Multi-channel Wireless Networks with Infrastructure Support: Capacity and Delay

In this paper, we propose a novel multi-channel network with infrastructure support, called an \textit{MC-IS} network, which has not been studied in the literature. To the best of our knowledge, we are the first to study such an \textit{MC-IS} network. Our \textit{MC-IS} network is equipped with a number of infrastructure nodes which can communicate with common nodes using a number of channels where a communication between a common node and an infrastructure node is called an infrastructure communication and a communication between two common nodes is called an ad-hoc communication. Our proposed \textit{MC-IS} network has a number of advantages over three existing conventional networks, namely a single-channel wireless ad hoc network (called an \textit{SC-AH} network), a multi-channel wireless ad hoc network (called an \textit{MC-AH} network) and a single-channel network with infrastructure support (called an \textit{SC-IS} network). In particular, the \textit{network capacity} of our proposed \textit{MC-IS} network is $\sqrt{n \log n}$ times higher than that of an \textit{SC-AH} network and an \textit{MC-AH} network and the same as that of an \textit{SC-IS} network, where $n$ is the number of nodes in the network. The \textit{average delay} of our \textit{MC-IS} network is $\sqrt{\log n/n}$ times lower than that of an \textit{SC-AH} network and an \textit{MC-AH} network, and $\min(C_I,m)$ times lower than the average delay of an \textit{SC-IS} network, where $C_I$ and $m$ denote the number of channels dedicated for infrastructure communications and the number of interfaces mounted at each infrastructure node, respectively.Comment: 12 pages, 6 figures, 3 table

On Capacity and Delay of Multi-channel Wireless Networks with Infrastructure Support

In this paper, we propose a novel multi-channel network with infrastructure support, called an MC-IS network, which has not been studied in the literature. To the best of our knowledge, we are the first to study such an MC-IS network. Our proposed MC-IS network has a number of advantages over three existing conventional networks, namely a single-channel wireless ad hoc network (called an SC-AH network), a multi-channel wireless ad hoc network (called an MC-AH network) and a single-channel network with infrastructure support (called an SC-IS network). In particular, the network capacity of our proposed MC-IS network is $\sqrt{n \log n}$ times higher than that of an SC-AH network and an MC-AH network and the same as that of an SC-IS network, where $n$ is the number of nodes in the network. The average delay of our MC-IS network is $\sqrt{\log n/n}$ times lower than that of an SC-AH network and an MC-AH network, and $\min\{C_I,m\}$ times lower than the average delay of an SC-IS network, where $C_I$ and $m$ denote the number of channels dedicated for infrastructure communications and the number of interfaces mounted at each infrastructure node, respectively. Our analysis on an MC-IS network equipped with omni-directional antennas only has been extended to an MC-IS network equipped with directional antennas only, which are named as an MC-IS-DA network. We show that an MC-IS-DA network has an even lower delay of $\frac{c}{\lfloor \frac{2\pi}{\theta}\rfloor \cdot C_I}$ compared with an SC-IS network and our MC-IS network. For example, when $C_I=12$ and $\theta=\frac{\pi}{12}$, an MC-IS-DA network can further reduce the delay by 24 times lower that of an MC-IS network and reduce the delay by 288 times lower than that of an SC-IS network.Comment: accepted, IEEE Transactions on Vehicular Technology, 201

The pricing of corporate debt and related issues

The purpose of this thesis is to study the pricing and credit risk of corporate debt using structural and reduced-form approaches. We discuss the theoretical aspects of three important topics in pricing risky debt: (i) the impact of stochastic interest rates, and hence the interaction between market risk and credit risk; (ii) the impact of diversifiable and non-diversifiable jump risks on pricing and default mechanisms, and (iii) a reduced-form model with a firm’s fundamental variables. To investigate the relationships between market risk and credit risk, we develop a flexible binomial framework for valuing credit-sensitive instruments by generalizing the valuation model of Geske [1977]. We price a defaultable coupon bond when interest rates and a firm’s asset value are stochastic. Our results confirm our belief that firms with low credit quality should have more market risk than firms with high credit quality. We discuss the implications of the results for capital adequacy. In addition to providing conceptual insights into the default behaviour, the flexibility of our method allows for efficient pricing of other credit-sensitive instruments. To improve the short-end properties of credit spreads, we model a firm’s asset value as a jump-diffusion process. We show several significant implications of the jump process for the term structure of credit spreads. We also discuss the effects of the disversifiability of jumps on corporate debt pricing. We prove that without considering systematic jump risk, theoretical models tend to underestimate credit spreads. Another contribution of this thesis is the incorporation of taxes into our model to show that taxes do have significant effects on levels of credit spread. Interestingly, the model implies that a decrease in the federal tax rate may precipitate an earlier default of low-grade bonds. Finally, we investigate a reduced-form model of corporate debt, by taking into account stochastic interest rates, a firm’s equity values, and hazard rates of default. Through a moving average of a log-transformation of equity prices, we introduce structural characteristics of the firm into the model. This is an innovation

Perceived Attributes of Music Teaching Effectiveness Among Kindergarten Teachers: Role of Personality

: Musical activity has been found to be beneficial to young children’s all-round development in kindergartens. The purpose of this study was to investigate the relationship between kindergarten teachers’ perceived attributes of music teaching effectiveness and personality. Eighty-eight in-service kindergarten teachers rated themselves using a set of Attributes of Music Teaching Effectiveness (AMTE) and the sensing-intuitive dimension of the Myers Briggs Type Indicator. Results showed that 75% (66 of 88) and 25% (22 of 88) of the teachers were sensing types and intuitive types, respectively. The former prefers a directive approach in music teaching to children, whereas the latter prefers a non-directive approach. While teachers’ personalities and work experience significantly predicted music teaching effectiveness, intuitive teachers rated themselves higher than did sensing teachers on the AMTE. Furthermore, the teachers of both personality types varied in their ratings of the importance of most effective attributes. Implications of these findings in relation to job allocation and professional development in effective music teaching for kindergarten teachers are discussed

Quantum spin fluctuations in dynamical quantum phase transitions

Quantum phase transitions have long been studied in their relation to quantum fluctuations. These fluctuations can be quantified as the degree of spin squeezing in spin models, where one of the two non-commutative observables breaks the standard quantum limit of measurement by minimizing its uncertainty. However, the understanding of their role in dynamical quantum phase transitions (DQPTs) is still incomplete. In this work, we combine the Loschmidt amplitude, which detects DQPTs, and the spin-squeezing parameter (SSP), the quantification of spin squeezing, to study the spin dynamics in a quenched interacting spin model around DQPT. We show that the extremal, mostly maximal, of SSP occurs near DQPTs when the system is quenched between different phases. These phenomena further unveil the spin correlations during DQPTs, for which the highest contribution aligns with the preferred direction of spin interactions in the post-quenched phase. We also demonstrate the time evolution of SSP differs for various quench scenarios. These findings provide us with physical insights into the dynamics of quantum fluctuations around DQPTs and their relation to the equilibrium phase diagrams.Comment: 12 pages, 15 figure