changes drastically, the driver receives a deviation warning. The results of this study suggest that the proposed algorithm is 1.96 times faster than the conventional algorithm