Statistical Estimation And Inference For Permutation Based Model

Statistics is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data. People spend lots of time dealing with different kinds of data sets. The structure of the data plays an important role in statistics. Among different structures of data, one interesting structure is the permutation, which involves in different kinds of problems, such as recommender system, online gaming, decision making and sports tournament. This thesis is motivated by my interest in understanding the permutation in statistics. Comparing to the wide applications of permutation related model, little is known to the property of permutation in statistics. There are a variety challenges that arise and lots of problems waiting for us to explore in the permutation based model. This thesis aims to solve several interesting problems of the permutation based model in statistics, which may help us to understand more about the property and characteristic of permutation. As a result of the various topics explored, this thesis is split into three parts. In Chapter 2, we discuss the estimation problem of unimodal SST model in the pairwise comparison problem. We prove that the CLS estimator is rate optimal up to a poly(log log n) factor and propose the computational efficient interval sorting estimator, as a computational efficient algorithm to the estimation problem. In Chapter 3, we shift our attention to the inference problem of the permutation based model. We study different kinds of inference problem, including the hypothesis testing problem in noisy sorting model and confidence set construction problems in generalized permutation based model. Network analysis is another important topic related to the permutation. In Chapter 4, we study the optimality of local belief propagation algorithm in the partial recovery problem of stochastic block model. We prove that local BP algorithm can reach the optimality in a certain regime. Moreover, in the regime where local BP algorithm may not achieve the optimal misclassified fraction, we will prove that local BP algorithm can be used in correcting other algorithms and get optimal algorithm to the partial recovery problem

AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversation Framework

This technical report presents AutoGen, a new framework that enables development of LLM applications using multiple agents that can converse with each other to solve tasks. AutoGen agents are customizable, conversable, and seamlessly allow human participation. They can operate in various modes that employ combinations of LLMs, human inputs, and tools. AutoGen's design offers multiple advantages: a) it gracefully navigates the strong but imperfect generation and reasoning abilities of these LLMs; b) it leverages human understanding and intelligence, while providing valuable automation through conversations between agents; c) it simplifies and unifies the implementation of complex LLM workflows as automated agent chats. We provide many diverse examples of how developers can easily use AutoGen to effectively solve tasks or build applications, ranging from coding, mathematics, operations research, entertainment, online decision-making, question answering, etc.Comment: 28 page

A virus-like particle of the hepatitis B virus preS antigen elicits robust neutralizing antibodies and T cell responses in mice

The preS antigen of hepatitis B virus (HBV) corresponds to the N-terminal polypeptide in the large (L) antigen in addition to the small (S) antigen. The virus-like particle (VLP) of the S antigen is widely used as a vaccine to protect the population from HBV infection. The presence of the S antigen and its antibodies in patient blood has been used as markers to monitor hepatitis B. However, there is very limited knowledge about the preS antigen. We generated a preS VLP that is formed by a chimeric protein between preS and hemagglutinin (HA), and the matrix protein M1 of influenza virus. The HBV preS antigen is displayed on the surface of preS VLP. Asn112 and Ser98 of preS in VLP were found to be glycosylated and O-glycosylation of Ser98 has not been reported previously. The preS VLP shows a significantly higher immunogenicity than recombinant preS, eliciting robust anti-preS neutralizing antibodies. In addition, preS VLP is also capable of stimulating preS-specific CD8+ and CD4+ T cell responses in Balb/c mice and HBV transgenic mice. Furthermore, preS VLP immunization provided protection against hydrodynamic transfection of HBV DNA in mice. The data clearly suggest that this novel preS VLP could elicit robust immune responses to the HBV antigen, and can be potentially developed into prophylactic and therapeutic vaccines

An Empirical Study on Challenging Math Problem Solving with GPT-4

Employing Large Language Models (LLMs) to address mathematical problems is an intriguing research endeavor, considering the abundance of math problems expressed in natural language across numerous science and engineering fields. While several prior works have investigated solving elementary mathematics using LLMs, this work explores the frontier of using GPT-4 for solving more complex and challenging math problems. We evaluate various ways of using GPT-4. Some of them are adapted from existing work, and one is \MathChat, a conversational problem-solving framework newly proposed in this work. We perform the evaluation on difficult high school competition problems from the MATH dataset, which shows the advantage of the proposed conversational approach

Can CD44+/CD24- Tumor Cells Be Used to Determine the Extent of Breast Cancer Invasion Following Neoadjuvant Chemotherapy?

breast cancers in relation to tumor size before and after the administration of neoadjuvant chemotherapy. Methods: CD44 + / CD24- tumor cells obtained from breast cancer specimens were characterized in vivo and in vitro using tumor formation assays and mammosphere generation assays, respectively. The distribution of CD44+/CD24- tumor cells in 78 breast cancer specimens following administration of neoadjuvant chemotherapy was also evaluated using immunofluorescence assays, and this distribution was compared with the extent of tumor invasion predicted by Response Evaluation Criteria in Solid Tumours (RECIST). Results: In 27/78 cases, complete remission (CR) was identified using RECIST. However, 18 of these CR cases were associated with a scattered distribution of tumor stem cells in the outline of the original tumor prior to neoadjuvant chemotherapy. After neoadjuvant chemotherapy, 24 cases involved cancer cells that were confined to the tumor outline, and 21 cases had tumor cells or tumor stem cells overlapping the tumor outline. In addition, there were 6 patients who were insensitive to chemotherapy, and in these cases, both cancer cells and stem cells were detected outside the contours of the tumor volume imaged prior to chemotherapy. Conclusion: CD44+/CD24- tumor cells may be an additional parameter to evaluate when determining the extent of breast cancer invasion. Key Words: Breast neoplasms, Neoadjuvant chemotherapy, Neoplasm invasion, Stem cell

Mapping and validation of sex-linked SNP markers in the swimming crab Portunus trituberculatus

Portunus trituberculatus is one of the most commercially important marine crustacean species for both aquaculture and fisheries in Southeast and East Asia. Production of monosex female stocks is attractive in commercial production since females are more profitable than their male counterparts. Identification and mapping of the sex-linked locus is an efficient way to elucidate the mechanisms of sex determination in the species and support the development of protocols for monosex female production. In this study, a sex-averaged map and two sex-specific genetic maps were constructed based on 2b-restriction site-associated DNA sequencing. A total of 6349 genetic markers were assigned to 53 linkage groups. Little difference was observed in the pattern of sex-specific recombination between females and males. Association analysis and linkage mapping identified 7 markers strongly associated with sex, four of which were successfully mapped on the extremity of linkage group 22. Females were homozygous and males were heterozygous for those 7 markers strongly suggesting an XX/XY sex determination system in this species. Three Markers were successfully validated in a wild population of P. trituberculatus and exhibited a specificity ranging from 93.3% to 100%. A high-resolution melting based assay was developed for sex genotyping. This study provides new knowledge and tools for sex identification which will help the development of protocols for monosex female production of P. trituberculatus and support future genomic studies

Drought intensity and post-drought precipitation determine vegetation recovery in a desert steppe in Inner Mongolia, China

Extreme drought events are expected to increase in frequency and severity, posing significant threats to ecosystems worldwide. While considerable research has been concentrated on the effects of climate extremes on the stability of grasslands, the process by which grassland productivity may recover after extreme drought events are still not well understood. Here, we conducted a four-year (2019–2022) recovery investigation after four-year's (2015–2018) extreme drought treatments of different intensities (control, press and pulse) to explore the vegetation recovery of desert-grassland ecosystems Inner Mongolia, China. Press drought involved a 66 % reduction in natural precipitation from May to August, while pulse drought reduced it by 100 % during June and July. We found that both press and pulse droughts led to a sharp decrease in aboveground net primary productivity (ANPP) after four years, primarily due to reduced growth, density, and productivity of annual and perennial plants. However, ANPP under pulse drought could recover fully after four years of stopping of drought treatment, and it could not under press drought. Additionally, community structure (i.e., species richness, plant density, and height) fully recovered within 1 year after the end of the two extreme drought treatments. Both plant density and height contributed to the ANPP recovery after press and pulse droughts. Structural equation modeling (SEM) results further revealed that the reduction in ANPP during the extreme drought was primarily due to a decrease in plant density caused by reduced soil water content. The recovery of ANPP in pulse drought was directly caused by increased soil water content in the post-extreme drought. These results suggest that drought intensity and precipitation determine ANPP recovery in a degraded desert steppe. Our findings are crucial for deepening understanding of the processes and mechanisms of ecosystem recovery after extreme drought, as well as for the successful management and protection of grassland ecosystems

Statistical Estimation and Inference for Permutation Based Model

Statistics is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data. People spend lots of time dealing with different kinds of data sets. The structure of the data plays an important role in statistics. Among different structures of data, one interesting structure is the permutation, which involves in different kinds of problems, such as recommender system, online gaming, decision making and sports tournament. This thesis is motivated by my interest in understanding the permutation in statistics. Comparing to the wide applications of permutation related model, little is known to the property of permutation in statistics. There are a variety challenges that arise and lots of problems waiting for us to explore in the permutation based model. This thesis aims to solve several interesting problems of the permutation based model in statistics, which may help us to understand more about the property and characteristic of permutation. As a result of the various topics explored, this thesis is split into three parts. In Chapter 2, we discuss the estimation problem of unimodal SST model in the pairwise comparison problem. We prove that the CLS estimator is rate optimal up to a poly(log log n) factor and propose the computational efficient interval sorting estimator, as a computational efficient algorithm to the estimation problem. In Chapter 3, we shift our attention to the inference problem of the permutation based model. We study different kinds of inference problem, including the hypothesis testing problem in noisy sorting model and confidence set construction problems in generalized permutation based model. Network analysis is another important topic related to the permutation. In Chapter 4, we study the optimality of local belief propagation algorithm in the partial recovery problem of stochastic block model. We prove that local BP algorithm can reach the optimality in a certain regime. Moreover, in the regime where local BP algorithm may not achieve the optimal misclassified fraction, we will prove that local BP algorithm can be used in correcting other algorithms and get optimal algorithm to the partial recovery problem

Monitoring the Plant Density of Cotton with Remotely Sensed Data

Abstract PDC (Plant Density of Cotton) was an essential parameter for estimating the cotton yield and developing the zone-management measurements. This paper proposed a new method to retrieve PDC from the satellite remote sensing data. The thirteen fields of Xinjiang Production and Construction Corps (XPCC) (total 630 hm 2 ) were selected as the study area, where the sowing date, emergence date, and PDC were investigated. Based on the investigation data the linear models to estimate PDC are established using EVI and DEVI respectively. The results indicated that the difference of seedling size caused by the emergence time decreased the estimation accuracy of PDC. To improve the estimation accuracy the partition functions were established in terms of sowing date. DEVI is capable of reducing the influence of soil background significantly and it can bring the monitoring time forward from June 9 th to May 24 th in this research. The results indicated that the optimal time monitoring PDC would be from squaring to full-flowering of cotton growing period. A demonstration to monitor PDC was taken on June 9 th in the 148 th farm of XPCC. It can be concluded that the emergence time and the non-cotton background were the main factors affecting the monitoring accuracy of PDC, and the partition function with the emergence time could improve the estimation accuracy, and DEVI could make the monitoring time forward, and the optimal monitoring time was from the squaring stage to the full-flowering stage. This research provides an efficient, rapid and intact way to monitor PDC, and it is significant for operational application at a regional scale