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Bayesian outcome selection modeling. 贝叶斯结果选择模型。
IF 1.7 Q1 Mathematics
Lms Journal of Computation and Mathematics
Pub Date : 2023-01-01 Epub Date: 2023-03-29 DOI: 10.1002/sta4.568
Khue-Dung Dang, Louise M Ryan, Richard J Cook, Tugba Akkaya Hocagil, Sandra W Jacobson, Joseph L Jacobson

In psychiatric and social epidemiology studies, it is common to measure multiple different outcomes using a comprehensive battery of tests thought to be related to an underlying construct of interest. In the research that motivates our work, researchers wanted to assess the impact of in utero alcohol exposure on child cognition and neuropsychological development, which are evaluated using a range of different psychometric tests. Statistical analysis of the resulting multiple outcomes data can be challenging, because the outcomes measured on the same individual are not independent. Moreover, it is unclear, a priori, which outcomes are impacted by the exposure under study. While researchers will typically have some hypotheses about which outcomes are important, a framework is needed to help identify outcomes that are sensitive to the exposure and to quantify the associated treatment or exposure effects of interest. We propose such a framework using a modification of stochastic search variable selection, a popular Bayesian variable selection model and use it to quantify an overall effect of the exposure on the affected outcomes. The performance of the method is investigated empirically and an illustration is given through application using data from our motivating study.

在精神病学和社会流行病学研究中，通常使用被认为与潜在兴趣结构相关的综合测试来测量多种不同的结果。在激励我们工作的研究中，研究人员想要评估子宫内酒精暴露对儿童认知和神经心理发展的影响，这是通过一系列不同的心理测试来评估的。对多重结果数据的统计分析可能具有挑战性，因为在同一个体上测量的结果不是独立的。此外，目前尚不清楚哪些结果会受到研究中暴露的影响。虽然研究人员通常会对哪些结果是重要的有一些假设，但需要一个框架来帮助确定对暴露敏感的结果，并量化相关的治疗或感兴趣的暴露效应。我们提出了这样一个框架，使用随机搜索变量选择的修改，一个流行的贝叶斯变量选择模型，并用它来量化暴露对受影响结果的总体影响。本文对该方法的性能进行了实证研究，并利用我们的激励研究数据进行了应用说明。
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引用次数: 0
The Relative Consistency of the Axiom of Choice Mechanized Using Isabelle⁄zf 利用Isabelle / zf机械化的选择公理的相对一致性
Q1 Mathematics
Lms Journal of Computation and Mathematics
Pub Date : 2021-04-26 DOI: 10.1112/S1461157000000449
Lawrence Charles Paulson
The proof of the relative consistency of the axiom of choice has been mechanized using Isabelle⁄ZF, building on a previous mechanization of the reflection theorem. The heavy reliance on metatheory in the original proof makes the formalization unusually long, and not entirely satisfactory: two parts of the proof do not fit together. It seems impossible to solve these problems without formalizing the metatheory. However, the present development follows a standard textbook, Kenneth Kunen's Set theory: an introduction to independence proofs , and could support the formalization of further material from that book. It also serves as an example of what to expect when deep mathematics is formalized.
选择公理的相对一致性的证明，在先前机械化的反射定理的基础上，用Isabelle / ZF机械化了。在原始证明中对元理论的严重依赖使得形式化异常长，并且不完全令人满意:证明的两个部分不适合在一起。如果不形式化元理论，似乎不可能解决这些问题。然而，目前的发展遵循了标准教科书，肯尼斯·库宁的集合论:独立性证明的介绍，并且可以支持从那本书中进一步材料的形式化。它也可以作为一个例子，说明当深度数学被形式化时将会发生什么。
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引用次数: 20
The Linear Programming Relaxation Permutation Symmetry Group of an Orthogonal Array Defining Integer Linear Program 定义整数线性规划的正交阵列的线性规划松弛置换对称群
Q1 Mathematics
Lms Journal of Computation and Mathematics
Pub Date : 2021-04-22 DOI: 10.1112/S1461157016000085
David M. Arquette, D. Bulutoglu
There is always a natural embedding of $S_{s}wr S_{k}$ into the linear programming (LP) relaxation permutation symmetry group of an orthogonal array integer linear programming (ILP) formulation with equality constraints. The point of this paper is to prove that in the $2$ -level, strength- $1$ case the LP relaxation permutation symmetry group of this formulation is isomorphic to $S_{2}wr S_{k}$ for all $k$ , and in the $2$ -level, strength- $2$ case it is isomorphic to $S_{2}^{k}rtimes S_{k+1}$ for $kgeqslant 4$ . The strength- $2$ result reveals previously unknown permutation symmetries that cannot be captured by the natural embedding of $S_{2}wr S_{k}$ . We also conjecture a complete characterization of the LP relaxation permutation symmetry group of the ILP formulation. Supplementary materials are available with this article.
具有相等约束的正交阵列整数线性规划(ILP)公式的线性规划(LP)松弛置换对称群中总是有$S_{s}wr S_{k}$的自然嵌入。本文的目的是证明在$2$ -级强度- $1$情况下，该公式的LP松弛置换对称群对所有$k$都同构于$S_{2}wr S_{k}$，在$2$ -级强度- $2$情况下，对$kgeqslant 4$都同构于$S_{2}^{k}rtimes S_{k+1}$。强度- $2$结果揭示了以前未知的排列对称性，这些对称性不能被$S_{2}wr S_{k}$的自然嵌入所捕获。我们还推测了ILP公式的LP松弛置换对称群的完整表征。本文附有补充材料。
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引用次数: 4
Lens Spaces, Isospectral on Forms but not on Functions 镜头空间，形式上的等谱，而不是函数上的等谱
Q1 Mathematics
Lms Journal of Computation and Mathematics
Pub Date : 2019-06-18 DOI: 10.1112/S1461157000001273
Ruth Gornet, J. McGowan
This paper means to correct an error by the authors for the composite $q$ case in the paper "Lens Spaces, Isospectral on Forms but not on Functions", published in LMS J. Comput. Math.} 9 (2006), 270-286. All calculations and examples presented in cite{GM} for prime $q$ remain valid, and we include detailed calculations below justifying this. Our original mistake was to conclude that Formula (3.11) cite[p. 399]{Ikeda} remained true for all $q$ when in fact it is only valid if $q$ is prime. This means formulas (3) and (4) in cite{GM} must be reworked to account for complications when $q$ is composite.
本文旨在纠正作者在LMS J.Comput上发表的论文“透镜空间，形式上的等光谱，而不是函数上的等谱”中对复合$q$情况的错误。数学。｝9（2006），270-286。引用｛GM｝中关于素数$q$的所有计算和示例仍然有效，我们在下面包括了证明这一点的详细计算。我们最初的错误是得出结论，公式（3.11）cite[p.399]｛Ikeda｝对所有$q$都是真的，而事实上只有当$q$是素数时它才有效。这意味着，当$q$是复合的时，必须重新设计｛GM｝中的公式（3）和（4），以考虑复杂性。
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引用次数: 17
A generalized scheme based on shifted Jacobi polynomials for numerical simulation of coupled systems of multi-term fractional-order partial differential equations 基于移位雅可比多项式的多项分数阶偏微分方程耦合系统数值模拟的广义格式
Q1 Mathematics
Lms Journal of Computation and Mathematics
Pub Date : 2017-01-01 DOI: 10.1112/S146115701700002X
K. Shah, H. Khalil, R. Khan
Due to the increasing application of fractional calculus in engineering and biomedical processes, we analyze a new method for the numerical simulation of a large class of coupled systems of fractional-order partial differential equations. In this paper, we study shifted Jacobi polynomials in the case of two variables and develop some new operational matrices of fractional-order integrations as well as fractional-order differentiations. By the use of these operational matrices, we present a new and easy method for solving a generalized class of coupled systems of fractional-order partial differential equations subject to some initial conditions. We convert the system under consideration to a system of easily solvable algebraic equation without discretizing the system, and obtain a highly accurate solution. Also, the proposed method is compared with some other well-known differential transform methods. The proposed method is computer oriented. We use MatLab to perform the necessary calculation. The next two parts will appear soon.
由于分数阶微积分在工程和生物医学过程中的应用越来越广泛，我们分析了一类分数阶偏微分方程耦合系统数值模拟的新方法。本文研究了两变量情况下的移位雅可比多项式，提出了分数阶积分和分数阶微分的运算矩阵。利用这些运算矩阵，我们给出了求解一类广义分数阶偏微分方程耦合系统的一种新的简便方法。在不使系统离散的情况下，将所考虑的系统转化为易解的代数方程系统，得到了高精度的解。最后，将该方法与其他一些著名的微分变换方法进行了比较。该方法是面向计算机的。我们使用MatLab进行必要的计算。接下来的两部分将很快出现。
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引用次数: 23
The Schwarzian equation for completely replicable functions 完全可复制函数的Schwarzian方程
Q1 Mathematics
Lms Journal of Computation and Mathematics
Pub Date : 2017-01-01 DOI: 10.1112/S1461157017000031
Abdelkrim El Basraoui, J. McKay
We describe the Schwarzian equations for the 328 completely replicable functions with integral $q$ -coefficients [Ford et al. , ‘More on replicable functions’, Comm. Algebra 22 (1994) no. 13, 5175–5193].
我们描述了328个具有积分q系数的完全可复制函数的Schwarzian方程[Ford et al.， ' More on可复制函数'，Comm. Algebra 22 (1994) no. 6]。13日,5175 - 5193]。
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引用次数: 3
Treatment for third-order nonlinear differential equations based on the Adomian decomposition method 基于Adomian分解法的三阶非线性微分方程处理
Q1 Mathematics
Lms Journal of Computation and Mathematics
Pub Date : 2017-01-01 DOI: 10.1112/S1461157017000018
Xueqin Lv, Jianfang Gao
The Adomian decomposition method (ADM) is an efficient method for solving linear and nonlinear ordinary differential equations, differential algebraic equations, partial differential equations, stochastic differential equations, and integral equations. Based on the ADM, a new analytical and numerical treatment is introduced in this research for third-order boundary-value problems. The effectiveness of the proposed approach is verified by numerical examples.
Adomian分解法(ADM)是求解线性和非线性常微分方程、微分代数方程、偏微分方程、随机微分方程和积分方程的有效方法。在此基础上，引入了一种新的三阶边值问题的解析和数值处理方法。数值算例验证了该方法的有效性。
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引用次数: 5
On the zeros of Dirichlet $L$ -functions – RETRACTION 狄利克雷$L$ -函数-缩回的零点
Q1 Mathematics
Lms Journal of Computation and Mathematics
Pub Date : 2017-01-01 DOI: 10.1112/S1461157018000013
Sami Omar, Raouf Ouni, Kamel Mazhouda
On the zeros of Dirichlet L-functions – RETRACTION Sami Omar, Raouf Ouni and Kamel Mazhouda (LMS J. Comput. Math. 14 (2011) 140–154) This paper [1], which was published online on 1 June 2011, has been retracted by agreement between the authors, the journal’s Editor-in-Chief Derek Holt, the London Mathematical Society and Cambridge University Press. The retraction was agreed to prevent other authors from using incorrect mathematical results.
Dirichlet l -函数的零点——缩回Sami Omar, Raouf Ouni和Kamel Mazhouda (LMS J.计算机学报)。数学14(2011)140-154这篇论文于2011年6月1日在网上发表，经作者、期刊主编Derek Holt、伦敦数学学会和剑桥大学出版社同意撤回。同意撤回是为了防止其他作者使用错误的数学结果。
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引用次数: 0
Finding 47:23 in the Baby Monster 在Baby Monster找到47:23
Q1 Mathematics
Lms Journal of Computation and Mathematics
Pub Date : 2016-05-18 DOI: 10.1112/S1461157016000024
J. Bray, R. Parker, R. Wilson
In this paper we describe methods for finding very small maximal subgroups of very large groups, with particular application to the subgroup 47:23 of the Baby Monster. This example is completely intractable by standard or naive methods. The example of finding 31:15 inside the Thompson group $text{Th}$ is also discussed as a test case.
本文描述了寻找非常大群的非常小的极大子群的方法，并特别应用于小怪物的47:23子群。这个例子是完全难以处理的标准或幼稚的方法。在Thompson组$text{Th}$中查找31:15的示例也作为测试用例进行了讨论。
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引用次数: 1
Computing -series of geometrically hyperelliptic curves of genus three 三属几何超椭圆曲线级数的计算
Q1 Mathematics
Lms Journal of Computation and Mathematics
Pub Date : 2016-05-01 DOI: 10.1112/S1461157016000383
David Harvey, Maike Massierer, Andrew V. Sutherland
Let C/Q be a curve of genus three, given as a double cover of a plane conic. Such a curve is hyperelliptic over the algebraic closure of Q, but may not have a hyperelliptic model of the usual form over Q. We describe an algorithm that computes the local zeta functions of C at all odd primes of good reduction up to a prescribed bound N. The algorithm relies on an adaptation of the "accumulating remainder tree" to matrices with entries in a quadratic field. We report on an implementation, and compare its performance to previous algorithms for the ordinary hyperelliptic case.
设C/Q为一条3属曲线，作为平面二次曲线的双重覆盖。这样的曲线在Q的代数闭包上是超椭圆的，但在Q上可能没有通常形式的超椭圆模型。我们描述了一种算法，该算法计算C在所有奇素数上的局部zeta函数，直到规定的界n。该算法依赖于“累积剩余树”对二次域中有条目的矩阵的适应。我们报告了一种实现，并将其性能与以前的普通超椭圆情况下的算法进行了比较。
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