We propose a unifying dynamic-programming framework to compute exact
literal-weighted model counts of formulas in conjunctive normal form. At the
center of our framework are project-join trees, which specify efficient
project-join orders to apply additive projections (variable eliminations) and
joins (clause multiplications). In this framework, model counting is performed
in two phases. First, the planning phase constructs a project-join tree from a
formula. Second, the execution phase computes the model count of the formula,
employing dynamic programming as guided by the project-join tree. We
empirically evaluate various methods for the planning phase and compare
constraint-satisfaction heuristics with tree-decomposition tools. We also
investigate the performance of different data structures for the execution
phase and compare algebraic decision diagrams with tensors. We show that our
dynamic-programming model-counting framework DPMC is competitive with the
state-of-the-art exact weighted model counters cachet, c2d, d4, and miniC2D.

提出了一种动态编程框架来计算 CNF 中公式的精确带权模型计数，其中包括 project-join 树的计划阶段和执行阶段，以及基于约束满足启发式与树分解工具的规划阶段，以及与张量比较的不同数据结构的执行阶段。与 cachet、c2d、d4 和 miniC2D 等最先进的精确带权模型计数器相比，该框架是有竞争力的。

DPMC：基于项目连接树的动态规划加权模型计数

DPMC: Weighted Model Counting by Dynamic Programming on Project-Join  Trees

We present an open source math-aware Question Answering System based on Ask
Platypus. Our system returns as a single mathematical formula for a natural
language question in English or Hindi. This formulae originate from the
knowledge-base Wikidata. We translate these formulae to computable data by
integrating the calculation engine sympy into our system. This way, users can
enter numeric values for the variables occurring in the formula. Moreover, the
system loads numeric values for constants occurring in the formula from
Wikidata. In a user study, our system outperformed a commercial computational
mathematical knowledge engine by 13%. However, the performance of our system
heavily depends on the size and quality of the formula data available in
Wikidata. Since only a few items in Wikidata contained formulae when we started
the project, we facilitated the import process by suggesting formula edits to
Wikidata editors. With the simple heuristic that the first formula is
significant for the article, 80% of the suggestions were correct.

我们提出了一种基于 Ask Platypus 的开源数学感知问答系统，它能够针对英语或印地语的自然语言问题返回单一的数学公式。这些公式来源于知识库 Wikidata，并通过 sympy 计算引擎将其转换为可计算的数据，用户可以为公式中出现的变量输入数值。在用户研究中，我们的系统性能优于商用计算数学知识引擎 13％。

引入 MathQA - 一种数学感知问答系统

Introducing MathQA -- A Math-Aware Question Answering System

Concrete is the most widely used engineered material in the world with more
than 10 billion tons produced annually. Unfortunately, with that scale comes a
significant burden in terms of energy, water, and release of greenhouse gases
and other pollutants. As such, there is interest in creating concrete formulas
that minimize this environmental burden, while satisfying engineering
performance requirements. Recent advances in artificial intelligence have
enabled machines to generate highly plausible artifacts, such as images of
realistic looking faces. Semi-supervised generative models allow generation of
artifacts with specific, desired characteristics. In this work, we use
Conditional Variational Autoencoders (CVAE), a type of semi-supervised
generative model, to discover concrete formulas with desired properties. Our
model is trained using open data from the UCI Machine Learning Repository
joined with environmental impact data computed using a web-based tool. We
demonstrate CVAEs can design concrete formulas with lower emissions and natural
resource usage while meeting design requirements. To ensure fair comparison
between extant and generated formulas, we also train regression models to
predict the environmental impacts and strength of discovered formulas. With
these results, a construction engineer may create a formula that meets
structural needs and best addresses local environmental concerns.

通过使用半监督生成模型（CVAE），该研究使用 UCI 机器学习库的开放数据和基于网络工具计算的环境影响数据对模型进行训练，以设计出满足结构要求且具有更低排放和更少自然资源使用的混凝土配方。