Energy-Efficient and Thermal-Aware Resource Management for Heterogeneous Datacenters Abstract: We propose in this paper to study the energy-, thermal-and performance-aware resource management in heterogeneous datacenters. Witnessing the continuous development of heterogeneity in datacenters, we are confronted with their different behaviors in terms of performance, power consumption and thermal dissipation: Indeed, heterogeneity at server level lies both in the computing infrastructure (computing power, electrical power consumption) and in the heat removal systems (different enclosure, fans, thermal sinks). Also the physical locations of the servers become important with heterogeneity since some servers can (over)heat others. While many studies address independently these parameters (most of the time performance and power or energy), we show in this paper the necessity to tackle all these aspects for an optimal resource management of the computing resources. This leads to improved energy usage in a heterogeneous datacenter including the cooling of the computer rooms. We build our approach on the concept of heat distribution matrix to handle the mutual influence of the servers, in heterogeneous environments, which is novel in this context. We propose a heuristic to solve the server placement problem and we design a generic greedy framework for the online scheduling problem. We derive several single-objective heuristics (for performance, energy, cooling) and a novel fuzzy-based priority mechanism to handle their tradeoffs. Finally, we show results using extensive simulations fed with actual measurements on heterogeneous servers. The last years have witnessed the development of heterogeneity in clusters and datacenters. Two main reasons have led to this situation today. The first one is due to the maintenance and evolution of the components in the datacenters: different generations of computers are commonly seen in production datacenters since the owners are not changing everything at each update. The second reason is driven by the idea that heterogeneity might be the key to achieving energy-proportional computing [5, 9] , especially for high-performance computing applications.. Many recent studies alert dramatically on the energy consumption of the datacenters. For instance, Koomey's report [21] claims that today's datacenters are consuming nearly 2% of the global energy, and up to half of that is spent on cooling-related activities [33] . This results generally in very poor Power Usage Effectiveness (PUE).. In this paper, we study the multi-objective resource management problem for heterogeneous datacenters. Besides the performance criterion, we also consider the energy consumption of the servers and their thermal impact on the datacenter cooling. The aim of our work is to optimize these objectives and to explore their tradeoffs. In particular, the energy consumption is partly due to the cooling efficiency in the datacenter [25, 38] , which is related to both the physical placement of the servers and the scheduling strategies when jobs dynamically enter and leave the system. The latter also affects the performance and the energy consumed by the servers.. Server placement in a computer room has been relatively less studied, especially its impact on the cooling efficiency. The reason for this lack of attention is mainly due to the fact that, when servers are homogeneous, their relative positions have no impact on the performance and computing energy. However, server placement can have an impact on the cooling infrastructure. The main observation is that one server might contribute to the temperature raise at the inlets of the other servers, due to the recirculation of heat in a datacenter. Such mutual influence can be modeled by a heat distribution matrix among the servers. If one wants to keep the inlet temperature under a given threshold, the supplied air temperature has to be decreased accordingly by the cooling system, which in turn increases its energy consumption. In the presence of heterogeneous servers with different power consumptions and hence heat dissipation, the problem of find the optimal placement becomes complicated and, to the best of our knowledge, has not been studied. Since it is not feasible to change dynamically the positions of the servers in a datacenter, we focus on static placement to minimize the cooling cost induced by different configurations.. With a given server placement, the traditional problem of job scheduling in the heterogeneous environment remains. Many previous work (e.g., [4, 40] ) considered only the performance criterion and hence focused on the jobs' execution times. In order to address the power consumption issue in datacenters, however, application scheduling must employ a multi-objective approach by considering performance, energy and cooling together. To account for the fact that a scheduler has no future knowledge (jobs arrive over time), we need an online scheduling strategy. Instead of designing different independent algorithms, we design a greedy online scheduling framework that can be adapted easily by redefining the cost function, from a single objective to two or more objectives. To tackle the energy-performance tradeoff, we further introduce a fuzzy-based priority approach, which allows to explore the potential improvement in one objective while relaxing the other objective up to an acceptable range. This approach can be extended to incorporate more than two objectives in the framework. Its principle is not limited to the case at hand and can potentially be applied to other multi-objective optimization problems.. The main contributions of this paper are the following:. • A static server placement heuristic to reduce the cooling cost for the servers in a datacenter.. • A greedy scheduling framework and several cost functions to tackle single-objective scheduling (for performance, energy, and cooling).. • A fuzzy-based priority approach to handle the tradeoff between two conflicting objectives, and its extension to multi-objective optimization.. These proposals are supported by extensive simulations conducted using real hardware specifications and software benchmarks, as well as experimentally verified cooling model and heat distribution matrix [39, 38] . Specifically for the hardware, a server system with high packing density and integrated cooling support is chosen for the experiments, which we believe represents well an emerging class of highly integrated energy-efficient servers. The results demonstrate the flexibility of our scheduling framework and confirm the effectiveness of the fuzzy-based approach for exploring the energy-performance tradeoff in heterogeneous datacenter environments. Our static server placement heuristic is also shown to provide much improved thermal distribution leading to significant reduction in cooling cost.. The rest of this paper is organized as follows. Section 2 formally states the system model and the scheduling problem. Section 3 describes our greedy server placement heuristic. Section 4 presents the job scheduling framework, various cost functions and the fuzzy-based priority approach. The simulation results are shown in Section 5. Section 6 reviews some related work, and Section 7 summarizes the paper and addresses future directions. In this paper, we have considered the energy-efficient and thermal-aware placements for both servers and workloads in heterogeneous datacenters. For the static server placement problem, we have shown that it is NP-hard and presented a greedy heuristic. To schedule the workloads, we have presented a greedy scheduling framework, which can be applied in an online manner with any well-defined cost function. Moreover, a novel fuzzy-based priority approach was proposed to simultaneously optimize two or more conflicting objectives. Simulations were conducted for a heterogeneous datacenter with heat recirculation effect. The results demonstrated the effectiveness of the proposed approaches for exploring the energy-performance tradeoff with cooling consideration. Our static server placement heuristic was also shown to provide better thermal balance, which directly leads to reductions in cooling cost.. For future work, other resource management techniques, such as DVFS or server consolidation, can be applied to achieve better energy and thermal efficiency. In this context, the tradeoff between the computing energy and cooling energy can be explored, possibly with the fuzzy-based priority approach. For the static server placement problem, it will be useful to design better heuristic solutions or good approximation algorithms, and to consider large datacenters with more rack slots than servers, which will provide additional space for optimization. Finally, we considered server placement and job scheduling separately in this paper; it may be helpful to consider the two aspects jointly to achieve further energy savings. The literature contains extensive studies on virtual machine placement (e.g., [6, 15, 44] ) for datacenters, but the placement of physical servers has received little attention. There are two main reasons. First, many traditional datacenters are homogeneous, so different placements of identical servers do not make a difference. Second, traditional metrics such as job performance and energy consumption (due to computing) are independent of the servers' relative positions, so they are unaffected by the different placement configurations.. As far as the cooling cost is concerned for heterogeneous datacenters, however, the placement of the physical servers will have an impact. In particular, the studies in [39, 38] have shown that the heat recirculation phenomenon in typical datacenters exhibits the following properties:. (1). Different rack positions tend to behave differently in terms of heat recirculation. Typically, servers located at the upper parts of the racks "inhale" more recirculated hot air while servers located at the lower parts "contribute" more hot air to recirculate in the room.. (2). In a closed computer room with fixed locations of all major objects and without moving objects, the airflow pattern that characterizes the heat recirculation among different rack positions is relatively stable.. While the first property suggests that the heat distribution matrix tends to be highly asymmetric, the second property assures that the matrix does not change significantly with different workloads in the servers or different positions of the servers. In the next section, we will rely on workload placement (or job scheduling) techniques to manage the cooling cost together with other objectives. Here, we focus on arranging the positions of the servers with different power profiles. The goal is to reduce the maximum inlet temperature of the servers so as to minimize the cooling cost under a given load condition.. To illustrate the effectiveness of this approach, consider a simple datacenter with two servers, two rack slots, and the following heat distribution matrix:. Suppose the two servers consume an average power of 100W and 200W, respectively. By placing the first server in slot 1 and the second server in slot 2, their inlet temperatures increase by 1 • C and 0.5 • C respectively according to Equation (3) . By simply swapping the positions of the two servers, their temperature increases will now become 0.4. • C and 0.8 • C. The 0.2 • C difference in the maximum inlet temperature of these two configurations directly determines the temperature of the supplied air by Equation (4) , and therefore impacts the cooling cost. For instance, consider a redline temperature of 25. • C and the following CoP model for a water-chilled CRAC unit in an HP datacenter [25, 38] :. According to Equations (4) and (5), the cooling costs for the two placement configurations are 68.275W and 67.269W, respectively. The impact will be more significant with a lower redline temperature or a more skewed heat distribution matrix, or when the servers are consuming more power. The problem will also become more challenging when there is a large number of servers/positions, since exhaustive search will no longer be possible. The next subsection considers this general case and proposes a heuristic algorithm for the problem. In this section, we review some related work in the literature on multi-objective scheduling and thermal-aware scheduling for datacenters.. Multi-objective scheduling Scheduling with multiple conflicting objectives has attracted much attention in many optimization problems. Section 4.3 described a few commonly used approaches. The following reviews some applications of these approaches in various problem domains.. (1). Simple priority. This is a simple priority-based approach to optimize multiple objectives in sequence. Assayad et al. [2] introduced a bi-criteria compromise function to set priorities between makespan and reliability for scheduling real-time applications. To minimize carbon emission and to maximize profit, two-step policies were proposed by Garg et al. [18] to map applications to heterogeneous datacenters based on the relative priority of the two objectives. Du et al. [12] proposed heuristics to optimize the QoS for interactive services before considering energy consumption on multicore processors with DVFS (Dynamic Voltage & Frequency Scaling) capability.. (2). Pareto frontier. This approach is often used in the offline setting to generate a set of nondominated solutions. Durillo et al. [13] applied this technique to tradeoff makespan and energy consumption for heterogeneous servers. Torabi et al. [41] used particle swarm optimization to approximate the pareto frontier for the unrelated machine scheduling problem with uncertainties in the inputs. Gao et al. [15] utilizes ant colony optimization to obtain the pareto frontier for resource wastage and power consumption in virtual machine placement. Evolutionary algorithms were employed in [45, 17] to obtain a set of alternative solutions for scheduling scientific workloads in the Grid environment.. (3). Constraint optimization. This approach optimizes one objective subject to constraint(s) on the other(s). Rizvandi et al. [31] applied it to minimize the energy consumption subject to the makespan achieved in an initial schedule. A mixed integer programming model was used by Petrucci et al. [29] to reduce the power consumption of virtualized servers subject to QoS requirements. Fard et al. [14] developed a double strategy to minimize the Euclidean distance between the generated solutions to a set of user-specified constraints in a four-objective optimization problem. The authors in [19] applied ǫ-constraint method to cloud scheduling, which optimizes each objective in turn with upper bounds specified for the others.. (4). Weighted combination. This approach combines multiple objectives into a single one. Lee and Zomaya [23] used DVFS to tradeoff makespan with energy consumption by considering a weighted sum of the two objectives. The same technique was used by the authors of [1, 36] in an online manner to minimize a combined objective of job response time and energy. A similar approach was taken by Sheikh and Ahmad [34] , who considered an additional objective of peak temperature in a multicore system, and hence optimizing three objectives at the same time. Instead of summation, some work (e.g., [7, 30] ) also used energy-delay product as a metric for scheduling applications in heterogeneous multicore systems.. Compared to these approaches, our fuzzy-based priority approach provides a rather flexible solution to handling two or more conflicting objectives. Although multi-objective scheduling with "fuzzy" or "good enough" solutions [44, 46] are known in the pareto-based approach, our fuzzy method is novel when (soft) priorities exist between different objectives. The principle can be potentially applied to other multi-objective optimization problems.. Thermal-Aware Scheduling As cooling energy constitutes a signifcant fraction of the total energy consumption in today's large-scale datacenter, thermal-aware scheduling for this environment has been the focus of many research in recent years.. Wang et al. [42, 43] considered thermal-aware workload placement in datacenters to reduce the server temperatures characterized by an RC-model, while minimizing the job response time. They proposed simple heuristics that allocate "hot" jobs to "cool" computing nodes, as well as backfilling techniques for scheduling parallel applications. In their study, the thermal map of the data center is assumed to be available through ambient and on-board sensors.. Moore et al. [25] first introduced the concept of heat recirculation effect and proposed workload placement algorithms, including MinHR, to reduce the recirculation of heat and the cooling cost in a datacenter. A prediction tool called Weatherman [24] was used to predict the data center thermal map using machine learning techniques. The authors showed that the tool accurately predicts the heat distribution of the datacenter without the need of static thermal configuration, and a scheduling algorithm based on Weatherman achieves similar performance as MinHR.. Tang et al. [38] also studied the problem of minimizing the cooling cost in datacenters with heat recirculation consideration. Based on an abstract heat flow model, they characterized the thermal behavior of datacenters via a heat distribution matrix. The model was validated by computational fluid dynamics (CFD) simulations in [39, 32] . They proposed offline scheduling solutions by using genetic algorithms and quadratic programming, which were evaluated using the heat distribution matrix captured for a small-scale datacenter. The same matrix is used in this paper for evaluating our online scheduling heuristics.. Instead of minimizing only the cooling cost, Pakbaznia and Pedram [27] considered minimizing the total energy of a datacenter from both computation and cooling. They showed that performing consolidation to turn off idle servers together with job scheduling to account for the heat recirculation can significantly reduce the total power usage. Banerjee et al. [3] further considered cooling-aware scheduling workload placement by exploring the dynamic cooling behavior of the CRAC unit in a datacenter.. While the above results considered only the energy consumption of a datacenter, the following also takes application performance into consideration. Mukherjee et al. [26] considered a similar problem as in [27] but further took the temporal dimension of the job placements into account. They formulated the problem as a non-linear program and proposed both offline and online heuristics to minimize the total energy subject to the deadline constraint for the jobs. Sansottera and Cremonesi [32] considered a datacenter environment hosting web services, and presented heuristics to minimize the total energy subject to service response time constraints. Kaplan et al. [20] studied the dual optimization of cooling and communication costs for HPC applications in a datacenter. They proposed a heuristic algorithm that achieves a good tradeoff between the two objectives, and subject to reliabity constraint specified by the processor junction temperature.. In contrast to the previous work, which focused on either offline scheduling or homogeneous datacenters, we studied the problem of online scheduling for heterogeneous datacenters with both energy and performance considerations, as well as their tradeoffs. Furthermore, we considered static server placement to balance the thermal distribution in the presence of nonuniform heat distribution matrix. In our previous work [37] , we have applied this concept to the arrangement of computing nodes in a smaller scale problem (at the server level). To the best of our knowledge, no prior work has considered this problem for heterogeneous datacenters.

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Normality and Nondegeneracy for Optimal Control Problems with State Constraints Abstract. In this paper, we investigate normal and nondegenerate forms of the maximum principle for optimal control problems with state constraints. We propose new constraint qualifications guaranteeing nondegeneracy and normality, that have to be checked on smaller sets of points of an optimal trajectory than those in known sufficient conditions. In fact, the constraint qualifications proposed impose the existence of an inward pointing velocity just on the instants of time for which the optimal trajectory has an outward pointing velocity. optimal control and maximum principle and state constraints and constraint qualifications and normality and degeneracy and nonsmooth analysis and oriented distance. We consider optimal control problems with pathwise state constraints. For these problems, we study necessary conditions of optimality in the form of a maximum principle that, in some situations, are able to provide more information, by avoiding the abnormality or the degeneracy phenomena.. We say that the maximum principle is abnormal if the scalar multiplier associated with the objective function (ahead denoted by λ) is equal to zero. In this case, the necessary conditions cannot use the information of the objective function to select minimizers.. The degeneracy phenomenon arises when the state constraint is active at the initial time. Then, a possible choice of multipliers is offered by the socalled degenerate multipliers, for which the adjoint multiplier (denoted by q) and therefore the Hamiltonian are equal to zero for almost every time. This implies that all conditions in the maximum principle are satisfied for any candidate to solution we might test. Thus, with the degenerate multipliers, the maximum principle is useless to select minimizers.. Nondegenerate and normal forms of the maximum principle are established for problems that satisfy a suitable constraint qualification. In addition to helping, in some situations, to find minimizers or to eliminate some candidates for optimality, the normal maximum principle is also useful to establish regularity properties of the minimizes (as in e.g. [8, 14, 19] ) or to deduce second order optimality conditions (see e.g. [13, 20, 21] ).. The degeneracy of the maximum principle for state constrained problems has already been well identified and studied in the literature even for nonsmooth data, see e.g. [1, 2, 3, 7, 10, 11, 26, 23, 24] . Previous investigations on nondegenerate and normal forms of the maximum principle involved various types of constraint qualifications. The relations between some of them is discussed for instance in [12, 16, 23] . In [24] , an integral-type constraint qualification was introduced. There, it was shown that, to avoid degeneracy, an inward pointing condition has to be satisfied for some, not all, instants of a neighborhood of the initial time.. In the present paper, we introduce new constraint qualifications that just have to be satisfied on a subset of times at which the optimal trajectory has an outward pointing velocity. Furthermore, we remove the convexity assumption on the problem data imposed in [24] . We also provide, in a corollary, additional sufficient conditions to avoid having the adjoint multiplier q equal to zero, or to avoid having q and λ both equal to zero. In this way, we show that a nondegeneracy condition derived previously in a different context in [5] holds true also in our case.. Normality for optimal control problems with state constraints has also been extensively studied, see for instance [12, 15, 18, 22, 26] and references therein. In the literature, it was shown that normality might be guaranteed by assuming constraint qualifications with the inward pointing inequalities imposed on neighborhoods of times τ for which the optimal trajectory belongs to the boundary of the state constraint. The new constraint qualification CQn requires the inward pointing inequality to be satisfied only for times t < τ from a neighborhood of τ at which the trajectory has an outward pointing velocity. We discuss here few consequences of this constraint qualification. The inward pointing condition from [18] is in the same spirit, however it uses also t > τ .. The constraints qualifications here proposed help also to understand the relations between previous constraints qualifications reported in the literature. Namely, we discuss conditions involving different generalized gradients and, in the smooth case, we compare different types of constraint qualifications.. The outline of the paper is as follows. In Section 2, we recall some notions of nonsmooth analysis, the nonsmooth maximum principle and compare various gradients of distance functions. In Section 3, we state our main results. This paper is devoted nondegenerate and normal versions of the maximum principle. New constraint qualifications, under which these versions hold true, are introduced. They differ from the existing in the literature constraint qualifications because the inward pointing condition has no longer to be satisfied for almost all times in an interval, but just on subsets for which the optimal trajectory has an outward pointing velocity.. Relations between the new and previous constraint qualifications are discussed. Also, relations between some known constraint qualifications reported in the literature are clarified.. The new constraint qualifications allow to avoid the degeneracy occurring when the state constraint is active at the initial state. Under further conditions, the adjoint multiplier is shown not to be equal to zero. Normality is guaranteed by imposing an inward pointing condition on neighbourhoods of times when the optimal trajectory belongs to the boundary of state constraints. Again it has to be verified just for almost all times for which the optimal trajectory has an outward pointing velocity.

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


A multivariable multiobjective predictive controller Predictive control of MIMO processes is a challenging problem which requires the specification of a large number of tuning parameters (the prediction horizon, the control horizon and the cost weighting factor). In this context, the present paper compares two strategies to design a supervisor of the Multivariable Generalized Predictive Controller (MGPC), based on multiobjective optimization. Thus, the purpose of this work is the automatic adjustment of the MGPC synthesis by simultaneously minimizing a set of closed loop performances (the overshoot and the settling time for each output of the MIMO system). First, we adopt the Weighted Sum Method (WSM), which is an aggregative method combined with a Genetic Algorithm (GA) used to minimize a single criterion generated by the WSM. Second, we use the NonDominated Sorting Genetic Algorithm II (NSGA-II) as a Pareto method and we compare the results of both the methods. The performance of the two strategies in the adjustment of multivariable predictive control is illustrated by a simulation example. The simulation results confirm that a multiobjective, Pareto-based GA search yields a better performance than a single objective GA. Industrial processes are essentially coupled multivariable systems. The Generalized Predictive Control (GPC) strategy offers an effective way to deal with problems in multivariable control systems by including the process model in the computation of control actions. Without any doubt, the ability of GPCs regarding this kind of processes attracted notable attention in industry over the past few years (Qin and Badgwell, 2003) .. In order to control a multivariable system, some works used multivariable predictive controllers in a completely decentralized fashion (Zenghui et al., 2006; Al-Gherwi et al., 2010) . To realize that, it is necessary to design decoupling compensators to eliminate the interactions, and then the MIMO system is treated as a set of independent SISO systems and individual GPC controllers for the different subsystems are operated. In such cases, satisfactory results are obtained if the interactions are negligible. But in many cases, industrial systems are strongly coupled and more than one input variable is coupled with the outputs. Consequently, closed-loop performances may be significantly decreased since some or all interactions are ignored (Al-Gherwi et al., 2010) . In this case, the system must be considered truly multivariable and some type of multivariable control has to be applied to achieve satisfactory performances.. It is evident that distributed GPC strategies have a simpler structure but their performance is expected to be generally poorer as compared with centralized GPC strategies which will be applied in this work. The design of multivariable predictive controllers requires the specification of synthesis parameters, namely, prediction horizons, control horizons and cost weighting factors. But there are not exact rules giving the values of the required parameters. In this context, some works (Bemporada and Munoz de la Penab, 2009; Muldera et al., 2009; Królikowski and Jerzy, 2001) were interested in tuning of the MPC parameters using multiobjective optimization.. A new Model Predictive Control (MPC) scheme based on multiparametric multiobjective linear programming was presented (Bemporada and Munoz de la Penab, 2009 ). In the work of Muldera et al. (2009) , a method for the synthesis of a simultaneous linear and anti-windup controller using multiobjective convex optimization is described and tested using a benchmark problem. Also, some works deal with the automatic tuning of MPC, e.g., Ben Abdennour et al. (1998) present an on-line adjustment of GPC synthesis parameters using fuzzy logic. Therefore the objective of this work is to adjust the synthesis parameters of multivariable predictive controllers to make a compromise between closed loop performances. To realize this the optimization problem treated in this work is a multiobjective one and the performance criteria of this problem correspond to the closed loop performances.. In this paper, we make use of Multi-Objective Optimization (MOO) based on the minimization of all performance criteria simultaneously. MOO leads to a set of optimal solutions, i.e., Pareto optimal solutions or non-dominated solutions (Colette and Siarry, 2002) . In this context, many works (e.g., Bemporada and Munoz de la Penab, 2009; Muldera et al., 2009; Popov et al., 2005; Yang and Pedersen, 2006; Behroozsarand and Shaffei, 2010) were focused on the synthesis of controllers based on multiobjective optimization, which has received growing interest.. In this work, we suggest two strategies to achieve our purpose. The first one is a combination of an aggregative method, namely, the weighted sum method, allowing the transformation of the criteria in only one criterion, and a GA whose role is to minimize the generated single criterion by the WSM. The second strategy uses NSGA-II as a multiobjective Pareto-based GA. NSGA-II is a modified version of the popular NSGA to rectify all the above issues of the latter. In fact, NSGA-II has a better sorting algorithm. , where M is the number of objectives and N is the population size), incorporates elitism and no sharing parameter needs to be chosen a priori (Deb, 2002; Srinivas and Deb, 1995) . The performance criteria to be simultaneously minimized are the overshoot and the settling time for each MIMO system output. This paper is organized as follows. The problem is formulated in Section 2, where the key elements needed to formulate a centralized MIMO predictive control law are given. Both strategies allowing the design of the multivariable multiobjective predictive controller are described in Section 3. The obtained simulation results and discussion are presented in Section 4. Conclusions and perspectives are given in the last section. Two GA search techniques, aggregation into a single objective (WSM) and a Pareto-method (real-coded NSGA-II), have been used to adjust a centralized multivariable predictive controller parameters. Simulation results prove that NSGA-II yields a better approximation of the Pareto front than the WSM. The numerical results show the performance of the tuned controller with the NSGA-II method to control the treated multivariable process and to obtain closed loop performances corresponding to the decision-maker preferences. Therefore, it is concluded that NSGA-II is very effective in the tuning of MGPC synthesis parameters, is able to maintain a better spread of solutions and converges better in the obtained non-dominated front compared with the WSM. These results encourage the application of NSGA-II to more complex and real world multiobjective optimization problems. It is also important to note that the controllers considered are unconstrained ones and the proposed methodology can be applied to constrained predictive controllers.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 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 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 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 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 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 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 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 B 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 B 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 B 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


A DSS generator for multiobjective optimisation of spreadsheet-based models AbstractWater management practice has benefited from the development of model-driven Decision Support Systems (DSS This study presents a general-purpose DSS generator, GANetXL, for developing specific DSS that require multiobjective optimisation of spreadsheet-based models. The DSS generator is a result of the desire to allow easier involvement of users in the development of DSS prototypes, which will lead to better DSS performance, acceptance and adoption in practice. It is argued here that this is possible by using GANetXL as a large number of users (decision makers and analysts), many of whom may be inexperienced in developing and using complex optimisation methods, are able to develop or at least understand spreadsheet models. Spreadsheets, such as Microsoft Excel, are considered ideal for small to medium-size modelling applications due to their ubiquitous presence, transparency of spreadsheet-based models, ease of use, availability of ready-to-use graphical interfaces and the fact that they can be programmed by using macro language.. The DSS generator, GANetXL, which integrates evolutionary multiobjective optimisation (EMO) with spreadsheet modelling capabilities, is demonstrated on two examples from water engineering practice. The first example involves the optimisation of a simple water supply reservoir operation model with two objectives. The functionality of the DSS generator and its intuitive interface allowed a quick implementation of the water supply reservoir simulation model within Excel, execution of the EMO algorithm and interactive visualisation of the objective and decision spaces thereby allowing a user to gain

O O O O B 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 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 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 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


spliceR:

an

R

package

for

classification

of

alternative

splicing

and

prediction

of

coding

potential

from

RNA-seq

data

Background:

RNA-seq

data

is

currently

underutilized,

in

part

because

it

is

difficult

to

predict

the

functional

impact

of

alternate

transcription

events.

Recent

software

improvements

in

full-length

transcript

deconvolution

prompted

us

to

develop

spliceR,

an

R

package

for

classification

of

alternative

splicing

and

prediction

of

coding

potential.

Results:

spliceR

uses

the

full-length

transcript

output

from

RNA-seq

assemblers

to

detect

single

or

multiple

exon

skipping,

alternative

donor

and

acceptor

sites,

intron

retention,

alternative

first

or

last

exon

usage,

and

mutually

exclusive

exon

events.

For

each

of

these

events

spliceR

also

annotates

the

genomic

coordinates

of

the

differentially

spliced

elements,

facilitating

downstream

sequence

analysis.

For

each

transcript

isoform

fraction

values

are

calculated

to

identify

transcript

switching

between

conditions.

Lastly,

spliceR

predicts

the

coding

potential,

as

well

as

the

potential

nonsense

mediated

decay

(NMD)

sensitivity

of

each

transcript.

Here,

we

have

introduced

the

R

package

spliceR,

which

increases

the

usability

and

power

of

RNA-seq

and

assembly

technologies

by

providing

a

full

overview

of

alternative

splicing

events

and

protein

coding

potential

of

transcripts.

spliceR

is

flexible

and

easily

integrated

in

existing

workflows,

supports

input

and

output

of

standard

Bioconductor

data

types,

and

enables

investigators

to

perform

many

different

downstream

analyses

of

both

transcript

abundance

and

differentially

spliced

elements.

We

demonstrate

the

power

and

versatility

of

spliceR

by

showing

how

new

conclusions

can

be

made

from

existing

RNA-seq

data.

Alternative

splicing

is

one

of

the

most

important

RNA

modifications,

leading

to

protein

diversification

and

contributing

to

the

complexity

of

higher

organisms

Recent

advances

in

RNA

sequencing

(RNA-seq),

combined

with

modern

RNA-seq

assembly

software

such

as

Cufflinks

allows

for

high-resolution

profiling

of

the

RNA

landscape.

The

technological

and

computational

advances

enables

identification

of

a

catalog

of

distinctly

spliced

transcripts

originating

from

the

same

transcription

unit/gene.

These

full-length

transcripts

are

however

underutilized,

in

part

because

it

is

difficult

to

predict

the

functional

impact

of

alternate

transcription

events

leading

to

the

different

transcripts.

In

addition

to

the

potential

for

impact

on

protein

domains,

alternate

splicing

may

also

alter

RNA

processing,

stability

and

localization.

Nonsense

mediated

decay

(NMD)

is

tightly

linked

to

alternate

splicing,

and

the

mechanism

by

which

even

small

changes

in

alternative

splicing

can

result

in

degradation

via

NMD

is

well

described

To

predict

splicing

events

that

may

lead

to

these

functional

changes,

it

is

necessary

to

classify

the

type

of

event

as

well

as

annotate

the

genomic

position

of

the

regions

that

are

differentially

spliced.

Such

classifications

also

enable

systematic

follow-up

analyses,

such

as

sequence

analysis

of

the

differentially

spliced

regions

to

infer

the

underlying

mechanisms.

However,

at

present

there

are

no

available

tools

that

adequately

perform

these

analyses.

Existing

methods,

including

MISO

Astalavista

and

DiffSplice

do

not

output

the

genomic

coordinates

of

differentially

spliced

regions

have

insufficient

classification

of

alternative

splicing

(i.e.,

only

a

subset

of

alternative

splicing

classes

are

supported)

or

cannot

assess

novel

features

Furthermore,

of

the

existing

tools

for

analyzing

alternative

splicing

support

NMD

predictions

This

prompted

us

to

develop

the

R

package

spliceR.

spliceR

uses

the

full-length

transcripts

created

by

RNA-seq

assemblers

to

detect

single-and

multiple

exon

skipping/

inclusion

(ESI,

MESI),

alternative

donor

and

acceptor

sites

intron

retention

(IR),

alternative

first

or

last

exon

usage

(ATSS,

ATTS),

and

mutually

exclusive

exon

events

(MEE).

spliceR

annotates

the

genomic

coordinates

of

the

differentially

spliced

elements,

facilitating

downstream

sequence

analysis.

Finally,

spliceR

predicts

the

coding

potential

of

transcripts,

calculates

untranslated

region

(UTR)

and

open

reading

frame

(ORF)

lengths

and

predicts

whether

transcripts

are

NMDsensitive

based

on

compatible

annotated

start

codon

positions

and

their

downstream

ORF.

Retrieval

of

data

spliceR

is

implemented

as

an

R

package

and

is

freely

available

from

the

Bioconductor

repository

It

is

based

on

standard

Bioconductor

classes

such

as

GRanges,

allowing

for

full

flexibility

and

modularity,

and

support

for

all

species

and

versions

supported

in

the

Bioconductor

annotation

packages.

An

example

dataset

is

included

to

allow

easy

exploration

of

the

package..

spliceR

is

compatible

with

the

output

from

any

fulllength

RNA-seq

assembler,

but

was

designed

to

integrate

with

Cufflinks

and

includes

a

dedicated

function

that

retrieves

all

relevant

information

from

the

SQL

database

generated

by

Cufflinks

axillary

R

package

cummeRbund.

In

future

versions

new

functions

dedicated

to

import

data

from

other

RNA-seq

assemblers

will

be

introduced.

The

R

code

for

a

standard

workflow

based

on

Cufflinks

data

is

illustrated

in

Figure

A

workflow

using

output

from

other

full-length

RNA-seq

assemblers

is

provided

in

the

spliceR

Bioconductor

documentation.

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


Algorithms for detecting and analysing autocatalytic sets Background: Autocatalytic sets are considered to be fundamental to the origin of life. Prior theoretical and computational work on the existence and properties of these sets has relied on a fast algorithm for detecting self-sustaining autocatalytic sets in chemical reaction systems. Here, we introduce and apply a modified version and several extensions of the basic algorithm: (i) a modification aimed at reducing the number of calls to the computationally most expensive part of the algorithm, (ii) the application of a previously introduced extension of the basic algorithm to sample the smallest possible autocatalytic sets within a reaction network, and the application of a statistical test which provides a probable lower bound on the number of such smallest sets, (iii) the introduction and application of another extension of the basic algorithm to detect autocatalytic sets in a reaction system where molecules can also inhibit (as well as catalyse) reactions, (iv) a further, more abstract, extension of the theory behind searching for autocatalytic sets. Results: (i) The modified algorithm outperforms the original one in the number of calls to the computationally most expensive procedure, which, in some cases also leads to a significant improvement in overall running time, (ii) our statistical test provides strong support for the existence of very large numbers (even millions) of minimal autocatalytic sets in a well-studied polymer model, where these minimal sets share about half of their reactions on average, (iii) "uninhibited" autocatalytic sets can be found in reaction systems that allow inhibition, but their number and sizes depend on the level of inhibition relative to the level of catalysis. Conclusions: (i) Improvements in the overall running time when searching for autocatalytic sets can potentially be obtained by using a modified version of the algorithm, (ii) the existence of large numbers of minimal autocatalytic sets can have important consequences for the possible evolvability of autocatalytic sets, (iii) inhibition can be efficiently dealt with as long as the total number of inhibitors is small. The modified RAF algorithm, based on the notion of pseudo-RAFs, clearly improves on the number of calls to the closure computation procedure, which is computationally the most expensive part of the algorithm. Depending on the structure of catalysis in a reaction network, this can also lead to a significant improvement in the overall running time of the algorithm. However, in a purely "random" system (as in the binary polymer model), the additional overhead of keeping track of the number of reactions that produce a given molecule seems to cancel out the gain obtained from a reduced number of closure computations, at least for polymers of the sizes studied here. But, in general, the modified algorithm is never worse -and in some cases it is faster -than the original version.. Our statistical test on the expected number of irrRAFs within a reaction network provides strong support for theexistence of very large numbers of irrRAFs. In instances of the binary polymer model, even for n = 8 with maxRAF sets of (on average) 375 reactions, is it highly likely (99% confidence) that at least hundreds of millions of irrRAFs exist. The overlap statistics show that these irrRAFs share, on average, about half of their reactions with each other, ranging from 25% to 80% overlap. In other words, there is always at least 20% (and up to 75%) difference between two arbitrary irrRAFs within the same reaction network. This large number and the relatively high variability could have important (and positive) consequences for the possible evolvability of autocatalytic sets [15, 21] .. Even though the general problem of finding RAF sets in systems that also allow inhibition (as well as catalysis) is NP-complete, we have shown that this problem becomes tractable when the total number of inhibitors is small (in absolute value). We have implemented and applied an extension of the basic RAF algorithm to search for such "uninhibited" RAF sets (u-RAFs), and have shown that their number and sizes depend largely on the level of inhibition (i.e., the probability that an inhibitor actually inhibits any given reaction) relative to the level of catalysis. So, at least in certain limited cases, inhibition can be dealt with efficiently. A full investigation of u-RAFs will be deferred to future work, however. The concept of autocatalytic sets was introduced by Kauffman [1] [2] [3] to study the idea of life as a functionally closed and self-sustaining chemical reaction system. This concept is closely related to other such models and ideas [4] [5] [6] [7] and is believed to have played a crucial role in the origin of life. It was later formalized mathematically in the form of RAF theory [8] [9] [10] .. To briefly review RAF theory, we first define a chemical reaction system (CRS) as a tuple (X, R, C) consisting of a set of molecule types X, a set of (possible or allowed) *Correspondence: wim@WorldWideWanderings.net 1 SmartAnalytiX.com, Lausanne, Switzerland Full list of author information is available at the end of the article chemical reactions R, and a catalysis set C indicating which molecule types can catalyse which reactions. Next, a food set F ⊂ X is defined as a subset of molecule types that are assumed to be freely available from the environment (i.e., they do not necessarily have to be produced by any of the reactions in R). Thus F is a subset of X, and we will denote a CRS with associated food set F as a quadruple Q = (X, R, C, F).. An autocatalytic set (or RAF set) for Q = (X, R, C, F) is a subset R ⊆ R of reactions which is:. 1. reflexively autocatalytic (RA): each reaction r ∈ R is catalysed by at least one molecule that is either present in F or can be formed from F by using a series of reactions only from R itself.

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


Asymptotic Global Confidence Regions in Parametric Shape Estimation Problems Abstract-We introduce confidence region techniques for analyzing and visualizing the performance of two-dimensional parametric shape estimators. Assuming an asymptotically normal and efficient estimator for a finite parameterization of the object boundary, Cramér-Rao bounds are used to define an asymptotic confidence region, centered around the true boundary. Computation of the probability that an entire boundary estimate lies within the confidence region is a challenging problem, because the estimate is a two-dimensional nonstationary random process. We derive lower bounds on this probability using level crossing statistics. The same bounds also apply to asymptotic confidence regions formed around the estimated boundaries, lower-bounding the probability that the entire true boundary lies within the confidence region. The results make it possible to generate asymptotic confidence regions for arbitrary prescribed probabilities. These asymptotic global confidence regions conveniently display the uncertainty in various geometric parameters such as shape, size, orientation, and position of the estimated object, and facilitate geometric inferences. Numerical simulations suggest that the new bounds are quite tight.Index Terms-Confidence regions, Cramér-Rao bounds, geometric inference, imaging, level crossing probability, maximumlikelihood estimation, parametric shape estimation, random process. In this paper, we proposed a new concept for analyzing the performance of two-dimensional parametric shape estimators using a confidence region visualization technique. Cramér-Rao bounds for estimation of unknown geometric parameters such as shape, size, orientation, and the position of objects are used to construct a confidence region within which the shape estimate resides with a prescribed probability. The geometric properties of the confidence region convey information about which parts of the shape are difficult to estimates and can be used to optimize imaging system parameters. Computing the actual probability that the estimate lies in the confidence region is, however, quite a challenging problem because a shape estimate is usually a two-dimensional nonstationary random process. We derived two bounds on this probability: the incomplete-gamma and level-crossing bounds. The incomplete-gamma bound was derived using the basic inequalities of a projection without considering the characteristics of the CRB matrix and the basis functions for parameterization. As expected, this bound turned out to be very conservative. However, using the level-crossing statistics, we derived a tighter level-crossing bound which can be obtained in a numerically stable way using QR decomposition. We also showed that our bounds are valid lower bounds for the probabilities that the true shape lies in a posteriori confidence regions which are created around the MLE, which is often encountered in practical estimation algorithms.. Numerical simulations for a nonlinear inverse scattering problem showed that our level-crossing bound is tight enough for a broad range of confidence levels and number of unknown parameters. Based on the theoretical results and several test applications, our global confidence region may prove useful in a variety of other applications of parametric shape estimation. Furthermore, owing to the generality of our model and approach, the result is applicable to linear and nonlinear shape representations, complicated observation models, etc. [10, pp. 76-77] ): Let be fixed. If the one-dimensional probability density function of the process is bounded at every , and if has, with probability one, a continuous sample derivative, , then the probability is zero that simultaneously, for any point in . where (C.8) The up-crossing rate of is given by [12] (C.9). The probability density function is computed from the joint probability of using the coordinate transformation (C.2) (C.10) since the Jacobian is . Note that in our formulation and in general, unlike Rice's original formulation for the stationary envelope process [14] , [15] . This makes the computation of and hence very complicated. Fortunately, can be made zero by an appropriate choice of in (36) and (37). After substituting (C.18) into (C.10), the probability density function for the level-crossing rate is obtained by integration (C. 19) If in (C.7), then , and (C.18) can be greatly simplified as (C.20) and the integration (C.19) is fairly easy, which was done in Rice's original work [14] , [15] . However, the simplification of (C.20) cannot be applied to our problem since the magnitudes of derivatives and are in general different. As expected from (C.18), a closed-form expression for the integral in (C. 19 where is the level-crossing rate of (C.9). Proof: The main idea of the proof is similar to the proof of Slepian's Lemma 1 [18] . Using (C.9) and (C.19), we have

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


A behavioral analysis for planning MIS implementation Planning for a successful MIS implementation requires understanding the effects of the introduction of a new system on the work lives of potential adopters. The effects can be assessed by the MIS practitioner/ change agent ff the agent will first obtain a thorough and specific understanding of the task activities performed by potential adopters, the interactions they engage in as they perform their tasks, and their preferences for, or feelings about, those activities and interactions. An interview based approach to gathering this data is described, and a short description of an implementation in which the approach was used is provided. Managing toward successful implementation of a new system requires understanding the effects of the new system on its potential adopters. In order to understand the effects, the change agent, who may be the MIS practitioner, must be able to obtain data which describes the current situation through the eyes of the potential adopter, so that changes adopters would feel as a result of a new system can be identified, and the consequences of the changes on the liklihood of a successful implementation can be assessed. This article describes in considerable detail an interview based approach to obtaining this useful descriptive data from potential adopters.. The approach described here is consistent with socio-technical theory, which holds that the organization's operating system is an emergent blend of its technical and social systems [24, 25] , and is a direct descendent of basic research in the behavioral sciences on communication networks and group structures.. The approach is disarmingly simple. There are three data components --all gathered through interviews with potential adopters. The components are 1) the specific task activities each potential adopter performs, 2) the interactions they have with others as they carry out these activities, and 3) their feelings about these task activities and interactions which define their "role." Since the label "user" is somewhat presumptuous when our concern is implementation, the clumsier, but more appropriate, phrase "potential adopter" will be used.. The article first outlines existing implementation research, then describes the three data components, provides guidelines on the interview process through which the information is gathered, describes how the data can be used, and concludes with a short case study of a system implementation in which the approach was used. The data, data gathering procedures, and guidelines for using it, are not offered as a surefire solution to implementation problems for the practitioner. It may be most appropriate to view the approach as a means to act upon all of the good and sensible things which socio-technical theorists and behavioral scientists have been saying we should be concerned about, and that MIS practitioners are coming to accept and want to act upon. The approach is offered as a step toward the goal of successful implementation when it is used relatively skillfully. Indeed, one of its advantages is that it is specific and straightforward, and can be used "relatively skillfully" by organizationally sensitive, if even ur~trained, change agents.. The interview procedure is the central feature of the approach which opens it to practitioners/ change agents who need not be organization development specialists.. The interview, if conducted as described, appears to be successful for several reasons:. 1. The questions about activities and interactions which serve as the heart of the interview are objective and nonthreatening.. 2. Potential adopters find the questions easy to respond to.. 3. The questions give potential adopters an opportunity to convey to an apparently interested person the rich detail of how they work and how much they do. 5. The approach helps convey the attitude that the interviewer needs to learn from the potential adopter, and is interested in basic and important things.. What the approach does then is place in the hands of the practitioner/change agent a rich source of insight into the effects of a new system on the working lives people would experience if the system were adopted by them. This insight can then help the analyst anticipate, avoid, or smooth potential adoption problems.. Besides the valuable uses for data on activities and interactions at several stages of the MIS development cycle, the process of gathering the data itself is beneficial. Behaviora~ scientists learned long ago in the famous Hawthorne studies that the mere expression of interest and concern by a researcher/change agent has a positive influence on behavior and attitudes [21 ] . Thus, it was not surprising to find in the field study that potential adopters responded very favorably to the interview itself; the management reported later that it had received supportive feedback from employees. The exact effect would be difficult to measure, but research has repeatedly shown it to be positive.

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


CENTROID TRIANGULATIONS FROM k-SETS ABSTRACT Given a set V of n points in the plane, no three of them being collinear, a convex inclusion chain of V is an ordering of the points of V such that no point belongs to the convex hull of the points preceding it in the ordering. We call k-set of the convex inclusion chain, every k-set of an initial subsequence of at least k points of the ordering. We show that the number of such k-sets (without multiplicity) is an invariant of V , that is, it does not depend on the choice of the convex inclusion chain. Moreover, this number is equal to the number of regions of the order-k Voronoi diagram of V (when no four points are cocircular).The dual of the order-k Voronoi diagram belongs to the set of so-called centroid triangulations that have been originally introduced to generate bivariate simplex spline spaces. We show that the centroids of the k-sets of a convex inclusion chain are the vertices of such a centroid triangulation. This leads to the currently most efficient algorithm to construct particular centroid triangulations of any given point set; it runs in O(n log n + k(n − k) log k) worst case time. Given a finite set V of n points in the plane, a k-set of V is a subset of k points of V that can be separated from the remaining points by a straight line. Since the 1970s, finding matching upper and lower bounds for the maximum number of k-sets of a set of n points in the plane has been an important problem in combinatorial geometry (see, e.g., Chapter 11 in Matoušek's textbook 1 , or Wagner's survey 2 ). The first (published) result is due to Lovász 3 who proved an upper bound of O(n 3 2 ) for k = n/2. Erdös, Lovász, Simmons and Straus 4 extended the result to general k, getting an upper bound of O(nk 1 2 ) and a lower bound of Ω(n log k). The currently best bounds have been given by Dey 5 and by Tóth 6 . Dey showed that no point set has more than O(nk Calling every i-set of V (i ≤ k) an (≤ k)-set of V , Peck 7 and, independently, Alon and Györi 8 , showed that the number of (≤ k)-sets of any set of n points is bounded by kn; the bound is achieved for points in convex position.. In this paper we obtain a new result on another summation of numbers of ksets. In opposition to previous works, we fix the value of k and consider the k-sets of different subsets of V (without multiplicity). The subsets are obtained in the following way: Let V = (v 1 , v 2 , ..., v n ) be an ordering of the points of V such that, for every i ∈ {2, ..., n}, v i does not belong to the convex hull of {v 1 , ..., v i−1 }. V is called a convex inclusion chain of V , and we call k-set of V any k-set of {v 1 , ..., v i }, for all i ∈ {k, ..., n}. We show that, when no three points of V are collinear, the number of distinct k-sets of a convex inclusion chain of V is an invariant of V , that is, it does not depend on the chosen convex inclusion chain. More precisely, it is equal to 2kn − n − k 2 + 1 − k−1 j=1 a j (V ), with a j (V ) the number of j-sets of V and with 0 1 = 0. Surprisingly, this number is equal to the number of regions of the order-k Voronoi diagram of V (when no four points of V are cocircular) 9 . This diagram is a partition of the plane whose every region is the set of points of the plane having the same k nearest neighbors in V . In order to establish another connection between convex inclusion chains and order-k Voronoi diagrams, we first recall how these diagrams occur in spline theory.. An (univariate) degree k B-spline is a piecewise polynomial function, every piece of which being a degree k polynomial 10 . This function is defined through a set of k + 2 reals, called knots. Given a set K of n knots, the B-splines defined by all subsets of k + 2 consecutive knots of K are linearly independent and form the basis of a degree k B-spline space. Spline functions are then obtained by linear combinations of B-splines. These functions have many properties that make them attractive, namely for curve modeling. In order to model surfaces, a multivariate generalization of B-splines is needed. In 1976, de Boor 11 introduced the notion of simplex spline: a degree k simplex spline is a piecewise polynomial function defined through a set of k + d + 1 knots, which are points in R d . Given a set K of n knots, different methods have then been proposed to select subsets of k + d + 1 knots of K (also called configurations) to form the basis of a simplex spline space; for an overview, see the survey of Neamtu 12 . In 2007, Neamtu 13 proposed the first solution that really reduces to B-splines when d = 1. The selected configurations are all (k + d + 1)-subsets of K for which there exists a sphere passing through d + 1 of these knots, having the k other knots inside, and the rest of K outside. The centers of these spheres form a subset of the vertices of the order-(k + 1) Voronoi diagram of K. An application of Neamtu's configurations to surface reconstruction can be found in 14 . However, Liu and Snoeyink 15 pointed out that Neamtu's solution is too restrictive on the types of splines that can be generated. They showed that there exist more general families of configurations that generalize B-splines. The simplex splines defined with these more general configurations are interesting notably to model sharp features 16 . In order to generate their configurations in the case d = 2, Liu and Snoeyink generalized the order-k Voronoi diagram in the following way. The order-k Voronoi diagram of a set V of points in the plane admits a straight line dual graph whose vertices are the centroids of the k-point subsets defining the order-k Voronoi regions 17, 18 . When no four points of V are cocircular, this dual graph is a triangulation called the order-k centroid Delaunay triangulation of V . Such a triangulation can be constructed by an iterative algorithm that deduces the order-k centroid Delaunay triangulation from the order-(k − 1) centroid Delaunay triangulation 9, 17 . Liu and Snoeyink extended this algorithm to construct more general triangulations, called order-k centroid triangulations. The extended algorithm is applied to any given order-(k − 1) centroid triangulation. When it succeeds in constructing a new triangulation (and not overlapping triangles) then the generated triangulation is an order-k centroid triangulation. An order-1 centroid triangulation is an arbitrary (classical) triangulation of V. The vertices of an order-k centroid triangulation are centroids of k-point subsets of V , and its triangles are of two types. The triangles of the first type are defined with subsets of k + 2 points of V , and these subsets are configurations defining a bivariate degree k − 1 simplex spline space. The triangles of the second type are defined with subsets of k + 1 points that define a bivariate degree k − 2 simplex spline space.. However, Liu and Snoeyink could prove that their algorithm really generates triangulations only for the cases k = 2 and k = 3. Even though experimental results indicate that it also works for higher values of k, the family of centroid Delaunay triangulations is still the only family of centroid triangulations for which it has been proved that it can be generated for all k. In this paper, we prove the existence of a new family of centroid triangulations, which are related to convex inclusion chains. In fact we show that, for all k, the centroids of the k-sets of a convex inclusion chain of V are the vertices of an order-k centroid triangulation of V .. Up to now, the algorithm of Liu and Snoeyink is the only algorithm that allows to generate every existing centroid triangulation. Its time complexity depends on the generated triangulation, but it cannot be less than Ω(n log n + k 2 (n − k)). A particular centroid triangulation, the order-k centroid Delaunay triangulation, can be generated using algorithms that construct the order-k Voronoi diagram. The algorithm of Agarwal and Matoušek 19 , for example, allows to construct this diagram in O(n 1+ǫ k) time, where ǫ > 0 is an arbitrarily small constant. The currently best randomized algorithm is the one given by Agarwal, de Berg, Matoušek, and Schwarzkopf 20 , improved by Chan 21 , which runs in O(n log n + k(n − k) log k) expected time.. We give here a deterministic algorithm that constructs different order-k centroid triangulations of any set of n points in the plane in O(n log n + k(n − k) log k) worst case time. Our algorithm is a generalization of the simple and fast Beneath-Beyond algorithm used to construct a triangulation of a point set, after a presort in some direction 22 . The triangulations generated by our algorithm can serve as input for an algorithm (for example a flip algorithm) that has to build a centroid triangulation optimizing various criteria. In this paper, we have shown that the number of k-sets of a convex inclusion chain of a set V of points in the plane is an invariant of V . Furthermore, it is equal to the number of regions of the order-k Voronoi diagram of V . We get that way a completely new method to compute the size of the order-k Voronoi diagram in the plane. We hope that the study of convex inclusion chains brings new insights into the important open problem of the size of order-k Voronoi diagrams in higher dimensions.. We have also shown that the centroids of the k-sets of a convex inclusion chain are the vertices of a triangulation that belongs to the set of centroid triangulations. This set also contains the order-k centroid Delaunay triangulation. Fully explaining the reason why the number of k-sets of a convex inclusion chain is equal to the number of order-k Voronoi regions comes then to showing that all centroid triangulations of a given point set have the same number of vertices. A sufficient condition for the result to hold has been given in 28 : If, in any centroid triangulation, every set of type-2 triangles defined with the same k + 1 points triangulates a convex polygon, then all centroid triangulations have the same number of vertices.. The difficulty of proving results on centroid triangulations comes from their recursive definition. The existence of an order-k centroid triangulation depends on the existence of a sequence of order-i centroid triangulations, for all i < k. We deem it necessary to find a direct geometric characterization of order-k centroid triangulations, not depending on lower order triangulations. We are currently proving that every vertex of an order-k centroid triangulation is the centroid of a k-point subset that can be separated from the remaining points by a convex curve. More precisely, the separating curves of the k-point subsets that define the vertices of such a triangulation form a set of convex pseudo-circles 29 . Finally, we have given an algorithm that allows to construct several order-k centroid triangulations of any given point set in O(n log n + k(n − k) log k) time. This is nearly optimal since the size of an order-k centroid triangulation is expected to be Θ(k(n − k)) and since the construction of an order-1 centroid triangulation is in Ω(n log n). However, the generated centroid triangulations should have some regularity properties to be of practical interest, namely for B-spline construction. Therefore, it is now important to investigate how they can be improved by local transformations, such as flips.

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


Receptive-Field Structure of Direction-Selective Ganglion Cells Projecting to the Goldfish Tectum The receptive field of a direction-selective unit of any type consists of an excitatory center that 3º-5º in size, a near inhibitory surround and a far surround upon which illumination exerts an influence for both spontaneous activity and specific cell response.KEYWORDS: direction-selective neurons; receptive field; lateral inhibition; ganglion cells; amacrine cells; horizontal cells; tectum opticum; goldfishThe receptive-field (RF) structure of direction-selective ganglion cells (DS GCs) is determined by specific retinal circuits including connections with various interneurons in the outer plexiform (OPL) and the inner plexiform (IPL) layers, the RF center being determined by direct pathways from receptors through bipolar cells within the dendritic field of the GC.In our electrophysiological experiments with extracellular recordings from axon terminals of DS GCs in the goldfish tectum, sizes of the RF center of the cells were evaluated in four ways: (1) a rough estimate as a product of the duration of spike train in response to contrast edges moving across the RF in preferred direction and the velocity of the movement; (2) more precisely, RF can be outlined with edges moving in many different directions, provided the temporal delay in the network is known; (3) tracing by small contrast spot moving on several parallel tracks allows to estimate the RF width by the number of spikes along each track and the RF length by the duration of spike train; when tracing in two mutually orthogonal directions (at 45° to the preferred one), the method permits calculation of a value for the delay from the same experiment; (4) since DS GCs respond well to "on" or "off" of small stationary spots, it is possible to use the canonical method of RF mapping with a flashing spot.All methods gave consistent results. Centers of the RF amounted to 3º-5º in all types of DS GCs.

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Cultivating a research agenda for data science I describe a research agenda for data science based on a decade of research and operational work in data-intensive systems at NASA, the University of Southern California, and in the context of open source work at the Apache Software Foundation. My vision is predicated on understanding the architecture for grid computing; on flexible and automated approaches for selecting data movement technologies and on their use in data systems; on the recent emergence of cloud computing for processing and storage, and on the unobtrusive and automated integration of scientific algorithms into data systems. Advancements in each of these areas are a core need, and they will fundamentally improve our understanding of data science, and big data. This paper identifies and highlights my own personal experience and opinion growing into a data scientist. I am committed to the above four areas of research and see them as both necessary and exciting if we are to advance the fields of Big Data and data science. I plan to attack the above research areas with a multi-disciplinary eye and to make a contribution in software architecture, design, reuse, and open source. I am excited to pursue these topics and am confident that the results of the pursuit will have a potential for tremendous impact in science and industry and the broader community.

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