Processing and analyzing of medical images is one of the priority research areas. At the same time, the processing of images of cells occupies a special place. This is due to the fact that such studies allow for a com...Processing and analyzing of medical images is one of the priority research areas. At the same time, the processing of images of cells occupies a special place. This is due to the fact that such studies allow for a comprehensive diagnosis of the state of human health, identify and prevent the development of diseases in the early stages. We investigate the effectiveness of using wavelet analysis in color models, taking into account the preliminary change in the contrast of the input image. We consider the HSV color model and the image contrast modification procedure, which is based on the histogram change in the specified range with gamma correction. As a criterion for choosing parameters for changing the contrast of the image, we consider the entropy of the image. We also showed the advisability of using the value of the entropy index for the subsequent improvement of image analysis based on the wavelet ideology. We examined the general sequence of action for the analysis of image of megaloblastic anemia cells. This sequence is based on the choice of parameters for changing the contrast of the image and application of wavelet ideology.展开更多
This paper describes an extension and a new foundation of the Standard Model of particle physics based on a SU(4)-force called hyper-color, and on preon subparticles. The hyper-color force is a generalization of the S...This paper describes an extension and a new foundation of the Standard Model of particle physics based on a SU(4)-force called hyper-color, and on preon subparticles. The hyper-color force is a generalization of the SU(2)-based weak interaction and the SU(1)-based right-chiral self-interaction, in which the W-and the Z-bosons are Yukawa residual-field-carriers of the hyper-color force, in the same sense as the pions are the residual-field-carriers of the color SU(3) interaction. Using the method of numerical minimization of the SU(4)-action based on this model, the masses and the inner structure of leptons, quarks and weak bosons are calculated: the mass results are very close to the experimental values. We calculate also precisely the value of the Cabibbo angle, so the mixing matrices of the Standard model, CKM matrix for quarks and PMNS matrix for neutrinos can also be calculated. In total, we reduce the 29 parameters of the Standard Model to a total of 7 parameters.展开更多
This paper presents a new face detection approach to real-time applications, which is based on the skin color model and the morphological filtering. First the non-skin color pixels of the input image are removed based...This paper presents a new face detection approach to real-time applications, which is based on the skin color model and the morphological filtering. First the non-skin color pixels of the input image are removed based on the skin color model in the YC rC b chrominance space, from which we extract candidate human face regions. Then a mathematical morphological filter is used to remove noisy regions and fill the holes in the candidate skin color regions. We adopt the similarity between the human face features and the candidate face regions to locate the face regions in the original image. We have implemented the algorithm in our smart media system. The experiment results show that this system is effective in real-time applications.展开更多
The color image segmentation problem has two main issues to be solved. The proper choice of a color model and the choice of an appropriate image model are the key issues in color image segmentation. In this work, Ohta...The color image segmentation problem has two main issues to be solved. The proper choice of a color model and the choice of an appropriate image model are the key issues in color image segmentation. In this work, Ohta (I<sub>1</sub>, I<sub>2</sub>, I<sub>3</sub>) is taken as the color model and different variants of Markov Random Field (MRF) models are proposed. In this regard, a Compound Markov Random Field (COMRF) model is porposed to take care of inter-color-plane and intra-color-plane interactions as well. In continuation to this model, a Constrained Compound Markov Random Field Model (CCOMRF) has been proposed to model the color images. The color image segmentation problem has been formulated in an unsupervised framework. The performance of the above proposed models has been compared with the standard MRF model and some of the state-of-the-art methods, and found to exhibit improved performance.展开更多
Recently automotive nets are adopted to solve increasing problems in automotive electronic systems.Technologies of automotive local area network from CAN and LIN can solve the problems of the increasing of wire bunch ...Recently automotive nets are adopted to solve increasing problems in automotive electronic systems.Technologies of automotive local area network from CAN and LIN can solve the problems of the increasing of wire bunch weight and lack in module installation space.However,the multilayer automotive nets software becomes more and more complex,and the development expense is difficult to predict and to keep in check.In this paper,the modeling method of hierarchical automotive nets and the substitution operation based on object-oriented colored Petri net(OOCPN) are proposed.The OOCPN model which analyzes the software structure and validates the collision mechanism of CAN/LIN bus can speed the automobile system development.First,the subsystems are divided and modeled by object-oriented Petri net(OOPN).According to the sets of message sharing relations,the message ports among them are set and the communication gate transitions are defined.Second,the OOPN model is substituted step by step until the inner objects in the automotive body control modules(BCM) are indivisible and colored by colored Petri net(CPN).And the color subsets mark the node messages for the collision mechanism.Third,the OOCPN model of the automotive body CAN/LIN nets is assembled,which keeps the message sets and the system can be expanded.The proposed model is used to analyze features of information sharing among the objects,and it is also used to describe each subsystem real-time behavior of processing messages and implemental device controllers operating,and puts forward a reasonable software framework for the automotive body control subsystem.The research can help to design the communication model in the automotive body system effectively and provide a convenient and rapid way for developing the logical hierarchy software.展开更多
A method of the forward operation of color appearance (from colorimetric attributes to color appearance attributes) using an artificial neural network (ANN) is presented The neural network model developed is a multila...A method of the forward operation of color appearance (from colorimetric attributes to color appearance attributes) using an artificial neural network (ANN) is presented The neural network model developed is a multilayer feedforward neural network model for predicting color appearance model (CAM). This method greatly decreased the mathematical computation in color appearance prediction. The error backed-propagation (BP) algorithm was applied in the training of the neural networks, and it was trained and tested by the LUTCHI color appearance datasets which are the most comprehensive one in testing color appearance model. CRT was selected as a typical example in experiment because it is usually used as self-luminous object in fact, and several ways for choosing training samples were included and compared each other. The testing results show that the color appearance prediction using artificial neural network is well consistent with visual evaluation.展开更多
Color appearance model (CAM) can be used to determine the required colors for repro- duction across changes in cross-media. CIECAM02 color appearance model prediction is implemen- ted by artificial neural networks i...Color appearance model (CAM) can be used to determine the required colors for repro- duction across changes in cross-media. CIECAM02 color appearance model prediction is implemen- ted by artificial neural networks in this paper, which includes forward and reversed prediction. 1333 color samples as training samples and other 1332 color samples as test samples are selected in the Chinese color system. In order to test the prediction accuracy of neural networks after simulation of CIECAM02 color appearance model, the color-difference formula can be used for the evaluation of forward and reversed models. Results have shown that BP neural-network has acceptable accuracy in simulation of CIECAM02 color appearance model for colors of Chinese color system.展开更多
A real-time photo-realistic rendering algorithm of ocean color is introduced in the paper, which considers the impact of ocean bio-optical model. The ocean bio-optical model mainly involves the phytoplankton, colored ...A real-time photo-realistic rendering algorithm of ocean color is introduced in the paper, which considers the impact of ocean bio-optical model. The ocean bio-optical model mainly involves the phytoplankton, colored dissolved organic material(CDOM), inorganic suspended particle, etc., which have different contributions to absorption and scattering of light. We decompose the emergent light of the ocean surface into the reflected light from the sun and the sky, and the subsurface scattering light. We establish an ocean surface transmission model based on ocean bidirectional reflectance distribution function(BRDF) and the Fresnel law, and this model's outputs would be the incident light parameters of subsurface scattering. Using ocean subsurface scattering algorithm combined with bio-optical model, we compute the scattering light emergent radiation in different directions. Then, we blend the reflection of sunlight and sky light to implement the real-time ocean color rendering in graphics processing unit(GPU). Finally, we use two kinds of radiance reflectance calculated by Hydrolight radiative transfer model and our algorithm to validate the physical reality of our method, and the results show that our algorithm can achieve real-time highly realistic ocean color scenes.展开更多
A parametric Colored Petri net model of the switched Ethernet network with the tree-like topology is developed. The model’s structure is the same for any given network and contains fixed number of nodes. The tree-lik...A parametric Colored Petri net model of the switched Ethernet network with the tree-like topology is developed. The model’s structure is the same for any given network and contains fixed number of nodes. The tree-like topology of a definite network is given as the marking of dedicated places. The model represents a network containing workstations, servers, switches, and provides the evaluation of the network response time. Besides topology, the parameters of the model are performances of hardware and software used within the network. Performance evaluation for the network of the railway dispatcher center is implemented. Topics of the steady-stable condition and the optimal choice of hardware are discussed.展开更多
Cognitive Radio(CR) system based on Orthogonal Frequency Division Multiple Access(OFDMA),such as Wireless Regional Area Networks(WRAN) and Worldwide Interoperability for Microwave Access(WiMAX),often attempt to improv...Cognitive Radio(CR) system based on Orthogonal Frequency Division Multiple Access(OFDMA),such as Wireless Regional Area Networks(WRAN) and Worldwide Interoperability for Microwave Access(WiMAX),often attempt to improve performance via dynamic radio resource management,which is characterized as concurrent processing of different traffic and nondeterministic system capacity.It is essential to design and evaluate such complex system using proper modeling and analysis tools.In the previous work,most of the communication systems were modeled as Markov Chain(MC) and Stochastic Petri Nets(SPN),which have the explicit limitation in evaluating adaptive OFDMA CR system with wide area traffic.In this paper,we develop an executable top-down hier-archical Colored Petri Net(CPN) model for adaptive OFDMA CR system,and analyze its performance using CPN tools.The results demonstrate that the CPN can model different radio resource manage-ment algorithms in CR Systems,and the CPN tools require less computational effort than Markov model using Matlab,with its flexibility and adaptability to the traffics which arrival interval and processing time are not exponentially distributed.展开更多
In this paper, a model based colored Petri net (CPN) to provide semantic support for web service composition is proposed, and the reliability and maintainability of composite services are improved. The composite con...In this paper, a model based colored Petri net (CPN) to provide semantic support for web service composition is proposed, and the reliability and maintainability of composite services are improved. The composite constructs in the model are sequence, concurrent, choice, loop and replace. The web service is formally defined by a CPN. A closed composing algebra is defined to obtain a framework which enables declarative composition of web services. Availability, confidentiality, and integrity of composite service are analyzed within the framework of the model based CPN.展开更多
Prediction of the formula for matching a given color standard by blending pre-dyed fibers is of considerable importance to the textile industry. This kind of formulation suffers from a lack of computer-aided tool to a...Prediction of the formula for matching a given color standard by blending pre-dyed fibers is of considerable importance to the textile industry. This kind of formulation suffers from a lack of computer-aided tool to assist the colorist attempting to find a good recipe to reproduce a target color. In this article a tristimulus color matching algorithm based on Stearns-Noechel model is proposed. This algorithm was run to predict recipes for 36 viscose blends. The maximum color difference is 0.97 CIELAB units. It is demonstrated that the algorithm can be used in color matching of fiber blends.展开更多
The steady states and the transient properties of an insect outbreak model driven by Gaussian colored noise are studied in this paper. According to the Fokker-Planck equation in the unified colored-noise approximation...The steady states and the transient properties of an insect outbreak model driven by Gaussian colored noise are studied in this paper. According to the Fokker-Planck equation in the unified colored-noise approximation, we analyse the stationary probability distribution and the mean first-passage time of this model. By numerical analysis, the effects of the self-correlation time of insect birth rate and predation rate respectively reveal a manifest population divergence on the insect density. The decrease of the mean first-passage time indicates an enhancement dynamic on the density divergency with colored noise of a large self-correlation time based on the insect outbreak model.展开更多
The classical TV (Total Variation) model has been applied to gray texture image denoising and inpainting previously based on the non local operators, but such model can not be directly used to color texture image inpa...The classical TV (Total Variation) model has been applied to gray texture image denoising and inpainting previously based on the non local operators, but such model can not be directly used to color texture image inpainting due to coupling of different image layers in color images. In order to solve the inpainting problem for color texture images effectively, we propose a non local CTV (Color Total Variation) model. Technically, the proposed model is an extension of local TV model for gray images but we take account of the coupling of different layers in color images and make use of concepts of the non-local operators. As the coupling of different layers for color images in the proposed model will in-crease computational complexity, we also design a fast Split Bregman algorithm. Finally, some numerical experiments are conducted to validate the performance of the proposed model and its algorithm.展开更多
颜色数字 N <SUB > 在在在二风味的四费米子的相互作用模型的真空的夸克反夸克冷凝物 q 和 diquark 冷凝物 qq 之间的相互影响的 c </SUB>-dependence 被研究。结果证明 G <SUB > S </SUB>-H<SUB > S &...颜色数字 N <SUB > 在在在二风味的四费米子的相互作用模型的真空的夸克反夸克冷凝物 q 和 diquark 冷凝物 qq 之间的相互影响的 c </SUB>-dependence 被研究。结果证明 G <SUB > S </SUB>-H<SUB > S </SUB>(分级的(q) <SUP>2</SUP>-scalar ( qq )的联合常数<SUP>2</SUP>隧道)阶段图将是与 N <SUB 的盒子一致的品质上> c </SUB>= 3 作为 N <SUB > c </SUB>在 4D Nambu Jona Lasinio 变化模型和 2D 粗野 Neveu ( GN )模型。然而在 3D GN 模型, G <SUB 的行为 > S </SUB>-H<SUB > P </SUB>( 假数量(qq ) 的联合常数 <SUP>2</SUP> 隧道) 阶段图将显然取决于 N <SUB > c </SUB> 。冷凝物 q 和 qq 的共存阶段被证明仅仅在 N <SUB 的情况中出现的一个 3D GN 模型没有的已知的特征 > c </SUB>≤
4。在所有模型,这些区域由在相应阶段图包含 diquark 冷凝物 hqqi 的阶段占据了将逐渐地作为 N <SUB 减少 > c </SUB> 长大并且最后去零如果 N <SUB > c </SUB>→
∞
,即在这限制,仅仅纯 qphase 能存在。展开更多
文摘Processing and analyzing of medical images is one of the priority research areas. At the same time, the processing of images of cells occupies a special place. This is due to the fact that such studies allow for a comprehensive diagnosis of the state of human health, identify and prevent the development of diseases in the early stages. We investigate the effectiveness of using wavelet analysis in color models, taking into account the preliminary change in the contrast of the input image. We consider the HSV color model and the image contrast modification procedure, which is based on the histogram change in the specified range with gamma correction. As a criterion for choosing parameters for changing the contrast of the image, we consider the entropy of the image. We also showed the advisability of using the value of the entropy index for the subsequent improvement of image analysis based on the wavelet ideology. We examined the general sequence of action for the analysis of image of megaloblastic anemia cells. This sequence is based on the choice of parameters for changing the contrast of the image and application of wavelet ideology.
文摘This paper describes an extension and a new foundation of the Standard Model of particle physics based on a SU(4)-force called hyper-color, and on preon subparticles. The hyper-color force is a generalization of the SU(2)-based weak interaction and the SU(1)-based right-chiral self-interaction, in which the W-and the Z-bosons are Yukawa residual-field-carriers of the hyper-color force, in the same sense as the pions are the residual-field-carriers of the color SU(3) interaction. Using the method of numerical minimization of the SU(4)-action based on this model, the masses and the inner structure of leptons, quarks and weak bosons are calculated: the mass results are very close to the experimental values. We calculate also precisely the value of the Cabibbo angle, so the mixing matrices of the Standard model, CKM matrix for quarks and PMNS matrix for neutrinos can also be calculated. In total, we reduce the 29 parameters of the Standard Model to a total of 7 parameters.
文摘This paper presents a new face detection approach to real-time applications, which is based on the skin color model and the morphological filtering. First the non-skin color pixels of the input image are removed based on the skin color model in the YC rC b chrominance space, from which we extract candidate human face regions. Then a mathematical morphological filter is used to remove noisy regions and fill the holes in the candidate skin color regions. We adopt the similarity between the human face features and the candidate face regions to locate the face regions in the original image. We have implemented the algorithm in our smart media system. The experiment results show that this system is effective in real-time applications.
文摘The color image segmentation problem has two main issues to be solved. The proper choice of a color model and the choice of an appropriate image model are the key issues in color image segmentation. In this work, Ohta (I<sub>1</sub>, I<sub>2</sub>, I<sub>3</sub>) is taken as the color model and different variants of Markov Random Field (MRF) models are proposed. In this regard, a Compound Markov Random Field (COMRF) model is porposed to take care of inter-color-plane and intra-color-plane interactions as well. In continuation to this model, a Constrained Compound Markov Random Field Model (CCOMRF) has been proposed to model the color images. The color image segmentation problem has been formulated in an unsupervised framework. The performance of the above proposed models has been compared with the standard MRF model and some of the state-of-the-art methods, and found to exhibit improved performance.
基金supported by National Natural Science Foundation of China (Grant No. 60873003)
文摘Recently automotive nets are adopted to solve increasing problems in automotive electronic systems.Technologies of automotive local area network from CAN and LIN can solve the problems of the increasing of wire bunch weight and lack in module installation space.However,the multilayer automotive nets software becomes more and more complex,and the development expense is difficult to predict and to keep in check.In this paper,the modeling method of hierarchical automotive nets and the substitution operation based on object-oriented colored Petri net(OOCPN) are proposed.The OOCPN model which analyzes the software structure and validates the collision mechanism of CAN/LIN bus can speed the automobile system development.First,the subsystems are divided and modeled by object-oriented Petri net(OOPN).According to the sets of message sharing relations,the message ports among them are set and the communication gate transitions are defined.Second,the OOPN model is substituted step by step until the inner objects in the automotive body control modules(BCM) are indivisible and colored by colored Petri net(CPN).And the color subsets mark the node messages for the collision mechanism.Third,the OOCPN model of the automotive body CAN/LIN nets is assembled,which keeps the message sets and the system can be expanded.The proposed model is used to analyze features of information sharing among the objects,and it is also used to describe each subsystem real-time behavior of processing messages and implemental device controllers operating,and puts forward a reasonable software framework for the automotive body control subsystem.The research can help to design the communication model in the automotive body system effectively and provide a convenient and rapid way for developing the logical hierarchy software.
基金the National Natural Science Foundation(60278022)
文摘A method of the forward operation of color appearance (from colorimetric attributes to color appearance attributes) using an artificial neural network (ANN) is presented The neural network model developed is a multilayer feedforward neural network model for predicting color appearance model (CAM). This method greatly decreased the mathematical computation in color appearance prediction. The error backed-propagation (BP) algorithm was applied in the training of the neural networks, and it was trained and tested by the LUTCHI color appearance datasets which are the most comprehensive one in testing color appearance model. CRT was selected as a typical example in experiment because it is usually used as self-luminous object in fact, and several ways for choosing training samples were included and compared each other. The testing results show that the color appearance prediction using artificial neural network is well consistent with visual evaluation.
基金Supported by the National Natural Science Foundation of China(61078048)
文摘Color appearance model (CAM) can be used to determine the required colors for repro- duction across changes in cross-media. CIECAM02 color appearance model prediction is implemen- ted by artificial neural networks in this paper, which includes forward and reversed prediction. 1333 color samples as training samples and other 1332 color samples as test samples are selected in the Chinese color system. In order to test the prediction accuracy of neural networks after simulation of CIECAM02 color appearance model, the color-difference formula can be used for the evaluation of forward and reversed models. Results have shown that BP neural-network has acceptable accuracy in simulation of CIECAM02 color appearance model for colors of Chinese color system.
基金jointly supported by the International Cooperation and Exchange Projects of the National Natural Science Foundation of China (No.61361163001)the National Key Scientific Instrument and Equipment Development Projects of National Natural Science Foundation of China (No.41527901)the National High-Tech R&D Program (863 Program) (No.2013AA09A505)
文摘A real-time photo-realistic rendering algorithm of ocean color is introduced in the paper, which considers the impact of ocean bio-optical model. The ocean bio-optical model mainly involves the phytoplankton, colored dissolved organic material(CDOM), inorganic suspended particle, etc., which have different contributions to absorption and scattering of light. We decompose the emergent light of the ocean surface into the reflected light from the sun and the sky, and the subsurface scattering light. We establish an ocean surface transmission model based on ocean bidirectional reflectance distribution function(BRDF) and the Fresnel law, and this model's outputs would be the incident light parameters of subsurface scattering. Using ocean subsurface scattering algorithm combined with bio-optical model, we compute the scattering light emergent radiation in different directions. Then, we blend the reflection of sunlight and sky light to implement the real-time ocean color rendering in graphics processing unit(GPU). Finally, we use two kinds of radiance reflectance calculated by Hydrolight radiative transfer model and our algorithm to validate the physical reality of our method, and the results show that our algorithm can achieve real-time highly realistic ocean color scenes.
文摘A parametric Colored Petri net model of the switched Ethernet network with the tree-like topology is developed. The model’s structure is the same for any given network and contains fixed number of nodes. The tree-like topology of a definite network is given as the marking of dedicated places. The model represents a network containing workstations, servers, switches, and provides the evaluation of the network response time. Besides topology, the parameters of the model are performances of hardware and software used within the network. Performance evaluation for the network of the railway dispatcher center is implemented. Topics of the steady-stable condition and the optimal choice of hardware are discussed.
基金Supported by the National Natural Science Foundation of China (No. 60702020)
文摘Cognitive Radio(CR) system based on Orthogonal Frequency Division Multiple Access(OFDMA),such as Wireless Regional Area Networks(WRAN) and Worldwide Interoperability for Microwave Access(WiMAX),often attempt to improve performance via dynamic radio resource management,which is characterized as concurrent processing of different traffic and nondeterministic system capacity.It is essential to design and evaluate such complex system using proper modeling and analysis tools.In the previous work,most of the communication systems were modeled as Markov Chain(MC) and Stochastic Petri Nets(SPN),which have the explicit limitation in evaluating adaptive OFDMA CR system with wide area traffic.In this paper,we develop an executable top-down hier-archical Colored Petri Net(CPN) model for adaptive OFDMA CR system,and analyze its performance using CPN tools.The results demonstrate that the CPN can model different radio resource manage-ment algorithms in CR Systems,and the CPN tools require less computational effort than Markov model using Matlab,with its flexibility and adaptability to the traffics which arrival interval and processing time are not exponentially distributed.
基金Project supported by the National Natural Science Foundation of China (Grant No.60403027)
文摘In this paper, a model based colored Petri net (CPN) to provide semantic support for web service composition is proposed, and the reliability and maintainability of composite services are improved. The composite constructs in the model are sequence, concurrent, choice, loop and replace. The web service is formally defined by a CPN. A closed composing algebra is defined to obtain a framework which enables declarative composition of web services. Availability, confidentiality, and integrity of composite service are analyzed within the framework of the model based CPN.
文摘Prediction of the formula for matching a given color standard by blending pre-dyed fibers is of considerable importance to the textile industry. This kind of formulation suffers from a lack of computer-aided tool to assist the colorist attempting to find a good recipe to reproduce a target color. In this article a tristimulus color matching algorithm based on Stearns-Noechel model is proposed. This algorithm was run to predict recipes for 36 viscose blends. The maximum color difference is 0.97 CIELAB units. It is demonstrated that the algorithm can be used in color matching of fiber blends.
基金Project supported by the Natural Science Basic Research Plan in Shaanxi Province,China (Grant No. SJ08A12)the Science Foundation of the Education Bureau of Shaanxi Province,China (Grant No. 12JK0962)the Science Foundation of Baoji University of Science and Arts of China (Grant No. ZK11053)
文摘The steady states and the transient properties of an insect outbreak model driven by Gaussian colored noise are studied in this paper. According to the Fokker-Planck equation in the unified colored-noise approximation, we analyse the stationary probability distribution and the mean first-passage time of this model. By numerical analysis, the effects of the self-correlation time of insect birth rate and predation rate respectively reveal a manifest population divergence on the insect density. The decrease of the mean first-passage time indicates an enhancement dynamic on the density divergency with colored noise of a large self-correlation time based on the insect outbreak model.
文摘The classical TV (Total Variation) model has been applied to gray texture image denoising and inpainting previously based on the non local operators, but such model can not be directly used to color texture image inpainting due to coupling of different image layers in color images. In order to solve the inpainting problem for color texture images effectively, we propose a non local CTV (Color Total Variation) model. Technically, the proposed model is an extension of local TV model for gray images but we take account of the coupling of different layers in color images and make use of concepts of the non-local operators. As the coupling of different layers for color images in the proposed model will in-crease computational complexity, we also design a fast Split Bregman algorithm. Finally, some numerical experiments are conducted to validate the performance of the proposed model and its algorithm.
基金supported by the National Natural Science Foundation of China under Grant No. 10475113
文摘颜色数字 N <SUB > 在在在二风味的四费米子的相互作用模型的真空的夸克反夸克冷凝物 q 和 diquark 冷凝物 qq 之间的相互影响的 c </SUB>-dependence 被研究。结果证明 G <SUB > S </SUB>-H<SUB > S </SUB>(分级的(q) <SUP>2</SUP>-scalar ( qq )的联合常数<SUP>2</SUP>隧道)阶段图将是与 N <SUB 的盒子一致的品质上> c </SUB>= 3 作为 N <SUB > c </SUB>在 4D Nambu Jona Lasinio 变化模型和 2D 粗野 Neveu ( GN )模型。然而在 3D GN 模型, G <SUB 的行为 > S </SUB>-H<SUB > P </SUB>( 假数量(qq ) 的联合常数 <SUP>2</SUP> 隧道) 阶段图将显然取决于 N <SUB > c </SUB> 。冷凝物 q 和 qq 的共存阶段被证明仅仅在 N <SUB 的情况中出现的一个 3D GN 模型没有的已知的特征 > c </SUB>≤
4。在所有模型,这些区域由在相应阶段图包含 diquark 冷凝物 hqqi 的阶段占据了将逐渐地作为 N <SUB 减少 > c </SUB> 长大并且最后去零如果 N <SUB > c </SUB>→
∞
,即在这限制,仅仅纯 qphase 能存在。