Multifidelity importance sampling Multifidelity importance samplingEstimating statistics of model outputs with the Monte Carlo method often requires a large number of model evaluations. This leads to long runtimes if the model is expensive to evaluate. Importance sampling is one approach that can lead to a reduction in the number of model evaluations. Importance sampling uses a biasing distribution to sample the model more efficiently, but generating such a biasing distribution can be difficult and usually also requires model evaluations. A different strategy to speed up Monte Carlo sampling is to replace the computationally expensive high-fidelity model with a computationally cheap surrogate model; however, because the surrogate model outputs are only approximations of the high-fidelity model outputs, the estimate obtained using a surrogate model is in general biased with respect to the estimate obtained using the high-fidelity model. We introduce a multifidelity importance sampling (MFIS) method, which combines evaluations of both the high-fidelity and a surrogate model. It uses a surrogate model to facilitate the construction of the biasing distribution, but relies on a small number of evaluations of the high-fidelity model to derive an unbiased estimate of the statistics of interest. We prove that the MFIS estimate is unbiased even in the absence of accuracy guarantees on the surrogate model itself. The MFIS method can be used with any type of surrogate model, such as projection-based reduced-order models and data-fit models. Furthermore, the MFIS method is applicable to black-box models, i.e., where only inputs and the corresponding outputs of the high-fidelity and the surrogate model are available but not the details of the models themselves. We demonstrate on nonlinear and time-dependent problems that our MFIS method achieves speedups of up to several orders of magnitude compared to Monte Carlo with importance sampling that uses the high-fidelity model only. Models of real-world engineering systems often depend on multiple inputs such as material properties and forcing terms. In most cases, these inputs are not known exactly due to measurement errors, noise, or small perturbations in the manufacturing processes, and thus they are modeled as random variables with a distribution that accounts for these uncertainties. The output of the model then also becomes a random variable, and one is typically interested in the statistics of the output. The Monte Carlo method evaluates the model at samples drawn from the distribution of the inputs, and estimates the statistics from the obtained outputs. Monte Carlo estimators converge slowly with the number of samples and thus many model evaluations are necessary to achieve a given error tolerance. A common remedy to reduce the runtime of the Monte Carlo method is to replace the high-fidelity model with a computationally cheap surrogate model with a lower fidelity; however, this leads in general to an estimator with a bias, see, e.g., [1] for a discussion. We therefore propose to speed up the Monte Carlo method by combining, instead of replacing, the high-fidelity model with the surrogate model. Even in the absence of accuracy guarantees on the surrogate model itself, our multifidelity estimator is unbiased with respect to the statistics of the high-fidelity model The proposed multifidelity importance sampling uses the surrogate model to construct a biasing distribution and the high-fidelity model to derive the actual estimate. This multifidelity approach leads to an unbiased estimator of the failure probability independent of the accuracy of the surrogate model.. outputs. A surrogate model that poorly approximates the high-fidelity model might not yield computational savings, but the unbiasedness of the multifidelity estimator is guaranteed.. We develop our multifidelity approach in the context of the computation of failure probabilities [2, 3] with the Monte Carlo method and importance sampling [4, 5, 6] . Failure probabilities are typically small and thus the Monte Carlo method requires many model evaluations to derive an accurate estimate. Importance sampling is a variance reduction technique that aims to reduce the number of required model evaluations by using a problem-dependent sampling strategy. The computation of failure probabilities is only one application of importance sampling. For example, importance sampling is also used to estimate statistics over distributions that cannot be sampled directly. We refer to, e.g., [4] for additional applications of importance sampling, and therefore potential applications of our multifidelity approach.. In its simplest form, the Monte Carlo method with importance sampling consists of two steps. In the first step, a biasing distribution is generated. In the second step, samples are drawn from the biasing distribution to derive an estimate of the failure probability. The key challenge is to construct an effective biasing distribution that leads to many samples for which a failure event occurs [4, 6] . Several approaches for constructing a biasing distribution have been presented. A common approach is the cross-entropy method [7, 8] . This iterative optimization algorithm fits a standard distribution with respect to the Kullback-Leibler divergence to inputs that correspond to failures of the system. There are also adaptive methods that break with the splitting of importance sampling into two steps and instead build the biasing distribution while the model is sampled and while the estimate is derived, see, e.g., [9, 10, 11, 12, 13] . A general overview of importance sampling and methods for constructing biasing distributions is given in [4, 6] .. We propose to use the surrogate model to construct the biasing distribution in the first step of the Monte Carlo method with importance sampling and the high-fidelity model to derive the estimate in the second step. This is a multifidelity approach because both models are used to compute an estimate of the failure probability, see Figure 1 .. Past work has used surrogate models to speed up the Monte Carlo method. The control variates method provides a framework for variance reduction, using additive corrections from an auxiliary random variable that is correlated to the high-fidelity model outputs [14] . One approach based on the control variate method is the multi-level Monte Carlo method [15, 16] , which combines the outputs of a hierarchy of coarse grid solutions using control variates. The multifidelity Monte Carlo method introduced in [17] allows arbitrary surrogate models that do not necessarily stem from coarse grid discretizations. In [18] the multifidelity Monte Carlo method is used in the context of optimization where intermediate results of the iterative optimization process are used instead of a surrogate model. In [19] , statistics of high-fidelity models are estimated, where a residual-based indicator is introduced to decide whether a surrogate model is evaluated or recourse to the high-fidelity model is necessary. All these approaches, however, do not explicitly target the speedup of the estimation of failure probabilities or importance sampling in general. In [1] , a multifidelity approach for computing failure probabilities is presented, which is extended in [20] with importance sampling and a crossentropy method to handle rare events. The multifidelity approaches in [1, 20] adaptively switch between the high-fidelity model and the surrogate model. An analysis shows unbiasedness of the corresponding estimators if tolerance parameters are chosen well. The approach for computing failure probabilities presented in [21] uses a posteriori error estimators of the surrogate model to decide whether the outputs of the surrogate or the high-fidelity model should be used. Surrogate models with rigorous and efficient a posteriori error estimators are currently available only for a limited class of problems [22, 23] .. In contrast, we use the surrogate model to construct the biasing distribution only, and thus do not rely on the availability of a priori error bounds or a posteriori error estimators. We show that the estimator of our multifidelity approach is an unbiased estimator of the failure probability independent of the accuracy of the surrogate model, although the speedup increases as the approximation quality of the surrogate model improves. The numerical results demonstrate runtime savings of orders of magnitude compared to the Monte Carlo method with importance sampling that uses the high-fidelity model only. Since our method requires only evaluations of the high-fidelity and the surrogate model, it applies to black-box models. Furthermore, our multifidelity approach is applicable to arbitrary surrogate models, including projection-based reducedorder models, data-fit and response surface models, and simplified physics models.. The following Section 2 gives a brief overview of the estimation of failure probabilities with the Monte Carlo method with importance sampling. Section 3 introduces the multifidelity approach and proves the unbiasedness of the multifidelity estimator. The numerical results in Section 4 confirm the unbiasedness of our estimator and demonstrate the runtime savings on linear and nonlinear problems. Finally, Section 5 draws conclusions. This paper introduced a multifidelity approach for failure probability computation with the Monte Carlo method and importance sampling. Our MFIS method employs a surrogate model to construct the biasing distribution and the high-fidelity model to compute the estimate. We have shown that this leads to an unbiased estimator of the failure probability. Numerical experiments on a wide range of linear and nonlinear problems demonstrated the significant runtime improvements gained with our MFIS method compared to the Monte Carlo method with importance sampling that invokes a single model only.. The key property of our MFIS method is that it speeds up the runtime of the Monte Carlo method by using a surrogate model, but it leads to an unbiased estimator even in the absence of accuracy guarantees on the surrogate model. Our multifidelity method shows that, in some situations, recourse to the high-fidelity model can compensate for the lack of a priori error bounds or a posteriori error estimators for the surrogate model. Furthermore, it demonstrates that accuracy guarantees on the surrogate model are not a prerequisite to derive guarantees on the Monte Carlo estimate. This is particularly useful in complex problem settings, for example in computational fluid dynamics and fluid-structure interaction, where surrogate models can often be derived but error bounds or error estimators for these surrogate models are unavailable due to a lack of mathematical theory.. For smaller failure probabilities (i.e., in the range of 10 −9 ), the number of samples in the failure domain of the surrogate model typically decreases significantly such that fitting a mixture model with the EM algorithm fails. Future work therefore includes an iterative approach, similar to the cross entropy method [7, 8] , where the biasing distribution is repeatedly refined using samples of the biasing distribution of the previous iteration.. as part of the DiaMonD Multifaceted Mathematics Integrated Capability Center. Some of the numerical examples were computed on the computer cluster of the Munich Centre of Advanced Computing.

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


Diffusion of Electric Vehicles and Novel Social Infrastructure from the Viewpoint of Systems Innovation Theory This paper describes diffusion of electric vehicles and novel social infrastructure from the viewpoint of systems innovation theory considering both human society aspects and elemental technological aspects. Firstly, fundamentals of the systems innovation theory and the platform theory are mentioned. Secondly, discussion on mobility from the viewpoint of the human-society layer and discussion of electrical vehicles from the viewpoint of the elemental techniques are carried out. Thirdly, based on those, R & D, measures are argued such as establishment of the ubiquitous noncontact feeding and authentication payment system is important. Finally, it is also insisted that after the establishment of this system the super smart grid with temporal and spatial control including demand itself with the low social cost will be expected. In the United States, the Ford Model T emerged about a century ago and marked a start of motorization. In Japan, a rapid motorization occurred after the 1950s and the postmotorization age is approaching. Revisions to Japanese traffic laws, strong traffic safety measures, and the development of driving assistance systems have contributed to the reduction of illegally-parked cars, traffic jams, and in the recent eight year period the halving the number of traffic fatalities [1] . There is a large environmental impact due to automobile usage and there is significant incentive to reduce this impact.. CO 2 is often pointed out as a cause of the global warming trend, and it has been discussed to cut social dependence on fossil fuels. With a view to the modal shift to non-fossil fuel power plant, the diffusion of electric vehicles that can utilize the regenerative electric power is expected to contribute reduction of the effects on the environment; many projects and discussions have addressed these topics, e.g., [2] .. On the other hand, from the viewpoint of human society, in addition to the CO 2 reduction, change in society's sense of values of vehicles as a status symbol has been observed recently. A trend in the urban young adult segment is not to desire vehicles with a decrease in car ownership and a partial modal shift to bicycles. Moreover, considering performance advances in batteries and payment systems as Manuscript received January 7, 2010 . † The author is with the Division of Mathematics, Electronics and Informatics Graduate School of Science and Engineering, Saitama University, Saitama-shi, 338-8570 Japan.. a) E-mail: takaaki@hslab.ees.saitama-u.ac.jp DOI: 10.1587/transfun.E93.A.672. elemental technology, we can see the future solution [3] . From the viewpoint of the systems innovation theory, considering the shift from car traffic to an electric vehicle society, this paper describes research and development in technology and measures that are desired to be taken to provide a solution; i.e., realization of the "Ubiquitous power feeding and authentication payment environment" by settlement of "Electric vehicles last 10 m's problem" with diffusion of the reasonable authentication payment systems; in addition, this paper also describes that "the super smart grid" issue will be important after the realization of the above mentioned environment. [3] - [9] 2.1 The Three Layer Model from Science and Engineering to Human Society This paper has described diffusion of electric vehicles and novel social infrastructure from the viewpoint of systems innovation theory; in particular, it has been argued the importance to establish the ubiquitous noncontact feeding and authentication payment system, and also has expected the super smart grid.. Firstly, fundamentals of the systems innovation theory including the platform theory have been mentioned. Secondly, based on this theory, consideration of mobility has been carried out from the viewpoint of the human society layer. Thirdly, an argument of electric vehicles has been done from the viewpoint of elemental technology. Fourthly, introduced by the previous discussion, development and measures including business models and employment structure have been discussed, and it has been insisted that the establishment of the ubiquitous noncontact feeding and authentication payment system is important. Finally, it has also been insisted that the super smart grid with temporal and spatial control including demand itself with the low social cost will be expected after the establishment of the ubiquitous noncontact feeding and authentication payment system.. For further research, the author would like to propose a problem formulation and to make a study of appropriate solutions for the various problems discussed in this paper.

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


Cross-Layer Protocol Combining Tree Routing and TDMA Slotting in Wireless Sensor Networks Being different from other networks, the load and direction of data traffic for wireless sensor networks are rather predictable. The relationships between nodes are cooperative rather than competitive. These features allow the design approach of a protocol stack to be able to use the cross-layer interactive way instead of a hierarchical structure. The proposed cross-layer protocol CLWSN optimizes the channel allocation in the MAC layer using the information from the routing tables, reduces the conflicting set, and improves the throughput. Simulations revealed that it outperforms SMAC and MINA in terms of delay and energy consumption. Wireless sensor networks (WSN) are widely used in many areas such as industry, environment, and military fields, but the limited amount of battery energy is the major constraint restricting the range of its applications. This motivates the proposal of many energy-saving strategies based on the hierarchical structure of protocols [1] , [2] . However, the hierarchical structure is a local optimization scheme. Each layer only accomplishes its own functions without taking the new characteristics of WSN into account.. The nodes in WSN usually implement a common task with limited energy, and this is different from traditional wireless networks, in which nodes have their own, separated tasks. The nodes in WSN should access the channel on schedule to avoid contentions for the holistic performance and the energy saving purposes. This means the nodes are cooperative rather than competitive.. Therefore, the protocols need to adopt a contentionfree mechanism such as scheduling and avoid contentions. In addition, the nodes in WSN have few point-to-point communications. Therefore, the direction and load of the data traffic are well-regulated. By adopting a suitable routing protocol with this situation in mind, the network performance is expected to be improved. Some routing protocols with simple structures were proposed such as dynamic tree routing protocols [3] . We propose a cross-layer protocol and architecture for wireless sensor networks in this paper called CLWSN, which is based on the above characteristics. CLWSN integrates the dynamic tree routing protocols with the TDMA MAC protocol such as those found in [4] - [6] , and accomplishes holistic optimization by exchanging information between different layers to improve the global performance. CLWSN proposes an efficient slot allocation scheme using the routing information to reduce the number of nodes in the conflicting set to increase the throughput. In addition, it can avoid the disadvantage of a large delay in the original TDMA by rearranging the order of the slots. CLWSN's structure is simple, energy-saving, and efficient. Scheduling and duty cycle mechanisms have been used in sensor networks to improve energy efficiency, but they also introduce a significant increase in the delivery latency. We proposed CLWSN as a TDMA-based distributed scheme to avoid collisions in MAC layer. In each time slot, CLWSN selects only one transmitter per conflicting set, which is defined as U(i) using the routing information. Therefore, all the nodes in the one-hop neighborhood of the transmitter are deemed to receive collision-free data. We also designed an algorithm that is capable of multi-hop data delivery in a single frame to accelerate the transmission. CLWSN rearranges the slot assignment using the routing information to allow more nodes in a path to set up a multihop schedule for subsequent forwarding of a packet in one frame. Therefore, each node along the forwarding path then wakes up at the correct time to receive and forward the data packet. Our theoretical analysis and simulation evaluation showed CLWSN's advantages in reducing delivery latency and avoiding contention. Moreover, CLWSN saves energy, and improves the delivery ratio and throughput as well. Our future work is to develop the protocol which is applicable for a more realistic propagation model and to do the experiment on the hardware platform. The cross-layer design for wireless sensor networks breaks the stack of the hierarchical structure of original protocols to achieve a better Quality of Service (QoS) for different applications. In recent years, various approaches on the crosslayer protocols have been proposed [7] .. LESOP [8] is a cross-layer design for better efficiency. In LESOP, direct interactions between the application and MAC layers are exploited. The transport and network layers are excluded to simplify the protocol stack and to control the tradeoff between the inspecting error and the energy consumption. Akyildiz et al. [9] developed a unified cross-layer protocol that melts the traditional layers, such as the transport, routing, medium access, and physical layers, into a single layer protocol. In [10] , Cui et al. proposed an iterative algorithm that performs adaptive link scheduling and computes optimal link rates and transmission powers for a fixed link schedule, given that the TDMA-based link schedules are non-orthogonal. Another related protocol is presented in [11] . Collision-free, deterministic, periodic flows are scheduled toward a data sink. This protocol uses cross-layer information to perform more efficient MAC layer transmission scheduling across the network. However, one disadvantage of this approach is that broadcasts cannot be scheduled since explicit ACKs are required to create a schedule, so this method is a poor choice in event driven networks.. MINA [12] is a cross-layer protocol that combines the routing and MAC protocols. The base station (BS) assigns slots for the nodes using a centralized algorithm to reduce Copyright c 2009 The Institute of Electronics, Information and Communication Engineers the length of the frame. Unfortunately, accurate location information is necessary and the centralized algorithm leads to too much communication overhead especially in a largerscaled network.. RMAC [13] exploits the cross-layer routing information to allow its control Pioneer frame to set up a multi-hop schedule for subsequent forwarding of a data frame. Each node along the forwarding path then wakes up at the correctly scheduled time to allow it to receive and forward the data frame. TEPA [14] takes into account the neighbor information from the MAC protocol and the topology information from the routing protocol. It optimizes the channel assignment to speed up the data transfer using centralized Differential Evolution (DE).. We propose CLWSN as a distributed scheme to optimize the channel utilization in the MAC layer using the routing information. Some protocols [12] , [14] believe that it is sufficient to be collision-free if nodes within two-hop or three-hop neighborhood do not transmit at the same time, while CLWSN defines the conflicting set as U(i) using the routing information and reduces the number of nodes in the conflicting set. Moreover, most of the above mentioned protocols use the centralized algorithm, while CLWSN uses a distributed scheme to optimize the channel utilization in the MAC layer using the routing information. The routing tree is generally static. For each time slot, CLWSN selects only one transmitter per conflicting set, and therefore, all the nodes in the set of one-hop neighborhood of the transmitter are deemed to receive collision-free data. The slot assignment in the path of the tree is optimized to accelerate the data transmission.. The rest part of this paper is organized as follows. Section 3 describes the definition of the conflicting set in the protocol. Section 4 describes the protocol details including the self-organization, slot allocation, and slot optimization algorithms. A performance analysis and simulation results are given in Sect. 5, and Sect. 6 concludes the paper.

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


Individualized closed-loop control of propofol anesthesia: A preliminary study This paper proposes an individualized approach to closed-loop control of depth of hypnosis during propofol anesthesia. The novelty of the paper lies in the individualization of the controller at the end of the induction phase of anesthesia, based on a patient model identified from the dose-response relationship during induction of anesthesia. The proposed approach is shown to be superior to administration of propofol based on population-based infusion schemes tailored to individual patients. This approach has the potential to outperform fully adaptive approaches in regards to controller robustness against measurement variability due to surgical stimulation. To streamline controller synthesis, two output filters were introduced (inverting the Hill dose-response model and the linear time-invariant sensor model), which yield a close-to-linear representation of the system dynamics when used with a compartmental patient model. These filters are especially useful during the induction phase of anesthesia in which a nonlinear dose-response relationship complicates the design of an appropriate controller. The proposed approach was evaluated in simulation on pharmacokinetic and pharmacodynamic models of 44 patients identified from real clinical data. A model of the NeuroSense, a hypnotic depth monitor based on wavelet analysis of EEG,was also included. This monitor is similar to the well-known BIS,but has linear time-invariant dynamics and does not introduce a delay. The proposed scheme was compared with a population-based controller, i.e. a controller only utilizing models based on demographic covariates for its tuning. On average, the proposed approach offered 25% improvement in disturbance attenuation, measured as the integrated absolute error following a step disturbance. The corresponding standard deviation from the reference was also decreased by 25%.Results are discussed and possible directions of future work are proposed. The purpose of administering anesthetic drugs during surgical procedures is to prevent unintended intra-operative awareness and to preserve stable suppression of noxious stimulation on the circulatory and hormonal systems, and on occasion to provide muscle relaxation [1] . Accordingly, anesthetic drugs are categorized into hypnotics, analgesics and neuromuscular blocking drugs. The fulfillment of the above-mentioned objectives is complicated by highly patient-specific and uncertain dose-response dynamics [2] , unpredictable disturbances introduced by surgical stimulation [3] and synergetic effects between drugs (e.g. hypnotic-opioid synergy) [4] . Additional constraints are imposed by the fact that some anesthetic drugs have undesirable side effects (e.g. cardiovascular depression, cognitive impairment, nausea, vomiting and respiratory depression). Thus, the drugs must be restrictively administered during surgical procedures [5] .. The hypnosis profile is divided into three temporal phases. During the induction phase of anesthesia, the patient is transferred from a fully awake state to a stable level of hypnosis. The surgical procedure takes place during the maintenance phase of anesthesia. Once the procedure is completed, drug administration is discontinued to yield the emergence phase of anesthesia. During this phase, the patient emerges from the anesthetized state to the fully awake state.. Classically, an anesthesiologist manually controls administration of anesthetic drugs in the operating room. Doses are determined based on measured and/or predicted patient response. The predictions are based on clinical experience complemented by anticipated response to surgical stimulation and synergetic effects between drugs. Expert knowledge and experience play an important role, because the process exhibits a high degree of uncertainty.. A computer application can be used for a priori computation of an adequate hypnotic dose profile. This is exploited in the Target Controlled Infusion (TCI) paradigm [6, 7] . TCI uses pharmacokinetic (PK) and pharmacodynamic (PD) models to regulate the predicted plasma or effect site (brain) drug concentration to a desired level set by the anesthesiologist. Considering that these concentrations are calculated rather than measured, TCI is regarded as an open-loop scheme. Thus, the performance of any TCI system relies heavily on the accuracy of the patient model. Furthermore, it is highly susceptible to disturbances caused by surgical stimulation and hypnotic-opioid synergy. Consequently, the TCI profile needs to be manually adjusted to counteract such disturbances.. An important step toward automated anesthesia drug delivery is to allow a computer application to make adjustments based on appropriate sensor measurements. In this scenario the anesthesiologist provides reference profiles for the measured quantity and the computer administers drugs to track the reference. This paradigm, known as closed-loop control, has been enabled with the introduction of clinical sensors for depth of hypnosis such as the Bispectral Index (BIS) [8] , Entropy monitor [9] and the waveletbased NeuroSense monitor [10] . In this paper a model of the commercially available NeuroSense monitor (NeuroWave Systems, Cleveland Heights, USA) is used. It provides the WAV CNS index, presented in Section 2.3, as a measure of clinical effect. It is shown that the WAV CNS correlates well with the BIS in steady state [10] , and in addition, it boasts improved time-invariant dynamic response. Fig. 1 outlines the components of a closed-loop controlled anesthesia system.. The minimum requirement for any controller is that the closedloop system is robust against measurement noise, disturbances (e.g. surgical stimulation) and model uncertainties. Improving robustness usually results in compromised controller performance and an appropriate trade-off between robustness and control performance is required. This compromise explains the existence of a multitude of control schemes and corresponding tuning procedures that have been evaluated for drug delivery in anesthesia. These schemes have included internal model control (IMC) [11] , modeling error compensation (MEC) [12] , model predictive control (MPC) [13] , neural-fuzzy control [14] , proportional integral derivative control (PID) [15] and robust control [15, 16] . An intensive list of previous work on closed-loop control of anesthesia can be found in a historic review [17] and more recently in [18] as well as in [3] . It was concluded in [19, 20] that closed-loop strategies might outperform manual infusion dosing. In particular, closed-loop administration of propofol is expected to lead to a mean decrease in drug dose, while providing adequately deep anesthesia.. The output (WAV CNS index provided by the NeuroSense monitor) and its corresponding input (dose) history can be used to adapt the control scheme to improve titration of drugs to the need of an individual patient. However, such adaptive approaches can fail if the behavior of the clinical front end is not fully explained by the dose, or if the output does not adequately excite the process to be controlled. In control of anesthesia, unknown surgical stimulations affect the clinical front end. With current technology, it is not possible to separate this effect from that of the drug. Hence, the clinical front end measurement is not fully explained by the dose during intubation or after incision, thereby posing a challenge for any adaptive scheme. This challenge is exacerbated by the fact that measurement noise is of comparable magnitude to output variability during the maintenance phase of anesthesia [3] .. This paper proposes an individualized approach to closed-loop control of depth of hypnosis during propofol anesthesia. Its novelty lies in the individualization of the controller at the end of the induction phase of anesthesia, based on a patient model identified from dose-response relationship during induction of anesthesia. The proposed approach is superior to population-based drug administration in titrating drug to the need of each individual patient. This novel approach also has potential to outperform fully adaptive approaches in regards to controller robustness against measurement variability due to surgical stimulation. An overview of the proposed approach is given in Fig. 2 .. To streamline controller synthesis, two output filters are introduced, which yield close-to-linear representation of the system dynamics when used with a compartmental patient model (the Hill dose-response model and the linear time-invariant sensor model). This synthesis is useful during the induction phase of anesthesia in which nonlinear dose-response relationship complicates the design of an appropriate controller. This paper is organized as follows: Section 2 describes the model of hypnosis used in this paper. Section 3 elaborates on the control design procedure employed once a plant model is given, whereas the system identification procedure to obtain the plant model is discussed in Section 4. Sections 5 and 6 describe the simulation setup and performance evaluation measures. Section 7 presents and discusses the results and Section 8 outlines the limitations of the study. Section 9 provides the conclusions. A robust individualized approach was proposed for closed-loop depth of hypnosis control with propofol. This novel approach can adapt the controller to individual patients to achieve desired control performance even in the presence of large inter-individual variability in hypnotic response to propofol. A comprehensive simulation-based study was conducted to assess the performance of the proposed approach with respect to the existing populationbased control. The individualized approach outperformed its population-based counterpart with improvement in a variety of performance measures with statistical significance.

O O O O 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 O O O O B 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 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 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 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 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 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 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 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 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 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 B 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 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 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


Packet Video Error Concealment With Gaussian Mixture Models Abstract-In this paper, Gaussian mixture modeling is applied to error concealment for block-based packet video. A Gaussian mixture model for video data is obtained offline and is thereafter utilized online in order to restore lost blocks from spatial and temporal surrounding information. We propose estimators on closed form for missing data in the case of varying available neighboring contexts. Our error concealment strategy increases peak signal-tonoise ratio compared to previously proposed schemes. Examples of improved subjective visual quality by means of the proposed method are also supplied.Index Terms-Error concealment, Gaussian mixture model (GMM), packet video, video modeling. We present a GMM-based method for solving the packet video error concealment problem. An estimator on closed form, that can be modified depending on the available neighborhood, is derived. The only introduced modeling assumptions are the order of the GMM, and the validity of repeated estimation in case of missing temporal information surrounding the loss.. GMM increases performance in PSNR compared to previously proposed methods for spatiotemporal error concealment. The results are valid for a wide range of stationary loss probabilities. It is verified that augmenting the number of mixture components increases performance compared to the usage of only one Gaussian, and also that a spatiotemporal context is beneficial for GMM-based estimation. Examples of improved subjective visual quality by means of the proposed method are also supplied.. A further increase in performance is expected if more neighboring data of the lost blocks would be incorporated into the model. The stochastic theory is general in the sense that data that are represented in different ways, for example in the pixel and transform domains, may be combined for error concealment without special arrangements. To what extent the two last claims may contribute to improvement of the method remains to be experimentally investigated.. Whereas the GMM is a well-accepted scheme that can describe densities asymptotically, it is possible that there exist other mixtures that work better for small numbers of mixture components, and give a better trade-off between performance and computational complexity. This issue is currently under investigation. He was appointed Professor of information theory with data communications at Chalmers University of Technology in 1988. His research interests cover several branches of information theory, signal processing, and related subjects. Four basic fields can be distinguished in his work, namely source and channel coding, estimation and optimal filtering, adaptive signal processing and, finally, modeling and speech processing. Speech coding is also often the subject of study. He has been working with a number of different schemes for speech compression such as sinusoidal coding, glottal-pulse coding, and CELP. He has also been active in language processing. The experiments are divided into four groups. First, the offline GMM parameter estimation is investigated. Then spatial, temporal, and spatiotemporal error concealment by means of GMM are compared. Further, the measures in case of missing modeled context discussed in Section II-C are addressed. Finally, we compare our scheme to previous state-of-the-art error concealment methods.. • GMM parameter estimation. In this experiment, offline GMM parameter estimation by means of the EM algorithm is considered. Models are obtained for in Fig. 2 . The MV is lost, and estimated by the median of the MVs of the neighboring blocks. For GMM training, 1 470 000 realizations of in Fig. 2 are drawn from the training set in a uniformly random manner and in such a way that no two vectors coincide. For the evaluation, 480 000 realizations of are drawn from the evaluation set in the same way. The log-likelihood for the realizations of in the evaluation set is shown in Fig. 5 for models with different numbers of mixture components . As we can see, the log-likelihood increases as a function of the number of mixture components. In Fig. 6 , the PSNR for the estimation of from according to (18) is shown for models with different numbers of mixture components . Confidence intervals have been calculated, assuming that the square Euclidean norm of the difference between and its estimate is distributed according to a normal distribution. The 0.95-confidence intervals are marked by dashed lines in Fig. 6 . By augmenting from 1 to 64, we increase PSNR by 2.6 dB while the computational complexity for the estimation increases linearly. Copying motion-compensated past information gives a PSNR of 29.4 dB if the MV is estimated by the median of the MVs of the surrounding blocks. We conclude that augmenting the number of mixture components in the GMM-based estimator is beneficial when there is access to spatial and temporal information. By comparing Figs. 5 and 6, we see that increasing the log-likelihood does not necessarily yield a corresponding increase in PSNR. In the case when the MV is correctly received, the PSNR values increase, but the conclusions remain the same.. • Spatial, temporal, and spatiotemporal error concealment by means of GMM. Fig. 7 shows estimation of from different modeled contexts in the case when the MV is estimated by the median of the MVs of the neighboring blocks. The PSNR given by an estimator with is shown in the figure. By comparing and , we see that temporal data are valuable for the creation of an estimate of the lost part. From a comparison of and , it is noticed that spatial data are also important. The PSNR in is almost as low as the PSNR obtained by copying motion-compensated previous pixels. This means that GMM does not improve performance compared to trivial error concealment if it only has access to temporal information. Through comparison of Figs. 6 and 7, we observe that a GMM with and access to both spatial and temporal context performs almost 3 dB better than a GMM with and access to temporal context only. We conclude that a combination of spatial and temporal information is beneficial for GMM-based estimation of the lost pixels. In the case when the MV is correctly received, the PSNR values increase, but the conclusions about the behavior of the GMM-based estimator remain the same.. • Measures in case of missing modeled context. In the case of temporally adjacent lost blocks, we utilize repeated estimation from previously corrected information. This strategy is applied by many others, e.g., in [12] and [13] . For spatially adjacent lost blocks, a comparison between marginalization according to (20) and repeated estimation according to (25) for different loss rates is presented in Fig. 8 . Each row of 16 16-blocks is separated into two packets according to Fig. 3 . A few tens of randomly chosen consecutive frames from each of the evaluation movies are coded. Packet errors are distributed in an independently random manner. The MV is estimated by the median of the MVs of the neighboring blocks. In the case when the MV is correctly received, the PSNR values increase, but the conclusions about the behavior of the GMM-based estimator remain the same. Since the performances of marginalization and repeated estimation are almost the same, marginalization should be chosen because it has lower computational complexity. If some spatially neighboring pixels are missing and previously estimated, the corresponding variables are marginalized according to (20) in the following experiments. Also in the following, in case of temporally adjacent lost blocks, we utilize repeated estimation from previously corrected pixels according to (25).. • Comparison to previous state-of-the-art error concealment schemes. Table I presents

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


Forecasting accuracy of behavioural models for participation in the arts In this paper, we assess the forecasting performance of count data models applied to arts attendance. We estimate participation models for two artistic activities that differ in their degree of popularity -museum and jazz concerts-with data derived from the 2002 release of the Survey of Public Participation in the Arts for the United States. We estimate a finite mixture model -a zero-inflated negative binomial model -that allows us to distinguish "true" non-attendants and "goers" and their respective behaviour regarding participation in the arts. We evaluate the predictive (in-sample) and forecasting (out-of-sample) accuracy of the estimated models using bootstrapping techniques to compute the Brier score. Overall, the results indicate good properties of the model in terms of forecasting. Finally, we derive some policy implications from the forecasting capacity of the models, which allows for identification of target populations. Cultural economics has contributed to our knowledge on participation in the arts by proposing and estimating economic models to explain the determinants of demand for cultural goods and services. Art managers have focused their interest on knowledge of their participants to design and implement effective marketing strategies for different artistic goods. In this paper, we try to relate both types of contributions by estimating a participation model and assessing its properties in terms of forecasting of cultural participation in jazz concerts and museum visits.. Participation in the arts, together with the consumption of cultural goods, corresponds to the last stage of the cultural process, as defined by UNESCO (2009) . It includes the activities of audiences and participants in consuming cultural products and taking part in cultural activities and experiences. Traditionally, participation in the arts has been divided into three categories depending on the way in which it takes place: attendance, active practice and the consumption of cultural content through the media.. The research interest of the field of cultural participation has gone through several stages, with each providing different types of knowledge on audience composition and motivation, which has added to previous contributions.. First, general descriptions of the socio-economic characteristics of the audiences with respect to non-audiences were explored. As noted in Seaman (2005) and McCarthy et al. (2001) , the initial interest was set on determining who was participating in the arts, and initial studies thus provided a description of which social groups participate more in relative terms, shedding light on the composition of audiences. That set of initial studies (participation studies; Seaman, 2005) confirmed some common traits of cultural audiences: audiences are more educated and enjoy higher income, there is evidence of some feminisation in the arts audiences, and attendance is a mostly urban phenomenon.. Those studies also reported that no particularities were found for different countries.. In a second step, a different set of studies (econometric studies, such as those reported in the survey by Seaman, 2005) began to incorporate individual decisionmaking models to understand why people participate in the arts and why differences arise. This type of study tries to estimate demand functions when price and income information is available (see, e.g. Prieto-Rodriguez et al. 2005) . Own-price elasticity, income (full-income) elasticity and the degree of complementarity-substitutability were researched. When modelling and estimating the demand for cultural goods, economists consider that factors others than prices and income determine the choice set of the cultural consumer and, subsequently, consumer demand. Additionally, the determinants of underlying tastes and its possible evolution are taken into account by some of those models. Notably, the presence of a certain stock of personal capital in terms of the ability to interpret and enjoy the symbolic characteristics of goods is considered. In this spirit, early exposure to the arts and artistic training are introduced in those individual decision models.. When prices and/or personal income are not available, participation equations are estimated to determine how personal constraints -in the form of personal capital / education, income, household burdens and so on -shape the observed choice of attendance. Participation equations, with the first equations in the form of probit/logit regression models, quantify the effect of marginal changes in the explanatory variables on the probability of being an attendee over a determined period of time (Gray 2003) .. The intensity of participation has sometimes been modelled by means of ordered probit/logit models (Borgonovi 2004) . Unobserved heterogeneity that may induce different behavioural patterns in the observed choice of the population has been addressed by latent class models (Ateca-Amestoy 2008; Fernandez-Blanco et al. 2009 ).. The testable hypotheses derived from the economic approach to cultural participation have thus been tested by estimating those types of econometric models using a wide variety of information on the cultural habits of the general population. Behavioural models not only assess the correlates of participation but also explain the determinants of those observed choices based on individual decision-making models.. However, in cultural economics, the forecasting properties of those behavioural estimated participation models have rarely been assessed. For instance, little attention has been devoted to the appropriateness of the models to describe what happens outside the sample used in the estimation: do people not included in the survey really behave as the estimated models establish? Moreover, the accuracy of the models is not often even assessed for those in the sample; researchers were more concerned with determining the relevant characteristics of participants rather than fully predicting their behaviours with regard to cultural participation. This can be thought of as an additional step of a study programme that has already systematically analysed the behaviour, as a model is needed to contrast it against reality in terms of its forecasting power, that is, its capacity to predict behaviour for those individuals not included in the sample used to estimate the model.. The achievement of this further step is interesting not only for researchers in cultural economics but also for cultural managers who attempt to better understand the characteristics of their audiences and the general population. We believe that a deeper knowledge may contribute to improving the targeting of audiences and lead to the more efficient programming and promotion of cultural activities.. The forecasting of future attendance in the area of cultural goods and services has been performed using different methods in the field of cultural management. One method corresponds to a consumer-oriented approach (Andreasen and Belk 1980; National Endowment for the Arts 1981; Holbrook and Schindler 1994) . This approach is based on the correlates of attendance, including attitudinal values, determinants of lifestyles and early exposure. However, because this approach does not always deal properly with endogeneity problems and causation, the usefulness of the findings for policy making cannot be addressed. A second approach focuses on the characteristics of the cultural event to forecast its audience. Some studies have taken a "manipulative approach to check the declare effect on future participation of a change in the attributes of the event" (National Endowment for the Arts 1981). Potential sales equations can be estimated, and the results are compared with expert forecasts (Putler and Lele 2003) .. Expert forecasts are part of the "managerial approach". Based on combinations of different techniques, such as the Delphi approach or forecasts based on the expertise of the managers, the potential audience of a particular event is estimated. This is one of the methods explored in the ARTSplan program (Weinberg 1986; Weinberg and Shachmut 1978) . Finally, Jones et al. (2007) used goal programming models to identify whether an individual ever goes to a movie theatre or does not using UK data.. In this paper, we want to explore the possibility of using behavioural models to gain further knowledge of consumers of art and to assess the predictive and forecasting performance of behavioural participation models applied to arts attendance. If behavioural models perform well in terms of forecasting, they will be useful for predicting potential and future attendance. To verify the robustness of our findings, we have decided to analyse two different cultural activities: attendance at jazz concerts and visiting art museums and art galleries. There are obvious differences between these activities, as one is a performing arts activity and the other one is related to the appreciation of cultural heritage. The dependent variable is defined as the number of times that a particular individual attends a museum or a live jazz performance.. Given this information, we estimate finite mixture models that allow us to distinguish "true" non-attendants and "goers" (even if they may show a zero corner behaviour). In doing so, we use data derived from the 2002 release of the Survey of Public Participation in the Arts (SPPA) for the United States. Furthermore, we evaluate the predictive (in-sample) and forecasting (out-of-sample) accuracy of the estimated models using bootstrapping techniques and computing Brier scores.. The paper is organised as follows. Section 2 discusses the data and the econometric issues in estimating cultural participation using finite mixture models.. Section 3 discusses estimation results and includes a brief interpretation of the findings.. The analysis of the forecasting power of the model using bootstrapping techniques to compute the Brier score is discussed in Section 4. Conclusions are discussed in Section 5. In this paper, we assessed the forecasting properties of the latent class count regression models for arts participation. The assessment of how well those behavioural models perform adds to the economic literature of cultural participation, and, further, this finding is also useful for decision makers and arts managers involved in marketing decisions.. After estimation, the in-sample and out-of-sample accuracies of the models were evaluated. Specifically, we verified the out-of-sample forecasting accuracy using bootstrapping techniques. In each trial, we estimated the jazz and museum attendance models by randomly sampling 25% of the original sample. We subsequently calculated the Brier scores for the other 75% of the sample. The results demonstrated that the predictions work well out-of-sample, as evidenced by the fact that out-of-sample Brier scores lie usually within the confidence intervals of the in-sample Brier scores in almost all cases. Therefore, we can rely on the forecasting accuracy of the estimated models and used them to extrapolate the behaviour of in-sample individuals to individuals not surveyed. This can be considered as a necessary condition for using the information given by econometric models as a basis of cultural policy.. Additionally, when comparing different activities, we have found that estimated models can help us to a larger extent to enhance our knowledge about the expected behaviour for those activities with a larger variability among the population, which in our case are visits to art museums and galleries. Obviously, additional information is especially valuable in these cases, as a larger variance makes it more difficult to establish any audience policy. Moreover, within activities, the estimated models imply a better knowledge that is larger for non-attendants and moderate attendees. These two groups are especially relevant, as they are the broadest categories and thus should be considered to be the most important targets of any cultural policy.. We have thus demonstrated that behavioural models are valid instruments to forecast cultural attendance. They allow improvements in the quality of the information available for scholars, policy makers and arts managers, which may contribute to improving the targeting of audiences and lead to more the efficient programming and promotion of cultural activities.

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


A New Approach to High-accuracy Road Orthophoto Mapping Based on Wavelet Transform Existing orthophoto map based on satellite photography and aerial photography is not precise enough for road marking. This paper proposes a new approach to high-accuracy orthophoto mapping. The approach uses inverse perspective transformation to process the image information and generates the orthophoto fragment. The offline interpolation algorithm is used to process the location information. It processes the dead reckoning and the EKF location information, and uses the result to transform the fragments to the global coordinate system. At last it uses wavelet transform to divides the image to two frequency bands and uses weighted median algorithm to deal with them separately. The result of experiment shows that the map produced with this method has high accuracy. Nowadays orthophoto map plays an important role in navigation, exploration and city planning. Meanwhile orthophoto map of urban environment is becoming a new hot demand. In urban environment, the environment is more complex and more informative. The road environment is the core of urban environment for its complexity, in which there are variety of static items and dynamic items, including road lanes, road signs, sidewalk, pedestrian and vehicles. The static items are important for vehicles driving, navigation and driving safety [1] [2] .. Orthophoto map produced by satellite and aerial photography such as google map cannot get highresolution image information of the road, which make it impossible to extract and identify the road signs. Therefore the image map data vendors now use artificial way for road marking. It decreases the efficiency of map refresh.. In this paper, the authors use road-vehicle system to produce the road orthophoto map. Compared with ordinary orthophoto map, it has obvious advantage in image accuracy.. International Journal of Computational Intelligence Systems, Vol. 4, No. 6 (December, 2011), 1367-1374 Received 10 July 2011; accepted 25 November 2011

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 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 B I 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 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 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 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