scholarly journals Building Expert Medical Prognostic Systems Using Voronoi Diagram

2015 ◽  
Vol 2015 ◽  
pp. 1-4
Author(s):  
Maria A. Ivanchuk ◽  
Igor V. Malyk
Keyword(s):  
Expert Systems ◽  
Voronoi Diagram ◽  
Voronoi Diagrams

The method of building expert systems for medical prediction of severity in patients is purposed. The method is based on using Voronoi diagrams. Examples of using the method are described in the paper.

CHEMICAL TESSELLATIONS — RESULTS OF BINARY AND TERTIARY REACTIONS BETWEEN METAL IONS AND FERRICYANIDE OR FERROCYANIDE LOADED GELS

2010 ◽  
Vol 20 (07) ◽  
pp. 2241-2252 ◽  
Author(s):  
B. P. J. DE LACY COSTELLO ◽  
I. JAHAN ◽  
P. HAMBIDGE ◽  
K. LOCKING ◽  
D. PATEL ◽  
...  
Keyword(s):  
Metal Ions ◽  
Voronoi Diagram ◽  
Metal Salt ◽  
Voronoi Diagrams ◽  
Reaction Rates ◽  
Cross Reactivity ◽  
Diffusion Reaction ◽  
Reactive Metal ◽  
Simple Chemical ◽  
Pattern Forming

In our recent letter [de Lacy Costello et al., 2009] we described the formation of spontaneous complex tessellations of the plane constructed in simple chemical reactions between drops of metal salts and ferricyanide or ferrocyanide loaded gels. In this paper, we provide more examples of binary tessellations and extend our analysis to tessellations constructed via tertiary mixtures of reactants. We also provide a classification system which describes the tessellation based on the reactivity of the metal salt with the substrate and also the cross-reactivity of the primary products. This results in balanced tessellations where both reactants have equal reactivity or unbalanced tessellations where one reactant has a lower reactivity with the gel. The products can also be partially or fully cross reactive which gives a highly complex tessellation. The tessellations are made up of colored cells (corresponding to different metal ferricyanides or ferrocyanides) separated by bisectors of low precipitate concentration. The tessellations constructed by these reactions constitute generalized Voronoi diagrams. In the case of certain binary or tertiary combinations of reactants where the diffusion/reaction rates differ, then multiplicatively weighted crystal growth Voronoi diagrams are constructed. Where one reactant has limited or no reactivity with the gel (or the products are cross reactive) then the fronts originating from the reactive metal ions cross the fronts originating from the partially reactive metal ions. The fronts can annihilate in the formation of a second Voronoi diagram relating to the relative positions of the reactive drops. Therefore, two or more generalised or weighted Voronoi diagrams can be calculated in parallel by these simple chemical systems. However when these reactions were used to calculate an additively weighted Voronoi diagram (the reaction was initiated at different time intervals) the diagram constructed did not correspond to the theoretical calculation. We use the failure of these reactions to construct an additively weighted Voronoi diagram to prove a mechanism of substrate competition for bisector formation. These tessellations are an important class of pattern forming reactions and are useful in modeling natural pattern forming phenomena in addition to being a great resource for scientific demonstrations.

Discrete Construction of Compoundly Weighted Voronoi Diagram

2013 ◽  
Vol 467 ◽  
pp. 545-548
Author(s):  
Hui Wang
Keyword(s):  
Production Process ◽  
Voronoi Diagram ◽  
Voronoi Diagrams ◽  
High Potential ◽  
Graphic Display ◽  
Potential Value ◽  
Discrete Algorithms ◽  
Traditional Algorithm ◽  
Definition Of

Compoundly weighted Voronoi diagram is difficult to construct because the bisector is fairly complex. In traditional algorithm, production process is always extremely complex and it is more difficult to graphic display because of the complex definition of mathematic formula. In this paper, discrete algorithms are used to construct compoundly weighted Voronoi diagrams. The algorithm can get over all kinds of shortcomings that we have just mentioned. So it is more useful and effective than the traditional algorithm. The results show that the algorithm is both simple and useful, and it is of high potential value in practice.

VORONOI DIAGRAMS FOR A TRANSPORTATION NETWORK ON THE EUCLIDEAN PLANE

2006 ◽  
Vol 16 (02n03) ◽  
pp. 117-144 ◽  
Author(s):  
SANG WON BAE ◽  
KYUNG-YONG CHWA
Keyword(s):  
Voronoi Diagram ◽  
Euclidean Plane ◽  
Transportation Network ◽  
Voronoi Diagrams ◽  
The Other ◽  
Constant Number ◽  
Time Path ◽  
The Given

This paper investigates geometric and algorithmic properties of the Voronoi diagram for a transportation network on the Euclidean plane. In the presence of a transportation network, the distance is measured as the length of the shortest (time) path. In doing so, we introduce a needle, a generalized Voronoi site. We present an O(nm2+ m3+ nm log n) algorithm to compute the Voronoi diagram for a transportation network on the Euclidean plane, where n is the number of given sites and m is the complexity of the given transportation network. Moreover, in the case that the roads in a transportation network have only a constant number of directions and speeds, we propose two algorithms; one needs O(nm + m2+ n log n) time with O(m(n + m)) space and the other O(nm log n + m2log m) time with O(n + m) space.

scholarly journals On Voronoi Diagrams on the Information-Geometric Cauchy Manifolds

Entropy ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. 713 ◽  
Author(s):  
Frank Nielsen
Keyword(s):  
Voronoi Diagram ◽  
Voronoi Diagrams ◽  
Information Geometry ◽  
Square Root ◽  
Chi Square ◽  
Scale Parameters ◽  
Leibler Divergence ◽  
Finite Set ◽  
Metric Distance ◽  
Rao Distance

We study the Voronoi diagrams of a finite set of Cauchy distributions and their dual complexes from the viewpoint of information geometry by considering the Fisher-Rao distance, the Kullback-Leibler divergence, the chi square divergence, and a flat divergence derived from Tsallis entropy related to the conformal flattening of the Fisher-Rao geometry. We prove that the Voronoi diagrams of the Fisher-Rao distance, the chi square divergence, and the Kullback-Leibler divergences all coincide with a hyperbolic Voronoi diagram on the corresponding Cauchy location-scale parameters, and that the dual Cauchy hyperbolic Delaunay complexes are Fisher orthogonal to the Cauchy hyperbolic Voronoi diagrams. The dual Voronoi diagrams with respect to the dual flat divergences amount to dual Bregman Voronoi diagrams, and their dual complexes are regular triangulations. The primal Bregman Voronoi diagram is the Euclidean Voronoi diagram and the dual Bregman Voronoi diagram coincides with the Cauchy hyperbolic Voronoi diagram. In addition, we prove that the square root of the Kullback-Leibler divergence between Cauchy distributions yields a metric distance which is Hilbertian for the Cauchy scale families.

A ROBUST TOPOLOGY-ORIENTED INCREMENTAL ALGORITHM FOR VORONOI DIAGRAMS

1994 ◽  
Vol 04 (02) ◽  
pp. 179-228 ◽  
Author(s):  
KOKICHI SUGIHARA ◽  
MASAO IRI
Keyword(s):  
Numerical Computation ◽  
Voronoi Diagram ◽  
Voronoi Diagrams ◽  
The Other ◽  
Geometric Algorithms ◽  
Incremental Algorithm ◽  
Single Precision ◽  
Careful Choice ◽  
Numerical Errors ◽  
Incremental Method

The paper presents a robust algorithm for constructing Voronoi diagrams in the plane. The algorithm is based on an incremental method, but is quite new in that it is robust against numerical errors. Conventionally, geometric algorithms have been designed on the assumption that numerical errors do not take place, and hence they are not necessarily valid for real computers where numerical errors are inevitable. The algorithm to be proposed in this paper, on the other hand, is designed with the recognition that numerical errors are inevitable in real computation; i.e., in the proposed algorithm higher priority is placed on topological structures than on numerical values. As a result, the algorithm is "completely" robust in the sense that it always gives some output however poor the precision of numerical computation may be. In general, the output cannot be more than an approximation to the true Voronoi diagram which we should have got by infinite-precision computation. However, the algorithm is asymptotically correct in the sense that the output converges to the true diagram as the precision becomes higher. Moreover, careful choice of the way of numerical computation makes the algorithm stable enough; indeed the present version of the algorithm can construct in single-precision arithmetic a correct Voronoi diagram for one million generators randomly placed in the unit square in the plane.

Dynamic Construction of Voronoi Diagram for a Set of Points and Straight Line Segments

2014 ◽  
Vol 533 ◽  
pp. 264-267
Author(s):  
Xin Liu
Keyword(s):  
Production Process ◽  
Voronoi Diagram ◽  
Voronoi Diagrams ◽  
High Potential ◽  
Line Segments ◽  
Potential Value ◽  
Straight Line ◽  
Traditional Algorithm ◽  
Set Of Points

Voronoi Diagram for a set of points and straight line segments is difficult to construct because general figures have uncertain shapes[. In traditional algorithm, when generator of general figure changes, production process will be extremely complex because of the change of regions neighboring with those generator changed. In this paper, we use dynamicconstruction of Voronoi diagrams. The algorithm can get over all kinds of shortcomings that we have just mentioned. So it is more useful and effective than the traditional algorithm[2]. The results show that the algorithm is both simple and useful, and it is of high potential value in practice.

scholarly journals The Voronoi theory of the normal liver lobular architecture and its applicability in hepatic zonation

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
C. Lau ◽  
B. Kalantari ◽  
K. P. Batts ◽  
L. D. Ferrell ◽  
S. L. Nyberg ◽  
...  
Keyword(s):  
Voronoi Diagram ◽  
Voronoi Diagrams ◽  
Normal Liver ◽  
Digital Tools ◽  
Liver Pathology ◽  
Two Dimensional ◽  
Lobular Architecture ◽  
Precise Characterization ◽  
Human Livers

AbstractThe precise characterization of the lobular architecture of the liver has been subject of investigation since the earliest historical publications, but an accurate model to describe the hepatic lobular microanatomy is yet to be proposed. Our aim was to evaluate whether Voronoi diagrams can be used to describe the classic liver lobular architecture. We examined the histology of normal porcine and human livers and analyzed the geometric relationships of various microanatomic structures utilizing digital tools. The Voronoi diagram model described the organization of the hepatic classic lobules with overall accuracy nearly 90% based on known histologic landmarks. We have also designed a Voronoi-based algorithm of hepatic zonation, which also showed an overall zonal accuracy of nearly 90%. Therefore, we have presented evidence that Voronoi diagrams represent the basis of the two-dimensional organization of the normal liver and that this concept may have wide applicability in liver pathology and research.

scholarly journals MULTI-AGENT SIMULATION OF ALLOCATING AND ROUTING AMBULANCES UNDER CONDITION OF STREET BLOCKAGE AFTER NATURAL DISASTER

2017 ◽  
Vol XLII-4/W4 ◽  
pp. 325-332 ◽  
Author(s):  
S. Azimi ◽  
M. R. Delavar ◽  
A. Rajabifard
Keyword(s):  
Natural Disasters ◽  
Voronoi Diagram ◽  
Smart City ◽  
Voronoi Diagrams ◽  
Multi Agent System ◽  
Medical Assistance ◽  
Agent System ◽  
Constraint Network ◽  
Multi Agent ◽  
The Difference

In response to natural disasters, efficient planning for optimum allocation of the medical assistance to wounded as fast as possible and wayfinding of first responders immediately to minimize the risk of natural disasters are of prime importance. This paper aims to propose a multi-agent based modeling for optimum allocation of space to emergency centers according to the population, street network and number of ambulances in emergency centers by constraint network Voronoi diagrams, wayfinding of ambulances from emergency centers to the wounded locations and return based on the minimum ambulances travel time and path length implemented by NSGA𝜫 and the use of smart city facilities to accelerate the rescue operation. Simulated annealing algorithm has been used for minimizing the difference between demands and supplies of the constrained network Voronoi diagrams. In the proposed multi-agent system, after delivering the location of the wounded and their symptoms, the constraint network Voronoi diagram for each emergency center is determined. This process was performed simultaneously for the multi-injuries in different Voronoi diagrams. In the proposed multi-agent system, the priority of the injuries for receiving medical assistance and facilities of the smart city for reporting the blocked streets was considered. Tehran Municipality District 5 was considered as the study area and during 3 minutes intervals, the volunteers reported the blocked street. The difference between the supply and the demand divided to the supply in each Voronoi diagram decreased to 0.1601. In the proposed multi-agent system, the response time of the ambulances is decreased about 36.7%.

scholarly journals Sequential Voronoi Diagram Calculations using Simple Chemical Reactions

2011 ◽  
Vol 3 (3) ◽  
pp. 29-41
Author(s):  
B. P. J. de Lacy Costello ◽  
I. Jahan ◽  
A. Adamatzky
Keyword(s):  
Voronoi Diagram ◽  
Chemical Reactions ◽  
Voronoi Diagrams ◽  
Cross Reactivity ◽  
Potassium Ferricyanide ◽  
Potassium Ferrocyanide ◽  
Metal Salts ◽  
Unconventional Computing ◽  
Simple Chemical ◽  
Calculation Results

In the authors’ recent paper (de Lacy Costello et al., 2010) the authors described the formation of complex tessellations of the plane arising from the various reactions of metal salts with potassium ferricyanide and ferrocyanide loaded gels. In addition to producing colourful tessellations these reactions are naturally computing generalised Voronoi diagrams of the plane. The reactions reported previously were capable of the calculation of three distinct Voronoi diagrams of the plane. As diffusion coupled with a chemical reaction is responsible for the calculation then this is achieved in parallel. Thus an increase in the complexity of the data input does not utilise additional computational resource. Additional benefits of these chemical reactions are that a permanent record of the Voronoi diagram calculation (in the form of precipitate free bisectors) is achieved, so there is no requirement for further processing to extract the calculation results. Previously it was assumed that the permanence of the results was also a potential drawback which limited reusability. This paper presents new data which shows that sequential Voronoi diagram calculations can be performed on the same chemical substrate. This is dependent on the reactivity of the original reagent and the cross reactivity of the secondary reagent with the primary product. The authors present the results from a number of binary combinations of metal salts on both potassium ferricyanide and potassium ferrocyanide substrates. The authors observe three distinct mechanisms whereby secondary sequential Voronoi diagrams can be calculated. In most cases the result was two interpenetrating permanent Voronoi diagrams. This is interesting from the perspective of mapping the capability of unconventional computing substrates. But also in the study of natural pattern formation per se.

Grow in accessible directions, like Voronoi diagrams

2020 ◽  
pp. 15-18
Author(s):  
Susan D'Agostino
Keyword(s):  
Voronoi Diagram ◽  
Regional Planning ◽  
Voronoi Diagrams ◽  
Real Life ◽  
Two Dimensional ◽  
Mathematics Students ◽  
Voronoi Tessellations ◽  
Dimensional Plane ◽  
A Cell

“Grow in accessible directions, like Voronoi diagrams” offers an accessible introduction to the mathematics of Voronoi diagrams—a separation of a two-dimensional plane into regions known as “cells” based on “sites.” In a Voronoi diagram, any point inside a cell is closer to the site of its cell than the site of any other cell. The discussion includes numerous real-life examples of Voronoi diagrams—also known as a Voronoi tessellations—in nature and regional planning. The discussion is supplemented with numerous hand-drawn sketches to enhance understanding. Mathematics students and enthusiasts are encouraged to draw inspiration from Voronoi diagrams by growing in accessible directions in mathematical and life pursuits. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.

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