Computational Quantification of Map Projection Distortion by Fractal Dimension of Coastlines

Maps, essential tools for portraying the Earth’s surface, inherently introduce distortions to geographical features. While various quantification methods exist for assessing these distortions, they often fall short when evaluating actual geographic features. In our study, we took a novel approach by analyzing map projection distortion from a geometric perspective. We computed the fractal dimensions of different stretches of coastline before and after projection using the divide-and-conquer algorithm and image processing. Our findings revealed that map projections, even when preserving basic shapes, inevitably stretch and compress coastlines in diverse directions. This analysis method provides a more realistic and practical way to measure map-induced distortions, with significant implications for cartography, geographic information systems (GIS), and geomorphology. By bridging the gap between theoretical analysis and real-world features, this method greatly enhances accuracy and practicality when evaluating map projections.

Three-dimensional stereotactic surface projection in the statistical analysis of single photon emission computed tomography data for distinguishing between Alzheimer's disease and depression

AIM To evaluate usefulness of single photon emission computed tomography(SPECT) with three-dimensional stereotactic surface projection(3D-SSP) in distinguishing between Alzheimer's disease(AD) and depression.METHODS We studied 43 patients who presented with both depressive symptoms and memory disturbance. Each subject was evaluated using the following:(1) the Minimal Mental State Examination;(2) the Hamilton Rating Scale for Depression;(3) Clinical Global Impression-Severity scale(CGI-S); and(4) SPECT imaging with 3D-SSP.RESULTS The MMSE scores correlated significantly with the maximum Z-scores of AD-associated regions. CGI-S scores correlated significantly with the maximum Z-scores of depression-associated regions. Factor analysis identified three significant factors. Of these, Factor 1 could be interpreted as favouring a tendency for AD, Factor 2 as favouring a tendency for pseudo-dementia, and Factor 3 as favouring a depressive tendency.CONCLUSION We investigated whether these patients could be categorized as types: Type A(true AD), Type B(pseudodementia), Type C(occult AD), and Type D(true depression). The factor scores in factor analysis supported the validity of this classification. Our results suggest that SPECT with 3D-SSP is highly useful for distinguishing between depression and depressed mood in the early stage of AD.

Application of Three-Dimensional Visualization Technology in Project Management of Offshore Platform Engineering Construction

Three-dimensional visualization technology converts engineering design drawings and data into graphics or images, realizes virtual reality perception of simulated users in future construction scene, enhances the interaction between project management and technical personnel and engineering construction achievement, and provides intuitive, flexible and strong realistic experience for project management. It can effectively improve the level of project communication, and assist the needs of project construction planning management, training, exhibition, etc. As a tool to help improve project management skills, it has good application effect and prospects.

Subspace Clustering in High-Dimensional Data Streams:A Systematic Literature Review

Clustering high dimensional data is challenging as data dimensionality increases the distance between data points,resulting in sparse regions that degrade clustering performance.Subspace clustering is a common approach for processing high-dimensional data by finding relevant features for each cluster in the data space.Subspace clustering methods extend traditional clustering to account for the constraints imposed by data streams.Data streams are not only high-dimensional,but also unbounded and evolving.This necessitates the development of subspace clustering algorithms that can handle high dimensionality and adapt to the unique characteristics of data streams.Although many articles have contributed to the literature review on data stream clustering,there is currently no specific review on subspace clustering algorithms in high-dimensional data streams.Therefore,this article aims to systematically review the existing literature on subspace clustering of data streams in high-dimensional streaming environments.The review follows a systematic methodological approach and includes 18 articles for the final analysis.The analysis focused on two research questions related to the general clustering process and dealing with the unbounded and evolving characteristics of data streams.The main findings relate to six elements:clustering process,cluster search,subspace search,synopsis structure,cluster maintenance,and evaluation measures.Most algorithms use a two-phase clustering approach consisting of an initialization stage,a refinement stage,a cluster maintenance stage,and a final clustering stage.The density-based top-down subspace clustering approach is more widely used than the others because it is able to distinguish true clusters and outliers using projected microclusters.Most algorithms implicitly adapt to the evolving nature of the data stream by using a time fading function that is sensitive to outliers.Future work can focus on the clustering framework,parameter optimization,subspace search techniques,memory-efficient synopsis structures,explicit cluster change detection,and intrinsic performance metrics.This article can serve as a guide for researchers interested in high-dimensional subspace clustering methods for data streams.

Numerical study on three-dimensional flow field of continuously rotating detonation in a toroidal chamber

Gaseous detonation propagating in a toroidal chamber was numerically studied for hydrogen/oxygen/nitrogen mixtures. The numerical method used is based on the three-dimensional Euler equations with detailed finiterate chemistry. The results show that the calculated streak picture is in qualitative agreement with the picture recorded by a high speed streak camera from published literature. The three-dimensional flow field induced by a continuously rotating detonation was visualized and distinctive features of the rotating detonations were clearly depicted. Owing to the unconfined character of detonation wavelet, a deficit of detonation parameters was observed. Due to the effects of wall geometries, the strength of the outside detonation front is stronger than that of the inside portion. The detonation thus propagates with a constant circular velocity. Numerical simulation also shows three-dimensional rotating detonation structures, which display specific feature of the detonation- shock combined wave. Discrete burning gas pockets are formed due to instability of the discontinuity. It is believed that the present study could give an insight into the interest- ing properties of the continuously rotating detonation, and is thus beneficial to the design of continuous detonation propulsion systems.

THREE-DIMENSIONAL MATHEMATICAL MODEL AND ITS APPLICATION IN THE NEIGHBORHOOD OF THE THREE GORGES RESERVOIR DAM IN THE YANGTZE RIVER

The calculation of flow and sediment transport is one of the most important tasks in river engineering. The task is particularly difficult because a number of complex physical phenomena should be accounted for more realistically in a model with a predictive power. Three-dimensional calculations of river flow and suspended sediment transport are performed in this paper with application in the Three Gorges Reservoir in the Yangtze River. A period of 76 years after the dam is built is simulated and the results are compared with laboratory measurements obtained by Tsinghua University whereby the model is verified and calibrated. Generally speaking, the calculated results agree well with the experiments, demonstrating that the present model can be used for flow and sediment transport prediction in rivers.

Three-dimensional reconstruction of human spinal cord based on histological serial sections

BACKGROUND： It is not possible to reconstruct the inner structure of the spinal cord, such as gray matter and spinal tracts, from the Visual Human Project database or CT and MRI databases, due to low image resolution and contrast in macrosection images. OBJECTIVE： To explore a semi-automatic computerized three-dimensional （3D） reconstruction of human spinal cord based on histological serial sections, in order to solve issues such as low contrast. DESIGN, TIME AND SETTING： An experimental study combining serial section techniques and 3D reconstruction, performed in the laboratory of Human Anatomy and Histoembryology at the Medical School of Nantong University during January to April 2008. SETTING： Department of Anatomy, Institute of Neurobiology, Jiangsu Province Key Laboratory of Neural Regeneration, Laboratory of Image Engineering. MATERIALS： A human lumbar spinal cord segment from fresh autopsy material of an adult male. METHODS： After 4% paraformaldehyde fixation for three days, serial sections of the lumbar spinal cord were cut on a Leica cryostat and mounted on slides in sequence, with eight sections aligned separately on each slide. All sections were stained with Luxol Fast Blue to reveal myelin sheaths. After gradient dehydration and clearing, the stained slides were coverslipped. Sections were observed and images recorded under a light microscope using a digital camera. Six images were acquired at x25 magnification and automatically stitched into a complete section image. After all serial images were obtained, 96 complete serial images of the human lumbar cord segment were automatically processed with ＂Curves＂, ＂Autocontrast＂, ＂Gray scale 8 bit＂, ＂Invert＂, ＂Image resize to 50%＂ steps using Photoshop 7.0 software. All images were added in order into 3D-DOCTOR 4.0 software as a stack, where serial images were automatically realigned with neighboring images and semi-automatically segmented for white matter and gray matter. Finally, simple surface and volume reconstruction were completed on a personal computer. The reconstructed human lumbar spinal cord segment was interactively observed, cut, and measured. MAIN OUTCOME MEASURES： The reconstructed human lumbar spinal cord segment. RESULTS： Compared with serial images obtained from other image modalities, such as CT, MRI, and macrosections from The Visual Human Project database, the Luxol Fast Blue stained histological serial section images exhibited higher resolution and contrast between gray and white matter. Image processing and 3D reconstruction steps were semi-automatically performed with related software. The 3D reconstructed human lumbar cord segment were observed, cut, and measured on a PC. CONCLUSION： A semi-automatically computerized method, based on histological serial sections, is an effective way to 3D-reconstruct the human spinal cord.

A combined numerical model of three-dimensional tidal motion and sediment transport in tidal current and its application

A calculation scheme, which combines a horizontal upwind finite element method with vertical implicit differences, is used to establish a three-dimensional mathematical model of tidal motion and sediment transport in tidal current. Compared with those of the relative theoretical formula, the results are satisfactory. The model mentioned above has been applied to the water area of the Lianzhou Bay, Guangxi Province. On the basis of the analysis and comparison with the field data, it shows clearly that the model calculation results are reasonable.

Speech emotion recognition via discriminant-cascading dimensionality reduction

In order to accurately identify speech emotion information, the discriminant-cascading effect in dimensionality reduction of speech emotion recognition is investigated. Based on the existing locality preserving projections and graph embedding framework, a novel discriminant-cascading dimensionality reduction method is proposed, which is named discriminant-cascading locality preserving projections （DCLPP）. The proposed method specifically utilizes supervised embedding graphs and it keeps the original space for the inner products of samples to maintain enough information for speech emotion recognition. Then, the kernel DCLPP （KDCLPP） is also proposed to extend the mapping form. Validated by the experiments on the corpus of EMO-DB and eNTERFACE＇05, the proposed method can clearly outperform the existing common dimensionality reduction methods, such as principal component analysis （PCA）, linear discriminant analysis （LDA）, locality preserving projections （LPP）, local discriminant embedding （LDE）, graph-based Fisher analysis （GbFA） and so on, with different categories of classifiers.

Exploring visual quality of multidimensional time series projections

Dimensionality reduction is often used to project time series data from multidimensional to two-dimensional space to generate visual representations of the temporal evolution.In this context,we address the problem of multidimensional time series visualization by presenting a new method to show and handle projection errors introduced by dimensionality reduction techniques on multidimensional temporal data.For visualization,subsequent time instances are rendered as dots that are connected by lines or curves to indicate the temporal dependencies.However,inevitable projection artifacts may lead to poor visualization quality and misinterpretation of the temporal information.Wrongly projected data points,inaccurate variations in the distances between projected time instances,and intersections of connecting lines could lead to wrong assumptions about the original data.We adapt local and global quality metrics to measure the visual quality along the projected time series,and we introduce a model to assess the projection error at intersecting lines.These serve as a basis for our new uncertainty visualization techniques that use different visual encodings and interactions to indicate,communicate,and work with the visualization uncertainty from projection errors and artifacts along the timeline of data points,their connections,and intersections.Our approach is agnostic to the projection method and works for linear and non-linear dimensionality reduction methods alike.

Nonlinear Dimensionality Reduction and Data Visualization:A Review

Dimensionality reduction and data visualization are useful and important processes in pattern recognition. Many techniques have been developed in the recent years. The self-organizing map （SOM） can be an efficient method for this purpose. This paper reviews recent advances in this area and related approaches such as multidimensional scaling （MDS）, nonlinear PC A, principal manifolds, as well as the connections of the SOM and its recent variant, the visualization induced SOM （ViSOM）, with these approaches. The SOM is shown to produce a quantized, qualitative scaling and while the ViSOM a quantitative or metric scaling and approximates principal curve/surface. The SOM can also be regarded as a generalized MDS to relate two metric spaces by forming a topological mapping between them. The relationships among various recently proposed techniques such as ViSOM, Isomap, LLE, and eigenmap are discussed and compared.

Computed tomography of Crohn's disease:The role of three dimensional technique

Crohn's disease,a transmural inflammatory bowel disease,remains a difficult entity to diagnose clinically.Over the last decade,multidetector computed tomography(CT) has become the method of choice for noninvasive evaluation of the small bowel,and has proved to be of significant value in the diagnosis of Crohn's disease.Advancements in CT enterography protocol design,three dimensional(3-D) post-processing software,and CT scanner technology have allowed increasing accuracy in diagnosis,and the acquisition of studies at a much lower radiation dose.The cases in this review will illustrate that the use of 3-D technique,proper enterography protocol design,and a detailed understanding of the different manifestations of Crohn's disease are all critical in properly diagnosing the full range of possible complications in Crohn's patients.In particular,CT enterography has proven to be effective in identifying involvement of the small and large bowel(including active inflammation,stigmata of chronic inflammation,and Crohn's-related bowel neoplasia) by Crohn's disease,as well as the extra-enteric manifestations of the disease,including fistulae,sinus tracts,abscesses,and urologic/hepatobiliary/osseous complications.Moreover,the proper use of 3-D technique(including volume rendering and maximum intensity projection) as a routine component of enterography interpretation can play a vital role in improving diagnostic accuracy.

Recursive super-convergence computation for multi-dimensional problems via one-dimensional element energy pro jection technique

This paper presents a strategy for computation of super-convergent solutions of multi-dimensional problems in the finite element method （FEM） by recursive application of the one-dimensional （1D） element energy projection （EEP） technique. The main idea is to conceptually treat multi-dimensional problems as generalized 1D problems, based on which the concepts of generalized 1D FEM and its consequent EEP formulae have been developed in a unified manner. Equipped with these concepts, multi-dimensional problems can be recursively discretized in one dimension at each step, until a fully discretized standard finite element （FE） model is reached. This conceptual dimension-by- dimension （D-by-D） discretization procedure is entirely equivalent to a full FE discretization. As a reverse D-by-D recovery procedure, by using the unified EEP formulae together with proper extraction of the generalized nodal solutions, super-convergent displacements and first derivatives for two-dimensional （2D） and three-dimensional （3D） problems can be obtained over the domain. Numerical examples of 3D Poisson＇s equation and elasticity problem are given to verify the feasibility and effectiveness of the proposed strategy.

Probabilistic joint remote preparation of a high-dimensional equatorial quantum state

This paper proposes a scheme for probabilistic joint remote preparation of an arbitrary high-dimensional equatorial quantum state by using high-dimensional single-particle orthogonal projective measurement and appropriate unitary operation. As a special case, a scheme of joint remote preparation of a single-qutrit equatorial state is presented in detail. The scheme is also generalized to the multi-party high-dimensional case. It shows that, only if when all the senders collaborate with each other, the receiver can reconstruct the original state with a certain probability.

Tensor Train Random Projection

This work proposes a Tensor Train Random Projection(TTRP)method for dimension reduction,where pairwise distances can be approximately preserved.Our TTRP is systematically constructed through a Tensor Train(TT)representation with TT-ranks equal to one.Based on the tensor train format,this random projection method can speed up the dimension reduction procedure for high-dimensional datasets and requires fewer storage costs with little loss in accuracy,comparedwith existingmethods.We provide a theoretical analysis of the bias and the variance of TTRP,which shows that this approach is an expected isometric projectionwith bounded variance,and we show that the scaling Rademacher variable is an optimal choice for generating the corresponding TT-cores.Detailed numerical experiments with synthetic datasets and theMNIST dataset are conducted to demonstrate the efficiency of TTRP.

Evolution of Two-Dimensional Correlation Spectroscopy

A number of useful techniques associated with two-dimensional correlation spectroscopy(2DCOS)to improve its performance and utility have been developed in the last 30years.Evolution of these 2DCOS techniques,including some of the very recent developments,is reviewed with examples.Topics include merged or modified asynchronous 2Dcorrelation spectrum,two-dimensional codistribution spectroscopy(2DCDS),Pareto scaling,and null-space projection treatment of spectral dataset.

Rainfall Assimilation Using a New Four-Dimensional Variational Method:A Single-Point Observation Experiment

Accurate forecast of rainstorms associated with the mei-yu front has been an important issue for the Chinese economy and society. In July 1998 a heavy rainstorm hit the Yangzi River valley and received widespread attention from the public because it caused catastrophic damage in China. Several numerical studies have shown that many forecast models, including Pennsylvania State University National Center for Atmospheric Research’s fifth-generation mesoscale model （MM5）, failed to simulate the heavy precipitation over the Yangzi River valley. This study demonstrates that with the optimal initial conditions from the dimension-reduced projection four-dimensional variational data assimilation （DRP-4DVar） system, MM5 can successfully reproduce these observed rainfall amounts and can capture many important mesoscale features, including the southwestward shear line and the low-level jet stream. The study also indicates that the failure of previous forecasts can be mainly attributed to the lack of mesoscale details in the initial conditions of the models.

Relative Ding Projective Modules over Formal Triangular Matrix Rings

Let U be a (B, A)-bimodule, A and B be rings, and be a formal triangular matrix ring. In this paper, we characterize the structure of relative Ding projective modules over T under some conditions. Furthermore, using the left global relative Ding projective dimensions of A and B, we estimate the relative Ding projective dimension of a left T-module.

A study of making use of computer-aided projection fringe system to measure breast dimension

To measure breast basic dimension by using computer-aided projection fringe system.Methods A system has been developed for measuring breast basic dimension based on computer-aided projection fringe measurement and programming software.Plastic manikins breast’s SN-N (sternal notch to nipple distance),N-ML (nipple to midline distance),N-N (internipple distance),MBW (base width of breast) and N-IMF (nipple to inframammary fold distance) are measured with this system.At the same time,these items are also measured with routine ruler.Results This study indicate that the system has some merits:① non-touching measurement;② it is very rapid,the patient measured need hold his breath only 0.5 second,and all the time it takes is about 2.5 minutes;③ the measurement’s sensitivity is as high as to 0.6 mm,which meets the clinic requirement entirely;④ the measurement’s accuracy of the system is not significantly when comparing to the routine ruler’s.Conclusion Computer-adided projection fringe system for measuring breast basic dimension is feasible and advanced.14 refs,1 fig.

机电系统网络控制课程的多维度混合式教学探索与实践

针对研究生课程机电系统网络控制的教学现状与发展需求,开展多维度混合式教学探索与实践。构建包含课堂讲授、资源库、专题研讨等在内的线上线下多维度教学体系;针对主题研讨实践环节引入翻转课堂,以项目驱动和研讨式教学引导学生分组完成课程相关的项目任务,掌握并运用所学知识分析解决问题,体验科学研究的过程与思维方法,形成理论知识到科研实践的闭环训练;最终建立形成性和终结性相结合的多元考核评价体系,旨在通过课程学习培养专业基础扎实、科研素养和工程实践能力突出的高端创新型人才。