Dimension and cut vertices: an application of Ramsey theory

Motivated by quite recent research involving the relationship between the dimension of a poset and graph-theoretic properties of its cover graph, we show that for every $d\geq 1$, if $P$ is a poset and the dimension of a subposet $B$ of $P$ is at most $d$ whenever the cover graph of $B$ is a block of the cover graph of $P$, then the dimension of $P$ is at most $d+2$. We also construct examples which show that this inequality is best possible. We consider the proof of the upper bound to be fairly elegant and relatively compact. However, we know of no simple proof for the lower bound, and our argument requires a powerful tool known as the Product Ramsey Theorem. As a consequence, our constructions involve posets of enormous size.Comment: Final published version with updated reference

Power system stability scanning and security assessment using machine learning

Future grids planning requires a major departure from conventional power system planning, where only a handful of the most critical scenarios is analyzed. To account for a wide range of possible future evolutions, scenario analysis has been proposed in many industries. As opposed to the conventional power system planning, where the aim is to find an optimal transmission and/or generation expansion plan for an existing grid, the aim in future grids scenario analysis is to analyze possible evolution pathways to inform power system planning and policy making. Therefore, future grids’ planning may involve large amount of scenarios and the existing planning tools may no longer suitable. Other than the raised future grids’ planning issues, operation of future grids using conventional tools is also challenged by the new features of future grids such as intermittent generation, demand response and fast responding power electronic plants which lead to much more diverse operation conditions compared to the existing networks. Among all operation issues, monitoring stability as well as security of a power system and action with deliberated preventive or remedial adjustment is of vital important. On- line Dynamic Security Assessment (DSA) can evaluate security of a power system almost instantly when current or imminent operation conditions are supplied. The focus of this dissertation are, for future grid planning, to develop a framework using Machine Learning (ML) to effectively assess the security of future grids by analyzing a large amount of the scenarios; for future grids operation, to propose approaches to address technique issues brought by future grids’ diverse operation conditions using ML techniques. Unsupervised learning, supervised learning and semi-supervised learning techniques are utilized in a set of proposed planning and operation security assessment tools

Essays on Financial Development in China : Political Connection, Fiscal Effect and Openness

早大学位記番号:新6790早稲田大

High dynamic range display systems

High contrast ratio (CR) enables a display system to faithfully reproduce the real objects. However, achieving high contrast, especially high ambient contrast (ACR), is a challenging task. In this dissertation, two display systems with high CR are discussed: high ACR augmented reality (AR) display and high dynamic range (HDR) display. For an AR display, we improved its ACR by incorporating a tunable transmittance liquid crystal (LC) film. The film has high tunable transmittance range, fast response time, and is fail-safe. To reduce the weight and size of a display system, we proposed a functional reflective polarizer, which can also help people with color vision deficiency. As for the HDR display, we improved all three aspects of the hardware requirements: contrast ratio, color gamut and bit-depth. By stacking two liquid crystal display (LCD) panels together, we have achieved CR over one million to one, 14-bit depth with 5V operation voltage, and pixel-by-pixel local dimming. To widen color gamut, both photoluminescent and electroluminescent quantum dots (QDs) have been investigated. Our analysis shows that with QD approach, it is possible to achieve over 90% of the Rec. 2020 color gamut for a HDR display. Another goal of an HDR display is to achieve the 12-bit perceptual quantizer (PQ) curve covering from 0 to 10,000 nits. Our experimental results indicate that this is difficult with a single LCD panel because of the sluggish response time. To overcome this challenge, we proposed a method to drive the light emitting diode (LED) backlight and the LCD panel simultaneously. Besides relatively fast response time, this approach can also mitigate the imaging noise. Finally yet importantly, we improved the display pipeline by using a HDR gamut mapping approach to display HDR contents adaptively based on display specifications. A psychophysical experiment was conducted to determine the display requirements

On the dimension of posets with cover graphs of treewidth 22

In 1977, Trotter and Moore proved that a poset has dimension at most $3$ whenever its cover graph is a forest, or equivalently, has treewidth at most $1$. On the other hand, a well-known construction of Kelly shows that there are posets of arbitrarily large dimension whose cover graphs have treewidth $3$. In this paper we focus on the boundary case of treewidth $2$. It was recently shown that the dimension is bounded if the cover graph is outerplanar (Felsner, Trotter, and Wiechert) or if it has pathwidth $2$ (Bir\'o, Keller, and Young). This can be interpreted as evidence that the dimension should be bounded more generally when the cover graph has treewidth $2$. We show that it is indeed the case: Every such poset has dimension at most $1276$.Comment: v4: minor changes made following helpful comments by the referee

Critical study of parallel programming frameworks for distributed applications

Parallel programming frameworks such as the Message Passing Interface (MPI), Partitioned Global Address Space (PGAS) languages, Charm++, Legion and High Performance Parallel X (HPX) have been used in several scientific domains -- such as bioinformatics, physics, chemistry, and others -- to implement distributed applications. These frameworks allow distributing data and computation across the different nodes (or machines) of a high-performance computing cluster. However, these frameworks differ in their programmability, performance, and suitability to different cluster settings. For example, some of these frameworks have been designed to support applications running on homogeneous clusters that include only general purpose CPUs, while others offer support for heterogeneous clusters that include accelerators, such as graphics processing units (GPUs). Hence, it is important for programmers to select the programing framework that is best suited to the characteristics of their application (i.e. its computation and communication patterns) and the hardware setup of the target high-performance computing cluster

Dimension of posets with planar cover graphs excluding two long incomparable chains

It has been known for more than 40 years that there are posets with planar cover graphs and arbitrarily large dimension. Recently, Streib and Trotter proved that such posets must have large height. In fact, all known constructions of such posets have two large disjoint chains with all points in one chain incomparable with all points in the other. Gutowski and Krawczyk conjectured that this feature is necessary. More formally, they conjectured that for every $k\geq 1$, there is a constant $d$ such that if $P$ is a poset with a planar cover graph and $P$ excludes $\mathbf{k}+\mathbf{k}$, then $\dim(P)\leq d$. We settle their conjecture in the affirmative. We also discuss possibilities of generalizing the result by relaxing the condition that the cover graph is planar.Comment: New section on connections with graph minors, small correction