A test problem for visual investigation of high-dimensional multi-objective search

An inherent problem in multiobjective optimization is that the visual observation of solution vectors with four or more objectives is infeasible, which brings major difficulties for algorithmic design, examination, and development. This paper presents a test problem, called the Rectangle problem, to aid the visual investigation of high-dimensional multiobjective search. Key features of the Rectangle problem are that the Pareto optimal solutions 1) lie in a rectangle in the two-variable decision space and 2) are similar (in the sense of Euclidean geometry) to their images in the four-dimensional objective space. In this case, it is easy to examine the behavior of objective vectors in terms of both convergence and diversity, by observing their proximity to the optimal rectangle and their distribution in the rectangle, respectively, in the decision space. Fifteen algorithms are investigated. Underperformance of Pareto-based algorithms as well as most state-of-the-art many-objective algorithms indicates that the proposed problem not only is a good tool to help visually understand the behavior of multiobjective search in a high-dimensional objective space but also can be used as a challenging benchmark function to test algorithms' ability in balancing the convergence and diversity of solutions

Equations involving fractional Laplacian operator: Compactness and application

In this paper, we consider the following problem involving fractional Laplacian operator: \begin{equation}\label{eq:0.1} (-\Delta)^{\alpha} u= |u|^{2^*_\alpha-2-\varepsilon}u + \lambda u\,\, {\rm in}\,\, \Omega,\quad u=0 \,\, {\rm on}\, \, \partial\Omega, \end{equation} where $\Omega$ is a smooth bounded domain in $\mathbb{R}^N$, $\varepsilon\in [0, 2^*_\alpha-2)$, $0<\alpha<1,\, 2^*_\alpha = \frac {2N}{N-2\alpha}$. We show that for any sequence of solutions $u_n$ of \eqref{eq:0.1} corresponding to $\varepsilon_n\in [0, 2^*_\alpha-2)$, satisfying $\|u_n\|_{H}\le C$ in the Sobolev space $H$ defined in \eqref{eq:1.1a}, $u_n$ converges strongly in $H$ provided that $N>6\alpha$ and $\lambda>0$. An application of this compactness result is that problem \eqref{eq:0.1} possesses infinitely many solutions under the same assumptions.Comment: 34 page

International Students\u27 Social Factors And Acculturative Stress

Each year, many international students come to the United States from all over the world to further their education, and they have contributed a significant part to the economy. Adapting to a new culture can be challenging and that puts international students at a greater risk for experiencing mental health issues than students in general. Thus, the need for understanding cross-cultural adaptation for international students is becoming increasingly important. Social factors are one of the coping resources that have been suggested to benefit international student cross-cultural adaptation. Studying aboard causes disruption in international students’ social relationships that is compounded by a change in culture, where language, social norms, values may make it more difficult to form strong social bonds in a new environment. One social construct that may help explain why international students can deal with the increased stress and risk of changing cultural environments is social connectedness (Lee & Robins, 1995). Therefore, in Chapter 1, I conducted a narrative review of 15 studies of international students exploring associations of social connectedness with psychological adaptation and sociocultural adaptation drawing from a cross-culture adaptation model (Searle & Ward, 1990). The review highlighted social connection effects on various predictors in psychological and sociocultural domains to understand social connectedness effects on the international student cross-cultural adaptation process. In Chapter 2, I examined the effects of social factors (e.g., social support and social connectedness) on international students\u27 acculturative stress from a bilinear perspective that was proposed by Berry et al.’s (1987) bi-dimensional model. A sample of 206 international students in the U.S. was collected from various resources. Hierarchical linear regression revealed that various types of social support and social connectedness are important predictors for acculturative stress as predicted. Specifically, social connectedness is the strongest predictor of acculturative stress. Also, I conducted a moderation analysis using the PROCESS Macro developed for SPSS to test the moderation effects proposed in Berry et al.’s (1987) theoretical work. I predicted that social connectedness would moderate the relationship between other social factors and acculturative stress. The results of moderation analysis were partially supported. Implications and recommendations are discussed

Three Essays on Hedge Fund Investments and Investment Banks

This dissertation focuses on studying how investment banks affect hedge fund equity investments through acting as prime brokers for hedge funds. The first chapter studies how the relationships between hedge funds and investment banks are maintained through equity issuance and prime brokerage business. Using a comprehensive dataset of hedge funds and IPO allocations, I examine IPO allocation decisions by investment banks to hedge funds. I find that investment banks whose prime brokers have strong relationships with hedge funds and are lead underwriters of IPOs tend to allocate more IPOs to these hedge funds. Moreover, the allocation to hedge funds is larger when IPOs are underpriced, and the allocations are larger during bearish periods compared to bullish periods. I further document that hedge fund investments in IPOs are determined by the strength of hedge fund-prime broker relationships, rather than by hedge fund manager skills. I also find that hedge funds which have multiple prime brokers tend to invest in more IPOs. As a result, prime brokers implicitly support hedge funds through favorable IPO allocations. The second chapter finds that hedge funds can profit from anticipating upcoming changes in analysts\u27 recommendations before they become public. I provide evidence supporting the hypothesis that hedge funds that have prime brokerage affiliations with analysts\u27 investment banks have access to information on upcoming analysts\u27 recommendations. Focusing on recommendations issued up to two days following stock holding report date, I find that large hedge funds that are clients of the investment bank (affiliated hedge funds) tend to buy upgrades and sell downgrades in a larger magnitude compared to other hedge funds before the public release of recommendations. Moreover, relative to non-affiliated hedge funds, affiliated hedge funds have a higher probability to trade in a way that is consistent with upcoming recommendation changes and earn higher (or avoid lower) short-term abnormal returns by buying (or selling) before upgrades (or downgrades). The results indicate that prime brokerage affiliation is an important source of private information on analysts\u27 reports for hedge funds. The third chapter studies hedge funds\u27 equity investment strategies by examining the investment value and risk consequence of their holdings concentration in large-cap and small-cap stocks. We find that stocks, especially small-cap ones, with concentrated hedge fund holdings earn higher future returns than those with less concentrated holdings. We also find that stocks with concentrated hedge fund holdings have higher downside risks, and the holdings concentration expedites the drop of stock performance, especially during financial crisis. In addition, small-cap stocks with higher holdings concentration are associated with hedge funds using higher leverage, consistent with Stein (2009) that deleverage leads to the negative return shock and downside risks in stocks. Our findings suggest that hedge fund managers are skilled in making equity investment under different market efficiency