Predicting and controlling the dynamics of infectious diseases

This paper introduces a new optimal control model to describe and control the dynamics of infectious diseases. In the present model, the average time of isolation (i.e. hospitalization) of infectious population is the main time-dependent parameter that defines the spread of infection. All the preventive measures aim to decrease the average time of isolation under given constraints

Dynamics of Ebola epidemics in West Africa 2014

This paper investigates the dynamics of Ebola virus transmission in West Africa during 2014. The reproduction numbers for the total period of epidemic and for different consequent time intervals are estimated based on a newly suggested linear model. It contains one major variable - the average time of infectiousness (time from onset to hospitalization) that is considered as a parameter for controlling the future dynamics of epidemics. Numerical implementations are carried out on data collected from three countries Guinea, Sierra Leone and Liberia as well as the total data collected worldwide. Predictions are provided by considering different scenarios involving the average times of infectiousness for the next few months and the end of the current epidemic is estimated according to each scenario

Turnpike theorem for an infinite horizon optimal control problem with time delay

An optimal control problem for systems described by a special class of nonlinear differential equations with time delay is considered. The cost functional adopted could be considered as an analogue of the terminal functional defined over an infinite time horizon. The existence of optimal solutions as well as the asymptotic stability of optimal trajectories (that is, the turnpike property) are established under some quite mild restrictions on the nonlinearities of the functions involved in the description of the problem. Such mild restrictions on the nonlinearities allowed us to apply these results to a blood cell production model. © 2014 Society for Industrial and Applied Mathematics

Structure learning of Bayesian Networks using global optimization with applications in data classification

Bayesian Networks are increasingly popular methods of modeling uncertainty in artificial intelligence and machine learning. A Bayesian Network consists of a directed acyclic graph in which each node represents a variable and each arc represents probabilistic dependency between two variables. Constructing a Bayesian Network from data is a learning process that consists of two steps: learning structure and learning parameter. Learning a network structure from data is the most difficult task in this process. This paper presents a new algorithm for constructing an optimal structure for Bayesian Networks based on optimization. The algorithm has two major parts. First, we define an optimization model to find the better network graphs. Then, we apply an optimization approach for removing possible cycles from the directed graphs obtained in the first part which is the first of its kind in the literature. The main advantage of the proposed method is that the maximal number of parents for variables is not fixed a priory and it is defined during the optimization procedure. It also considers all networks including cyclic ones and then choose a best structure by applying a global optimization method. To show the efficiency of the algorithm, several closely related algorithms including unrestricted dependency Bayesian Network algorithm, as well as, benchmarks algorithms SVM and C4.5 are employed for comparison. We apply these algorithms on data classification; data sets are taken from the UCI machine learning repository and the LIBSVM. © 2014, Springer-Verlag Berlin Heidelberg

Structure learning of Bayesian networks using a new unrestricted dependency algorithm

Bayesian Networks have deserved extensive attentions in data mining due to their efficiencies, and reasonable predictive accuracy. A Bayesian Network is a directed acyclic graph in which each node represents a variable and each arc a probabilistic dependency between two variables. Constructing a Bayesian Network from data is the learning process that is divided in two steps: learning structure and learning parameter. In many domains, the structure is not known a priori and must be inferred from data. This paper presents an iterative unrestricted dependency algorithm for learning structure of Bayesian Networks for binary classification problems. Numerical experiments are conducted on several real world data sets, where continuous features are discretized by applying two different methods. The performance of the proposed algorithm is compared with the Naive Bayes, the Tree Augmented Naive Bayes, and the

An optimization approach to the study of drug-drug interactions

Drug-drug interaction is one of the important problems of Adverse Drug Reaction (ADR). In this paper we develop an optimization approach for the study of this problem. This approach is based on drug-reaction relationships represented in the form of a vector of weights, which can be defined as a solution to some global optimization problem. Although this approach can be used for solving many ADR problems, we concentrate here only on drug-drug interactions. Based on drug-reaction relationships, we formulate this problem as an optimization problem. The approach is applied to different classes of reactions from the Australian Adverse Drug Reaction Advisory Committee (ADRAC) database

From convex to nonconvex: A loss function analysis for binary classification

Problems of data classification can be studied in the framework of regularization theory as ill-posed problems. In this framework, loss functions play an important role in the application of regularization theory to classification. In this paper, we review some important convex loss functions, including hinge loss, square loss, modified square loss, exponential loss, logistic regression loss, as well as some non-convex loss functions, such as sigmoid loss, ø-loss, ramp loss, normalized sigmoid loss, and the loss function of 2 layer neural network. Based on the analysis of these loss functions, we propose a new differentiable non-convex loss function, called smoothed 0-1 loss function, which is a natural approximation of the 0-1 loss function. To compare the performance of different loss functions, we propose two binary classification algorithms for binary classification, one for convex loss functions, the other for non-convex loss functions. A set of experiments are launched on several binary data sets from the UCI repository. The results show that the proposed smoothed 0-1 loss function is robust, especially for those noisy data sets with many outliers. © 2010 IEEE

Optimization of parameters of the Kelvin element in vibration analysis

In this paper we consider the problem of finding optimal parameters of the Kelvin element in vibration analysis. This problem is based on finding analytical solution of the initial ODE for development of the optimization model. Such technique allows us to compute optimal parameters of Kelvin element

Profiling phishing emails based on hyperlink information

In this paper, a novel method for profiling phishing activity from an analysis of phishing emails is proposed. Profiling is useful in determining the activity of an individual or a particular group of phishers. Work in the area of phishing is usually aimed at detection of phishing emails. In this paper, we concentrate on profiling as distinct from detection of phishing emails. We formulate the profiling problem as a multi-label classification problem using the hyperlinks in the phishing emails as features and structural properties of emails along with whois (i.e.DNS) information on hyperlinks as profile classes. Further, we generate profiles based on classifier predictions. Thus, classes become elements of profiles. We employ a boosting algorithm (AdaBoost) as well as SVM to generate multi-label class predictions on three different datasets created from hyperlink information in phishing emails. These predictions are further utilized to generate complete profiles of these emails. Results show that profiling can be done with quite high accuracy using hyperlink information. © 2010 Crown Copyright

Improving Naive Bayes classifier using conditional probabilities

Naive Bayes classifier is the simplest among Bayesian Network classifiers. It has shown to be very efficient on a variety of data classification problems. However, the strong assumption that all features are conditionally independent given the class is often violated on many real world applications. Therefore, improvement of the Naive Bayes classifier by alleviating the feature independence assumption has attracted much attention. In this paper, we develop a new version of the Naive Bayes classifier without assuming independence of features. The proposed algorithm approximates the interactions between features by using conditional probabilities. We present results of numerical experiments on several real world data sets, where continuous features are discretized by applying two different methods. These results demonstrate that the proposed algorithm significantly improve the performance of the Naive Bayes classifier, yet at the same time maintains its robustness. © 2011, Australian Computer Society, Inc