Optimal Simplification Research Articles

Role of gas–molecular cluster–aerosol dynamics in atmospheric new-particle formation

New-particle formation from vapors through molecular cluster formation is a central process affecting atmospheric aerosol and cloud condensation nuclei numbers, and a significant source of uncertainty in assessments of aerosol radiative forcing. While advances in experimental and computational methods provide improved assessments of particle formation rates from different species, the standard approach to implement these data in aerosol models rests on highly simplifying assumptions concerning gas–cluster–aerosol dynamics. To quantify the effects of the simplifications, we develop an open-source tool for explicitly simulating the dynamics of the complete particle size spectrum from vapor molecules and molecular clusters to larger aerosols for multi-compound new-particle formation. We demonstrate that the simplified treatment is a reasonable approximation for particle formation from weakly clustering chemical compounds, but results in overprediction of particle numbers and of the contribution of new-particle formation to cloud condensation nuclei for strongly clustering, low-concentration trace gases. The new explicit approach circumvents these issues, thus enabling robust model–measurement comparisons, improved assessment of the importance of different particle formation agents, and construction of optimal simplifications for large-scale models.

Geometric Modeling of Rosa roxburghii Fruit Based on Three-Dimensional Point Cloud Reconstruction

Fruit three-dimensional (3D) model is crucial to estimating its geometrical and mechanical properties and improving the level of fruit mechanical processing. Considering the complex geometrical features and the required model accuracy, this paper proposed a 3D point cloud reconstruction method for the Rosa roxburghii fruit based on a three-dimensional laser scanner, including 3D point cloud generation, point cloud registration, fruit thorns segmentation, and 3D reconstruction. The 3D laser scanner was used to obtain the original 3D point cloud data of the Rosa roxburghii fruit, and then the fruit thorns data were removed by the segmentation algorithm combining the statistical outlier removal and radius outlier removal. By analyzing the effects of five-point cloud simplification methods, the optimal simplification method was determined. The Poisson reconstruction algorithm, the screened Poisson reconstruction algorithm, the greedy projection triangulation algorithm, and the Delaunay triangulation algorithm were utilized to reconstruct the fruit model. The number of model vertices, the number of facets, and the relative volume error were used to determine the best reconstruction algorithm. The results indicated that this model can better reconstruct the actual surface of Rosa roxburghii fruit. The method provides a reference for the related application.

High-volume point cloud data simplification based on decomposed graph filtering

Recent studies on three-dimensional (3D) point cloud data (PCD) simplification have played significant roles in computer-aided models for alleviating computational and storage burden. However, existing simplification methods are not suitable for the high-volume PCD with billions of point number, especially in construction industry. In this paper, a decomposed simplification method is developed to handle the high-volume buildings' PCD. Based on the divide-and-conquer philosophy, the new decomposed approach effectively reduces the memory usage. In the proposed approach, PCD is divided into several subsets according to the relationship of natural neighbor, and decomposed graph filtering with adaptive resampling rate is designed. It can be proved that the decomposed simplification results have no variance in the comparison with the optimal simplification of entire PCD. Verification experiments are conducted on different sizes of PCD, which indicate the effectiveness and feasibility of the proposed approach.

On optimal polyline simplification using the Hausdorff and Fréchet distance

We revisit the classical polygonal line simplification problem and study it using the Hausdorff distance and Frechet distance. Interestingly, no previous authors studied line simplification under these measures in its pure form, namely: for a given e > 0, choose a minimum size subsequence of the vertices of the input such that the Hausdorff or Frechet distance between the input and output polylines is at most e.We analyze how the well-known Douglas-Peucker and Imai-Iri simplification algorithms perform compared to the optimum possible, also in the situation where the algorithms are given a considerably larger error threshold than we require for the optimum solution. Furthermore, we show that computing an optimal simplification using the undirected Hausdorff distance is NP-hard. The same holds when using the directed Hausdorff distance from the input to the output polyline, whereas the reverse can be computed in polynomial time. Finally, to compute the optimal simplification from a polygonal line consisting of n vertices under the (continuous) Frechet distance, we give an $O(kn^5)$ time algorithm that requires $O(kn^2)$ space, where $k$ is the output complexity of the simplification.

Resilient training of neural network classifiers with approximate computing techniques for hardware‐optimised implementations

As Machine Learning applications increase the demand for optimised implementations in both embedded and high-end processing platforms, the industry and research community have been responding with different approaches to implement these solutions. This work presents approximations to arithmetic operations and mathematical functions that, associated with a customised adaptive artificial neural networks training method, based on RMSProp, provide reliable and efficient implementations of classifiers. The proposed solution does not rely on mixed operations with higher precision or complex rounding methods that are commonly applied. The intention of this work is not to find the optimal simplifications for specific deep learning problems but to present an optimised framework that can be used as reliably as one implemented with precise operations, standard training algorithms and the same network structures and hyper-parameters. By simplifying the ‘half-precision’ floating point format and approximating exponentiation and square root operations, the authors’ work drastically reduces the field programmable gate array implementation complexity (e.g. −43 and −57% in two of the component resources). The reciprocal square root approximation is so simple it could be implemented only with combination logic. In a full software implementation for a mixed-precision platform, only two of the approximations compensate the processing overhead of precision conversions.

Regression modeling of reduction in spatial accuracy and detail for multiple geometric line simplification procedures

ABSTRACTOne of the important stages of map generalization is the selection of optimal simplification procedure for each spatial feature or feature type. Selected algorithms are then applied collaboratively to simplify the whole set of features. However, there is a lack of investigations that report a systematic approach of deriving a similar reduction in accuracy and detail by using different algorithms. In current paper we propose the solution to this problem on the basis of regression modeling between tolerance value of each algorithm and the value of some geometric measure which describes changes in accuracy and detail of the line. This allows fitting the regression model between tolerance values of the two selected algorithms which can be used to obtain similar simplification results. Regressions between Douglas-Peucker, Li-Openshaw and Visvalingam-Whyatt algorithm tolerance values are investigated. Application of methodology is illustrated on the example of three coastlines with significantly different spatial character. Results of the study show that regression coefficients depend highly both on the combination of the two algorithms, and on the character of the line. Finally, it is shown that a weighted combination of accuracy and detail regression models can be used to model the changes in level of detail of the line.

The Coleman Diagram, Small N Inquiry and Ethnographic Causality

Certain key ideas have served to stimulate thought about the nature of sociological inquiry by presenting frameworks which are adjustable to the varying demands of different sorts of data. They provide, as it were, heuristics which enable a systematic debate about the optimal simplifications that are enjoined by varying types of data, notably what are sometimes labelled as quantitative and qualitative. In so doing they facilitate a variety of analyses, generate hypotheses and eventually lead to discoveries that transcend inherited boundaries. Our claim is that the Coleman diagram, though largely interpreted within a quantitative tradition, is one such framework for formalizing qualitative methods and for understanding the interplay between different types of data in the social sciences.

Near Optimal Control Based on the Tensor-Product Technique

This brief investigates the near optimal control problem and targets at the rigid body attitude dynamic system that are characterized by its typical nonlinearity. In order to apply the linear matrix inequality-based optimization, a second-order linear-parameter-varying model is specifically derived from the attitude system by means of the tensor-product transformation. Furthermore, an adaptive attitude tracking control law is designed to achieve both the offline optimization and online control simplification. The final control law is provided in a combined form. As a result, the dynamic response of the system mainly depends on the near optimal virtual controller and the stability can be further guaranteed by the adaptive tracking controller. Numerical simulations are conducted to verify the effectiveness of the proposed algorithms.

A Graph-Based Min-# and Error-Optimal Trajectory Simplification Algorithm and Its Extension towards Online Services

Trajectory simplification has become a research hotspot since it plays a significant role in the data preprocessing, storage, and visualization of many offline and online applications, such as online maps, mobile health applications, and location-based services. Traditional heuristic-based algorithms utilize greedy strategy to reduce time cost, leading to high approximation error. An Optimal Trajectory Simplification Algorithm based on Graph Model (OPTTS) is proposed to obtain the optimal solution in this paper. Both min-# and min-ε problems are solved by the construction and regeneration of the breadth-first spanning tree and the shortest path search based on the directed acyclic graph (DAG). Although the proposed OPTTS algorithm can get optimal simplification results, it is difficult to apply in real-time services due to its high time cost. Thus, a new Online Trajectory Simplification Algorithm based on Directed Acyclic Graph (OLTS) is proposed to deal with trajectory stream. The algorithm dynamically constructs the breadth-first spanning tree, followed by real-time minimizing approximation error and real-time output. Experimental results show that OPTTS reduces the global approximation error by 82% compared to classical heuristic methods, while OLTS reduces the error by 77% and is 32% faster than the traditional online algorithm. Both OPTTS and OLTS have leading superiority and stable performance on different datasets.

Disjoint factor analysis with cross-loadings

Disjoint factor analysis (DFA) is a new latent factor model that we propose here to identify factors that relate to disjoint subsets of variables, thus simplifying the loading matrix structure. Similarly to exploratory factor analysis (EFA), the DFA does not hypothesize prior information on the number of factors and on the relevant relations between variables and factors. In DFA the population variance–covariance structure is hypothesized block diagonal after the proper permutation of variables and estimated by Maximum Likelihood, using an Coordinate Descent type algorithm. Inference on parameters on the number of factors and to confirm the hypothesized simple structure are provided. Properties such as scale equivariance, uniqueness, optimal simplification of loadings are satisfied by DFA. Relevant cross-loadings are also estimated in case they are detected from the best DFA solution. DFA has also the option to constrain a variable to load on a pre-specified factor so that the researcher can assume, a priori, some relations between variables and loadings. A simulation study shows performances of DFA and an application to optimally identify the dimensions of well-being is used to illustrate characteristics of the new methodology. A final discussion concludes the paper.

Three-dimensional terrain model multiview quality assessment considering human visual system

In the current remote sensing big data era, the huge amount of data, especially the expansion of spatial dimension, brings challenges to the traditional processing and applications in data transferring, processing and visualization. Model quality assessment is usually employed to evaluate the yielding model and select the optimal simplification method, which is used to improve the efficiency of big data processing. The existing three-dimensional (3-D) terrain model assessment methods mainly exploit the data accuracy or geometric features while ignoring the impact of humans or users. We mainly investigate the quality assessment for the 3-D terrain model. The proposed method provides an integration of structural similarity and the human vis- ual system from the multiview angles for the image quality assessment. The visual impact of observers and the structural information retention of the 3-D terrain model have been fully con- sidered. In the experiments, two kinds of models with different simplification ratios are utilized for the terrain model evaluation. The results confirm that the proposed algorithm has a better performance of terrain model quality assessment than other traditional methods. © 2015 Society of Photo-Optical Instrumentation Engineers (SPIE) (DOI: 10.1117/1.JRS.9.097290)

Criminal Procedure: Optimization or Unjustified Simplification? The Round Table Discussion Review Dated September 24, 2015

Criminal Procedure: Optimization or Unjustified Simplification? The Round Table Discussion Review Dated September 24, 2015

Using the uncertainty principle to design simple interactions for targeted self-assembly

We present a method that systematically simplifies isotropic interactions designed for targeted self-assembly. The uncertainty principle is used to show that an optimal simplification is achieved by a combination of heat kernel smoothing and Gaussian screening of the interaction potential in real and reciprocal space. We use this method to analytically design isotropic interactions for self-assembly of complex lattices and of materials with functional properties. The derived interactions are simple enough to narrow the gap between theory and experimental implementation of theory based designed self-assembling materials.

Computing polygonal path simplification under area measures

In this paper, we consider the restricted version of the well-known 2D line simplification problem under area measures and for restricted version. We first propose a unified definition for both of sum-area and difference-area measures that can be used on a general path of n vertices. The optimal simplification runs in O(n3) under both of these measures. Under sum-area measure and for a realistic input path, we propose an approximation algorithm of On2ϵ time complexity to find a simplification of the input path, where ϵ is the absolute error of this algorithm compared to the optimal solution. Furthermore, for difference-area measure, we present an algorithm that finds the optimal simplification in O(n2) time. The best previous results work only on x-monotone paths while both of our algorithms work on general paths. To the best of our knowledge, the results presented here are the first sub-cubic simplification algorithms on these measures for general paths.

MSMSE-based optimal beamforming design and simplification on AF MIMO two-way relay channels

An optimal cooperative beamforming for the amplify-and-forward (AF) MIMO two-way relay channels was designed. Supposing the channel state information (CSI) was perfectly known by the receiver and transmitter as well as the relay, optimal beamforming vectors (matrices) of all nodes were jointly designed based on the criterion of minimizing the sum mean square errors (MSMSE). The analysis result shows that the performance effect of transmitting and receiving beamforming pairs is to maximize the receive signal-to-noise ratio (SNR) at two communication nodes, and the rank of the optimal relay beamforming matrix is no larger than two when there is only one data stream at each source node. A simplified algorithm was put forward to accomplish the design based on the analysis conclusions. Simulation results provide that the system performance, which is characterized in terms of bit error rates (BER), is significantly improved by cooperative beamforming, and the performance of the simplified method is not only very close to the optimal one but also with faster iteration speed and much lower computational complexity.

Streaming Algorithms for Line Simplification

We study the following variant of the well-known line-simplification problem: we are getting a (possibly infinite) sequence of points p 0,p 1,p 2,… in the plane defining a polygonal path, and as we receive the points, we wish to maintain a simplification of the path seen so far. We study this problem in a streaming setting, where we only have a limited amount of storage, so that we cannot store all the points. We analyze the competitive ratio of our algorithms, allowing resource augmentation: we let our algorithm maintain a simplification with 2k (internal) points and compare the error of our simplification to the error of the optimal simplification with k points. We obtain the algorithms with O(1) competitive ratio for three cases: convex paths, where the error is measured using the Hausdorff distance (or Fréchet distance), xy-monotone paths, where the error is measured using the Hausdorff distance (or Fréchet distance), and general paths, where the error is measured using the Fréchet distance. In the first case the algorithm needs O(k) additional storage, and in the latter two cases the algorithm needs O(k 2) additional storage.

Optimal simplification of polygonal chains for subpixel-accurate rendering

For a given polygonal chain, we study the min-# problem, which consists of finding an approximate and ordered subchain with a minimum number of vertices under a given approximation criterion. We propose the first near-linear time algorithm for the min-# problem that ensures optimality in the number of vertices and that retains the shape of the input polygonal chain at the same time. Previous algorithms with near-linear time performance produced geometrical inconsistencies and former methods used to preserve the features of the original chain required a quadratic time complexity. When we set the approximation error equal to the pixel pitch, our simplification criterion guarantees that the rendering of the simplification lies at most half a pixel away from the original chain, contrary to other methods that do not offer a direct control over the rendering. Thus, we avoid producing visible topological inconsistencies. Moreover, our method is based on basic data structures, which leads to a simple and efficient implementation.

Wiener Filter-Based Error Resilient Time-Domain Lapped Transform

In this paper, the design of the error resilient time-domain lapped transform is formulated as a linear minimal mean-squared error problem. The optimal Wiener solution and several simplifications with different tradeoffs between complexity and performance are developed. We also prove the persymmetric structure of these Wiener filters. The existing mean reconstruction method is proven to be a special case of the proposed framework. Our method also includes as a special case the linear interpolation method used in DCT-based systems when there is no pre/postfiltering and when the quantization noise is ignored. The design criteria in our previous results are scrutinized and improved solutions are obtained. Various design examples and multiple description image coding experiments are reported to demonstrate the performance of the proposed method.

Near-Linear Time Approximation Algorithms for Curve Simplification

We consider the problem of approximating a polygonal curve P under a given error criterion by another polygonal curve P' whose vertices are a subset of the vertices of P. The goal is to minimize the number of vertices of P' while ensuring that the error between P' and P is below a certain threshold. We consider two different error measures: Hausdorff and Frechet. For both error criteria, we present near-linear time approximation algorithms that, given a parameter ź > 0, compute a simplified polygonal curve P' whose error is less than ź and size at most the size of an optimal simplified polygonal curve with error ź/2. We consider monotone curves in ź2 in the case of the Hausdorff error measure under the uniform distance metric and arbitrary curves in any dimension for the Frechet error measure under Lp metrics. We present experimental results demonstrating that our algorithms are simple and fast, and produce close to optimal simplifications in practice.

Advising parents on time telling for children who have learning difficulties

Parents of children, who have learning problems often seek advice from teachers about time telling. There is only limited consensus on how to instruct this skill and with what sort of timepieces. This paper reviews the literature and current classroom practice to consider what goals are functionally appropriate, what typical learning difficulties affect time comprehension, presenting time language, mapping time with timetables and the complex choice between analogue and digital timepieces. For each type a consensus is presented on optimal sequencing, possible simplifications and effective strategies. Digital time, increasingly more prevalent and faster to read may be the better first option for teaching such children functional time telling skills. Analogue may better represent the passage of time but this is not essential for students who exhibit significant learning problems. Children need exposure to both types and classrooms should display both types in adjacent positions.