Asymptotic Behavior of Colored Jones polynomial and Turaev-Viro Invariant of figure eight knot

In this paper we investigate the asymptotic behavior of the colored Jones polynomials and the Turaev-Viro invariants for the figure eight knot. More precisely, we consider the $M$-th colored Jones polynomials evaluated at $(N+1/2)$-th root of unity with a fixed limiting ratio, $s$, of $M$ and $(N+1/2)$. We find out the asymptotic expansion formula (AEF) of the colored Jones polynomials of the figure eight knot with $s$ close to $1$. Nonetheless, we show that the exponential growth rate of the colored Jones polynomials of the figure eight knot with $s$ close to $1/2$ is strictly less than those with $s$ close to $1$. It is known that the Turaev Viro invariant of the figure eight knot can be expressed in terms of a sum of its colored Jones polynomials. Our results show that this sum is asymptotically equal to the sum of the terms with $s$ close to 1. As an application of the asymptotic behavior of the colored Jones polynomials, we obtain the asymptotic expansion formula for the Turaev-Viro invariants of the figure eight knot. Finally, we suggest a possible generalization of our approach so as to relate the AEF for the colored Jones polynomials and the AEF for the Turaev-Viro invariants for general hyperbolic knots.Comment: 40 pages, 0 figure

Topics in portfolio management

In this thesis, two topics in portfolio management have been studied: utility-risk portfolio selection and a paradox in time consistency in mean-variance problem. The first topic is a comprehensive study on utility maximization subject to deviation risk constraints. Under the complete Black-Scholes framework, by using the martingale approach and mean-field heuristic, a static problem including a variational inequality and some constraints on nonlinear moments, called Nonlinear Moment Problem, has been obtained to completely characterize the optimal terminal payoff. By solving the Nonlinear Moment Problem, the various well-posed mean-risk problems already known in the literature have been revisited, and also the existence of the optimal solutions for both utility-downside-risk and utility-strictly-convex-risk problems has been established under the assumption that the underlying utility satisfies the Inada Condition. To the best of our knowledge, the positive answers to the latter two problems have long been absent in the literature. In particular, the existence of an optimal solution for utility-semivariance problem, an example of the utility-downside-risk problem, is in substantial contrast to the nonexistence of an optimal solution for the mean-semivariance problem. This existence result allows us to utilize semivariance as a risk measure in portfolio management. Furthermore, it has been shown that the continuity of the optimal terminal wealth in pricing kernel, thus the solutions in the binomial tree models converge to the solution in the continuous-time Black-Scholes model. The convergence can be applied to provide a numerical method to compute the optimal solution for utility-deviation-risk problem by using the optimal portfolios in the binomial tree models, which are easily computed; such numerical algorithm for optimal solution to utility-risk problem has been absent in the literature. In the second part of this thesis, a paradox in time consistency in mean-variance has been established. People often change their preference over time, so the maximizer for current preference may not be optimal in the future. We call this phenomenon time inconsistency or dynamic inconsistency. To manage the issues of time inconsistency, a game-theoretic approach is widely utilized to provide a time-consistent equilibrium solution for dynamic optimization problem. It has been established that, if investors with mean-variance preference adopt the equilibrium solutions, an investor facing short-selling prohibition can acquire a greater objective value than his counterpart without the prohibition in a buoyant market. It has been further shown that the pure strategy of solely investing in bond can sometimes simultaneously dominate both constrained and unconstrained equilibrium strategies. With numerical experiments, the constrained investor can dominate the unconstrained one for more than 90% of the time horizon. The source of paradox is rooted from the nature of game-theoretic approach on time consistency, which purposely seeks for an equilibrium solution but not the ultimate maximizer. Our obtained results actually advocate that, to properly implement the concept of time consistency in various financial problems, all economic aspects should be critically taken into account at a time.Open Acces

Effects of low-frequency, low-acceleration motion on manual task performance

The current criteria and recommendations for assessing the acceptability of wind-induced building motion were largely established based on human perception thresholds and/or tolerance to wind-induced building motion. Therefore, they may not be able to ensure the performance of manual tasks is unaffected by wind-induced building motion. Few studies have investigated the effects of wind-induced building motion on manual task performance, and the findings of these studies are inconclusive. Hence the relationships between manual task performance and the wind-induced building motion and the mechanisms causing manual task performance degradation are yet to be explored and fully understood. Sopite syndrome describes a set of symptom centering around drowsiness due to exposure of healthy individuals to real or apparent motion. Recent studies have shown that symptoms of sopite syndrome are the most frequent manifestations of the effects of wind-induced building motion and decrease subjective work performance and objective cognitive task performance of building occupants. However, no study has investigated the effects of sopite syndrome on manual task performance. This thesis investigates the effects of low-frequency, low-acceleration motion and sopite syndrome on manual task performance based on a series of motion simulator experiments. Twelve low-frequency, low-acceleration motion conditions were generated using four frequencies (0.125, 0.25, 0.5, and 1 Hz) and three acceleration magnitudes (8, 16, and 30 milli-g) for both fore-aft and lateral directions. A continuous tracking task (CTT) was used as a paradigm to investigate the effects of the motion on manual task performance. Aiming accuracy of the CTT is the dependent measure. Twenty (10 males and 10 females) participants completed the experiment under fore-aft motion conditions and another 20 participants (10 males and 10 females) under lateral motion conditions. A Motion Sickness Assessment Questionnaire (MSAQ) was used to measure motion sickness severity, in particular sopite syndrome severity, of the participants before and after the exposure to the motion conditions. Activation levels of soleus (SOL) and tibialis anterior (TA), the lower leg muscles involved in maintaining balance in the fore-aft direction, were measured using electromyography (EMG) to provide supporting evidences for the effects of motion and sopite syndrome on manual task performance from a physiological perspective. Both acceleration and frequency were found to contribute to the degradations of manual task performance. Acceleration shows a strong inverse relationship with manual task performance; manual task performance decreases as the acceleration increases from 8 milli-g to 30 milli-g. The acceleration effect is attributable to an increase in inertial force. The activation levels of the SOL and TA also increase as acceleration increases from 8 milli-g to 30 milli-g. Evidently, the increase in inertial force can, in turn, induce visual impairment, disrupt balance, increase vibration breakthrough, and/or trigger motion sickness or sopite syndrome. In contrast, frequency has a complex nonlinear relationship with manual task performance. The worst manual task performance was measured at 0.5 Hz among the test frequencies ranging from 0.125 Hz to 1 Hz. This frequency effect is associated with the frequency response characteristic of the human body. Body sway increases as frequency approaches the resonant frequency of a standing human, which occurs at near 0.5 Hz. The activation levels of SOL and TA increase as frequency increases from 0.125 Hz to approximately 0.5 Hz, then drop as frequency increases from 0.5 Hz to 1 Hz. This affirms that the body sways the most at 0.5 Hz. The increases in body sway can cause discomfort, divert attention resources from performing a manual task, and trigger anxiety that increases difficulty to response to manual tasks

Real Time Support Systems

With the huge grow of networked computer, the traditional way of network monitoring by walk to each computer to check the configuration may not be effective and efficient to monitor network traffic on the network infrastructure and there are highly percentages of human error. The Project aim to deliver an efficient and effective system to replace the traditional way of network monitoring. With this Real Time Support System enable the person in charge of computer resources and networking especially the Network Administrator to monitoring the network performance and make the necessary changes to tune the network performance hence save the resources. Beside that, this project also aims to develop a low cost, easy to maintain and user-friendly windows based Real Time Support System for Small Medium Enterprise (SMEs) in Malaysia

De novo human genome assemblies reveal spectrum of alternative haplotypes in diverse populations.

The human reference genome is used extensively in modern biological research. However, a single consensus representation is inadequate to provide a universal reference structure because it is a haplotype among many in the human population. Using 10× Genomics (10×G) "Linked-Read" technology, we perform whole genome sequencing (WGS) and de novo assembly on 17 individuals across five populations. We identify 1842 breakpoint-resolved non-reference unique insertions (NUIs) that, in aggregate, add up to 2.1 Mb of so far undescribed genomic content. Among these, 64% are considered ancestral to humans since they are found in non-human primate genomes. Furthermore, 37% of the NUIs can be found in the human transcriptome and 14% likely arose from Alu-recombination-mediated deletion. Our results underline the need of a set of human reference genomes that includes a comprehensive list of alternative haplotypes to depict the complete spectrum of genetic diversity across populations

A Weapon of Legitimacy: China’s Integrative Power and its Impact on its Reactions on Domestic Conflicts

The rise of China has provided a plethora of different powers it can use to its advantage, continues its rise, or punish noncompliance. Throughout the years of China\u27s rising, it has been accumulating considerable hard power in its military and economic capabilities, while also trying to improve on its soft power of cultural values. However one often overlooked, and under-appreciated power of China is the integrative power of Chinese nationalism. This integrative power that comes from China’s acute usage of nationalism to support the legitimacy of its one-party system. This study argues that China has an excess of integrative power and that China has skillfully used it to turn unfavorable events and threats, such as the Hong Kong protests of 2019, back to their advantage; even if this would mean that China is a primary facilitator of conflict and also at times an inhibitor to the de-escalation of conflict

Joint Quantization and Diffusion for Compressed Sensing Measurements of Natural Images

Recent research advances have revealed the computational secrecy of the compressed sensing (CS) paradigm. Perfect secrecy can also be achieved by normalizing the CS measurement vector. However, these findings are established on real measurements while digital devices can only store measurements at a finite precision. Based on the distribution of measurements of natural images sensed by structurally random ensemble, a joint quantization and diffusion approach is proposed for these real-valued measurements. In this way, a nonlinear cryptographic diffusion is intrinsically imposed on the CS process and the overall security level is thus enhanced. Security analyses show that the proposed scheme is able to resist known-plaintext attack while the original CS scheme without quantization cannot. Experimental results demonstrate that the reconstruction quality of our scheme is comparable to that of the original one.Comment: 4 pages, 4 figure