Discrimination and allocation using a mixture of discrete and continuous variables with some empty states

The natural performance of the location model is a potential tool for allocating an object into one of the two observed groups involving mixtures of continuous and binary variables. In constructing location model, continuous variable is used to estimate parameters while binary variable is utilized to create segmentation in each group. Such segmentation is called as multinomial cells. Basically, the multinomial cells will grow exponentially according to the number of the binary variable. These multinomial cells will become empty when there is no object can be assigned into some of them. Then the occurring of empty cells will lead to unreliable parameter estimation. Consequently, the construction of the discriminant rule based on location model is impossible. Therefore, this paper attempts to discuss how the location model based on maximum likelihood estimation can be constructed even dealing with many measured binary variables. In other word, how is location model able to deal with the issue of many empty ...

Thrombocytosis associated with malignant ovarian lesions within a pediatric and adolescent population

Traditionally quantum information research has centred on discrete quantum variables, particularly binary variables (qubits). However, recently much attention has focused on quantum information manipulations with continuous variables such as the amplitude and phase of the electromagnetic field. As well as offering the possibility of high data rates, continuous variables also exhibit greater versatility in realizing certain operations. For example teleportation, in which quantum information is passed intact through a classical channel with the assistance of shared entanglement, can be achieved more efficiently using continuous variable techniques. I review recent work on the characterization of teleportation and entanglement swapping and present new work on interferometric tests of teleportation. These interferometric tests are important because they allow the efficacy of teleportation to be checked without knowledge of the input quantum state. They can be applied equally to the cases of discrete and continuous variable inputs and in so doing highlight unexpected similarities. I contrast the various classical limits which emerge from the different ways of assessing teleportation. An obvious omission from the list of continuous variable quantum information manipulations is any proposal for direct analogues of 2 photon interference effects, especially those that lead to Bell inequality type tests of local realism. Bell-type correlations are the defining feature of discrete variable entanglement experimentally. I discuss new work that shows how entanglement of the Bell-type can be observed in continuous variable, homodyne measurement schemes.

It is common in applied research to have large numbers of variables measured on a modest number of cases. Even with low rates of missingness of individual variables, such data sets can have a large number of incomplete cases with a mix of data types. Here, we propose a new joint modeling approach to address the high-dimensional incomplete data with a mix of continuous and binary data. Specifically, we propose a multivariate normal model encompassing both continuous variables and latent variables corresponding to binary variables. We apply a parameter-extended Metropolis–Hastings algorithm to generate the covariance matrix of a mixture of continuous and binary variables. We also introduce prior distribution families for unstructured covariance matrices to reduce the dimension of the parameter space. In several simulation settings, the method is compared with available-case analysis, a rounding method, and a sequential regression method.

This paper discusses the integrated topology and sizing optimization of frame structures where beam elements are used in the structural analysis model. Based on the ground structure approach, discrete variables (0, 1) representing the absence or presence of beam members and continuous sizing variables for beam cross sections are involved in the problem. A two-level multipoint approximation strategy is introduced to address this mixed-variable problem. A first-level approximate problem is first constructed using the branched multipoint approximate function involving both discrete and continuous variables. For solving this problem, discrete variables are optimized through a genetic algorithm, and when calculating the fitness in the genetic algorithm, a second-level approximate problem solved by the dual method is established to optimize the cross sections for the retained beam members. Temporal deletion techniques are used for displacement and stress constraints. Meanwhile, by considering local vibration modes in frequency-constrained problems, material density is assigned with an extremely small value for the removed beams to avoid these local modes. Thence, the singularities encountered in stress, displacement, and frequency constraints are overcome. Typical examples and a satellite application are given to verify the feasibility and efficiency of this method in handling the integrated topology and sizing optimization for frame structures.

Host area, potential pest impact and probability of pest presence are frequently displayed on maps by pest risk assessors. These variables can be mapped separately, but it is also important to map combinations of these variables in order to define the area of potential establishment and the endangered area to assist decision‐making processes. This paper presents different methods for combining maps, and discusses their advantages and disadvantages. Different methods are shown that can be used to combine maps depending on whether the individual maps were derived from continuous quantitative variables or from discrete variables. The authors suggest combining maps derived from continuous variables using simple mathematical equations in order to compute expected invaded areas and expected potential impacts. Maps derived from discrete variables (e.g. scores) can be combined using a risk matrix, but the results may be highly dependent on the chosen matrix. The practical interest of these methods is illustrated in a case study on Diabrotica virgifera virgifera. The authors recommend combining the original continuous variables when such variables are available. The combination of categories defined from continuous variables led to a loss of information and may decrease the values of the maps. Risk matrices should be used only if the individual variables are discrete and if the underlying continuous variables are not available.

This paper presents an efficient mixed-integer particle swarm optimization (MIPSO) for solving the constrained optimal power flow (OPF) with a mixture of continuous and discrete control variables and discontinuous fuel cost functions. In the MIPSO-based method, the individual that contains the real-value mixture of continuous and discrete control variables is defined, two mutation schemes are proposed to deal with the continuous and discrete control variables, respectively. Different objective functions with the valve-point loading effects constraints considered were employed to test the robustness of the proposed method. The feasibility of the proposed method is demonstrated for a 9-bus system and a 26-bus system, and it is compared with other stochastic methods in terms of solution quality, convergence property, and computation efficiency. The experimental results show that the MIPSO-based OPF method has suitable mutation schemes, resulting in robustness and effectiveness in solving constrained mixed-integer OPF problems.

Integrating Genetic Risk Factors with Age, Presenting White Cell Count and MRD Response As Continuous Variables to Predict Relapse in Paediatric Acute Lymphoblastic Leukemia (ALL)

A practical approach for hybrid distributed MPC

An improved mixed-integer particle swarm optimization (MI-PSO) algorithm is presented, which is called asynchronous updating particle swarm optimization (AU-PSO). The proposed algorithm speeds up convergence rate of PSO by handling discrete and continuous decision variables differently. The discrete variables have a possibility holding previous values, while the continuous variables are treated normally. This kind of treatment provides more chances to find a better solution. The proposed AU-PSO is then examined by test functions and successfully applied in a design of circular antenna array.

Engineering design problems often involve global optimization of functions that are supplied as ’black box‘ functions. These functions may be nonconvex, nondifferentiable and even discontinuous. In addition, the decision variables may be a combination of discrete and continuous variables. The functions are usually computationally expensive, and may involve finite element methods. An engineering example of this type of problem is to minimize the weight of a structure, while limiting strain to be below a certain threshold. This type of global optimization problem is very difficult to solve, yet design engineers must find some solution to their problem – even if it is a suboptimal one. Sometimes the most difficult part of the problem is finding any feasible solution. Stochastic methods, including sequential random search and simulated annealing, are finding many applications to this type of practical global optimization problem. Improving Hit-and-Run (IHR) is a sequential random search method that has been successfully used in several engineering design applications, such as the optimal design of composite structures. A motivation to IHR is discussed as well as several enhancements. The enhancements include allowing both continuous and discrete variables in the problem formulation. This has many practical advantages, because design variables often involve a mixture of continuous and discrete values. IHR and several variations have been applied to the composites design problem. Some of this practical experience is discussed.

Bayesian networks (BNs) are being studied in recent years for system diagnosis, reliability analysis, and design of complex engineered systems. In several practical applications, BNs need to be learned from available data before being used for design or other purposes. Current BN learning algorithms are mainly developed for networks with only discrete variables. Engineering design problems often consist of both discrete and continuous variables. This paper develops a framework to handle continuous variables in BN learning by integrating learning algorithms of discrete BNs with Gaussian mixture models (GMMs). We first make the topology learning more robust by optimizing the number of Gaussian components in the univariate GMMs currently available in the literature. Based on the BN topology learning, a new multivariate Gaussian mixture (MGM) strategy is developed to improve the accuracy of conditional probability learning in the BN. A method is proposed to address this difficulty of MGM modeling with data of mixed discrete and continuous variables by mapping the data for discrete variables into data for a standard normal variable. The proposed framework is capable of learning BNs without discretizing the continuous variables or making assumptions about their conditional probability densities (CPDs). The applications of the learned BN to uncertainty quantification and model calibration are also investigated. The results of a mathematical example and an engineering application example demonstrate the effectiveness of the proposed framework.

Quantum teleportation, a transfer protocol of quantum states, is the essence of many sophisticated quantum information protocols. There have been two complementary approaches to optical quantum teleportation: discrete variables (DVs) and continuous variables (CVs). However, both approaches have pros and cons. Here we take a “hybrid” approach to overcome the current limitations: CV quantum teleportation of DVs. This approach enabled the first realization of deterministic quantum teleportation of photonic qubits without post-selection. We also applied the hybrid scheme to several experiments, including entanglement swapping between DVs and CVs, conditional CV teleportation of single photons, and CV teleportation of qutrits. We are now aiming at universal, scalable, and fault-tolerant quantum computing based on these hybrid technologies.

Inference in hybrid Bayesian networks with large discrete and continuous domains

If the row and column categories of a contingency table sequentially seen, as objects and variables, then they are object data with discrete variables. Often from objects obtained additional data in the form of continuous variables. Based on these discrete and continuous variables, the more accurate method is necessary to analyse the associations between these variables. Treating discrete data as continuous is wrong, so this article aims to analyse the association of data in the form of / x 2 contingency tables with additional data that is continuous. From the data in the form of / x 2 contingency table, it converted using the simplification of correspondence analysis (SoCA), so that continuous principal coordinates obtained. Furthermore, the association between continuous variables was analysed using the cosine value of the angle between the two vectors. Case studies use poverty data in Indonesia, which published by the Central Statistics Agency (BPS-Statistics Indonesia). Data in the form of contingency tables are people population lived in poverty based on province and area of residence (urban or rural). Additional variables are poverty depth index, severity index, Gini ratio, food poverty line and non-food poverty line. The results of the analysis obtained information that in urban areas tend to have high Gini ratio, food poverty lines and non-food poverty lines, for rural areas tend to have a high poverty depth and severity index.