One of the many successful applications of Gaussian Mixture Models (GMMs) is in image segmentatio... more One of the many successful applications of Gaussian Mixture Models (GMMs) is in image segmentation, where spatially constrained mixture models have been used in conjuction with the Expectation-Maximization (EM) framework. In this paper, we propose a new methodology for the M-step of the EM algorithm that is based on a novel constrained optimization formulation. Numerical experiments using simulated and real images illustrate the superior performance of our methodology in terms of the attained maximum value of the objective function and segmentation accuracy compared to previous implementations of this approach.
Forbidden states and the three-body bound state collapse
Physical Review C, 2001
ABSTRACT The appearance of bound states with large binding energies of several hundred MeV in the... more ABSTRACT The appearance of bound states with large binding energies of several hundred MeV in the three-body system, known as bound state collapse, is investigated. For this purpose three classes of two-body potentials are employed; local potentials equivalent to nonlocal interactions possessing a continuum bound state, in addition to the usual negative-energy bound state; local potentials with a strong attractive well sustaining a forbidden state; and supersymmetric transformation potentials. It is first shown that local potentials equivalent to the above nonlocal ones have a strong attractive well in the interior region which supports, in addition to the physical deuteron state, a second bound state (usually called a pseudobound state) with a large binding energy, which is responsible for the bound state collapse in the three-body (and in general to the N-body) system. Second, it is shown that local potentials with a forbidden state also generate a three-body bound state collapse, implying that the role played by the forbidden state is similar to the one played by the pseudobound state. Finally, it is shown that the removal of the forbidden state via supersymmetric transformations also results in the disappearance of the collapse. Thus one can safely argue that the presence of unphysical bound states with large binding energies in the two-body system is responsible for the bound state collapse in the three-body system.
Partial differential equations (PDEs) with boundary conditions (Dirichlet or Neumann) defined on ... more Partial differential equations (PDEs) with boundary conditions (Dirichlet or Neumann) defined on boundaries with simple geometry have been successfully treated using sigmoidal multilayer perceptrons in previous works. This article deals with the case of complex boundary geometry, where the boundary is determined by a number of points that belong to it and are closely located, so as to offer a reasonable representation. Two networks are employed: a multilayer perceptron and a radial basis function network. The later is used to account for the exact satisfaction of the boundary conditions. The method has been successfully tested on two-dimensional and three-dimensional PDEs and has yielded accurate results.
In this paper, we propose a new methodology for analysis of microarray images. First, a new gridd... more In this paper, we propose a new methodology for analysis of microarray images. First, a new gridding algorithm is proposed for determining the individual spots and their borders. Then, a Gaussian mixture model (GMM) approach is presented for the analysis of the individual spot images. The main advantages of the proposed methodology are modeling flexibility and adaptability to the data, which are well-known strengths of GMM. The maximum likelihood and maximum a posteriori approaches are used to estimate the GMM parameters via the expectation maximization algorithm. The proposed approach has the ability to detect and compensate for artifacts that might occur in microarray images. This is accomplished by a model-based criterion that selects the number of the mixture components. We present numerical experiments with artificial and real data where we compare the proposed approach with previous ones and existing software tools for microarray image analysis and demonstrate its advantages.
In a previous article we have shown how one can employ Artificial Neural Networks (ANNs) in order... more In a previous article we have shown how one can employ Artificial Neural Networks (ANNs) in order to solve non-homogeneous ordinary and partial differential equations. In the present work we consider the solution of eigenvalue problems for differential and integrodifferential operators, using ANNs. We start by considering the Schrödinger equation for the Morse potential that has an analytically known solution, to test the accuracy of the method. We then proceed with the Schrödinger and the Dirac equations for a muonic atom, as well as with a non-local Schrödinger integrodifferential equation that models the n + α system in the framework of the resonating group method. In two dimensions we consider the well studied [2] Henon-Heiles Hamiltonian and in three dimensions the model problem of three coupled anharmonic oscillators. The method in all of the treated cases proved to be highly accurate, robust and efficient. Hence it is a promising tool for tackling problems of higher complexity and dimensionality.
Abstract. A new training algorithm is presented for delayed reinforcement learning problems,that ... more Abstract. A new training algorithm is presented for delayed reinforcement learning problems,that does not assume,the existence of a critic model and employs the polytope optimization algorithm to adjust the weights of the action network so that a simple direct measure,of the training performance is maximized. Experimental results from the application of the method,to the pole balancing prob- lem indicate improved,training performance,compared,with critic-based and genetic reinforcement approaches. Key words: reinforcement learning, neurocontrol, optimization, polytope algorithm, pole balancing,
Gaussian mixture models (GMMs) constitute a well-known type of probabilistic neural networks. One... more Gaussian mixture models (GMMs) constitute a well-known type of probabilistic neural networks. One of their many successful applications is in image segmentation, where spatially constrained mixture models have been trained using the expectation-maximization (EM) framework. In this letter, we elaborate on this method and propose a new methodology for the M-step of the EM algorithm that is based on a
One of the many successful applications of Gaussian Mixture Models (GMMs) is in image segmentatio... more One of the many successful applications of Gaussian Mixture Models (GMMs) is in image segmentation, where spatially constrained mixture models have been used in conjuction with the Expectation-Maximization (EM) framework. In this paper, we propose a new methodology for the M-step of the EM algorithm that is based on a novel constrained optimization formulation. Numerical experiments using simulated and real images illustrate the superior performance of our methodology in terms of the attained maximum value of the objective function and segmentation accuracy compared to previous implementations of this approach.
Forbidden states and the three-body bound state collapse
Physical Review C, 2001
ABSTRACT The appearance of bound states with large binding energies of several hundred MeV in the... more ABSTRACT The appearance of bound states with large binding energies of several hundred MeV in the three-body system, known as bound state collapse, is investigated. For this purpose three classes of two-body potentials are employed; local potentials equivalent to nonlocal interactions possessing a continuum bound state, in addition to the usual negative-energy bound state; local potentials with a strong attractive well sustaining a forbidden state; and supersymmetric transformation potentials. It is first shown that local potentials equivalent to the above nonlocal ones have a strong attractive well in the interior region which supports, in addition to the physical deuteron state, a second bound state (usually called a pseudobound state) with a large binding energy, which is responsible for the bound state collapse in the three-body (and in general to the N-body) system. Second, it is shown that local potentials with a forbidden state also generate a three-body bound state collapse, implying that the role played by the forbidden state is similar to the one played by the pseudobound state. Finally, it is shown that the removal of the forbidden state via supersymmetric transformations also results in the disappearance of the collapse. Thus one can safely argue that the presence of unphysical bound states with large binding energies in the two-body system is responsible for the bound state collapse in the three-body system.
Partial differential equations (PDEs) with boundary conditions (Dirichlet or Neumann) defined on ... more Partial differential equations (PDEs) with boundary conditions (Dirichlet or Neumann) defined on boundaries with simple geometry have been successfully treated using sigmoidal multilayer perceptrons in previous works. This article deals with the case of complex boundary geometry, where the boundary is determined by a number of points that belong to it and are closely located, so as to offer a reasonable representation. Two networks are employed: a multilayer perceptron and a radial basis function network. The later is used to account for the exact satisfaction of the boundary conditions. The method has been successfully tested on two-dimensional and three-dimensional PDEs and has yielded accurate results.
In this paper, we propose a new methodology for analysis of microarray images. First, a new gridd... more In this paper, we propose a new methodology for analysis of microarray images. First, a new gridding algorithm is proposed for determining the individual spots and their borders. Then, a Gaussian mixture model (GMM) approach is presented for the analysis of the individual spot images. The main advantages of the proposed methodology are modeling flexibility and adaptability to the data, which are well-known strengths of GMM. The maximum likelihood and maximum a posteriori approaches are used to estimate the GMM parameters via the expectation maximization algorithm. The proposed approach has the ability to detect and compensate for artifacts that might occur in microarray images. This is accomplished by a model-based criterion that selects the number of the mixture components. We present numerical experiments with artificial and real data where we compare the proposed approach with previous ones and existing software tools for microarray image analysis and demonstrate its advantages.
In a previous article we have shown how one can employ Artificial Neural Networks (ANNs) in order... more In a previous article we have shown how one can employ Artificial Neural Networks (ANNs) in order to solve non-homogeneous ordinary and partial differential equations. In the present work we consider the solution of eigenvalue problems for differential and integrodifferential operators, using ANNs. We start by considering the Schrödinger equation for the Morse potential that has an analytically known solution, to test the accuracy of the method. We then proceed with the Schrödinger and the Dirac equations for a muonic atom, as well as with a non-local Schrödinger integrodifferential equation that models the n + α system in the framework of the resonating group method. In two dimensions we consider the well studied [2] Henon-Heiles Hamiltonian and in three dimensions the model problem of three coupled anharmonic oscillators. The method in all of the treated cases proved to be highly accurate, robust and efficient. Hence it is a promising tool for tackling problems of higher complexity and dimensionality.
Abstract. A new training algorithm is presented for delayed reinforcement learning problems,that ... more Abstract. A new training algorithm is presented for delayed reinforcement learning problems,that does not assume,the existence of a critic model and employs the polytope optimization algorithm to adjust the weights of the action network so that a simple direct measure,of the training performance is maximized. Experimental results from the application of the method,to the pole balancing prob- lem indicate improved,training performance,compared,with critic-based and genetic reinforcement approaches. Key words: reinforcement learning, neurocontrol, optimization, polytope algorithm, pole balancing,
Gaussian mixture models (GMMs) constitute a well-known type of probabilistic neural networks. One... more Gaussian mixture models (GMMs) constitute a well-known type of probabilistic neural networks. One of their many successful applications is in image segmentation, where spatially constrained mixture models have been trained using the expectation-maximization (EM) framework. In this letter, we elaborate on this method and propose a new methodology for the M-step of the EM algorithm that is based on a
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