Uncertainty management in multiobjective hydro-thermal self-scheduling under emission considerations In this paper, a stochastic multiobjective framework is proposed for a day-ahead short-term Hydro Thermal Self-Scheduling (HTSS) problem for joint energy and reserve markets. An efficient linear formulations are introduced in this paper to deal with the nonlinearity of original problem due to the dynamic ramp rate limits, prohibited operating zones, operating services of thermal plants, multi-head power discharge characteristics of hydro generating units and spillage of reservoirs. Besides, system uncertainties including the generating units' contingencies and price uncertainty are explicitly considered in the stochastic market clearing scheme. For the stochastic modeling of probable multiobjective optimization scenarios, a lattice Monte Carlo simulation has been adopted to have a better coverage of the system uncertainty spectrum. Consequently, the resulting multiobjective optimization scenarios should concurrently optimize competing objective functions including GENeration COmpany's (GENCO's) profit maximization and thermal units' emission minimization. Accordingly, the -constraint method is used to solve the multiobjective optimization problem and generate the Pareto set. Then, a fuzzy satisfying method is employed to choose the most preferred solution among all Pareto optimal solutions. The performance of the presented method is verified in different case studies. The results obtained from -constraint method is compared with those reported by weighted sum method, evolutionary programming-based interactive Fuzzy satisfying method, differential evolution, quantum-behaved particle swarm optimization and hybrid multi-objective cultural algorithm, verifying the superiority of the proposed approach. For several years Unit Commitment (UC) has been used to determine the optimal scheduling of power producers for different horizons (daily, weekly and etc.). The Independent System Operator (ISO) implements Security-Constrained Unit Commitment (SCUC) problem that its objective function is minimization of cost while considering system security and meeting system load. GENeration COmpanies (GENCOs) uses Price-Based Unit Commitment (PBUC) to maximize their profit but they are not concerning about providing the system load [1] . The UC and PBUC are respectively termed as the Hydro-Thermal Scheduling (HTS) and Hydro-Thermal Self Scheduling (HTSS) [2] for the system with the hydro and thermal units. Different solution methods of the HTSS problem are comprehensively classified into heuristic and analytical methods in Ref. [3] . In Ref. [4] , a novel mixed-integer nonlinear approach is proposed to solve the short-term hydro scheduling problem in the day-ahead electricity market, considering not only head-dependency, but also start/stop of units, discontinuous operating regions and discharge ramping constraints.. In Ref. [5] , a stochastic programming formulation is proposed for trading wind energy in a market environment under uncertainty of shut-down cost of unit i ($) A j start-up cost of unit j ($) b n (i) slope of block n of fuel cost curve of unit i ($/MWh) b n (j) slope of the volume block n of the reservoir associated to unit j (m 3 /s/Hm 3 ) b k n (j) slope of the block n of the performance curve k of unit j (MW/m 3 /s) be n (i) slope of segment n in emission curve of unit i (lbs/MWh) e i ,f i coefficients of valve loading cost function E min (i) generated emission by off-unit while providing nonspinning reserve (lbs) E(p u n−1 (i)) generated emission of n − 1th upper limit in the emission curve of unit i (lbs) EGR emission group (SO 2 orNO x ) E QUOTA emission quota (lbs) F(p u n−1 (i)) generation cost of n-1th upper limit in the fuel cost curve of unit i ($/h) F(j,t,s). forecasted natural water inflow of the reservoir associated to unit j (Hm 3 /h) L number of performance curves M number of prohibited operating zones NL number of blocks of the piecewise linearized startup fuel function NP number of price levels NS number of scenario after scenario reduction NA number of areas in the network p b (t) power capacity of bilateral contract (MW) P(s) probability of scenario s Pr(s) normalized probability of scenario s p min (i), p max (i) minimum and maximum power output of unit i (MW) p -n (j) minimum power output of unit j for performance curve n (MW) p(j) capacity of unit j (MW) p d n (i) lower limit of nth prohibited operating zone of unit i (MW) p u n−1 (i) upper limit of n − 1th prohibited operating zone of unit i (MW) Q -(j),Q (j) minimum and maximum water discharge of unit j (m 3 /s) RDL n (i), RUL n (i) ramp down and ramp up limit for block n (MW) SUE(i),SDE(i) start-up and shut-down emission generated by unit i (lbs) SU(i),SD(i) start-up and shut-down ramp rate limit of unit i (MW/h) RDL(p(i,t,s)), RUL(p(i,t,s)) ramping down and ramping up limit of unit i (MW) v 0 (j) minimum content of the reservoir associated to unit j (Hm 3 ) v n (j) maximum content of the reservoir j associated to nth performance curve (Hm 3 ). Variables ı n (i,t,s) generation of block n of fuel cost curve for unit i (MW). n (i,t,s) generation of block n of unit i for valve loading effect curve (MW) sp (t,s), sr (t,s), and ns (t,s) market price for energy, spinning and non-spinning reserve ($/MWh), respectively r n individual membership function (the degree of optimality) for the nth objective function in the rth Pareto optimal solution w n the weight factor of the nth objective function in the MMP problem r total membership function of the rth Pareto optimal solution B(i,t,s). start-up cost of unit i ($) C(i,t,s). valve loading effect cost of unit i ($) F(i,t,s) fuel cost of unit i ($) EP main objective function (expected profit of GENCO) EA GENCO's total expected profit in dollars after arbitrage EE expected generated emission for each Pareto optimal solution (lbs) N d (i,t,s),N u (i,t,s) non-spinning reserve of thermal unit i in the spot market when unit is off and on, respectively (MW) N d (j,t,s), N u (j,t,s) non-spinning reserve of a hydro unit j in the spot market when unit is off and on, respectively (MW) p(i,t,s) power output of thermal unit i (MW) p(i, t, s) maximum power output of unit i (MW) p(j,t,s) power output of hydro unit j (MW) p sp (t,s) power for bid on the spot market (MW) PROFIT(s) profit of scenario s q n (j,t,s) water discharge of hydro unit j and block n (m 3 /s) R(i,t,s), R(j,t,s) spinning reserve of a thermal unit i and hydro unit j in the spot market (MW), respectively v(j,t,s) water content of the reservoir associated with unit. Binary variables I(i,t,s) 1 if thermal unit i is on I(j,t,s) 1 if hydro unit j is on I d (i,t,s) 1 if unit i provide non-spinning reserve when unit is off.. n (i,t,s) 1 if block n of fuel cost curve of unit i is selecteď n (j,t,s) 1 if volume of reservoir water is greater than v n (j) n (i,t,s) 1 if power output of unit i has exceeded block n of valve loading effect curve W P k,t,s obtained from the roulette wheel mechanism in the scenario generation stage indicating whether kth price level in the sth scenario occurred (w P k,t,s energy market prices as well as the volatile and intermittent nature of wind energy. Optimal hydro scheduling for the short-term time horizon is proposed in Ref. [6] wherein a mixed-integer nonlinear programming framework including the head effect on power production, start-up costs of units, multiple operating regions, and discharge variation constraints is considered. Also in Ref. [6] , as new contributions to the field, the market price uncertainty is introduced in the model via price scenarios. Also, the risk management is included in Ref. [6] using Conditional Value-at-Risk (CVR) to limit profit volatility. In Ref. [7] , Monte Carlo Simulation (MCS) method is implemented to generate random hourly prices for energy, ancillary services, and fuel in the stochastic PBUC framework. A stochastic midterm risk-constrained hydrothermal scheduling algorithm is proposed for profit maximization of GENCOs in Ref. [8] . In Refs. [9, 10] , the stochastic SCUC is implemented for the electricity market clearing problem while reserve services are determined based on the expected-load-not-served. Two methodologies are suggested to reduce computational burden of the stochastic UC in Ref. [11] . The stochastic nature of the electricity price is modeled in a multi-stage stochastic framework for thermal units' self-scheduling in Ref. [12] . Ref [13] used a deterministic MIP approach for solving the HTSS problem of generating units. Also, [14] presents a mixed-integer stochastic framework for a hydro-wind power system scheduling. Ref. [15] presents the techno-economic factor for distributed generation units based on the effect of their generation on the network losses. The MCS method is used for the outages of generating units and transmission lines together with the load forecasting inaccuracies in the SCUC problem in Ref. [16] . A stochastic self-scheduling for thermal units based on the ARIMA model is utilized in Ref. [17] . In Ref. [18] , an interval-fuzzy two-stage stochastic programming method is developed for the carbon dioxide (CO2) emission trading under uncertainty. It is worth to mention that, in the above-mentioned papers, the valve loading effect and dynamic ramp rate are not taken into account. On the other hand, to the best of our knowledge, no research work in the area considers a stochastic multiobjective multiperiod framework for the HTSS problem. In other words, the uncertainty sources (generating unit contingencies and price forecast uncertainty) have been taken into account in this work. Accordingly, the main contribution of this paper is to present a multiperiod stochastic multiobjective framework for the short term HTSS. In the proposed model, the expected profit is maximized based on the MIP optimization formulation while at the same time the expected emission is minimized in the form of multiobjective stochastic problem. Furthermore, the price uncertainty is considered using the Probability Distribution Function (PDF) of price forecast error. Concurrently, the roulette wheel mechanism is implemented to generate the price of energy and spinning/nonspinning reserve for each hour and Lattice Monte Carlo simulation (LMCS) method is applied to consider Forced Outage Rate (FOR) of units. For the sake of accuracy, more practical constraints of thermal and hydro units are taken into account. In Refs. [19] [20] [21] , the valve loading effect cost is modeled in the form of a nonlinear sinusoidal function which is linearized in our framework. Based on the work [22] , different dynamic ramp rate is also proposed in the HTSS framework. Finally, a general formulation is recommended for the multi-performance curve of hydro units based on [23] . Different solution methods for the optimization problem can be found in Refs. [24] [25] [26] [27] . Accordingly, the proposed HTSS includes a linear formulation for valve loading effect, fuel cost, emission function, fuel constraint, and multi-performance power-discharge curves of hydro units as well as units' minimum up/down time. A GENCO can use the proposed methodology in their day-ahead scheduling to find the optimal decision for the UC for the next day. The new contributions of this paper with respect to the previous works can be briefly summarized as follows: The remainder of this paper is organized as follows: In section II, the proposed stochastic modeling of HTSS problem is formulated concerning system's uncertainties. In section III, the MIP formulation for the stochastic multiobjective HTSS has been presented. Solution approach of the multiobjective optimization problem is discussed in section IV. In the next section, the IEEE 118-bus test system is studied to demonstrate effectiveness of the proposed scheme. Some relevant conclusions are drawn in the section VI. This paper presents a stochastic multiobjective HTSS framework in the form of MIP optimization problem in which the valve loading effect cost, dynamic ramp rate, POZs, fuel limitation are modeled all in linear form. It also includes multi-performance curves for hydro units making the HTSS framework more realistic. With the proposed method, each GENCO can cope with the uncertainties of the HTSS problem, i.e. price forecast error and generating units' outage. Besides, each GENCO can compromise the conflicting objectives of the expected profit maximization in such a way that the GENCO's concerns about the emission are to some extent relieved. Furthermore, the stochastic approach leads to a more efficient utilization of generating units, allowing the GENCOs to estimate the effects of units' contingencies and price uncertainty on the HTSS results. Covering the uncertainties by the proposed stochastic multiobjective HTSS, each GENCO can bid in the day-ahead market so as to gain profit as much as possible. Using the arbitrage approach make it possible for the GENCO to purchase its required emission or sell its emission quota to obtain more profit.. The research work under way to (a) present a stochastic model with other scenario reduction techniques; (b) consider financial risk associated with the market price uncertainty, and (c) use accelerated benders decomposition to reduce computational burden.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O


A linear approach for sparse coding by a two-layer neural network Many approaches to transform classification problems from nonlinear to linear by feature transformation have been recently presented in the literature. These notably include sparse coding methods and deep neural networks. However, many of these approaches require the repeated application of a learning process upon the presentation of unseen data input vectors, or else involve the use of large numbers of parameters and hyper-parameters, which must be chosen through cross-validation, thus increasing running time dramatically. In this paper, we propose and experimentally investigate a new approach for the purpose of overcoming limitations of both kinds. The proposed approach makes use of a linear auto-associative network (called SCNN) with just one hidden layer. The combination of this architecture with a specific error function to be minimized enables one to learn a linear encoder computing a sparse code which turns out to be as similar as possible to the sparse coding that one obtains by re-training the neural network. Importantly, the linearity of SCNN and the choice of the error function allow one to achieve reduced running time in the learning phase. The proposed architecture is evaluated on the basis of two standard machine learning tasks. Its performances are compared with those of recently proposed non-linear auto-associative neural networks. The overall results suggest that linear encoders can be profitably used to obtain sparse data representations in the context of machine learning problems, provided that an appropriate error function is used during the learning phase. Various approaches to transform classification problems from non-linear to linear by a feature transformation have been recently investigated. These notably include sparse coding methods [1, 2, 3, 4, 5] and deep neural networks [6, 7] . However, two remarkable limitations usually affect these approaches: (i) most of the current sparse coding methods [1, 3, 4, 8, see, for example,] require the repeated application of some learning process in order to compute an input sparse representation, whenever the algorithm is fed with an input vector which was never used during the training phase; (ii) even though auto-associative neural networks enable one to overcome limitation (i), many of them, such as deep belief networks, present several levels of complexity or non-linearity. In fact, their learning methods usually involve a large number of parameters and hyper-parameters, such as the number of hidden units for more than one hidden layer, learning rates, momentum, weight decay, and so on. These parameters must be chosen through cross-validation, thus leading to a dramatic increase of running time. Interestingly, some authors [8, 9] suggest that simpler architectures, requiring a reduced number of parameters to be found, may enable one to achieve state-of-the-art performance. Following up this suggestion, the use of a relatively "simple" neural network approach, overcoming limitations (i) and (ii), is proposed here and experimentally investigated in terms of a trade-off between computational costs and performances.. The problem of overcoming limitations (i) and (ii) was addressed (a) by selecting an auto-associative neural network which enables one to learn a mapping between data and code space (the encoder) during the learning phase so that the learned mapping can be subsequently used on unseen data; and (b) by choosing just one linear hidden layer with identity as output function, jointly with an error function which allows one to learn at the same time both the encoder and the decoder by taking explicitly into account the contributions given by the two mappings. Given the linearity of the hidden layer and the selected error function, "good" learning rate parameters, ensuring linear rates of convergence in the minimization of error function, can be chosen in an explicit form without using cross-validation.. Points (a) and (b) guarantee that a reduced number of parameters must be determined during the learning phase: these are the number of hidden nodes and the sparsity parameter value which controls the extent to which the coding is sparse. On account of this fact, the present approach turns out to be computationally less expensive than deep neural networks and standard sparse coding approaches alike. Importantly, the present approach enables one to compute a linear encoder by means of which, during the test phase (on unseen data), one obtains a sparse code which is as similar as possible to the sparse code that one obtains by re-training the neural network. By applying a non-linear operation such as soft-thresholding or soft-max on this code one obtains a non-linear feature transformation. The rest of the paper is organized as follows.The selected auto-associative neural network and its relation to previously proposed approaches are discussed in Section 2 and 3, respectively. The experiment and its outcomes are presented in Section 4. In particular, in 4.1 tests showing the capability of our approach to reproduce PCA behaviour are described and discussed, whereas the ability to obtain appropriate sparse data representations enabling one to solve two standard machine learning tasks is evaluated in 4.2, 4.3.1 and 4.3.2. Our approach is additionally compared with two auto-associative neural networks recently proposed in literature ( [10] , [11] and with current results presented in the literature). Finally, Section 5 is devoted to an analysis of experimental results and their significance. In this paper we showed that a linear two-layer neural netwok (SCNN) can be profitably used to achieve sparse data representations for solving machine learning problems.. In our approach hidden layer linearity and the specific choice of error function allow one to explicitly define learning rate values which ensure linear rates of convergence in the minimization of error function and convergence of Table 3 : Error rates (%) of MNIST classification by SCNN + linear SVM with a number of hidden units equal to 400 against different noise values. These value are also compared with those obtained by raw images and SCNN with a re-learning phase on the test set (without using a projection dictionary). both reconstruction (decoder) and projection (encoder) dictionaries towards a minimizer [18, 28, see] . Moreover, we have to set the number of units of just one hidden layer, unlike deep network approaches, and the linearity of the hidden layer allows one to perform a learning process which is computationally less expensive than a non-linear approach for a time constant. In this sense, we claim that our architecture is a comparatively " simple" one.. SCNN reaches a very similar reconstruction error compared to PCA as described in Section 4.1. Interestingly, by means of our approach, we obtained performances that are comparable to or better than non-linear methods. More specifically, the experiments in Section 4.2 and 4.3.1 show that our approach produces sparse data representations enabling one to solve standard machine learning problems. SCNN outperforms ASCNN and SAANN in all cases; and its performances are comparable to those of Sparsenet, which does not use an encoder to project unseen data to sparse code, but requires iteration of a learning process. In the hand-written digit classification problem (see Section 4.3.2), our results are competitive with respect to state-of-the-art results that are based on unsupervised feature learning plus linear classification without using additional image geometric information. In addition, our approach seems to be little affected by noise.. It is worth noting, in connection with Section 4.2, that during the test phase our approach (SCNN) reaches high sparsity values comparable with or better than the values obtained by ASCNN and Sparsenet that make use of non linear activation functions and a new learning process, respectively. SAANN has sparsity values that are much lower than those obtained by all other methods. Figure 4 shows that the SCNN linear encoder projects input data with a degree of sparsity greater than or equal to that obtained by ASCNN and Sparsenet for different noise levels. In connection with Section 4.3.1, it is worth noting that both SCNN and Sparsenet achieve high accuracy values (more than 0.80) preserving high sparsity values in terms of sparsity area. ASCNN and SAANN exhibit also high sparsity values but in correspondence of lower values of classification accuracy. In the hand-written digit classification problem (see Section 4.3.2, linear projection dictionary followed by soft-thresholding operator enable one to obtain an error rate equal to about 2%, that is, a better value than that obtained by other approaches such as Local Kernel smoothing, VQ coding and Laplacian eigenmap. Furthermore, this value is comparable to standard sparse coding approaches and deep network (see Table 1 and 2).. It is worth noting that the learning process based on an alternate updating of the dictionaries C and D (see ASCNN and SCNN learning processes, sections 2 and 3) appears to lead to better results than the update involving two dictionaries simultaneously (see SAANN learning process, Section 2). In fact, SAANN achieves in many cases worse results than SCNN and ASCNN (see for example figures 2, 3, and 6).. Altogether, these results suggest that linear encoders can be used to obtain sparse data representations that are useful in the context of machine learning problems, providing that an appropriate error function is used during the learning phase. In particular, on the basis of some suggestions made in [29, 2] we introduced a term in the error function which enables one to obtain a sparse code which is as similar as possible to the output of the encoder. Experiments of two different kinds were conducted. The first series of experiments is aimed at evaluating the capability of the networks to reproduce PCA behaviour (see Subsection 4.1). In the second series of experiments, . we evaluated the performance of our approach on the basis of two standard machine learning tasks. The first task is a missing-pixels problem (see Subsection 4.2). Here, we focused on evaluating the ability of the selected networks to obtain appropriate sparse data representations which enable one to solve the task. The second task concerns hand-written digit classification (see subsections 4.3.1). In this latter task we first compared SCNN with the selected networks (see subsections 4.3.1), and then we measured the error rate of our approach at varying the number of hidden nodes. Our results were compared with major extant approaches (see Subsection 4.3.2). Moreover, we evaluated the effect of noise on the performance of SCNN. The main neural network parameters were set up as follows:. • initialization of the weights. The initial weights were randomly chosen in the set [−1, 1];. • learning rates were chosen for SCNN to be the Lipschitz constants. The maximum number of iteration were always fixed to: 1000 for step (a), 500 for step (b), 500 for step (c), and 50 for external loop (see 1);. • learning rate and maximum number of iterations for ASCNN and SAANN have been chosen in accordance with [10] and [11] , respectively;. • threshold was selected as stop condition. We heuristically tried different choices for all methods, and best results are reported;. • λ was chosen according to what is specified in each experiment.

O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O B I O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Bio and health informatics meets cloud : BioVLab as an example The exponential increase of genomic data brought by the advent of the next or the third generation sequencing (NGS) technologies and the dramatic drop in sequencing cost have driven biological and medical sciences to data-driven sciences. This revolutionary paradigm shift comes with challenges in terms of data transfer, storage, computation, and analysis of big bio/medical data. Cloud computing is a service model sharing a pool of configurable resources, which is a suitable workbench to address these challenges. From the medical or biological perspective, providing computing power and storage is the most attractive feature of cloud computing in handling the ever increasing biological data. As data increases in size, many research organizations start to experience the lack of computing power, which becomes a major hurdle in achieving research goals. In this paper, we review the features of publically available bio and health cloud systems in terms of graphical user interface, external data integration, security and extensibility of features. We then discuss about issues and limitations of current cloud systems and conclude with suggestion of a biological cloud environment concept, which can be defined as a total workbench environment assembling computational tools and databases for analyzing bio/medical big data in particular application domains.Keywords: Bioinformatics, Cloud computing, Big data, Workflow, User interface, Data integration, Analysis, SecurityHigh throughput, massive parallel sequencing technologies, called the next generation sequencing (NGS) technologies, were first introduced in the late 1990s. The leap of sequencing technology by NGS dropped sequencing cost dramatically and caused the exponentially increasing volume of data. Comparing NGS to the traditional Sanger sequencing technology that was used for the first human genome project, a three billion dollar project over a span of 10 years, the cost and time for sequencing a single human genome has dropped by 3,000,000 and 3000 times respectively[1,2]. As a result, the nucleotide sequence resource in the EMBL-Bank DB has approximately doubled over the past 5 years [3, 4] . The sequencing throughput rate has increased five fold per year, whereas computer performance generally follows the Moore's Law, doubling only every 18 or 24 months. Thus the gap The analysis of big data in the bio and medical fields requires very big computing power and many research facilities and clinics are unable to afford such computing facilities. Thus cloud computing has gained great interest in the bio and medical fields to analyze big data and a growing number of bioinformatics cloud systems have been developed. In this paper we surveyed current bioinformatics cloud systems and discussed design issues. To handle big data of multiple types, analysis tasks require use of appropriate tools and databases from a vast number of tools and databases. Thus simply using cloud computing does not resolve the issue of big data analysis in the bio and medical fields. We discussed this issue by introducing a concept of cloud environment for specific scientific research goals. Chae (XSEDE) . In this role he is responsible for specialized scientific community interfaces to large scale cyberinfrastructure. Marru is also the principal research systems architect within Pervasive Technology Institute of Indiana University and is a founding member of the Apache Airavata project management committee. Marru's current research focuses on working alongside multidisciplinary experts in the field of eScience to developed open community driven web and service-based scientific workflow and gateway systems for individual research, collaboration, outreach, and cross-disciplinary collaboration. These systems assist scientists to focus on their research without the need to be distracted my emerging information technology and cyberinfrastructure.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B I B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O B B I B I B B I B I B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B I O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O B I O O O O O B O O O O O O O O O O O B O O O O O O O O B I O O O B O O O O O O O O O O O O O O O O O O O B I O O O O O O B I B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Controlling chaos in a chaotic neural network The chaotic neural network constructed with chaotic neuron shows the associative memory function, but its memory searching process cannot be stabilized in a stored state because of the chaotic motion of the network. In this paper, a pinning control method focused on the chaotic neural network is proposed. The computer simulation proves that the chaos in the chaotic neural network can be controlled with this method and the states of the network can converge in one of its stored patterns if the control strength and the pinning density are chosen suitable. It is found that in general the threshold of the control strength of a controlled network is smaller at higher pinned density and the chaos of the chaotic neural network can be controlled more easily if the pinning control is added to the variant neurons between the initial pattern and the target pattern. q Recently the chaotic neural network constructed with chaotic neurons has received much attention because of its complex dynamics and its potential application in the associative dynamics, optimization and information processing, etc. (Adachi & Aihara, 1997; Aihara, Takabe, & Toyoda, 1990; Tokuda, Nagashima, & Aihara, 1997) . Besides, the electrophysiological experiments of animals have proved that chaos dynamics exists in real neurons and neural networks play an important role in neuron activity (Degn, Holden, & Olsen, 1987; Freeman, 1987; Tsuda, 1991) . It is believed that the investigation of the dynamics characters of chaotic neural networks is helpful to an understanding of the memory rules of the brain.. In Adachi and Aihara (1997) , the non-periodic associative dynamics of the chaotic neural network was studied in detail. The network can retrieve the stored patterns, but they appear nonperiodically since the network is in chaos. So it is difficult to distinguish the stored patterns from each other in the chaotic neural network (Kobori, Ikoda, & Nakayama, 1996) , which limits the applications of the associative memory function of the network. If one wants to realize the information processing in the associative dynamics system, the chaotic orbit of the network should be controlled in a certain expected way and the network should be stabilized in a stored pattern. The problem of controlling the chaos of the chaotic neural network therefore is put forward.. Since the initial work on chaotic control was made by Ott, Grebogi, and Yorke (1990) (OGY) , much progress has been achieved in this field. Several control methods were put forward, such as chaos synchronization (Pecora & Carroll, 1990) , OPF (Hunt, 1991) and delayed controlling feedback (Pyragas, 1992) . But all the above methods only suited to the low dimension chaotic systems. For a high dimension spatial-temporal chaotic system, Hu proposed a control method, i.e. the chaotic pinning control method, which has been used to successfully control the chaos of a coupled map lattice systems in one dimension (Hu & Qu, 1994) .. The chaotic neural network shows the more complex spatial-temporal chaotic dynamics compared to the coupled map lattice system in which each lattice site of coupled map lattice systems is only coupled to its nearest ones. Besides the neurons in the chaotic neural networks are connected to each other in whole spatial, the delay feedback of the networks is more complicated than the coupled map lattice system. We applied Hu's pinning control method to the chaotic neural network and found that the method was not succeeded in controlling the chaos of the chaotic neural network. Several other attempts have been made to control the chaos of the network, but the target of the control are spatially uniform or periodic states which are far from some states useful for information processing (Adachi, 1995; Mizutani, Sato, Uchiyama, & Sonehara, 1995) . In this work, we propose a pinning method focused on the chaotic neural network. The feedback control in our pinning method is imposed on the internal state of neurons while the feedback control in Hu's method is put to the output of the system. The computer simulation proved that the chaos of the chaotic neural network could be controlled by the pinning control method and the output of the network could be stabilized in a stored pattern. In Section 2, the chaotic neural network used as a controlling object in the work is described. Our pinning control method and its mathematical model are proposed in Section 3. In Section 4 are given the computer simulation results and the discussion about two control parameters, pinning distance and strength of control. Conclusion and discussion are in Section 5.

B I O O B I I O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O B I I O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O B I I O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O B I I O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Twitter data analysis by means of Strong Flipping Generalized Itemsets Twitter data has recently been considered to perform a large variety of advanced analysis. Analysis of Twitter data imposes new challenges because the data distribution is intrinsically sparse, due to a large number of messages post every day by using a wide vocabulary. Aimed at addressing this issue, generalized itemsets -sets of items at different abstraction levels -can be effectively mined and used to discover interesting multiple-level correlations among data supplied with taxonomies. Each generalized itemset is characterized by a correlation type (positive, negative, or null) according to the strength of the item correlation.This paper presents a novel data mining approach to supporting different and interesting targeted analysis -topic trend analysis, context-aware service profiling -by analyzing Twitter posts. We aim at discovering contrasting situations by means of generalized itemsets. Specifically, we focus on comparing itemsets discovered at different abstraction levels and we select large subsets of specific (descendant) itemsets that show correlation type changes with respect to their common ancestor. To this aim, a novel kind of pattern, namely the Strong Flipping Generalized Itemset (SFGI), is extracted from Twitter messages and contextual information supplied with taxonomy hierarchies. Each SFGI consists of a frequent generalized itemset X and the set of its descendants showing a correlation type change with respect to X.Experiments performed on both real and synthetic datasets demonstrate * Corresponding author.the effectiveness of the proposed approach in discovering interesting and hidden knowledge from Twitter data. In recent years, social networks and online communities have become a powerful source of knowledge. Social network sites, such as Twitter and Facebook, are accessed by millions of people every day and their users usually publish and continuously update multimedia resources, posts, and blogs.. Since actions undertaken by Web users reflect their habits, personal interests, and professional skills, a particular attention has been paid to the analysis of data acquired from Twitter. Although a large body of research addresses social network data mining [11, 12, 14, 26, 31, 32, 34, 45] , the potential business impact of mining social data is still largely unexplored. Service providers (e.g., TV channels, radio stations) may explore and analyze Twitter posts to improve service provision according to the knowledge hidden in Twitter data. From a business point of view, it is worth profiling Twitter user trends and message topics to plan targeted promotions or to identify exceptional situations. For example, let us consider a music tour organizer. To plan a singer tour in Italy, it is important to known in which Italian cities and in which time periods people are most likely to attend concerts. The analysis of the Twitter messages posted by Italian users about a given singer may support organizers in planning tours and advertising sessions. For example, they can promote album or songs to specific user segments. Innovative analytics solutions are needed to effectively and efficiently support service profiling and topic trend analysis as well as to discover exceptional situations from large social data collections. However, Twitter data is intrinsically sparse because posts range over many different topics and use a wide vocabulary. To address this issue, a promising research direction is to exploit semantics-based models (e.g., ontologies, taxonomies) to drive the data mining process and to discover interesting correlations among Twitter data at different abstraction levels.. Generalized itemset mining [40] is an exploratory data mining technique that allows us to discover multiple-level correlations among data supplied with an analyst-provided taxonomy. The taxonomy (i.e., a set of is-a hierar-chies) is used to aggregate low-level data items into higher-level concepts. For example, a city (e.g., Milan) can be generalized as the corresponding country (e.g., Italy). A generalized itemset (e.g., {(Location,Italy),(Day,Working day)}) consists of a set of items that either occur in the source dataset or represent data item generalizations according to the given taxonomy. However, the potentially large set of extracted itemsets could be hardly manageable by domain experts for manual inspection. By comparing itemsets extracted at different abstraction levels we focus the analysis on worthwhile itemset subsets, representing only contrasting or unexpected situations, because in social data analysis targeted actions are often triggered by exceptional or surprising events [20, 33] . Specifically, itemsets can be further evaluated and compared by using established correlation indexes (e.g., Kulc, interest, lift [44] ), which indicate the item correlation type (i.e., positive, negative, or null) and strength. If the correlation type of an ancestor (high-level) itemset is in contrast with those of many of its low-level descendant itemsets, then an anomalous situation may come out. For example, if items in {(Location,Italy),(Day,Working day)} are positively correlated with each other, we expect that itemsets such as {(Location,Milan),(Day,Working day)} have the same correlation type. Otherwise, the comparison between the two itemsets can be worth investigating more in detail. Even though itemsets with contrasting correlation have already been studied in [5] , to the best of our knowledge an approach to mining large groups of itemsets in contrast with a common ancestor in terms of correlation type has never been proposed so far. This paper presents the TFC Analyzer (Twitter Flipping Correlation Analyzer) system to support different and interesting targeted analysis, i.e., topic trend analysis, context-aware service profiling, outlier detection. It aims at analyzing Twitter posts to discover subsets of frequent generalized itemsets that potentially represent contrasting situations. Given the Twitter posts (i.e., the tweets) enriched with their publication context (i.e., date, time, place), a novel kind of pattern, namely the Strong Flipping Generalized Itemset (SFGI), is mined. SFGIs are patterns in the form X ∼ Ψ, where X is a frequent generalized itemset having a large set Ψ of low-level exceptions, i.e., frequent descendant itemsets of X whose correlation type changes with respect to X. The existence of a large group of contrasting low-level itemsets may indicate the presence of an unexpected situation in Twitter data. To extract all SFGIs whose number of contrasting low-level correlations is equal to or exceeds a given (analyst-provided) threshold, TFC Analyzer exploits an efficient LCM-based (Linear Time Closed Itemset Miner-based) itemset mining algorithm combined with an ad-hoc post-pruning phase. Experiments performed on real-life data coming from Twitter demonstrate the effectiveness of the proposed system in discovering interesting knowledge. Furthermore, the performance and scalability of the adopted mining strategy have been evaluated on real and synthetic datasets.. Even though this work focuses on Twitter data analysis, it is worth mentioning that the proposed patterns can be successfully mined and exploited to support knowledge discovery from data coming from different contexts. This paper is organized as follows. Section 2 presents a motivating example. Section 3 compares our work with related approaches. Section 4 thoroughly describes the characteristics of the TFC Analyzer system, while Section 5 describes the experiments performed. Section 6 discusses the extension of TFC Analyzer in a distributed environment. Finally, Section 7 draws conclusions and discusses future work. This paper presents Twitter Flipping Correlation Analyzer(TFC Analyzer), a novel data mining approach to efficiently supporting business applications based on social network data mining, e.g., context-aware service profiling and topic trend analysis. TFC Analyzer aims at discovering contrasting and unexpected situations from Twitter dataset equipped with taxonomies by extracting Strong Flipping Generalized Itemsets (SFGIs), a newly proposed type of patterns. The experiments performed on Twitter datasets demonstrate the applicability of the proposed approach to perform advanced analysis, such as topic trend analysis, context-aware service profiling, and outlier detection. The efficiency and effectiveness of the proposed system can be enhanced in several directions.. The two most promising future research perspectives are: System scalability towards big data. As discussed in Section 6, since Twitter messages are being posted at an ever increasing rate, new and distributed solutions to extend the proposed approach towards big data issues need to be investigated.. SFGI mining from data coming from other research contexts. Given a taxonomy built over data items, SFGIs can be potentially extracted from any transactional dataset. Despite in this work we focus our analysis on Twitter datasets, because their characteristics are particularly suitable for data generalization and item correlation analysis, we aim at studying also the applicability of SFGIs to data coming from diverse application domains (e.g., network traffic data, sports data, financial data). A significant research effort has been devoted to analyzing the content and structure of online communities and social networks. For example, in [6, 35] the authors analyze click-stream and blog data to identify most common Web user activities, such as universal searches, message sending, and community creation. Similarly, in [20, 33] the evolution of online communities and the lifetime of their User-Generated Content (UGC) are investigated. Sentiment analysis techniques (e.g., [28] ) have also been used to detect attitudes and opinions of social network and online community users. In recent years, the application of data mining techniques to discover relevant social knowledge from the UGC has become an appealing research topic [31, 45, 24] . In [19, 43] a particular attention has been paid to microblogging websites, such as Twitter, which represent rapidly evolving communities. The extraction of hidden associations from Twitter UGC has already been investigated in [11, 14] . Specifically, the authors in [14] discover trend patterns from Twitter data to identify the users who contribute towards the discussions on specific trends. The approach presented in [11] addresses topic trend analysis from Twitter data by exploiting generalized association rules. Unlike [11, 14] , this paper focuses on discovering unexpected situations from Twitter data by exploiting a new type of generalized patterns, namely the Strong Flipping Generalized Itemsets.. A parallel research issue is frequent itemset and association rule mining driven by item correlation measures [1, 5, 8, 39] . The frequent itemset and association rule mining problems were first introduced in [2] to discover hidden item correlations from potentially large market basket data. The first attempt to evaluate association rule significance by means of the chi square test for correlation has been made in [8] . To avoid generating all candidate frequent itemsets, the upward closure of the chi square measure is exploited to early prune part of the search space. Since negatively correlated itemsets are usually characterized by a low support value [42] , their extraction becomes a challenging task when coping with large and complex datasets. To overcomes this issue, in [1, 39] the authors propose two novel itemset quality measures, namely the collective strength and support expectation, which can be used to indirectly mine negative associations among data. Unfortunately, since chi square, support expectation, and collective strength are not null-invariant, their value depends on the dataset size. In [44] the authors investigate the use of null-invariant correlation measures [25] in frequent itemset mining. The approach proposed in [5] focuses on exploiting the null-invariant Kulczynsky measure to discover flipping correlations among data supplied with taxonomies. Flipping correlations are itemsets whose correlation type flips from positive to negative (or vice versa) when items are generalized to a higher level of abstraction for every generalization step. However, in case many sibling itemsets flip their correlation type with respect to a common ancestor, many different patterns are generated and thus the result could become redundant and hardly readable. Furthermore, in real-world data the itemset correlation type (i) rarely changes at every generalization step and (ii) may also change from correlated to uncorrelated (and not only from positive to negative or vice versa). To overcome these issues, we propose a new type of generalized pattern, namely the Strong Flipping Generalized Itemsets (SFGIs). A SFGI consists of a generalized itemset and its corresponding set of frequent descendant itemsets with contrasting correlation type (positive, negative, or null). SFGIs differ from flipping correlations [5] because (i) they do not consider one itemset per abstraction level, but groups of sibling itemsets with contrasting correlation type with respect to their common ancestor, (ii) they also consider uncorrelated descendants and not only positive or negative item correlations. SFGIs that contain many descendant itemsets with contrasting correlation are selected because they may represent unexpected situations in the analyzed data.. A parallel effort has been devoted to efficiently extracting generalized frequent itemsets and association rules. The first generalized frequent itemset mining algorithm has been proposed in [40] in the context of market basket analysis. It generates itemsets by considering for each item all its parents in the hierarchy. To avoid generating all the possible candidates in the taxonomy the authors in [3, 41] propose to push (analyst-provided) constraints into the mining process. Many algorithm optimizations have also been proposed [4, 13, 21, 29] . For example, the approach presented in [21] proposes an optimization strategy based on a top-down hierarchy traversal. It identifies in advance itemsets that cannot be frequent in a transactional dataset by exploiting the Apriori principle [2] . In [29] the authors propose to mine closed and maximal [36] generalized itemsets. More recently, support-driven approaches to mining generalized itemsets and analyzing their changes over time have been presented [4, 9, 10] . In [4, 9] only the itemsets infrequent with respect to the support threshold are generalized at a higher level of abstraction, whereas in [10] only the descendant itemsets with different correlation contribute to the support counting of a high-level ancestor. Unlike [10, 4, 9] , our approach does not rely on a support-driven generalized pattern selection strategy. Conversely, we discover large groups of sibling itemsets with contrasting correlation with respect to their common ancestor.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


A finite volume method solution for the bidomain equations and their application to modelling cardiac ischaemia This paper presents an implementation of the finite volume method with the aim of studying subendocardial ischaemia during the ST segment. In this implementation, based on hexahedral finite volumes, each quadrilateral sub-face is split into two triangles to improve the accuracy of the numerical integration in complex geometries and when fibre rotation is included.The numerical method is validated against previously published solutions obtained from slab and cylindrical models of the left ventricle with subendocardial ischaemia and no fibre rotation.Epicardial potential distributions are then obtained for a half-ellipsoid model of the left ventricle.In this case it is shown that for isotropic cardiac tissue the degree of subendocardial ischaemia does not affect the epicardial potential distribution, which is consistent with previous findings from analytical studies in simpler geometries.The paper also considers the behaviour of various preconditioners for solving numerically the resulting system of algebraic equations resulting from the implementation of the finite volume method. It is observed that each geometry considered has its own optimal preconditioner. Solving the bidomain [1] equations [2, 3] has become the predominant method of obtaining insight into the electrical activity of the human heart. These solution methods are generally numerical in nature and are based on the finite difference method [4, 5, 6] , the finite element method [7, 8, 9, 10] and the finite volume method [11, 12] . Most of these studies consider propagation of the action potential through various two and three dimensional shapes of healthy cardiac tissue. However, the bidomain equations have also been used to study subendocardial ischaemia during the ST segment [13, 14, 15] . The ST segment being the isoelectric portion of the electrocardiogram between the QRS complex, where the ventricles of the heart depolarise, and the T wave, where the ventricles repolarise [16] . At the cellular level, this interval corresponds to the plateau phase of the action potential [17] where each cell is at the same potential, thus giving rise to the isoelectric status of the tissue.. The modelling of cardiac ischaemia, both subendocardial and transmural, is important in understanding how it relates to coronary heart disease and its predictive value for sudden cardiac death. A recent excellent review [18] highlights many of the benefits and limitations of modelling in this area.. This situation has also been the focus of experimental studies [19, 20] and direct numerical simulation [21] .. Previous studies of the effect of subendocardial ischaemia during the ST segment have been limited to simple geometries [13, 14, 15] . Due to the simple geometries considered, solutions could be obtained using analytical techniques with only minimal augmentation by numerical methods. This is a limitation of these studies, so to consider more realistic geometries, a full numerical method is required.. In this paper, an implementation of the finite volume method is presented with the aim of studying the effect of subendocardial ischaemia during the ST segment. The implementation is based on that described by Penland et. al [11] , but is extended by subdividing quadrilateral control volume sub-faces into triangles to better account for cardiac fibre rotation and to better approximate more complex geometries. The bidomain equations are solved in a steady state situation, reflecting the static behaviour during the ST segment [16] .. The first part of this paper describes in detail the construction of the finite volume method solution of the bidomain equations and highlights the differences from previous implementations. Iterative solution strategies to solve the resulting system of algebraic equations are then discussed. The finite volume method solution is then validated in both slab and cylindrical geometries by comparing with solutions obtained previously [13, 14] . Next, solutions are obtained in an ellipsoidally shaped approximation to the left ventricle, where it is verified that the degree of subendocardial ischaemia does not affect the epicardial potential distribution in an isotropic model. Finally, there is a comparison of the benefits of several iterative solution techniques, including timing and convergence issues. This paper has presented an implementation of the finite volume method to solve the bidomain equations governing electric potential in cardiac tissue. The numerical model is tested and validated in three geometries representing the ventricular wall with subendocardial ischaemia.. The approach taken here varies slightly from previous implementations [11, 12] in that the computational domain is meshed in hexahedrons with each face of the hexahedral control volume broken down into sets of triangles. This idea allows for more accurate integration in the finite volume method and better accounts for complicated geometries and fibre rotation.. The numerical method has been validated by comparisons with previously published analytical solutions [13, 14, 26] in terms of epicardial potential distributions. The numerical solutions show good agreement with the analytical ones when fibre rotation is ignored. Also, the semi-ellipsoidal model of the left ventricle shows that for isotropic tissue the degree of ischaemia does not affect the epicardial potential distribution, as noted in simple geometries [15] .. Computation times for solving the system of algebraic equations arising from the finite volume method discretisation were also studied in detail. It was found that different preconditioners behaved differently depending on the geometry considered. This behaviour is put down to the slightly different structures of the coefficient matrix obtained for each geometry. For the slab geometry, the ILUT preconditioner is recommended, but for the cylindrical and ellipsoidal geometries, the ILUC preconditioner is recommended. It is still a matter of trial and error to obtain optimal lf il values depending on the computer architecture and size of the problem.. One clear advantage of the approach presented here is that it can handle arbitrary geometries.. However, another advantage is that it would be possible to calculate the surface Laplacian [31, 32] in a straight forward manner. The point c is the centroid of the volume element, the points f represent centroids of the three relevant faces of the element and the points e represent the centroids of the relevant edges of the element. To validate the solution method discussed above, comparisons will be made with previously published analytical models of subendocardial ischaemia. Unless otherwise stated, the bidomain conductivities are those given by Clerc [28] : σ

O B I I O O O B I O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O B I O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


On the Efficiency of Cluster-based Approaches for Motion Detection using Body Sensor Networks Abstract. Body Sensor Networks (BSN) are an emerging application that places sensors on the human body. Given that a BSN is typically powered by a battery, one of the most critical challenges is how to prolong the lifetime of all sensor nodes. Recently, using clusters to reduce the energy consumption of BSN has shown promising results. One of the important parameters in these cluster-based algorithms is the selection of cluster heads (CHs). Most prior works selected CHs either probabilistically or based on nodes' residual energy. In this work, we first discuss the efficiency of cluster-based approaches for saving energy. We then propose a novel cluster head selection algorithm to maximize the lifetime of a BSN for motion detection. Our results show that we can achieve above 90% accuracy for the motion detection, while keeping energy consumption as low as possible. In recent years Body Sensor Networks (BSNs) have attracted increasing attention for their use in remote healthcare such as remotely monitoring the elderly and children. A BSN is composed of a number of tiny wireless sensors placed on the user's body. Sensor nodes can transmit data to a remote server for online or offline analysis via various wireless technologies (e.g., IEEE 802. 15.4 [1] or Bluetooth) so that doctors can monitor the patient's physiological states in real-time. BSNs have been widely used for various healthcare applications [2, 3, 4, 5] , motion detection/analysis [6, 7, 8, 9] , and gaming [10] . A critical issue when designing a BSN is the energy consumption, since wireless sensors typically employ small batteries for ease of deployment. A number of works have studied the issue of reducing the energy consumption of BSN. For example, Xiao et al. [3] proposed a method to reduce the transmission power at the physical layer without sacrificing the reliability for a considering the required power level for sending a packet from the cluster nodes to the cluster head for a given posture. 3) We implement our clusterhead selection algorithm on a testbed for motion detection using KNN and show that we can achieve high accuracy (above 90%) while saving energy for a body sensor network.. The remainder of this paper is organized as follows. In Section II we review the related work. We briefly describe different motion detection methodologies in Section III. In section IV, we propose a methodology to minimize the transmission cost in a BSN while balancing each node's energy consumption. The results of the experiment are shown in section V and we conclude this paper in Section VI. In this paper, we provide a detailed analysis of how different parameters in a cluster-based algorithm can affect the amount of energy saving. Additionally, we propose a novel CH selection algorithm by considering the required power level for sending a packet from the CN to the CH. Furthermore, we use a threshold-based approach to evenly distribute the energy load among nodes by considering the number of times a node has acted as a CN and a CH. We implement our cluster-based algorithm on a testbed using the KNN algorithm and show that it can achieve high accuracy (above 90%). We are currently working on a prediction mechanism to reduce the number of transmissions required when motions of CNs can be predicted. In this section, we describe the related work. Our work builds on prior research on body sensor networks, motion detection, and energy conservation. To evaluate the performance of our protocol, we compare it with the case of PT, as in Section 4, (in which all nodes use the same power level, one that is sufficient reach the entire BSN). We look at the real packet format in TinyOS in which sensing data is a small part (6 Bytes) of the whole packet (26 Bytes) and thus conservatively choose a compression ratio r=0.5 in our analysis. In addition, in our analysis we model the energy consumption for transmission and reception based on the specifications of a CC2420 transceiver. As shown in Fig. 8 , our protocol can achieve more energy saving when the ratio of / mn increases. Here n is the number of nodes in the network and m is the number of static (non-moving) nodes. For a 10-node network, our protocol can achieve up to 90% less energy consumption as compared to PT. Here the saved energy is defined as. . In other words, in the best case, our protocol can prolong the lifetime of the network to be ten times longer as compared to PT. We used KNN algorithm for the motion detection and implemented a testbed using the TelosB mote [52] which has a TI MSP430 [53] processor and a Chipcon CC2420 RF transceiver [51] that supports the IEEE 802.15.4 for communication. A pair of AA batteries are used for power supply. The data rate is 250 kbps when operating at the frequency of 2.4 GHz. We employed four triaxial MEMS accelerometer sensors placed on the wrists and ankles of a person to capture the subject's motions. The BS receives sensing data from the BSN and forwards it to a PC server where KNN is executed. We developed our program under TinyOS [54] , which is a component-based and embedded operating system written in the nesC programming language. Our experiments were run in real time. In Fig. 9 , each point represents the results from 50 repetitions of each motion (250 times in total). Sample size (ss) and k are important parameters for the KNN algorithm, so both of them are dynamically tuned to find the highest accuracy. Generally, when k is fixed, the accuracy will go up with the increase in sample size, but the reverse is not true. There is a tradeoff between (ss, k) and the accuracy, since we need to consider the computation cost/time depending on the characteristics of the applications. The results indicate our cluster-based algorithm (known as PT) can achieve similar performance as that of FT. When ss=300 and k=10, the accuracy is 94.8% for FT and 91% for PT respectively. The performance is slightly better when we increase the sample size to 400. The accuracies for FT and PT are 94% and 92%, respectively. Generally, the accuracy of FT is higher than that of PT, since it provides more information to the KNN.

O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B


Coherence and recurrency: maintenance, control and integration in working memory Abstract Working memory (WM), including a 'central executive', is used to guide behavior by internal goals or intentions. We suggest that WM is best described as a set of three interdependent functions which are implemented in the prefrontal cortex (PFC). These functions are maintenance, control of attention and integration. A model for the maintenance function is presented, and we will argue that this model can be extended to incorporate the other functions as well. Maintenance is the capacity to briefly maintain information in the absence of corresponding input, and even in the face of distracting information. We will argue that maintenance is based on recurrent loops between PFC and posterior parts of the brain, and probably within PFC as well. In these loops information can be held temporarily in an active form. We show that a model based on these structural ideas is capable of maintaining a limited number of neural patterns. Not the size, but the coherence of patterns (i.e., a chunking principle based on synchronous firing of interconnected cell assemblies) determines the maintenance capacity. A mechanism that optimizes coherent pattern segregation, also poses a limit to the number of assemblies (about four) that can concurrently reverberate. Top-down attentional control (in perception, action and memory retrieval) can be modelled by the modulation and re-entry of top-down information to posterior parts of the brain. Hierarchically organized modules in PFC create the possibility for information integration. We argue that large-scale multimodal integration of information creates an 'episodic buffer', and may even suffice for implementing a central executive. When we return home from work we sometimes find ourselves deeply engaged in thinking about an unsolved problem. Yet, at the same time we manage to find our way home and avoid accidents. This indicates that apparently we are able to automatically control our behavior without needing conscious attention. If suddenly an obstacle appears, however, we are also able to switch attention in a split second. Given the right cues, we may also remember that in the morning we planned to do some shopping on the way home. That too would put solving the problem to a halt and bring us to figure out the best route to the shop. This shows that control may be taken over by retrieving a plan, and that in order to carry it out we need access to a large database, including a route planner. If later on we resume thinking about the problem, we may figure out a solution by combining known elements in a novel configuration, and then start thinking how to use it in the future.. The description given above is an example of the coordinated and goal-directed thoughts and actions that are generated in our brains all the time. Clearly, such coordinated behavior requires a versatile system of cognitive control for which as yet there does not seem to exist an adequate concept. Some of the contours of such a control system, however, are discernable in the example given above, like the ability to maintain representations, to direct attention and to combine previously unrelated information.. An early and influential framework for the study of control and coordination of cognitive behavior is the multicomponent model of working memory (Baddeley and Hitch 1974) . Working memory (WM) refers to a limited capacity system for temporary holding and manipulating information, that is required for performing a wide range of cognitive tasks such as comprehension, learning and reasoning. Originally the model distinguished three-components. A general control system, or 'central executive', and two subsidiary slave systems, a phonological loop and a visuo-spatial sketch pad, each capable of maintaining a limited amount of information. More recently (Baddeley 2003) , an episodic buffer was added to connect working memory with long-term memory and to allow binding together information from different sources into integrated episodes. The central executive is the most important but least understood component of WM, and it looks conspicuously like a homunculus. Baddeley is well aware of this criticism, but he defends the central executive concept by pointing out that it defines a problem area for which the processes have to be specified. An important conceptual model was suggested by Norman and Shallice (1986) . They proposed a 'data base system' for automatic habitual action routines, containing well-learned stimulus-response associations and cognitive and behavioral skills, and a 'supervisory attentional system' capable of controlling behavior by selectively biasing and reconfiguring the available skills and schemas. Automatic control develops gradually through practice as learning processes create associative pathways between perception and action. The conscious form of control is applied when we are confronted by novel and unexpected stimuli, and when we have the intention to attain specific goals. In this case, automatic actions to stimulus patterns in the environment have to be suppressed and replaced by novel task-and goal-directed actions.. The model of Norman and Shallice aimed to explain deficits of executive control that are often observed in patients with damage in prefrontal cortical areas. It is now generally accepted that the prefrontal cortex (PFC) is of crucial importance when behavior must be guided and controlled by internal states and intentions, when automatic responses have to be suppressed, and when tasks require the establishment of new or rapidly changing mappings between perception and action (e.g., Goldman-Rakic 1996; Miller and Cohen 2001; Smith and Jonides 1999; Wood and Grafman 2003) . Anatomically, the PFC is well positioned to coordinate processing in the rest of the brain. It consists of a number of strongly interconnected areas that collectively have reciprocal connections with virtually all other neocortical and subcortical structures. It is also an area that shows late development, both phylogenetically and ontogenetically, reaching maturity only in adolescence (Fuster 2001) .. Based on these anatomical considerations, we have suggested (Phaf and Wolters 1997) that working memory or, more general, executive functions, may have emerged as a consequence of an evolutionary development of the PFC. This development may have created the possibility for neural processes that could run (partly) independent of present input and output, but that also could modulate, and thus control, perception-action relations in the rest of the cortex. In this view, the role of PFC in controlling behavior is modulatory rather than transmissive, which is similar to the role assigned to PFC in several other models (e.g., Norman and Shallice 1986; Miller and Cohen 2001; O'Reilly et al. 1999) . Whereas simple adaptive behavior rests on a cycle of perception, action, and perception-ofaction results, the added PFC would allow an internalization of this loop, freeing the organism of the restriction of being aware of, or acting upon, physically present objects or situations only. In fact, it would implement a medium for creating a virtual world, i.e., manipulating internal representations that are independent of the present environment (for a similar idea, describing thinking as simulated behavior and perception, see Hesslow 2002) .. More specifically, we suggested that the development of PFC created the possibility to maintain physically absent information in an active state by recurrent connections (loops) between PFC and the rest of the cortex. The recurrent activity in these loops may affect subsequent perceptual and motor processing, i.e., it can redirect attention and control actions by activating or inhibiting particular motor programs. By assuming interactions and integration between loops, more complex forms of representation and control may develop. For instance, recurrent connections with memory systems would allow access to all stored information, and mechanisms for combining information in the loops would allow the formation and updating of future goal states, and ways to achieve them. Of course, the model suggested here is extremely simplified and it does not capture many of the complexities and intricate details of the real system. For instance, we did not try to incorporate modulatory effects of neurotransmitters and we have not discussed the many possible interactions of the PFC with subcortical systems, like the basal ganglia and amygdala, and the cerebellum. It may also be noted that we discussed, but did not try to incorporate, the possibly important role of a dopamine gating system for maintaining high level integrative activation states (O'Reilly et al. 1999 (O'Reilly et al. , 2002 .. One of our aims to develop the model was to try to find out how the structural and functional characteristics of the PFC may explain the central executive component of working memory assumed by Baddeley (2003) . In the latest version of this model an additional component, an episodic buffer, was proposed. This component was thought necessary to explain interactions between working memory and LTM, for example to explain how chunking may supplement the capacity for immediate serial recall. A continuous interaction between working memory and LTM is a basic assumption in our model, and we have shown that chunking is a natural consequence of this interaction.. According to Baddeley (2003) , the episodic buffer allows information from different systems to be integrated, and it may be regarded as the 'storage component of the executive'. Moreover, Baddeley suggested that the buffer is a separate temporary store in which long-term memory information is downloaded in order to be manipulated and used for creating new representations. In our view, the structure of such an episodic buffer would actually be a hierarchy of PFC modules maintaining and integrating information at successively higher levels. Information is not copied and downloaded in PFC, but selected task-relevant perceptual and memory information in posterior cortical areas is kept in an active state by recurrent loops. We assume that at the highest integration levels, presumably located in anterior and dorsolateral areas of PFC, information can be integrated over space and time. At this level, general goals, and plans to achieve them, would be generated. We suggest that this may be the implementation of an episodic buffer and even of a central executive. The creation of short-term and long-term goals at high levels of integration, allows to control behavior by top-down regulation of activation in subordinate modules and eventually by modulating perception-action systems. Current goals and tasks would have to be maintained here in order to control ongoing behavior. More distant goals, however, may be stored in LTM to be retrieved later on.. We do not imply that control is always hierarchical. Because the PFC is assumed to be a modulatory system, simple tasks may be executed automatically without PFC involvement. Only controlled processing requires modulation of automatic processes by PFC feedback. Also here, however, control does not need to be completely hierarchical. Depending on the type and complexity of a task, control may be executed by specialized modules at subordinate levels. Automatic processing and controlled processing under the guidance of subordinate levels in PFC, is a requirement to free higher integrative areas to engage in the kind of simulated actions and perceptions, and using anticipated outcomes, that are the contents of conscious thought and planning.. So there are things we can do automatically, using previously established associations between perceptual events and effective responses, and there are things we can do in a controlled way, using the possibility of PFC to modulate and thus control perception and action. The possibility of PFC to work off-line, to use and integrate all present and past knowledge for creating virtual worlds and for making plans and carry them out if conditions are appropriate, has generated a tremendously flexible potential for control. The model we propose is vastly insufficient to simulate such cognitive feats that we engage in daily. We believe, however, that the principles for a controlling system we have suggested may be a first step towards a better understanding of what is until now a cognitive Terra Incognita.

O O O B O O B O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O B B I I O B O O O O B O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Bell polynomials and generalized Blissard problems We introduce two possible generalizations of the classical Blissard problem and we show how to solve them by using the second order and multi-dimensional Bell polynomials, whose most important properties are recalled. The importance and utility of ordinary Bell [1] polynomials -which are a classical mathematical tool for representing the nth derivative of a composite function -in many different frameworks of mathematics is well known.. They are often used in Combinatorial Analysis [2, 3] and Statistics [4, 5] and also in mathematical applications, such as the Blissard problem, the representation of Lucas polynomials of the first and second kind [6, 7] , the representation of symmetric functions of a countable set of numbers, i.e. the generalization of the Newton-Girard formulas [8] .. Recently, some extensions of the Bell polynomials to the case of multi-variable composite functions and to the functions with several variables have been carried out (see [9] [10] [11] ).. Still open is the issue of determining whether with such extensions it is possible to generalize the applications already known for the ordinary Bell polynomials. This paper takes the applications of second order Bell polynomials and multi-dimensional Bell polynomials to an extension of the Blissard problem into consideration.. In Section 2 we recall the ordinary, the second order and multi-dimensional Bell polynomials.. In Sections 3 and 4 we apply respectively second order Bell polynomials and multi-dimensional Bell polynomials to generalized Blissard problem.. This problem occurs in the symbolic calculus in order to find the inverse of exponential series.

B I O O O O O O O O O O O O B I O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O B I O O B I O O O O O B I O O O O O O O O O O O O O O B I O O O O O O O O O O B I O O B I O O B I O O O O O O O O O O O O O O O O