Voronoi Diagram Research Articles

Comparative assessment of projection and clustering method combinations in the analysis of biomedical data

BackgroundClustering on projected data is common in biomedical research analysis. Principal component analysis (PCA) is widely used for projection, focusing on data dispersion (variance), while clustering identifies data concentrations (neighborhood). These are conflicting aims. This study re-evaluates combinations of PCA and other projection methods with common clustering algorithms. MethodsSix projection methods (PCA, ICA, isomap, MDS, t-SNE, UMAP) were combined with five clustering algorithms (k-means, k-medoids, single link, Ward's method, average link). Projections and clusterings were evaluated using a numerical criterion for evaluating clustering performance and a visual criterion based on plotting the projected data on a Voronoi tessellation plane with class-wise coloring. Nine artificial and five real biomedical datasets were analyzed. ResultsNo combination consistently captured prior classifications in projections and clusters. Visual inspection proved essential. PCA was often but not always outperformed or equaled by neighborhood-based methods (UMAP, t-SNE) and manifold learning techniques (isomap). ConclusionsThe results dissaprove PCA as a standard projection method prior to clustering. Therefore, method selection should be data specific as a tailored approach to data projection and clustering in biomedical analysis. To aid this process, we propose a novel visualization technique that combines Voronoi tessellation with color coding.

Design and Validation of Cyber-Physical Systems Through Co-Simulation: The Voronoi Tessellation Use Case

Design and Validation of Cyber-Physical Systems Through Co-Simulation: The Voronoi Tessellation Use Case

Innovative tools and methods for digitizing both visible and non-visible attributes of cultural heritage items. Part II: a multiscale approach

The process of object digitization marks the initial step toward digital transformation, focusing on discretizing specific geometric entities according to predefined level of detail. The degree of detail, depending on the scale of representation and visualization, is important for two critical steps: segmentation and classification. These stages aim to partition the object into regions with homogeneous properties and assigning labels to each region based on its characteristics. The geometrical model implementation follows, serving different objectives including the structural analyses of the digitized object. Within this framework three mechanical methods will be presented: the lattice-based model dating back to Hrennikoff (1943), the Discrete Element Method (Cundal, 1971) and the microplane method (Bažant and Oh, 1985). These methods will be discussed alongside applications concerning brick walls, concrete element and Fiber Reinforced Polymer (FRP) materials utilized for reinforcement of existing concrete elements as well as new FRP element. Depending on the chosen scale, the numerical model can be implemented based on Voronoi Diagram (1908) and Delaunay triangulation (1934). These techniques find applications in various fields, including cluster analysis, record access scheduling, and collision detection.

Comprehensive study of the synthetic tychite, Na6Mg2(CO3)4SO4: synthesis, structure and conductive properties.

The structural and conductive properties of the synthetic tychite Na6Mg2(CO3)4SO4 (space group: Fd3̄) were explored. Optimal synthesis parameters were selected by varying the molar ratio of reagents, synthesis temperature and time. For structural descriptions, we carried out scanning electron microscopy, thermal analysis, and Raman and Fourier-transform infrared spectroscopy. We carried out theoretical and experimental studies of conductivity. Theoretical calculations were obtained using geometrical-topological analysis based on Voronoi partitioning (the evaluation of geometrical sizes of voids and channels), the bond valence site energy (BVSE) method (the fast calculation of migration energies, Em), kinetic Monte Carlo simulation (the estimation of ionic conductivity at different temperatures), and density functional theory (the precise assessment of Em and vacancy formation energies). The experimental techniques included electrochemical impedance spectroscopy EIS (total conductivity determination) and direct current DC polarization (electronic conductivity assessment) measurements. Na6Mg2(CO3)4SO4 was found to have a three-periodic Na+-ion migration map with an Em of 0.37 eV and 0.18 eV from BVSE and DFT results, respectively. The theoretical value of cationic conductivity was 2.6 × 10-7 S cm-1 at 100 °C. The experimental total conductivity was equal to 6.0 × 10-7 S cm-1 at 100 °C, which is close to theoretical results. Using additional DC polarization, the electronic contribution to the total conductivity was characterized as insignificant.

A novel class of multivalent ionic conductors with the La3CuSiS7 structure type: results of stepwise ICSD screening.

The results of high-throughput screening of the inorganic crystal structure database for new promising Ca2+-, Mg2+-, Zn2+- and Al3+-ion conducting ternary and quaternary sulfides, selenides, and tellurides are presented (∼1500 compounds). A geometrical-topological approach based on the Voronoi partition was initially used and yielded 104 compounds, which were unknown as conductors with possible cation migration. All compounds were passed through the bond valence site energy analysis to determine the migration energy Em. Furthermore, we established the logarithmic dependencies of Em on the geometrical parameters of the migration pathways. As a result, 16 out of 104 structures were filtered out as promising conductors. Finally, density functional theory simulations yielded the 11 most prospective compounds with Em < 1.0 eV. Among them, we found a novel class of ionic conductors with the La3CuSiS7 structure, for which ab initio molecular dynamic calculations were performed, revealing diffusion coefficients of ∼10-7 cm2 s-1 and ionic conductivity of ∼10-2 S cm-1 at 300 K.

Towards Codebook-Free Deep Probabilistic Quantization for Image Retrieval.

As a classical feature compression technique, quantization is usually coupled with inverted indices for scalable image retrieval. Most quantization methods explicitly divide feature space into Voronoi cells, and quantize feature vectors in each cell into the centroids learned from data distribution. However, Voronoi decomposition is difficult to achieve discriminative space partition for semantic image retrieval. In this paper, we explore semantic-aware feature space partition by deep neural network instead of Voronoi cells. To this end, we propose a new deep probabilistic quantization method, abbreviated as DeepIndex, which constructs inverted indices without explicit centroid learning. In our method, the deep neural network takes an image as input and outputs its probability of being put into each inverted index list. During training, we progressively quantize each image into the inverted lists with the top- T maximal probabilities, and calculate the reward of each trial based on retrieval accuracy. We optimize the deep neural network to maximize the probability of the inverted list with maximal reward. In this way, the retrieval performance is directly optimized, leading to a more semantically discriminative space partition than other quantization methods. The experiments on public image datasets demonstrate the effectiveness of our DeepIndex method on semantic image retrieval.

Об оценках интегрального риска предиктора липшицевых функций в моделях машинного обучения

Class imbalance in available training samples for solving machine learning problems in most practical cases complicates the training of predictors that effectively generalize patterns from the training dataset to the general population. This paper investigates the theoretical foundations of the effectiveness of adding synthetic data to the training set. In the assessment of overall risk, two types of errors are highlighted: representation error and deviation error. Practical recommendations are formulated for creating synthetic samples that deviate in their distribution from the representative ones by the density distribution of the argument, with more frequent samples in those areas where the density distribution of the argument has relatively low values, leading to a reduction in the size of the corresponding Voronoi cells and a reduction in the contribution of deviation error to total risk.

The influence of clustering in homogeneous isotropic turbulence on the ignition behavior of iron particles

We conduct carrier-phase direct numerical simulations (CP-DNS) to investigate the ignition of iron particles in homogeneous isotropic turbulence, and characterize the connection between particle clustering and particle ignition. A pseudo-spectral reacting multiphase flow solver using a low Mach number approximation is employed. It features an established point-particle sub-model for reacting iron particles and describes the mass, heat and momentum transfer across the particle boundary layers in a two-way coupled regime. Within this setup, we perform a series of simulations covering a broad range of Reynolds and Stokes numbers. The results confirm the well-known observation from incompressible dispersed multiphase flows that particle clustering is most pronounced for particle clouds with Stokes numbers of order one. Here, strong particle clustering additionally facilitates the earlier ignition of heterogeneously burning iron particles. This is because groups of neighboring particles locally deposit more heat per volume than a single isolated particle, thus more strongly increasing the local fluid temperature and shifting particle reactions from kinetically-limited to diffusion-limited particle conversion. A Voronoi tessellation analysis shows that the particles packed together in clusters tend to ignite first, even for small Stokes numbers, at which clustering is less prominent. An increase in Reynolds number reduces the ignition delay times, especially for high Stokes numbers, since particles with higher inertia are more sensitive to the larger scales of the turbulent motion. The present findings are of practical importance for the design and flame stabilization mechanisms in future iron combustion burners.

Characterization of domain formation in complex membranes.

A widely known property of lipid membranes is their tendency to undergo a separation into disordered (Ld) and ordered (Lo) domains. This impacts the local structure of the membrane relevant for the physical (e.g., enhanced electroporation) and biological (e.g., protein sorting) significance of these regions. The increase in computing power, advancements in simulation software, and more detailed information about the composition of biological membranes shifts the study of these domains into the focus of classical molecular dynamicssimulations. In this chapter, we present a versatile yet robust analysis pipeline that can be easily implemented and adapted for a wide range of lipid compositions. It employs Gaussian-based Hidden Markov Modelsto predict the hidden order states of individual lipids by describing their structure through the area per lipid and the average SCC order parameters per acyl chain. Regions of the membrane with a high correlation between ordered lipids are identified by employing the Getis-Ord local spatial autocorrelation statistic on a Voronoi tessellation of the lipids. As an example, the approach is applied to two distinct systems at a coarse-grained resolution, demonstrating either a strong tendency towards phase separation (1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC), 1,2-dilinoleoyl-sn-glycero-3-phosphocholine (DIPC), cholesterol) or a weak tendency toward phase separation (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), 1-palmitoyl-2-docosahexaenoyl-sn-glycero-3-phosphocholine (PUPC), cholesterol). Explanations of the steps are complemented by coding examples written in Python, providing both a comprehensive understanding and practical guidance for a seamless integration of the workflow into individual projects.

On the numerical approximation of Blaschke–Santaló diagrams using Centroidal Voronoi Tessellations

Blaschke–Santaló diagrams are images of maps defined on a set of parameters, taking values into an Euclidean space. Typically, the dimension of the source space is high, possibly infinite, while the target space is two or three dimensional. These diagrams help characterize geometrically various inequalities and are of particular interest in the field of shape optimization. We propose a numerical method, based on Centroidal Voronoi Tessellations, which produces sample points in the parameter space that have uniformly distributed images in the Blaschle–Santaló diagram, therefore providing an accurate description of the latter. Compared with the classical Monte Carlo methods, which simply use a large number of images corresponding to random parameters, the method proposed is computationally efficient and precise. Simulations for two and three dimensional diagrams are presented involving examples in algebra and shape optimization.

First-principles molecular dynamics study on the behaviors of Cs in a mixed system of liquid metal and LiCl-KCl molten salt.

The structure and dynamic properties of Cs in the mixed system of LiCl-KCl molten salt and a liquid metal (Bi and Pb) electrode are investigated through first-principles molecular dynamics simulation. It is found that the dynamic properties of different ions in molten salt could be significantly affected when the liquid metal electrode is coupled and this influence varies with the type of liquid metal applied. The microstructures of the mixed systems of molten salt and liquid metal electrode: MS-Cs-Bi, MS-CsCl-Bi, MS-Cs-Pb, and MS-CsCl-Pb, are also investigated by the bond angle distribution function, Voronoi tessellation analysis, five-fold symmetry parameter, and bond-orientational order parameter. The comparison study of the microstructures of the mixed systems when different liquid metal electrodes are applied provides information on the liquid metal electrode selection when conducting electrolysis. The present study represents the first demonstration of the study of a mixed system of salt and liquid electrode for practical applications and would be greatly beneficial to the development of pyroprocessing of spent nuclear fuel.

Adaptive Centroidal Voronoi Tessellation With Agent Dropout and Reinsertion for Multi-Agent Non-Convex Area Coverage

Adaptive Centroidal Voronoi Tessellation With Agent Dropout and Reinsertion for Multi-Agent Non-Convex Area Coverage

Non destructive control of permanent magnet rotors in a perspective of electric motor circularity

This work presents an innovative non destructive control process in order to guide for the end of life (re-use or recycling) of permanents magnets (PM) rotors of electric motors. The process is based on the measurement of the external field produced by the PM rotors. A Finite Element model of the rotor and its environment has been used to simulate a process of classification of the geometry of PM rotors, crucial information for the disassembling of the PM. Firstly, using a finite element model, we were able to investigate the field distribution outside the rotor of the magnetic flux density for different PM rotors designs. From this information, we can set up a classification methodology, based on the Central Voronoi Tessellation (CVT) method, which can help to identify how the PM are inserted within the rotor. This information can be very useful to choose PM disassembling process that should be applied.

Precipitation Study in Flood Zones: San Mateo Atenco, State of Mexico, Mexico Case Study

This work is focused on analyzing the causes of flooding in the sub-basin belonging to the municipality of San Mateo Atenco: Almoloya-Otzolotepec, because the municipal territory is constantly threatened by hydrometeorological phenomena, such as hailstorms, frost and torrential rains. The maximum precipitation was analyzed in neighboring climatological stations and the precipitation at different return periods (2 to 1000) was determined through the Gumbel distribution, and its impact according to the Thiessen polygon method. With the information of the 24-hour intensities, the Intensity Duration Frequency (IDF) curves and the hietogram of the study area were plotted using the alternating block method. The above procedure was applied to the precipitation data from the 9 stations that affect the basin. The approach proposed in this work considers all the precipitation variables for the best approximation of the phenomena that may occur in the basin; it is an innovative model because it considers the weighted averages of precipitation for each area of influence and its surroundings; this information is useful for the implementation of flood protection projects, adequate design of drainage and sewage systems, and a rational use of the resource to guarantee better living conditions for the inhabitants. According to the results obtained, there is a slow hydrological response and the areas with the greatest runoff potential (8383&lt;CN&lt;100) are located towards the central part of the basin where there is a significant concentration of bare soil.

О покрытии поверхности цилиндра и конуса равными шарами

The article concerns the problem of covering the lateral surface of a right circular cylinder or a cone with equal balls. The surface is required to belong to their union, and the balls’ radius is minimal. The centers of the balls must lie on the covered surface. The problem is relevant for mathematics and for applications since it arises in security and communications. We develop heuristic algorithms for covering construction based on a geodesic Voronoi diagram. The construction of a covering is a non-trivial task since the line of intersection of a cylinder or a cone with a sphere is a closed curve of the fourth order. To compare the numerical results with the known ones, we unroll the surface of revolution onto a plane. Another feature is that, we use both Euclidean distance and a special non-Euclidean metric, which can describe the speed of signal propagation in a heterogeneous medium. We also perform a numerical experiment and discuss its results. Meanwhile, it is shown that with a small number of circles covering a planification of the cylindrical surface, their radius is significantly less than for a similar rectangle.

Notice of Violation of IEEE Publication Principles: Connected Optimal Two-Coverage of Sensor Networks

Notice of Violation of IEEE Publication Principles<br><br>"Connected Optimal Two-Coverage of Sensor Networks,"<br>by Z. Yun, J. Teng, Z. Yu, D. Xuan, B. Chen, W. Zhao,<br>in the IEEE/ACM Transactions on Networking, vol.PP, no.99<br><br>After careful and considered review of the content and authorship of this paper by a duly constituted expert committee, this paper has been found to be in violation of IEEE's Publication Principles.<br><br>This paper contains significant portions of original text from the paper cited below. The original text was copied without attribution (including appropriate references to the original author(s) and/or paper title) and without permission. One author (Ziqiu Yun) was responsible for the violation, and this violation was done without the knowledge of the other authors.<br><br>"Planar Thinnest Deployment Pattern of Congruent Discs which Achieves 2-coverage"<br>by Ge Jun,<br>in his thesis presented at the School of Mathematical Sciences, Soochow University, Suzhou 215006, P. R. China, June 2010.<br><br> <br/> In wireless sensor networks, multiple-coverage, in which each point is covered by more than one sensor, is often required to improve detection quality and achieve high fault tolerance. However, finding optimal patterns that achieve multiple-coverage in a plane remains a long-lasting open problem. We first derive the optimal deployment density bound for two-covered deployment patterns where Voronoi polygons generated by sensor nodes are congruent. We then propose optimal two-coverage patterns based on the optimal bound. We further extend these patterns by considering the connectivity requirement and design a set of optimal patterns that achieve two-coverage and one-, two-, and three-connectivity. We also study optimal patterns under practical considerations. To our knowledge, our work is the very first that proves the optimality of multiple-covered deployment patterns.

Multifractal structure of cholinergic innervation in the tunica albuginea of rat testis. Comparison with different models simulating nerve networks

The complexity of the distribution of cholinergic innervation of the albuginea suggests that its structural pattern may exhibit multiple scaling rules rather than a single global scale. Therefore, the study of nerve fibers could be approached through multifractal analysis. The cholinergic fiber plexuses of the rat testicular albuginea, visualized by a histochemical technique for the detection of acetylcholine sterases, will be analyzed for the possible detection of their multifractal structure, calculating several types of multifractal spectra, namely multifractal spectrum f(α) versus α, and the generalized dimension DQ versus Q. In the present study, the results will be compared with the multifractal spectra of plexus models consisting of the elaboration of interconnected line lattices generated, either employing a binary matrix or using a tessellation matrix, and according to various realizations of randomly distributed points in a two-dimensional space. The results of this study suggest that the cholinergic nerve plexuses of the testicular albuginea of the rat show a multifractal behavior, and the multifractality of the real data is greater than that of the simulated networks. However, Voronoi tessellations models show a more remarkable similarity of the multifractal scale with the real data in comparison with those generated by a binary matrix.

Study of a high-precision complex 3D geological modelling method based on a fine KNN and kriging coupling algorithm: a case study for Jiangsu, China

A high-precision, complex, three-dimensional (3D) geological model can directly express the attributes of stratum thickness, geological structure, lithology and spatial form, which can provide a reliable basis for the development and utilization of underground space and planning decisions. However, it is difficult to perform accurate modelling due to the lack of basic data. As such, this paper proposes coupling a machine learning algorithm (K-nearest neighbour (KNN)) with the kriging algorithm to construct the topological relationship between the Delaunay triangle and the Thiessen polygon in order to perform the simulation and prediction of virtual drilling. Based on KNN, support vector machine (SVM) and neural network algorithms as well as the virtual borehole encryption data, data standardization processing and analysis are carried out. Through model verification, algorithm optimization is realized, and the optimal modelling method is explored. The results show that the fine KNN algorithm improved by Bayesian optimization can effectively improve the modelling accuracy through 0.1-m encryption, standardization processing and 5-fold cross-validation. Stratum modelling combined with the fine KNN and kriging algorithms can obtain a more accurate modelling without adding virtual boreholes. The improved levels of upper and lower hybrid modelling with an appropriate number of profile boreholes can also effectively optimize model accuracy. Both modelling accuracy and efficiency can be significantly improved by using Delaunay triangles and Thiessen polygons with virtual boreholes. Stratum modelling can effectively express the geological pinch-out in areas with adequate degrees of stratification, and hybrid modelling performs well in irregular geological bodies such as karsts and lenses.

C-VoNNI: a precise fingerprint construction for indoor positioning systems using natural neighbor methods with clustering-based Voronoi diagrams

C-VoNNI: a precise fingerprint construction for indoor positioning systems using natural neighbor methods with clustering-based Voronoi diagrams

Design of 3D anisotropic Voronoi porous structure driven by stress field

Porous structures exhibit excellent mechanical properties and are widely utilized in engineering design. However, there is still substantial potential for enhancing the mechanical performance of these structure. By customizing the anisotropic design of each pore in the porous structure, the strength and stiffness of the structure can be significantly enhanced. In this work, we present a novel method for designing 3D anisotropic Voronoi porous structures (AVPSs). To construct these structures, we propose a novel algorithm for generating 3D anisotropic Voronoi diagrams (AVDs) based on Riemannian distance. The geometries of Voronoi cells are controlled to conform with both the stress distribution and the principal stress directions. The distribution of Voronoi cells are graded using a stress-based site sampling strategy, the orientation of Voronoi cells are modified by introducing stress-mapped Riemann tensor fields. The AVPSs are then modeled by computing implicit surfaces based on AVDs. The AVPSs conform closely to the geometric profile of the input model by clipping AVDs using the tetrahedral mesh. Furthermore, the results obtained from numerical simulations and experimental tests indicate that the AVPSs possess both high strength and high stiffness.