From Simplest Recursion to the Recursion of Generalizations of Cross Polytope Numbers

My research project involves investigations in the mathematical field of combinatorics. The research study will be based on the results of Professors Steven Edwards and William Griffiths, who recently found a new formula for the cross-polytope numbers. My topic will be focused on Generalizations of cross-polytope numbers . It will include the proofs of the combinatorics results in Dr. Edwards and Dr. Griffiths\u27 recently published paper. $E(n,m)$ and $O(n,m)$, the even terms and odd terms for Dr. Edward\u27s original combinatorial expression, are two distinct combinatorial expressions that are in fact equal. But there is no obvious algebraic evidence to show that they are equal. There are induction proofs in the paper. But I wondered if there is a better way to explain that at the undergraduate level, so I proved it algebraically with combinatorial identities. $E_k(n,m)$ and $O_k(n,m)$, which are the generalized forms for $E(n,m)$ and $O(n,m)$, are in fact equal and share the same recurrence formula with $E(n,m)$ and $O(n,m)$. We can call those numbers from the table of $E_k$ and $O_k$ the generalizations of the cross-polytope numbers

The political economy of migration in China.

Since opening up its economy to international trade and investment in the 1970s, China has undergone the largest transfer of rural populations to urban eras in modern history. In order to achieve these growth levels, massive migration was necessary in order to provide the armies of cheap labor that has been China's comparative economic advantage and the very core of its economic development strategy. This thesis examines the history of, and tensions within, China migration policy, and its implication for China's long-term position in the global economy. This thesis argues that China's migration policy is attempting to reconcile two conflicting goals of the ruling elite. On the one hand, migration flows are necessary to fulfill China's export-oriented industrial strategy, which requires vast amounts of cheap labor. On the other hand, the freedom of movement which migration requires poses a potential threat to social and political instability, especially if it sets the stage for independent civic mobilizations over the longer term. Maintaining the Hukou registration system as a form of residual control also encourages the existence of a large underclass of low wage workers who possess minimal rights in the areas to which they have migrated. The resulting income inequalities are themselves a source of social discontent that may well threaten the legitimacy of Communist governance.--Abstract

Impedance Measurement of Small Antennas Over a Ground Plane Without Direct Cable Attachment

An indirect impedance measurement approach that does not require direct cable attachment or large space using a two-port network is presented. Using a straight wire monopole as an interrogating antenna and measured impedances of three calibration standards, the input impedance of a small spherical helix dipole over a ground plane is retrieved. It is found that accurate result is obtained around the dipole resonance frequency. The accuracy and sources of error are discussed

Design Analysis of Chinese Classical Garden

Mentor: Arthur H Chen; Academic advisor: Mary Shannon BocockClassical Chinese gardens emphasize the harmony of nature, architecture, and human. They are picturesque gardens that developed from the charming moments in nature. A Classical garden seems to be a chaos of vegetation, water, and buildings inside a gate, but besides the chaos, there are systems of design principles that are worth to analysis and learn. This research analyzes and compares the design and building methods of Classical Chinese gardens to find their meaning in heritage protection and design. Four gardens from Suzhou and two gardens from Beijing are used as specific examples.This research was supported by the Undergraduate Research Opportunities Program (UROP)

OEBench: Investigating Open Environment Challenges in Real-World Relational Data Streams

How to get insights from relational data streams in a timely manner is a hot research topic. This type of data stream can present unique challenges, such as distribution drifts, outliers, emerging classes, and changing features, which have recently been described as open environment challenges for machine learning. While existing studies have been done on incremental learning for data streams, their evaluations are mostly conducted with manually partitioned datasets. Thus, a natural question is how those open environment challenges look like in real-world relational data streams and how existing incremental learning algorithms perform on real datasets. To fill this gap, we develop an Open Environment Benchmark named OEBench to evaluate open environment challenges in relational data streams. Specifically, we investigate 55 real-world relational data streams and establish that open environment scenarios are indeed widespread in real-world datasets, which presents significant challenges for stream learning algorithms. Through benchmarks with existing incremental learning algorithms, we find that increased data quantity may not consistently enhance the model accuracy when applied in open environment scenarios, where machine learning models can be significantly compromised by missing values, distribution shifts, or anomalies in real-world data streams. The current techniques are insufficient in effectively mitigating these challenges posed by open environments. More researches are needed to address real-world open environment challenges. All datasets and code are open-sourced in https://github.com/sjtudyq/OEBench

Pregnancy outcomes in women with active anorexia nervosa: a systematic review

Background: It is a common misconception that women with active anorexia nervosa (AN) are less likely to conceive. Pregnancies in women with AN are considered high risk. The purpose of this systematic review was to explore pregnancy complications in women with active AN, including maternal, fetal, and neonatal complications. Methods: The authors conducted a systematic review in accordance with PRISMA statement guidelines with stringent selection criteria to include studies on patients with active AN during pregnancy. Results: There were 21 studies included in our review. Anaemia, caesarean section, concurrent recreational substance use, intrauterine growth restriction, preterm birth, small-for-gestation (SGA) birth, and low birth weight were the most reported pregnancy complications in women with active AN, while the rates of gestational diabetes and postpartum haemorrhage were lower. Discussion: Women with active AN have a different profile of pregnancy complications comparing to malnourished women and women in starvation. We recommend early discussion with women diagnosed with AN regarding their fertility and pregnancy complications. We recommend clinicians to aim to improve physical and psychological symptoms of AN as well as correction of any nutritional deficiency ideally prior to conception. Management of pregnancies in women with active AN requires regular monitoring, active involvement of obstetricians and psychiatrist. Paediatric follow-up postpartum is recommended to ensure adequate feeding, wellbeing and general health of the infants. Psychiatric follow-up is recommended for mothers due to risk of worsening symptoms of AN during perinatal period

Attention Mechanisms in Medical Image Segmentation: A Survey

Medical image segmentation plays an important role in computer-aided diagnosis. Attention mechanisms that distinguish important parts from irrelevant parts have been widely used in medical image segmentation tasks. This paper systematically reviews the basic principles of attention mechanisms and their applications in medical image segmentation. First, we review the basic concepts of attention mechanism and formulation. Second, we surveyed over 300 articles related to medical image segmentation, and divided them into two groups based on their attention mechanisms, non-Transformer attention and Transformer attention. In each group, we deeply analyze the attention mechanisms from three aspects based on the current literature work, i.e., the principle of the mechanism (what to use), implementation methods (how to use), and application tasks (where to use). We also thoroughly analyzed the advantages and limitations of their applications to different tasks. Finally, we summarize the current state of research and shortcomings in the field, and discuss the potential challenges in the future, including task specificity, robustness, standard evaluation, etc. We hope that this review can showcase the overall research context of traditional and Transformer attention methods, provide a clear reference for subsequent research, and inspire more advanced attention research, not only in medical image segmentation, but also in other image analysis scenarios.Comment: Submitted to Medical Image Analysis, survey paper, 34 pages, over 300 reference