Line Simplification

As an important practice of map generalization, the aim of line simplification is to reduce the number of points without destroying the essential shape or the salient character of a cartographic curve. This subject has been well-studied in the literature. This entry attempts to introduce how line simplification can be guided by fractal geometry, or the recurring scaling pattern of far more small things than large ones. The line simplification process involves nothing more than removing small things while retaining large ones based on head/tail breaks.Comment: 6 pages, 3 figure

Integrating Transformer and Paraphrase Rules for Sentence Simplification

Sentence simplification aims to reduce the complexity of a sentence while retaining its original meaning. Current models for sentence simplification adopted ideas from ma- chine translation studies and implicitly learned simplification mapping rules from normal- simple sentence pairs. In this paper, we explore a novel model based on a multi-layer and multi-head attention architecture and we pro- pose two innovative approaches to integrate the Simple PPDB (A Paraphrase Database for Simplification), an external paraphrase knowledge base for simplification that covers a wide range of real-world simplification rules. The experiments show that the integration provides two major benefits: (1) the integrated model outperforms multiple state- of-the-art baseline models for sentence simplification in the literature (2) through analysis of the rule utilization, the model seeks to select more accurate simplification rules. The code and models used in the paper are available at https://github.com/ Sanqiang/text_simplification

Static Contract Simplification

Contracts and contract monitoring are a powerful mechanism for specifying properties and guaranteeing them at run time. However, run time monitoring of contracts imposes a significant overhead. The execution time is impacted by the insertion of contract checks as well as by the introduction of proxy objects that perform delayed contract checks on demand. Static contract simplification attacks this issue using program transformation. It applies compile-time transformations to programs with contracts to reduce the overall run time while preserving the original behavior. Our key technique is to statically propagate contracts through the program and to evaluate and merge contracts where possible. The goal is to obtain residual contracts that are collectively cheaper to check at run time. We distinguish different levels of preservation of behavior, which impose different limitations on the admissible transformations: Strong blame preservation, where the transformation is a behavioral equivalence, and weak blame preservation, where the transformed program is equivalent up to the particular violation reported. Our transformations never increase the overall number of contract checks.Comment: Technical Repor

Global Curve Simplification

Due to its many applications, \emph{curve simplification} is a long-studied problem in computational geometry and adjacent disciplines, such as graphics, geographical information science, etc. Given a polygonal curve $P$ with $n$ vertices, the goal is to find another polygonal curve $P'$ with a smaller number of vertices such that $P'$ is sufficiently similar to $P$. Quality guarantees of a simplification are usually given in a \emph{local} sense, bounding the distance between a shortcut and its corresponding section of the curve. In this work, we aim to provide a systematic overview of curve simplification problems under \emph{global} distance measures that bound the distance between $P$ and $P'$. We consider six different curve distance measures: three variants of the \emph{Hausdorff} distance and three variants of the \emph{Fr\'echet} distance. And we study different restrictions on the choice of vertices for $P'$. We provide polynomial-time algorithms for some variants of the global curve simplification problem and show NP-hardness for other variants. Through this systematic study we observe, for the first time, some surprising patterns, and suggest directions for future research in this important area.Comment: 33 pages, 16 figure

A Constrained Sequence-to-Sequence Neural Model for Sentence Simplification

Sentence simplification reduces semantic complexity to benefit people with language impairments. Previous simplification studies on the sentence level and word level have achieved promising results but also meet great challenges. For sentence-level studies, sentences after simplification are fluent but sometimes are not really simplified. For word-level studies, words are simplified but also have potential grammar errors due to different usages of words before and after simplification. In this paper, we propose a two-step simplification framework by combining both the word-level and the sentence-level simplifications, making use of their corresponding advantages. Based on the two-step framework, we implement a novel constrained neural generation model to simplify sentences given simplified words. The final results on Wikipedia and Simple Wikipedia aligned datasets indicate that our method yields better performance than various baselines

Multiresolution topological simplification

Persistent homology has been devised as a promising tool for the topological simplification of complex data. However, it is computationally intractable for large data sets. In this work, we introduce multiresolution persistent homology for tackling large data sets. Our basic idea is to match the resolution with the scale of interest so as to create a topological microscopy for the underlying data. We utilize flexibility-rigidity index (FRI) to access the topological connectivity of the data set and define a rigidity density for the filtration analysis. By appropriately tuning the resolution, we are able to focus the topological lens on a desirable scale. The proposed multiresolution topological analysis is validated by a hexagonal fractal image which has three distinct scales. We further demonstrate the proposed method for extracting topological fingerprints from DNA and RNA molecules. In particular, the topological persistence of a virus capsid with 240 protein monomers is successfully analyzed which would otherwise be inaccessible to the normal point cloud method and unreliable by using coarse-grained multiscale persistent homology. The proposed method has also been successfully applied to the protein domain classification, which is the first time that persistent homology is used for practical protein domain analysis, to our knowledge. The proposed multiresolution topological method has potential applications in arbitrary data sets, such as social networks, biological networks and graphs.Comment: 22 pages and 14 figure

Efficient LTL Decentralized Monitoring Framework Using Formula Simplification Table

This paper presents a new technique for optimizing formal analysis of propositional logic formulas and Linear Temporal Logic (LTL) formulas, namely the formula simplification table. A formula simplification table is a mathematical table that shows all possible simplifications of the formula under different truth assignments of its variables. The advantages of constructing a simplification table of a formula are two-fold. First, it can be used to compute the logical influence weight of each variable in the formula, which is a metric that shows the importance of the variable in affecting the outcome of the formula. Second, it can be used to identify variables that have the highest logical influences on the outcome of the formula. %The simplification table can be used to optimize %existing solutions for several interesting %LTL verification problems. We demonstrate the effectiveness of formula simplification table in the context of software verification by developing efficient framework to the well-known decentralized LTL monitoring problem

Simple and Effective Text Simplification Using Semantic and Neural Methods

Sentence splitting is a major simplification operator. Here we present a simple and efficient splitting algorithm based on an automatic semantic parser. After splitting, the text is amenable for further fine-tuned simplification operations. In particular, we show that neural Machine Translation can be effectively used in this situation. Previous application of Machine Translation for simplification suffers from a considerable disadvantage in that they are over-conservative, often failing to modify the source in any way. Splitting based on semantic parsing, as proposed here, alleviates this issue. Extensive automatic and human evaluation shows that the proposed method compares favorably to the state-of-the-art in combined lexical and structural simplification

Semantic Structural Evaluation for Text Simplification

Current measures for evaluating text simplification systems focus on evaluating lexical text aspects, neglecting its structural aspects. In this paper we propose the first measure to address structural aspects of text simplification, called SAMSA. It leverages recent advances in semantic parsing to assess simplification quality by decomposing the input based on its semantic structure and comparing it to the output. SAMSA provides a reference-less automatic evaluation procedure, avoiding the problems that reference-based methods face due to the vast space of valid simplifications for a given sentence. Our human evaluation experiments show both SAMSA's substantial correlation with human judgments, as well as the deficiency of existing reference-based measures in evaluating structural simplification

Mastering Sketching: Adversarial Augmentation for Structured Prediction

We present an integral framework for training sketch simplification networks that convert challenging rough sketches into clean line drawings. Our approach augments a simplification network with a discriminator network, training both networks jointly so that the discriminator network discerns whether a line drawing is a real training data or the output of the simplification network, which in turn tries to fool it. This approach has two major advantages. First, because the discriminator network learns the structure in line drawings, it encourages the output sketches of the simplification network to be more similar in appearance to the training sketches. Second, we can also train the simplification network with additional unsupervised data, using the discriminator network as a substitute teacher. Thus, by adding only rough sketches without simplified line drawings, or only line drawings without the original rough sketches, we can improve the quality of the sketch simplification. We show how our framework can be used to train models that significantly outperform the state of the art in the sketch simplification task, despite using the same architecture for inference. We additionally present an approach to optimize for a single image, which improves accuracy at the cost of additional computation time. Finally, we show that, using the same framework, it is possible to train the network to perform the inverse problem, i.e., convert simple line sketches into pencil drawings, which is not possible using the standard mean squared error loss. We validate our framework with two user tests, where our approach is preferred to the state of the art in sketch simplification 92.3% of the time and obtains 1.2 more points on a scale of 1 to 5.Comment: 12 pages, 14 figure