Positivity of chromatic symmetric functions associated with Hessenberg functions of bounce number 3

We give a proof of Stanley-Stembridge conjecture on chromatic symmetric functions for the class of all unit interval graphs with independence number 3. That is, we show that the chromatic symmetric function of the incomparability graph of a unit interval order in which the length of a chain is at most 3 is positively expanded as a linear sum of elementary symmetric functions.Comment: 32 page

Coupled 3D Dislocation Modeling at Nano- and Micro-Scales

The performance of crystalline materials varies depending on the considered scale. To understand the size dependence of materials properties, the interaction and evolution of defects are essential. As such, the role played by dislocations is crucial for modeling metallic materials. In essence, a dislocation is a default in the crystalline periodicity that creates long-range stress fields, which makes the modeling of dislocation dynamics a challenging problem. This thesis concentrates on the development of a novel multiscale method, which couples concurrently dislocation dynamics at nano- and micro-scales. A version of this method, the \textit{Coupled Atomistic and Discrete Dislocations} (CADD), exists for two-dimensional problems. Its three-dimensional extension (CADD3d) is developed theoretically, and then implemented including the necessary parallel computing aspects. The proposed model requires two main building blocks, which are linked to general dislocation properties. The first component is the correction field of the linear elasticity solution for dislocation cores. The core structures are pre-computed by modeling straight dislocations with arbitrary mixed angles using atomistic simulations. The obtained results are validated by extending the variational Peierls-Nabarro method. Finally, the templates including the core correction field are generated from the calculated core structures. The second building block is the mobility law of dislocations. The dislocation mobilities for several orientations and temperatures are studied with atomistic simulations, and validated by comparisons to theoretical models. The mobility law is characterized by two damping mechanisms, the phonon viscosity and the phonon radiation effects. CADD3d is then examined by studying several benchmark problems, which prove that the CADD3d method is a valid approach to couple atomistic and discrete dislocation dynamics including when multiple curved dislocations dynamics have to be considered. Furthermore, to highlight the applicability of CADD3d for material plasticity problems, a Frank-Read source in an aluminum alloy is studied. The application result provides interesting insights on the mechanisms of solid-solution strengthening and grain-hardening effects at the nano and micro scales

Financial Intermediation, Heterogeneous Investors, and Asset Pricing

This dissertation consists of three essays in financial intermediation, heterogeneous agents, and asset pricing. In the first essay, I extract mutual fund flows that respond to the active change in equity share of mutual funds and show that they have significant predictability of market return. These “market timing-sensitive (MT-sensitive) flows” have predictability of the overall market over the next two to twelve months, without evidence of reversal. This predictability holds even when controlling for other macroeconomic variables and market sentiment index. I report that mutual fund managers who enjoy MT-sensitive inflows outperform the managers with MT-sensitive outflows over the next quarter. Also, I show that investors whose mutual fund investments mimic MT-sensitive flows have market timing ability, and outperform investors with mutual fund investments in the opposite direction to MT-sensitive flows. In the second essay, I analyze mutual fund investors' responses to changes in funds' allocations to emerging markets. I show that such flows predict positive abnormal returns in emerging markets at quarterly and annual horizons. When there is one standard deviation shock to the EMT-sensitive flows, a six-month equal-weighted emerging market return is expected to be 3.58% in excess of risk-free rate in the US, and 1.69% in excess of US stock market excess return. This predictability holds even when controlling for other macroeconomic variables. The evidence suggests fund investors collectively possess valuable information about emerging markets. The third essay proposes a general equilibrium model with bounded rationality that explains both endogenous learning and price. If agents are bounded rational, in that they do not have complete processing capacity as assumed in rational expectations models, there is a role for endogenous allocation of resources to learning about the economy. Investors trade off learning about different elements, such as terminal dividend (asset fundamental) vs. market structure (aggregate demand schedules). I found that investors prefer to learn what others do not learn, and this explains why there is specialization in the investment. Investors tend to be fundamentalists when market is uncertain, but learning also depends on capacity, ratio of sophisticated investors, risk aversion, etc. I analyze the trade-off between these information sources, and the implications for price efficiency, risk, and return, in a general equilibrium

Bases of the equivariant cohomologies of regular semisimple Hessenberg varieties

We consider bases for the cohomology space of regular semisimple Hessenberg varieties, consisting of the classes that naturally arise from the Bialynicki-Birula decomposition of the Hessenberg varieties. We give an explicit combinatorial description of the support of each class, which enables us to compute the symmetric group actions on the classes in our bases. We then successfully apply the results to the permutohedral varieties to explicitly write down each class and to construct permutation submodules that constitute summands of a decomposition of cohomology space of each degree. This resolves the problem posed by Stembridge on the geometric construction of permutation module decomposition and also the conjecture posed by Chow on the construction of bases for the equivariant cohomology spaces of permutohedral varieties

Permutation module decomposition of the second cohomology of a regular semisimple Hessenberg variety

Regular semisimple Hessenberg varieties admit actions of associated Weyl groups on their cohomology space of each degree. In this paper, we consider the module structure of the cohomology spaces of regular semisimple Hessenberg varieties of type $A$. We define a subset of the Bialynicki-Birula basis of the cohomology space so that they become a module generator set of the cohomology module of each degree. We then use those generators to construct permutation submodules of the degree two cohomology module and show that they form a permutation module decomposition. Our construction is consistent with a known combinatorial result by Chow on chromatic quasisymmetric functions

Dislocations 2016

Dislocation dynamics are important to understand material plasticity in small-sized materials. In case of face-centered cubic crystalline systems, densities of initial dislocations, dislocation nucleations and starvations processes influence material strengths at micro- and nano-scales [1]. To model these multi-scale physics in concurrent manners, 2D Coupled Atomistic and Discrete Dislocation dynamics (CADD) [2] is the only available computational tool. However, in CADD, the described dislocation dynamics are limited to 2 dimensional systems. In this presentation, we propose a new method for coupling MD and DD simulations in 3D (CADD3D) to resolve the limitations of CADD. We introduce its required building blocks (core templates [3] and mobility law) and the coupling-communication scheme. The dynamics of a hybrid dislocation, which is a dislocation structure composed of atomic and discrete dislocations, will be shown to demonstrate the workability of the proposed communication scheme. Furthermore, several applications will be presented using CADD3D such as an expanding dislocation loop nucleated from a Frank-Read source

A Study on Improving the Operation of Naeil Irum School for Out-of-School Youth

In this study, a comprehensive re-evaluation of the existing Naeil Lee Room School operating system was conducted to diagnose problems, and based on this, specific improvement plans were presented to seek to expand participation of out-of-school youth and increase the completion rate and employment rate. To this end, first, previous studies related to the operation status of Naeil Lee Room School and development plans were collected and analyzed, and implications were drawn. Second, in-depth interviews were conducted with 85 trainees, 12 graduates, 8 dropouts, and 16 workers from 9 Naeil Lee Room Schools nationwide to identify current operating conditions and problems, and to collect and analyze improvement ideas. Third, the study conducted on-site visits to Job Corps centers in Washington and Philadelphia, USA, and collected related data to benchmark them. Fourth, a survey was conducted on 709 out-of-school youths using out-of-school youth support centers, youth shelters, unlicensed alternative schools, protective disposal facilities, etc., including Naeil Lee Room School, to draw implications. Fifth, academy, field, and government experts and youth advisory groups were formed, and the final plan to improve the operation of Naeil Lee Room School was proposed by reflecting the review opinions

Bayesian Belief Network Model Quantification Using Distribution-Based Node Probability and Experienced Data Updates for Software Reliability Assessment

Since digital instrumentation and control systems are expected to play an essential role in safety systems in nuclear power plants (NPPs), the need to incorporate software failures into NPP probabilistic risk assessment has arisen. Based on a Bayesian belief network (BBN) model developed to estimate the number of software faults considering the software development lifecycle, we performed a pilot study of software reliability quantification using the BBN model by aggregating different experts' opinions. In this paper, we suggest the distribution-based node probability table (D-NPT) development method which can efficiently represent diverse expert elicitation in the form of statistical distributions and provides mathematical quantification scheme. Besides, the handbook data on U.S. software development and V&V and testing results for two nuclear safety software were used for a Bayesian update of the D-NPTs in order to reduce the BBN parameter uncertainty due to experts' different background or levels of experience. To analyze the effect of diverse expert opinions on the BBN parameter uncertainties, the sensitivity studies were conducted by eliminating the significantly different NPT estimates among expert opinions. The proposed approach demonstrates a framework that can effectively and systematically integrate different kinds of available source information to quantify BBN NPTs for NPP software reliability assessment

Potential for transmission of naturally mutated H10N1 avian influenza virus to mammalian hosts and causing severe pulmonary disease

Subtype H10 avian influenza viruses (AIV) are distributed worldwide in wild aquatic birds, and can infect humans and several other mammalian species. In the present study, we investigated the naturally mutated PB2 gene in A/aquatic bird/South Korea/SW1/2018 (A/SW1/18, H10N1), isolated from wild birds during the 2018–2019 winter season. This virus was originally found in South Korea, and is similar to isolates from mainland China and Mongolia. It had low pathogenicity, lacked a multi-basic cleavage site, and showed a binding preference for α2,3-linked sialic acids. However, it can infect mice, causing severe disease and lung pathology. SW1 was also transmitted by direct contact in ferrets, and replicated in the respiratory tract tissue, with no evidence of extrapulmonary spread. The pathogenicity and transmissibility of SW1 in mouse and ferret models were similar to those of the pandemic strain A/California/04/2009 (A/CA/04, H1N1). These factors suggest that subtype H10 AIVs have zoonotic potential and may transmit from human to human, thereby posing a potential threat to public health. Therefore, the study highlights the urgent need for closer monitoring of subtype H10 AIVs through continued surveillance of wild aquatic birds