Optimal Tests of Treatment Effects for the Overall Population and Two Subpopulations in Randomized Trials, using Sparse Linear Programming

We propose new, optimal methods for analyzing randomized trials, when it is suspected that treatment effects may differ in two predefined subpopulations. Such sub-populations could be defined by a biomarker or risk factor measured at baseline. The goal is to simultaneously learn which subpopulations benefit from an experimental treatment, while providing strong control of the familywise Type I error rate. We formalize this as a multiple testing problem and show it is computationally infeasible to solve using existing techniques. Our solution involves a novel approach, in which we first transform the original multiple testing problem into a large, sparse linear program. We then solve this problem using advanced optimization techniques. This general method can solve a variety of multiple testing problems and decision theory problems related to optimal trial design, for which no solution was previously available. In particular, we construct new multiple testing procedures that satisfy minimax and Bayes optimality criteria. For a given optimality criterion, our new approach yields the optimal tradeoff? between power to detect an effect in the overall population versus power to detect effects in subpopulations. We demonstrate our approach in examples motivated by two randomized trials of new treatments for HIV

The Computational Complexity of Quantum Determinants

In this work, we study the computational complexity of quantum determinants, a $q$-deformation of matrix permanents: Given a complex number $q$ on the unit circle in the complex plane and an $n\times n$ matrix $X$, the $q$-permanent of $X$ is defined as $$\mathrm{Per}_q(X) = \sum_{\sigma\in S_n} q^{\ell(\sigma)}X_{1,\sigma(1)}\ldots X_{n,\sigma(n)},$$ where $\ell(\sigma)$ is the inversion number of permutation $\sigma$ in the symmetric group $S_n$ on $n$ elements. The function family generalizes determinant and permanent, which correspond to the cases $q=-1$ and $q=1$ respectively. For worst-case hardness, by Liouville's approximation theorem and facts from algebraic number theory, we show that for primitive $m$-th root of unity $q$ for odd prime power $m=p^k$, exactly computing $q$-permanent is $\mathsf{Mod}_p\mathsf{P}$-hard. This implies that an efficient algorithm for computing $q$-permanent results in a collapse of the polynomial hierarchy. Next, we show that computing $q$-permanent can be achieved using an oracle that approximates to within a polynomial multiplicative error and a membership oracle for a finite set of algebraic integers. From this, an efficient approximation algorithm would also imply a collapse of the polynomial hierarchy. By random self-reducibility, computing $q$-permanent remains to be hard for a wide range of distributions satisfying a property called the strong autocorrelation property. Specifically, this is proved via a reduction from $1$-permanent to $q$-permanent for $O(1/n^2)$ points $z$ on the unit circle. Since the family of permanent functions shares common algebraic structure, various techniques developed for the hardness of permanent can be generalized to $q$-permanents

Exploring Methods for Building Dialects-Mandarin Code-Mixing Corpora: A Case Study in Taiwanese Hokkien

In natural language processing (NLP), code-mixing (CM) is a challenging task, especially when the mixed languages include dialects. In Southeast Asian countries such as Singapore, Indonesia, and Malaysia, Hokkien-Mandarin is the most widespread code-mixed language pair among Chinese immigrants, and it is also common in Taiwan. However, dialects such as Hokkien often have a scarcity of resources and the lack of an official writing system, limiting the development of dialect CM research. In this paper, we propose a method to construct a Hokkien-Mandarin CM dataset to mitigate the limitation, overcome the morphological issue under the Sino-Tibetan language family, and offer an efficient Hokkien word segmentation method through a linguistics-based toolkit. Furthermore, we use our proposed dataset and employ transfer learning to train the XLM (cross-lingual language model) for translation tasks. To fit the code-mixing scenario, we adapt XLM slightly. We found that by using linguistic knowledge, rules, and language tags, the model produces good results on CM data translation while maintaining monolingual translation quality.Comment: The paper was accepted by EMNLP 2022 finding

COMPARISON OF EMG ACTIVITY WITH DYNAMIC MOVEMENT AND STATIC POSTURE ON VIBRATION PLATFORM

The aim of this study is to investigate the difference among dynamic movement and static posture on vibration platform as well as no vibration. For this purpose, six healthy male subjects were recruited in this study. Each subject was instructed to maintain four situations: dynamic movement with vibration (frequency: 40 Hz, amplitude: 1 mm), and no-vibration; static posture with vibration (frequency: 40 Hz, amplitude: 1 mm), and novibration. Result showed statistically significant increase at EMG rms of whole body vibration treatment and EMG rms value of dynamic movement was significantly larger than that of static posture (

Collection of anthropometry from older and physically impaired persons: traditional methods versus TC2 3-D body scanner

With advances in technology it is now possible to collect a wide range of anthropometric data, to a high degree of accuracy, using 3D light-based body scanners. This gives the potential to speed up the collection of anthropometric data for design purposes, to decrease processing time and data input required, and to reduce error due to inaccuracy of measurements taken using more traditional methods and equipment (anthropometer, stadiometer and sitting height table). However, when the data collection concerns older and/or physically impaired people there are serious issues for consideration when deciding on the best method to collect anthropometry. This paper discusses the issues arising when collecting data using both traditional methods of data collection and a first use by the experimental team of the TC2 3D body scanner, when faced with a ‘non-standard’ sample, during an EPSRC funded research project into issues surrounding transport usage by older and physically impaired people. Relevance to industry: Designing products, environments and services so that the increasing ageing population, as well as the physically impaired, can use them increases the potential market. To do this, up-to-date and relevant anthropometry is often needed. 3D light-based bodyscanners offer a potential fast way of obtaining this data, and this paper discusses some of the issues with using one scanner with older and disabled people

Muon mass correction in partial wave analyses of charmed meson semi-leptonic decays

We derive the parameterization formula for partial wave analyses of charmed meson semi-leptonic decays with consideration of the effects caused by the lepton mass. As the proposed super-tau-charm factory will reach much enhanced luminosity and BESIII is taking $\psi(3770)\to D\bar{D}$ data, our results are helpful to improve the measurement precision of future partial wave analyses of charmed meson semi-muonic decays