A Representation Theorem for Domains with Discrete and Continuous Variables.

This paper proves a new representation theorem for domains with both discrete and continuous variables. The result generalizes Debreu's well-known representation theorem on connected domains. A strengthening of the standard continuity axiom is used in order to guarantee the existence of a representation. A generalization of the main theorem and an application of the more general result are also presented.

A modified Primal-Dual Logarithmic-Barrier Method for solving the Optimal Power Flow problem with discrete and continuous control variables

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A modified Primal-Dual Logarithmic-Barrier Method for solving the Optimal Power Flow problem with discrete and continuous control variables

The aim of solving the Optimal Power Flow problem is to determine the optimal state of an electric power transmission system, that is, the voltage magnitude and phase angles and the tap ratios of the transformers that optimize the performance of a given system, while satisfying its physical and operating constraints. The Optimal Power Flow problem is modeled as a large-scale mixed-discrete nonlinear programming problem. This paper proposes a method for handling the discrete variables of the Optimal Power Flow problem. A penalty function is presented. Due to the inclusion of the penalty function into the objective function, a sequence of nonlinear programming problems with only continuous variables is obtained and the solutions of these problems converge to a solution of the mixed problem. The obtained nonlinear programming problems are solved by a Primal-Dual Logarithmic-Barrier Method. Numerical tests using the IEEE 14, 30, 118 and 300-Bus test systems indicate that the method is efficient. (C) 2012 Elsevier B.V. All rights reserved.

Discrete Conditional Phase-type models utilising classification trees: Application to modelling health service capacities

Discrete Conditional Phase-type (DC-Ph) models consist of a process component (survival distribution) preceded by a set of related conditional discrete variables. This paper introduces a DC-Ph model where the conditional component is a classification tree. The approach is utilised for modelling health service capacities by better predicting service times, as captured by Coxian Phase-type distributions, interfaced with results from a classification tree algorithm. To illustrate the approach, a case-study within the healthcare delivery domain is given, namely that of maternity services. The classification analysis is shown to give good predictors for complications during childbirth. Based on the classification tree predictions, the duration of childbirth on the labour ward is then modelled as either a two or three-phase Coxian distribution. The resulting DC-Ph model is used to calculate the number of patients and associated bed occupancies, patient turnover, and to model the consequences of changes to risk status.

Discrete Conditional Phase-type model (DC_Ph) for patient waiting time with a logistic regression component to predict patient admission to hospital

Discrete Conditional Phase-type (DC-Ph) models are a family of models which represent skewed survival data conditioned on specific inter-related discrete variables. The survival data is modeled using a Coxian phase-type distribution which is associated with the inter-related variables using a range of possible data mining approaches such as Bayesian networks (BNs), the Naïve Bayes Classification method and classification regression trees. This paper utilizes the Discrete Conditional Phase-type model (DC-Ph) to explore the modeling of patient waiting times in an Accident and Emergency Department of a UK hospital. The resulting DC-Ph model takes on the form of the Coxian phase-type distribution conditioned on the outcome of a logistic regression model.

Discrete squeezed states for finite-dimensional spaces

We show how discrete squeezed states in an N-2-dimensional phase space can be properly constructed out of the finite-dimensional context. Such discrete extensions are then applied to the framework of quantum tomography and quantum information theory with the aim of establishing an initial study on the interference effects between discrete variables in a finite phase space. Moreover, the interpretation of the squeezing effects is seen to be direct in the present approach, and has some potential applications in different branches of physics.

Discrete generator coordinate: Symmetry restoration in finite-dimensional spaces

Group theoretical-based techniques and fundamental results from number theory are used in order to allow for the construction of exact projectors in finite-dimensional spaces. These operators are shown to make use only of discrete variables, which play the role of discrete generator coordinates, and their application in the number symmetry restoration is carried out in a nuclear BCS wave function which explicitly violates that symmetry. © 1999 Published by Elsevier Science B.V. All rights reserved.

Penalty-based nonlinear solver for optimal reactive power dispatch with discrete controls

The optimal reactive dispatch problem is a nonlinear programming problem containing continuous and discrete control variables. Owing to the difficulty caused by discrete variables, this problem is usually solved assuming all variables as continuous variables, therefore the original discrete variables are rounded off to the closest discrete value. This approach may provide solutions far from optimal or even unfeasible solutions. This paper presents an efficient handling of discrete variables by penalty function so that the problem becomes continuous and differentiable. Simulations with the IEEE test systems were performed showing the efficiency of the proposed approach. © 1969-2012 IEEE.

Classification of Chenopodium Genus Populations and Species Based on Continuous and Categorical Variables

2000 Mathematics Subject Classification: 62P10, 62H30

Bayesian Dependence Tests for Continuous, Binary and Mixed Continuous-Binary Variables

Tests for dependence of continuous, discrete and mixed continuous-discrete variables are ubiquitous in science. The goal of this paper is to derive Bayesian alternatives to frequentist null hypothesis significance tests for dependence. In particular, we will present three Bayesian tests for dependence of binary, continuous and mixed variables. These tests are nonparametric and based on the Dirichlet Process, which allows us to use the same prior model for all of them. Therefore, the tests are “consistent” among each other, in the sense that the probabilities that variables are dependent computed with these tests are commensurable across the different types of variables being tested. By means of simulations with artificial data, we show the effectiveness of the new tests.

Vector evaluated particle swarm optimization (VEPSO) for multi-objective design optimization of composite structures

We present a generic method/model for multi-objective design optimization of laminated composite components, based on vector evaluated particle swarm optimization (VEPSO) algorithm. VEPSO is a novel, co-evolutionary multi-objective variant of the popular particle swarm optimization algorithm (PSO). In the current work a modified version of VEPSO algorithm for discrete variables has been developed and implemented successfully for the, multi-objective design optimization of composites. The problem is formulated with multiple objectives of minimizing weight and the total cost of the composite component to achieve a specified strength. The primary optimization variables are - the number of layers, its stacking sequence (the orientation of the layers) and thickness of each layer. The classical lamination theory is utilized to determine the stresses in the component and the design is evaluated based on three failure criteria; failure mechanism based failure criteria, Maximum stress failure criteria and the Tsai-Wu failure criteria. The optimization method is validated for a number of different loading configurations - uniaxial, biaxial and bending loads. The design optimization has been carried for both variable stacking sequences, as well fixed standard stacking schemes and a comparative study of the different design configurations evolved has been presented. (C) 2007 Elsevier Ltd. All rights reserved.

Artificial Bee Colony (ABC) for multi-objective design optimization of composite structures

In this paper, we present a generic method/model for multi-objective design optimization of laminated composite components, based on Vector Evaluated Artificial Bee Colony (VEABC) algorithm. VEABC is a parallel vector evaluated type, swarm intelligence multi-objective variant of the Artificial Bee Colony algorithm (ABC). In the current work a modified version of VEABC algorithm for discrete variables has been developed and implemented successfully for the multi-objective design optimization of composites. The problem is formulated with multiple objectives of minimizing weight and the total cost of the composite component to achieve a specified strength. The primary optimization variables are the number of layers, its stacking sequence (the orientation of the layers) and thickness of each layer. The classical lamination theory is utilized to determine the stresses in the component and the design is evaluated based on three failure criteria: failure mechanism based failure criteria, maximum stress failure criteria and the tsai-wu failure criteria. The optimization method is validated for a number of different loading configurations-uniaxial, biaxial and bending loads. The design optimization has been carried for both variable stacking sequences, as well fixed standard stacking schemes and a comparative study of the different design configurations evolved has been presented. Finally the performance is evaluated in comparison with other nature inspired techniques which includes Particle Swarm Optimization (PSO), Artificial Immune System (AIS) and Genetic Algorithm (GA). The performance of ABC is at par with that of PSO, AIS and GA for all the loading configurations. (C) 2009 Elsevier B.V. All rights reserved.

On the Dirichlet Prior and Bayesian Regularization

A common objective in learning a model from data is to recover its network structure, while the model parameters are of minor interest. For example, we may wish to recover regulatory networks from high-throughput data sources. In this paper we examine how Bayesian regularization using a Dirichlet prior over the model parameters affects the learned model structure in a domain with discrete variables. Surprisingly, a weak prior in the sense of smaller equivalent sample size leads to a strong regularization of the model structure (sparse graph) given a sufficiently large data set. In particular, the empty graph is obtained in the limit of a vanishing strength of prior belief. This is diametrically opposite to what one may expect in this limit, namely the complete graph from an (unregularized) maximum likelihood estimate. Since the prior affects the parameters as expected, the prior strength balances a "trade-off" between regularizing the parameters or the structure of the model. We demonstrate the benefits of optimizing this trade-off in the sense of predictive accuracy.

Computational learning of the conditional phase-type (C-Ph) distribution: Learning C-Ph distributions

This paper presents a new algorithm for learning the structure of a special type of Bayesian network. The conditional phase-type (C-Ph) distribution is a Bayesian network that models the probabilistic causal relationships between a skewed continuous variable, modelled by the Coxian phase-type distribution, a special type of Markov model, and a set of interacting discrete variables. The algorithm takes a dataset as input and produces the structure, parameters and graphical representations of the fit of the C-Ph distribution as output.The algorithm, which uses a greedy-search technique and has been implemented in MATLAB, is evaluated using a simulated data set consisting of 20,000 cases. The results show that the original C-Ph distribution is recaptured and the fit of the network to the data is discussed.