The densest <Emphasis Type="Italic">k</Emphasis>-subgraph problem on clique graphs

The Densest k-Subgraph (DkS) problem asks for a k-vertex subgraph of a given graph with the maximum number of edges. The problem is strongly NP-hard, as a generalization of the well known Clique problem and we also know that it does not admit a Polynomial Time Approximation Scheme (PTAS). In this paper we focus on special cases of the problem, with respect to the class of the input graph. Especially, towards the elucidation of the open questions concerning the complexity of the problem for interval graphs as well as its approximability for chordal graphs, we consider graphs having special clique graphs. We present a PTAS for stars of cliques and a dynamic programming algorithm for trees of cliques. M.L. is co-financed within Op. Education by the ESF (European Social Fund) and National Resources. V.Z. is partially supported by the Special Research Grants Account of the University of Athens under Grant 70/4/5821.     

Health Risk Assessment of a Modern Municipal Waste Incinerator

During the modernization of the municipal waste incinerator (MWI, maximum capacity of 180,000 tons per year) of Metropolitan Grenoble (405,000 inhabitants), in France, a risk assessment was conducted, based on four tracer pollutants: two volatile organic compounds (benzene and 1, 1, 1 trichloroethane) and two heavy metals (nickel and cadmium, measured in particles). A Gaussian plume dispersion model, applied to maximum emissions measured at the MWI stacks, was used to estimate the distribution of these pollutants in the atmosphere throughout the metropolitan area. A random sample telephone survey (570 subjects) gathered data on time-activity patterns, according to demographic characteristics of the population. Life-long exposure was assessed as a time-weighted average of ambient air concentrations. Inhalation alone was considered because, in the Grenoble urban setting, other routes of exposure are not likely. A Monte Carlo simulation was used to describe probability distributions of exposures and risks. The median of the life-long personal exposures distribution to MWI benzene was 3.2·10^–5 g/m³ (20th and 80th percentiles = 1.5·10^–5 and 6.5·10^–5 g/m³), yielding a 2.6·10^–10 carcinogenic risk (1.2·10^–10–5.4·10^–10). For nickel, the corresponding life-time exposure and cancer risk were 1.8·10^–4 g/m³ (0.9.10^–4 – 3.6·10^–4 g/m³) and 8.6·10^–8 (4.3·10^–8–17.3·10^–8); for cadmium they were respectively 8.3·10^–6 g/m³ (4.0·10^–6–17.6·10^–6) and 1.5·10^–8 (7.2·10^–9–3.1·10^–8). Inhalation exposure to cadmium emitted by the MWI represented less than 1% of the WHO Air Quality Guideline (5 ng/m³), while there was a margin of exposure of more than 10⁹ between the NOAEL (150 ppm) and exposure estimates to trichloroethane. Neither dioxins nor mercury, a volatile metal, were measured. This could lessen the attributable life-long risks estimated. The minute (VOCs and cadmium) to moderate (nickel) exposure and risk estimates are in accord with other studies on modern MWIs meeting recent emission regulations, however.     

On the Complexity of Constructing Evolutionary Trees

In this paper we study a few important tree optimization problems with applications to computational biology. These problems ask for trees that are consistent with an as large part of the given data as possible. We show that the maximum homeomorphic agreement subtree problem cannot be approximated within a factor of , where N is the input size, for any 0 in polynomial time unless P = NP, even if all the given trees are of height 2. On the other hand, we present an O(N log N)-time heuristic for the restriction of this problem to instances with O(1) trees of height O(1) yielding solutions within a constant factor of the optimum. We prove that the maximum inferred consensus tree problem is NP-complete, and provide a simple, fast heuristic for it yielding solutions within one third of the optimum. We also present a more specialized polynomial-time heuristic for the maximum inferred local consensus tree problem.     

Economic and economic statistical designs for three-level control charts

In some situations, an appropriate quality measure uses three or more discrete levels to classify a product characteristic. For these situations, some control charts have been developed based on statistical criteria regardless of economic considerations. In this paper, we develop economic and economic statistical designs (ESD) for 3-level control charts. We apply the cost model proposed by Costa and Rahim.[Economic design of X charts with variable parameters: the Markov chain approach, J Appl Stat 28 (2001), 875–885] Furthermore, we assume that the length of time that the process remains in control is exponentially distributed which allows us to apply the Markov chain approach for developing the cost model. We apply a genetic algorithm to determine the optimal values of model parameters by minimizing the cost function. A numerical example is provided to illustrate the performance of the proposed models and to compare the cost of the pure economic and ESD for three-level control charts. A sensitivity analysis is also conducted in this numerical example.     

On testes for threshold–type nonlinearity in irregulaly spaced time series

Formulating the model first in continuous time, we have developed a state space approach to the problem of testing for threshold-type nonlinearity when the data are irregularly spaced.     

Bootstrap LR tests of stationarity,common trends and cointegration

This paper considers the likelihood ratio (LR) tests of stationarity, common trends and cointegration for multivariate time series. As the distribution of these tests is not known, a bootstrap version is proposed via a state- space representation. The bootstrap samples are obtained from the Kalman filter innovations under the null hypothesis. Monte Carlo simulations for the Gaussian univariate random walk plus noise model show that the bootstrap LR test achieves higher power for medium-sized deviations from the null hypothesis than a locally optimal and one-sided Lagrange Multiplier (LM) test that has a known asymptotic distribution. The power gains of the bootstrap LR test are significantly larger for testing the hypothesis of common trends and cointegration in multivariate time series, as the alternative asymptotic procedure – obtained as an extension of the LM test of stationarity – does not possess properties of optimality. Finally, it is shown that the (pseudo-)LR tests maintain good size and power properties also for the non-Gaussian series. An empirical illustration is provided.     

Bayesian X̄ control limits for exponentially distributed measurements

This article deals with the construction of an X? control chart using the Bayesian perspective. We obtain new control limits for the X? chart for exponentially distributed data-generating processes through the sequential use of Bayes’ theorem and credible intervals. Construction of the control chart is illustrated using a simulated data example. The performance of the proposed, standard, tolerance interval, exponential cumulative sum (CUSUM) and exponential exponentially weighted moving average (EWMA) control limits are examined and compared via a Monte Carlo simulation study. The proposed Bayesian control limits are found to perform better than standard, tolerance interval, exponential EWMA and exponential CUSUM control limits for exponentially distributed processes.     

Adaptive order selection for autoregressive models

Autoregressive model is a popular method for analysing the time dependent data, where selection of order parameter is imperative. Two commonly used selection criteria are the Akaike information criterion (AIC) and the Bayesian information criterion (BIC), which are known to suffer the potential problems regarding overfit and underfit, respectively. To our knowledge, there does not exist a criterion in the literature that can satisfactorily perform under various situations. Therefore, in this paper, we focus on forecasting the future values of an observed time series and propose an adaptive idea to combine the advantages of AIC and BIC but to mitigate their weaknesses based on the concept of generalized degrees of freedom. Instead of applying a fixed criterion to select the order parameter, we propose an approximately unbiased estimator of mean squared prediction errors based on a data perturbation technique for fairly comparing between AIC and BIC. Then use the selected criterion to determine the final order parameter. Some numerical experiments are performed to show the superiority of the proposed method and a real data set of the retail price index of China from 1952 to 2008 is also applied for illustration.