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This paper proposes a new method called depth difference (DeD), for estimating the optimal number of clusters ( k ) in a dataset based on data depth. The DeD method estimates the k parameter before actual clustering is constructed. We define the depth within clusters, depth between clusters, and depth difference to finalize the optimal value of k , which is an input value for the clustering algorithm. The experimental comparison with the leading state-of-the-art alternatives demonstrates that the proposed DeD method outperforms.

This study proposes an approximate dynamic programming (ADP) method for a stochastic home energy management system (HEMS) that aims to minimise the electricity cost and discomfort of a household under uncertainties. The study focuses on a HEMS that optimally schedules heating, ventilation, and air conditioning, water heater, and electric vehicle, while accounting for uncertainties in outside temperature, hot water usage, and non-controllable net load. The authors approach the ADP-based HEMS via an effective combination of Sobol sampling backward induction and a K–D tree nearest neighbour techniques for the value function approximation. A subset of possible states is sampled and used to create an approximation of the value of being in aggregated states. They compare the ADP approach with other prevailing HEMS methods, including dynamic programming (DP) and mixed-integer linear programming (MILP), in a model predictive control framework. Simulation results show that the proposed ADP approach can yield near-optimal appliance schedules under uncertainties when finely discretised. Merits and drawbacks of the proposed ADP method in comparison with DP and MILP are also revealed.

Uncertain random variables are tools to deal with a mixture of uncertainty and randomness. A new concept of order statistics associated with uncertain random variables is proposed, and is applied to analyze k -out-of- n systems with uncertain random lifetimes. The chance distributions of order statistics of uncertain random variables are derived from the operational law of uncertain random variables. Finally, the reliability of k -out-of- n systems with uncertain random lifetimes is discussed.

In this study, monomials with odd integer powers are proposed for blind multiuser detection of code-division multiple access signals with long spreading codes, in the near–far situation. The performance of the new non-linear detectors are substantiated asymptotically and confirmed via simulations. It is demonstrated that the proposed non-linear detectors significantly outperform the matched filter detector in the block fading and Ricean fading channels, at the cost of a small increase in computational complexity. The optimum integer power value for the block fading channel with a limited interferer level, the Ricean channel with a given K factor and asynchronous channel is determined. The proposed multiuser detectors are blind in the sense that they require neither training nor the spreading code of the interferers. The detectors also do not require long convergence time for decision making in contrast to conventional blind multiuser detectors.

Objectives: To evaluate the diet of 16-18-y-old boys and girls with particular reference to intakes of nutrients believed to affect bone health and dietary acid-base balance. Design: A 7-day food diary was completed between the months of October and December. Setting: Cambridge, UK Subjects: A total of 111 boys and 101 girls aged 16-18 y who were recruited into the Cambridge Bone Studies. Main outcome measures: Mean daily intakes of foods and selected nutrients (protein, calcium, phosphorus, magnesium, potassium, vitamins C and K) were calculated. Two estimates of acid-base balance were calculated from the diet using the formulae of Remer (net acid excretion, estimated indirectly; NAE(ind)) and Frassetto (protein/potassium ratio). Results: Mean calcium and phosphorus intakes were above the UK Reference Nutrient intake (RNI). In all, 39% of the boys and 36% of the girls had vitamin K intakes lower than 1 microgram/kg body weight/day. Calcium intake was positively correlated with all other nutrients except vitamins C and K. Boys had a significantly higher estimated net acid excretion (NAE(ind)) than girls (P<0.001). Although a strong correlation (r=0.76, P<0.001) was found between the two methods, at higher acid levels a divergence was observed. A significant positive correlation was found between NAE(ind) and the weight consumed per day of milk, cheese, meat and cereal foods and a negative correlation was found with the weight of potatoes and fruit. Diet composition is such that a lower NAE(ind) is accompanied by a lower calcium intake. Conclusions: The interpretation of the effects of calcium and other nutrients on bone cannot be considered in isolation from the other components of the diet. These results challenge some of the accepted perceptions about what constitutes an optimal diet for the promotion of bone health in adolescents. Sponsorship: Medical Research Council, Department of Health/Medical Research Council Nutrition Research Initiative and Mead Johnson Research Fund.

In this paper, we consider the following random version of Shepp's urn scheme: A player is given an urn with n balls. p of these balls have value +1 and n-p have value -1. The player is allowed to draw balls randomly, without replacement, until he or she wants to stop. The player knows n, the total number of balls, but knows only that p, the number of balls of value +1, is a number selected randomly from the set 0, 1,2,...,n. The player wishes to maximize the expected value of the sum of the balls drawn. We first derive the player's optimal drawing policy and an algorithm to compute the player's expected value at the stopping time when he or she uses the optimal drawing policy. Since the optimal drawing policy is rather intricate and the computation of the player's optimal expected value is quite cumbersome, we present a very simple drawing policy, which is asymptotically optimal. We also show that this random urn scheme is equivalent to a random coin tossing problem.

Enzyme reactions depend strongly on pH and temperature. The direct dependence of the enzyme becomes obvious, when the enzyme activity is measured at the respective pH or temperature, while preincubation for a distinct time yields the stability of the enzyme against these influences. A pH‐optimum curve is characteristic for the pH behavior, while the activity increases with temperature until denaturation of the enzymes counteracts the increase. The temperature increase can be linearized in an Arrhenius diagram, the slope of which gives the activation energy.