Abstract

In structural biology, single particle of cryo-electron microscopy (cryo-EM) has been a popular method of determining biological structures. In particular, computation analysis plays an important role in solving structure from a highly noisy cryo-EM image set. Henderson (2013) pointed out that the computer-based image process needs a careful check to ensure the valid of the progress. Otherwise, it can cause an over-fitting problem of single particle cryo-EM in which the solved structure from a highly noise cryo-EM image set can be strongly biased toward the reference model. It is referred as the model bias. An interesting example of the model bias is ``Einstein from noise'', that is, the face of Einstein can be reconstructed from pure noise. This surprising example prompted our interest in investigating the phenomenon from a theoretical point of view. In this talk, we will present a series of simulation results in order to illustrate this phenomenon. Further, we will also give clear mathematical explanations of these results.

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大家都知道「You are what you eat!」這句話！吃的好，身體中會充滿健康的元素，整個人會散發出青春活力，不易生病！以公共衛生的術語來說，吃的健康的人疾病風險低、生活品質高、健康壽命長！

然而要如何吃的健康，似乎眾說紛紜，雖有衛生福利部頒佈的「每日飲食指南」，一般人可能也沒有留意；即使注意到，可能也一知半解，不知如何應用。

這個通俗演講的目的在介紹一個簡易的健康飲食原則，並討論如何在生活中行出此一原則。「吃」真的不只是為了果腹充飢，而是關乎你的身心健康與幸福！健康吃的原則，有複雜的理論基礎，但專家們已歸納出簡易的施行原則，不過這簡單的原則的實作需要些巧思。歡迎你來學習！

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The Cox proportional hazards (PH) model is a common statistical technique employed for analyzing time-to-event data. The assumption of proportional hazards, however, is not always appropriate in real applications. In cases where the assumption is not tenable, threshold regression (TR) and other survival methods, which do not require the PH assumption, are available and widely used. These alternative methods generally assume that the study data constitute simple random samples. In particular, threshold regression has not been studied in the setting of complex surveys that involve 1) differential selection probabilities of study subjects and 2) intra-cluster correlations induced by multistage cluster sampling. In this paper, we extend TR procedures to account for complex sampling designs. The pseudo-maximum likelihood estimation technique is applied to estimate the TR model parameters. Computationally efficient Taylor linearization variance estimators that consider both the intra-cluster correlation and the differential selection probabilities are developed. The proposed methods are evaluated using simulation experiments with various complex designs and illustrated empirically using mortality-linked NHANES III Phase II genetic data.

This is a joint work with Yan Li, Tao Xiao, and Dandan Liao. The manuscript has recently been accepted for publication in the journal of Statistics in Medicine.

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The Riemann zeta function is an important function in mathematics. In particular, the Riemann Hypothesis is a conjecture about the roots of this function. A multiple zeta value (MZV) can be viewed as a generalization of the Riemann zeta function which is defined only for positive integer. The history of MZVs dated back to the time of Euler. Indeed, it was a problem proposed by Goldbach in a letter to Euler in an attempt to evaluate double zeta star values in terms of the Riemann zeta function at positive integer. In recent year, the theory of MZVs has opened up quite a lot connections to other branches of mathematics, such as the knot theory, measure theory and the theory of motives. Also, mathematical physicists need relations among MZVs to express some Feynman integrals. Our principle in the study of this theory is to find all algebraic relations among MZVs. In this talk, I should pay special attention to the sum formula of MZVs and introduce the method of adding additional factors to the integral representation of MZVs, and then show some generalizations of the duality theorem and analogous sum relations.

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Modern theories in educational assessment are rapidly transforming testing from unaccommodating ranking measures into flexible and informative tools that can be used to address the compelling needs of various stakeholders in education. The presentation will start with a brief introduction to smart learning, including some of the trending movements, such as individualized learning and MOOCs. Then, we will discuss how some of the cutting-edge smart testing technologies, such as Computerized Adaptive Testing and Cognitive Diagnostic Measurement, can facilitate smart learning. Our focus will be on how to build a reliable, and also affordable, web-based diagnostic tool for schools to classify students' mastery levels for any given set of cognitive skills that students need to succeed. In addition, we will show how Computerized Adaptive Testing can be employed to support individualized learning on a mass scale.

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考慮一場賠率(odds)為b的賭局，我們證明在最佳下注比例方法下，賭局的平均對數報酬為KL(R||P(b))-KL(R||P)。其中R為實際的輸贏分配比例，P(b)為公平機率，P為賭客個人認為的機率。此論證證明一場固定賠率的賭局，預測輸贏機率決定你會虧損多少，而賭局的最大期望報酬卻是由賠率所決定，我們無法做任何改進。我們亦將此概念應用於選擇權價差交易策略上，價差交易由於固定住最大虧損與最大獲利，故我們只需將策略研發工作用於預測大盤結算點位分部，便能繼算最佳部位與價差組合。

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In this talk, I will discuss some examples of sparse signal detection problems in the context of binary outcomes. These will be motivated by examples from next generation sequencing association studies, understanding heterogeneities in large scale networks, and exploring opinion distributions over networks. Moreover, these examples will serve as templates to explore interesting phase transitions present in such studies. In particular, these phase transitions will be aimed at revealing a difference between studies with possibly dependent binary outcomes and Gaussian outcomes. The theoretical developments will be further complemented with numerical results.

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