Determination of Axonal and Dendritic Orientation Distributions Within the Developing Cerebral Cortex by Diffusion Tensor Imaging Abstract-As neurons of the developing brain form functional circuits, they undergo morphological differentiation. In immature cerebral cortex, radially-oriented cellular processes of undifferentiated neurons impede water diffusion parallel, but not perpendicular, to the pial surface, as measured via diffusion-weighted magnetic resonance imaging, and give rise to water diffusion anisotropy. As the cerebral cortex matures, the loss of water diffusion anisotropy accompanies cellular morphological differentiation. A quantitative relationship is proposed here to relate water diffusion anisotropy measurements directly to characteristics of neuronal morphology. This expression incorporates the effects of local diffusion anisotropy within cellular processes, as well as the effects of anisotropy in the orientations of cellular processes. To obtain experimental support for the proposed relationship, tissue from 13 and 31 day-old ferrets was stained using the rapid Golgi technique, and the 3-D orientation distribution of neuronal proceses was characterized using confocal microscopic examination of reflected visible light images. Coregistration of the MRI and Golgi data enables a quantitative evaluation of the proposed theory, and excellent agreement with the theoretical results, as well as agreement with previously published values for locally-induced water diffusion anisotropy and volume fraction of the neuropil, is observed.Index Terms-Brain modeling, diffusion tensor imaging (DTI), inverse problems, optical microscopy. P ROPER morphological development of neurons is essential for the formation of functional neural circuits [1] , [2] . In the cerebral cortex, pyramidal neurons undergo morphological differentiation after migrating from germinal zones near the lateral ventricles to the cortical plate [3] . Immediately following migration, cell bodies of these neurons are elongated, and their dominant structural feature is a radially-oriented apical dendrite. Subsequently, collaterals branch from the primary apical dendrites, basal dendrites grow from cell bodies at varying orientations relative to the radially-oriented primary apical dendrite, and axons invade the cortex from the subplate. In several experimental models of neurodevelopmental disorders, including examples caused by environmental (e.g., fetal alcohol spectrum disorder [4] , [5] ) or genetic (e.g., Rett syndrome [6] , [7] ) factors, the axonal/dendritic arbor complexity is reduced in affected individuals compared to age-matched controls. A noninvasive method to characterize cellular morphology in the developing cerebral cortex could therefore be of value in characterizing neurodevelopmental disorders in humans, and potentially offer a strategy for detecting disease in affected individuals and/or for assessing disease severity.. Magnetic-resonance-based techniques for measuring directional dependence in translational diffusion of water, i.e., diffusion anisotropy [8] - [10] , have proven valuable for characterizing the cellular-level microstructure of brain white matter (WM) [11] , [12] . In WM of mature individuals, diffusion anisotropy results from the presence of densely packed, coherently oriented axons and myelin sheaths [13] . This is because water displacements due to diffusion are more restricted in directions perpendicular to an axon tract than in directions parallel to the tract. Due to this relationship, diffusion tensor imaging (DTI) measurements provide the basis for several investigations of microstructural changes associated with development and aging [14] , [15] , and with various neuropathological [16] , [17] and neuropsychiatric [18] , [19] disorders.. The strategy of utilizing water diffusion anisotropy can also be extended to characterization of the cerebral cortex. Although water diffusion within mature cortical gray matter is only very slightly anisotropic [20] , [21] , at early stages of morphological development, cortical diffusion anisotropy is comparable in magnitude to that within myelinated WM fiber tracts [22] - [25] . The directional dependence of diffusion in the immature cortex corresponds to the characteristic radial pattern of the undifferentiated neuropil [22] - [26] . Diffusion is relatively unhindered 0278-0062/$26.00 © 2011 IEEE in the direction perpendicular to the pial surface (and thus parallel to elongated cell bodies and apical dendrites), as opposed to diffusion in the parallel direction where membranes of cellular processes impede molecular displacement [24] . In systematic studies of prematurely-delivered human infants [24] , [27] , postmortem human fetal brains [28] , [29] , and in several animal model systems [30] - [37] , temporal aspects of the transition from high to low cortical diffusion anisotropy have been characterized [38] . This comparative approach has consistently demonstrated that loss in cortical diffusion anisotropy temporally coincides with axonal and dendritic morphological development. Further, a comparison between normally-reared and neonatally enucleated ferrets has shown that cerebral cortical areas with visual-deprivation-induced reductions in axonal/dendritic arbor complexity exhibit elevated anisotropy in water diffusion [39] . These empirical findings suggest that DTI is a potentially sensitive strategy to characterize the developing cerebral cortical neuropil; however, a quantitative understanding of this relationship is lacking. In studies of brain WM, much progress has been made in characterizing heterogeneous distributions of axon orientations by DTI [40] - [47] . Specifically, characterization of multimodal distributions of axonal orientations within individual voxels shows great potential for analyzing diffusion MRI data within areas in which WM fiber pathways intersect [40] - [48] . Within the developing cerebral cortex however, the orientation distribution of axonal and dendritic structures is different. Neighboring axonal and dendritic processes are generally much less aligned in cortical gray matter than axon segments are in WM. In addition, the overall orientation distribution of axonal and dendritic elements within the cerebral cortex is expected to be clustered around a primary (radial) direction, which is in contrast to the multimodal distribution found within regions of crossing WM fibers [49] . Thus, distinct approaches will need to be developed to analyze diffusion MRI data in the cerebral cortex [50] - [52] beyond those used to study WM.. Herein, we propose a theoretical relation between the diffusion tensor and the distribution of structural elements within the developing cerebral cortical neuropil. We have previously derived an expression for the diffusion-attenuated MR signal intensity produced by water diffusing within impermeable cylinders of arbitrary orientational distribution [51] . Here, this expression is used to obtain an analytical relationship between anisotropy in the water diffusion tensor, and anisotropy in the distribution of axonal and dendritic orientations within the cerebral cortical neuropil. This relationship expresses quantitatively how diffusion tensor structure is induced in part by the intrinsic diffusion anisotropy within neuronal processes, and in part by the anisotropy of the orientation distribution of these processes. In order to experimentally evaluate the proposed relation, we compare diffusion tensor measurements to quantitatively analyzed histological preparations. Ideally, DTI and histological comparisons would test the proposed theory using tissue that exhibits a wide range of morphological characteristics. In a recent study of diffusion anisotropy changes in the normally developing ferret cerebral cortex [34] , systematic laminar and regional variability in cortical diffusion anisotropy was found to be maximal approximately two weeks after birth. This variability arises from laminar and regional gradients in neuronal birthdates, and is expected to give rise to corresponding variability in anisotropy of the cerebral cortical axonal/dendritic process orientation distributions. Here, 3-D confocal analyses were performed on Golgi-stained brain tissue derived from postnatal day 13 (P13) and P31 ferrets, and the distribution in the anisotropy of axonal and dendritic element orientations was confirmed to be broader at P13 than at P31. Therefore, the P13 cerebral cortical tissue was characterized in multiple histological sections, and image registration procedures were applied to directly compare diffusion anisotropy measurements performed on the post mortem material immediately prior to Golgi staining and analysis. An experimental framework based on confocal microscopy for quantitative comparisons of histology to MRI was described, and used to evaluate a novel relation between the MR diffusion tensor and axonal/dendritic architecture. This relation was a mathematical expression of how microstructural anisotropy in gray matter shapes the diffusion tensor. The proposed microstructural underpinnings of the diffusion tensor were experimentally validated on a fixed ferret brain by confocal microsocopy using reflected visible light of Golgi-stained tissue following diffusion tensor imaging. Quantitative comparisons following coregistration of the Golgi and DTI data support the proposed theoretical relationship between the water diffusion tensor and the orientation tensor of neuronal processes. These results provide a framework for interpreting DTI measurements of the cerebral cortex in terms of cellular morphological properties that can be influenced by environmental experience, or perturbed in neurodevelopmental disorders. In this work we have investigated the structural origins of diffusion anisotropy in the immature ferret cerebral cortex by comparing DTI measurements to quantitative analyses of Golgistained tissue. The early postnatal ferret brain is suitable for this comparison because it exhibits a high degree of similarity to fetal human cerebral cortex, including the development of sulcal and gyral structures at a developmental stage that is temporally coincident with the loss of cortical diffusion anisotropy. Additionally, the trajectory of DTI changes with development has been extensively characterized in this species [31] , [34] . We derived a direct mathematical relation between the diffusion tensor and the axonal and dendritic architecture in the neuropil, expressing quantitatively how diffusion anisotropy is induced by intrinsic diffusion anisotropy within axons and dendrites and anisotropy in their orientation distribution. A methodological framework for quantitative characterization of histologicallyprepared tissue was described, and applied to tissue from a P13 and a P31 ferret. In accordance with predictions based on previous studies of cortical diffusion anisotropy, a larger amount of variance in was observed at P13 than at P31. Therefore, to assess the veracity of the proposed theoretical relationship in (9) , scatter matrices were measured throughout the P13 cerebral cortex, and these were demonstrated to be significantly correlated to diffusion tensor measurements performed on the same brain as predicted by (9) .. To experimentally determine cortical orientation distributions of neuronal processes, it was necessary to choose a staining technique that enables visualization of dendritic and axonal structures. An ideal technique for providing comparisons to cortical DTI measurements stains cortical cells in an unbiased manner, provides data from several cells within each MRI voxel, and will stain cells in a manner that will enable individual axonal and dendritic processes to be resolved. The Golgi technique is one of very few methods that meet these criteria. By staining a small, random subset ( 1%) of cells in a complete manner [71] , the Golgi technique enables an overall representation of cellular architecture to be characterized, but the staining is not so dense that it is impossible to resolve neighboring fibers. For these reasons, the Golgi method has been in use for over a century as a general method for characterizing neuronal morphology (e.g., see [72] and references cited therein), and has previously been used to document dendritic development in pyramidal neurons of ferret cerebral cortex [73] . For these reasons, the Golgi technique was selected here for comparisons to DTI measurements. However, it is also noted that the procedures described here can be extended to other methods for visualization of cellular processes in the future.. There was a strong mutual alignment between the directions of the principal eigenvectors of the scatter and DTI matrices, in agreement with theory. The theoretical relationship was further supported by comparing centralized eigenvalues of the neurite orientation and water diffusion tensors to one another, as well as measures of fractional anisotropy. The straight line which best fit the pairs of centralized eigenvalues had a slope corresponding to of 0.53 , according to (10) and (12) . Typical values of were previously reported in measurements of water diffusion within post mortem baboon cerebral cortex [52] resulting in an estimate of neurite density on the order of -0.8, consistent with literature values of the neuropil volume fraction of 0.7 (rat, [74] ) and 0.8 (rhesus macaque, [75] ). Thus the observed slope estimated using (10) to the data is in excellent agreement with previous measurements by us and others.. Several factors potentially contribute to the variance in the Fig. 12 plots. Variations in neurite volume fraction or intrinsic diffusion anisotropy among the different Golgi fields were not taken into account, which likely explains some of the scatter in the data points around the straight lines in Fig. 12 . Additionally, slight misregistration of the Golgi and DTI reference frames is also expected to contribute to scatter in the Fig. 12 plots. Specifically, histological preparation procedures introduce nonlinear deformations of the tissue that are not fully accounted for by the linear registration approach described in Section III-D. However, efforts were made to minimize these effects, such as manual in-plane adjustments to match each Golgi ROI to a specific DTI voxel. Although nonlinear methods could in principle improve the registration procedures, we found the adopted approach to provide considerable accuracy (the mean distance between DTI-frame landmarks and the corresponding planes in Fig. 4 (a) was found to be 0.20 mm). Due to the lack of similarity in image contrast patterns between the Golgi and DTI data, nonlinear registration strategies were not pursued here. Last, although the volumes of the Golgi regions were nearly matched to the volume of a single DTI voxel, the shapes of the Golgi regions differed from DTI voxels (250--sided cubes) due to constraints of the Golgi imaging technique. This distinction could lead to differences in the manner in which the two methods sample cerebral cortical neuronal morphology. Despite these potential complications, a highly statistically significant correlation between DTI derived parameters and neurite orientation matrix was observed, in agreement with the proposed theory.. In addition to factors expected to contribute to variance in Fig. 12 , systematic effects related to simplifying assumptions of the (1) model may also influence the relationship between the measured diffusion tensor and the orientation distribution in neuronal processes. Several of these factors have been discussed in previous studies [39] , [50] , [51] . For example, only neuronal processes were accounted for in the histological measurements, whereas vasculature, glial processes and anisotropy of the extracellular space could, in principle, contribute to diffusion anisotropy. It should be noted, however, that the volume fraction of capillaries and glial cells are each estimated to be less than 5% [74] , and the contribution of these components to diffusion anisotropy is thus expected to be minor. In addition, since intra-and extracellular spaces are complementary to one another, the anisotropy of the extracellular space will very likely mimic the variation in the neuritic anisotropy, and the net effect may thus amount to a rescaling of the proportionality constant in (9) . In the future, experiments with other histological or immunohistochemical stains will be of value to specifically determine the extent that e.g., glial processes contribute to the observed measurements, and to separate the axonal and dendritic contributions.. Recent investigations have shown that diffusion MRI is sufficiently sensitive to detect differences between cortical areas within an individual [50] and between cerebral cortices of different treatment groups, such as visually-deprived and control animal subjects within visual cortex [39] . Despite the obstacles encountered in characterizing the link between MRI measurements on intact tissue and measurements performed on the same tissue following histological processing, the work presented here demonstrates it is possible to interpret directionally-dependent diffusion MRI measurements in terms of the 3-D orientation distribution function of cellular processes in the developing neuropil. This capability is particularly significant in the contexts of neurodevelopmental disorders, in which affected individuals exhibit simplified dendritic arbors within the developing brain [4] - [7] , as well as for studies of the relationship between environmental factors and neuronal morphology, such as the effect of stress on hippocampal pyramidal dendrite structure [76] . Therefore, it is anticipated that measurements of diffusion anisotropy within the cerebral cortex will be of increasing value for extending the diagnostic capabilities of MRI in studies of neuropsychiatric disorders in the future. It has previously been shown in ferrets that reductions in cerebral cortical diffusion anisotropy associated with brain development take place primarily between the first and fourth weeks of life [34] . It was therefore expected that anisotropy in scatter matrices in the cerebral cortex from a P31 animal would be lower, on average, than anisotropy observed within cerebral cortex of a P13 animal. However, the reduction in cortical diffusion anisotropy takes place according to an inside-out laminar gradient, such that deep cortical layers exhibit lower diffusion anisotropy than superficial layers; and a rostral-caudal regional gradient, such that rostral cortical regions exhibit lower diffusion anisotropy than caudal regions. Due to the presence of these gradients, it was also expected that more variability in anisotropy of scatter matrices would be observed in the P13 brain than in the P31 brain. To experimentally test these predictions, the 32 sites (containing a total of 128 sub-ROIs) within five axial sections of the P13 brain were compared to a set of 14 sites (56 sub-ROIs) characterized within a single axial section of the P31 brain. Mean and standard deviations of the distributions of values were 0.46 0.15 and 0.34 0.12 for the P13 and P31 sections, respectively, which confirms the expectation that is higher and more variable at P13 than at P31. Subsequent analysis was therefore focused on the P13 brain, to determine whether variability in the values is reflected in variability of cerebral cortical diffusion anisotropy, as predicted by (12) .. To provide a visual comparison of Golgi and DTI data, and to evaluate the hypothesis that neurite orientation anisotropy is a major determinant of diffusion anisotropy, a model independent comparison of anisotropy in diffusion and axon/dendrite orientation distributions was made. An intuitive approach is based on comparing the behavior of the diffusion signal and the neurite orientation density as functions on the unit sphere. We use spherical interpolation such that both may be evaluated at any point on the sphere. This can be done e.g., on the basis of an expansion in spherical harmonics , As described for example in [50] , [51] , [69] , any sufficiently smooth function on the sphere can be represented as a Laplace series (19) with coefficients determined by (20) where the asterisk denotes complex conjugation. When used to represent the axon/dendrite segment orientation distribution , we see from the equation above that the coefficients are the average value of the corresponding complex conjugated spherical harmonic. This average is estimated empirically by using the observed neurite directions (21) where is the number of neurites and is a unit vector in the direction of the th neurite. Similarly, coefficients are used to represent the normalized diffusion-weighted MRI signal intensity and were estimated by the linear least squares solution of (22) see e.g., [70] , where here is the th diffusion weighting direction. In our implementation, we keep terms up to and including . Data from four pairs of neuronal process orientation distributions and diffusion tensors are shown in detail in Fig. 9 . For fields labeled I-IV in Fig. 4(b) , transmitted light images are shown in the left column of Fig. 9 . The set of line segments used to estimate the scatter matrix for cellular processes within one quadrant for each of the four fields is displayed as 3-D surface models in the adjacent column of Fig. 9 . The right two columns of Fig. 9 show Schmidt plots, an equal area stereographic projection [57] method, of the neuronal process orientation distribution and diffusion MRI data. Each Schmidt plot is shown in the Golgi reference frame (e.g., the azimuthal angle for each Schmidt plot corresponds to the in-plane direction in the Golgi images). The orientation distribution plots reflect the probability that a neuronal process is oriented according to polar and azimuthal angles shown, whereas the diffusion MRI plots (Fig. 9, Fig. 9 . Model independent comparison of the angular dependencies of the neuronal process orientation distribution and negative log of the diffusion signal for four quadrants. Images in rows I-IV are taken from corresponding fields labeled I-IV in Fig. 4(b) . From left to right, the first column shows transmitted light images for each field. The quadrant shown in the remaining three columns is outlined with a black box. The second column shows 3-D surface models of the set of line segments used to estimate the scatter matrix for the stained cellular processes. Images are rotated slightly to show the boundaries of the quadrants. An equal area stereographic projection method (Schmidt plot) has been used to render the 3-D probability density distributions in a manner that is suitable for 2-D graphs in the third and fourth columns. In each plot, the polar angle ranges from 0 (center of plot) to 90 (outer perimeter of the circle). Concentric circles within the outer perimeter of each plot correspond to polar angles of 30 and 60 . The azimuthal angles for each plot are aligned with the first and second columns of the figure. Orientation distributions are expressed using (19) in the third column, and the negative log of the diffusion signal intensity is expressed using (22) in the fourth column. Numbers in upper left corners of the third and fourth columns are and , respectively, as defined in (11) .. right plots showing the negative log of the diffusion signal) reflect the apparent diffusion coefficient measured along a direction specified by a given set of polar and azimuthal angles. These plots display qualitatively similar features. In each row, peak intensities for orientation distributions and diffusion-weighted MRI signal intensity are observed for similar polar and azimuthal angles. In addition, Golgi quadrants in which the neuronal process orientation distribution peak is narrow (within fields I and II) generally correspond to narrow peaks in the diffusion-weighted signal, whereas broad orientation distribution peaks (quadrants within fields III and IV) are generally matched with broad peaks in the diffusion weighted signal. For comparison, fractional anisotropy values (third column) or (fourth column), are given in the upper left corner of each Schmidt plot. Overall, the Golgi peaks appear sharper than the DTI peaks, and we believe there are two main reasons for this. First, diffusion anisotropy is affected also by water in the extracellular space which is arguably less anisotropic than the intracellular space. Second, even for a single neurite direction, the diffusion peak would be blurred since the diffusion direction (the diffusion wave vector) has a component parallel to the neurite for most directions. The degree of agreement between the principal DTI and scatter matrix eigenvectors was used as one way to quantitatively assess whether the prediction of (9) was upheld in our data. Fig. 10 provides a graphical comparison of primary eigenvectors of the DTI data for voxels within the cerebral cortex, expressed in the Golgi frame (yellow vectors), with primary eigenvectors of the 128 Golgi field quadrants (red vectors). As expected, the orientations of the two sets of vectors generally coincide. The distribution of relative angles between the corresponding directions was examined to determine whether a statistically significant correlation exists between the two sets of tensor eigenvectors. The null hypothesis is that no correlation between these directions exists. Under conditions of the null hypothesis, , which is the z-component of the primary DTI eigenvector in a coordinate system in which the Golgi primary eigenvector defines the z-axis, would be uniformly distributed between zero and one. Fig. 11 shows the cumulative distribution of , compared to the uniform distribution. The actual distribution is clearly different from the uniform, in particular there is a tendency for the relative angles to be close to zero, indicating general alignment between the principal directions of the diffusion tensor and the scatter matrix. Indeed, the Kolmogorov-Smirnov test rejects the null hypothesis . The average angle between the diffusion principal direction and scatter matrix principal direction is approximately 36 , and the scatter characterized by the length of the resultant vector is 0.93. Note that would correspond to maximal scattering over the unit circle, whereas would correspond to maximal coherence.. To test the prediction in (10) of a linear relationship between the eigenvalues of the two matrices, the centralized eigenvalues of the scatter matrix were matched pairwise to the centralized eigenvalues of the DTI matrix according to rank. These pairs are plotted in the Fig. 12 upper panel where a clear linear relationship is observed, as predicted by the theory, corresponding The slope of the lines shown for all panels corresponds to the product , as described in the text, and is set to a value of 0.53, determined from the data shown in (a). In (b), radial and axial diffusivities versus corresponding numbers using the scatter matrix eigenvalues are plotted, and the solid line is the predicted linear relationship using the fit from (a) and the observed mean diffusivity . In (c), fractional anisotropy of water diffusion is plotted against fractional anisotropy of the axon/dendrite scatter matrix , and the line corresponds to the fit determined in panel (a).. to a significant Spearman correlation using either the largest or smallest eigenvalues. The best linear fit (using the robust fitting function "robustfit" in Matlab), resulted in a slope of . A second analysis was performed in which the diffusion eigenvalues were represented as radial diffusivity, defined to be the average of the two smallest diffusion eigenvalues, and axial diffusivity, defined to be the largest diffusion eigenvalue. Similarly, radial and axial eigenvalues were defined for the scatter matrix, and the resulting 2 128 pairs of points were plotted against each other in the Fig. 12 middle panel. Given that the mean diffusivity across the voxels is relatively constant (average , standard deviation 0.027), (10) predicts a linear relationship between this set of numbers, with slope and y-axis intercept . This is shown as a solid line in the middle panel, using the values obtained from the fit above ( and intercept 0.13). An independent fit gave similar values ( and intercept 0.11). In the Fig. 12 lower panel, fractional diffusion anisotropy is plotted against the fractional orientation anisotropy , cf. (12), and again a significant linear correlation is found with a correlation coefficient of , and an estimate of .

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O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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Power-aware broadcasting and activity scheduling in ad hoc wireless networks using connected dominating sets In ad hoc mobile wireless networks, due to host mobility, broadcasting is expected to be more frequently used to nd a route to a particular host, to page a host, and alarm all hosts. A straightforward broadcasting by ooding is usually very costly and will result in substantial redundancy and more energy consumption. Power consumption is an important issue since most mobile hosts operate on battery. Broadcasting based on a connected dominating set is a promising approach, where only nodes in the dominating set need to relay the broadcast packet. A set is dominating if all the nodes in the system are either in the set or neighbors of nodes in the set. Wu and Li proposed a simple and e cient distributed algorithm for calculating connected dominating set in ad hoc wireless networks, where connections of nodes are determined by their geographical distances. In general, nodes in the connected dominating set consume more energy to handle various bypass tra cs than nodes outside the set. To prolong the life span of each node and, hence, the network by balancing the energy consumption in the system, nodes should bealternated in being chosen to form a connected dominating set. Activity scheduling deals with the way to rotate the role of each node among a set of given operation modes (dominating nodes versus dominated nodes in this paper). In this paper, we propose to apply power-aware connected dominating set notions to broadcasting and activity scheduling. The e ectiveness of the proposed method in prolonging the life span of the network is con rmed through simulation. An ad hoc wireless network is a special type of wireless network in which a collection of mobile hosts with wireless network interfaces may form a temporary network, without the aid of any established infrastructure or centralized administration. Examples of such networks are used in military, disaster rescue, wireless conferences, and monitoring in some kind of dangerous, remote or unaccessible environment.. We can use a simple graph G = (V E) to represent an ad hoc wireless network, where V represents a set of wireless mobile hosts and E represents a set of edges. An edge between host pairs (v u) indicates that bothhosts v and u are within their wireless transmitter ranges. To simplify our discussion, we assume all mobile hosts are homogeneous, i.e., their wireless transmitter ranges are the same. In other word, if there is an edge e = ( v u) in E, it indicates u is within v's range and v is within u's range. Thus the corresponding graph will be an undirected graph. In this case, a mobile host may not beable to communicate directly with other hosts in a single-hop fashion and a m ulti-hop scenario occurs, where the packets sent by the source host are relayed by several intermediate hosts before reaching the destination host. Dominating-set-based broadcasting 21] is based on the concept of dominating set in graph theory. A subset of the vertices is a dominating set if every vertex not in the subset is adjacent to at least one vertex in the subset. In Figure 1 , fv wg forms a dominating set in a graph with ve vertices. The main idea of this approach is to limit the broadcast process to a subgraph induced from the dominating set. Moreover, the dominating set should be connected for the ease of the broadcast process within the induced graph consisting of dominating nodes only. Vertices in a dominating set are called gateway hosts while vertices that are outside a dominating set are called non-gateway hosts. The main advantage of connected dominating-set-based broadcasting is that it simpli es the decision of retransmission to the one in a smaller subnetwork generated from the connected dominating set. This means that only gateway hosts need to relay the broadcast packet. Since non-gateway host is prevented from retransmitting, this mechanism will reduce power consumption, redundant retransmission and, hence, network contention.. Clearly, the e ciency of this approach depends largely on the process of nding a connected dominating set and the size of the corresponding subnetwork. Unfortunately, nding a minimum connected dominating set is NP-complete for most graphs 8]. Wu and Li 25] proposed a simple distributed algorithm, called marking process, that can quickly determine a connected dominating set in a given connected graph, which represents an ad hoc wireless network. Speci cally, a host is marked as a gateway if it has two unconnected neighbors. This approach also outperforms several classical approaches, such as the cluster approach 3, 12] and MCDS (minimum connected dominating set) 7, 19] , in terms of nding a small connected dominating set and/or does so quickly 25]. Movement of one single node in clustering structure may trigger global structural updates, thus its maintenance is expensive. MCDS 19] is clustering type structure. Centralized algorithms such as 7] produce smaller sets but with unacceptable overhead even for static networks. Dominating sets have small overhead since movement of one node only a ects the structure in its neighborhood.. In ad hoc wireless networks, the limitation of power of each host poses a unique challenge for power-aware design 16]. There has been an increasing focus on low cost and reduced node power consumption in ad hoc wireless networks. Even in standard networks such as IEEE 802.11, requirements are included to sacri ce performance in favor of reduced power consumption 4]. In order to prolong the life span of each node and, hence, the network, power consumption should beminimized and balanced among nodes. Unfortunately, nodes in the dominating set in general consume more energy in handling various bypass tra c than nodes outside the set. Therefore, a static selection of dominating nodes will result in a shorter life span for certain nodes, which in turn result in a shorter life span of the whole network.. In this paper, we study dynamic selection of dominating nodes, also called activity scheduling. Activity s c heduling deals with the way to rotate the role of each node among a set of given operation modes. For example, one set of operation modes is sending, receiving, idles, and sleeping. Di erent modes have di erent energy consumptions. Activity s c heduling judiciously assigns a mode to each node to save overall energy consumptions in the networks and/or to prolong life span of each individual node. Note that saving overall energy consumptions does not necessarily prolong life span of a particular individual node.. We propose to save o verall energy consumptions by a l l o wing only dominating nodes (i.e., gateway nodes) to retransmit the broadcast packet. In addition, in order to maximize the lifetime of all nodes, an activity scheduling method is used that dynamically selects nodes to form a connected dominating set. Speci cally, in the selection process of a gateway node, we give preference to a node with a higher energy level. The e ectiveness of the proposed method in prolonging the life span of the network is con rmed through simulation. This paper is organized as follows: Section 2 reviews the related work, Wu and Li's decentralized formation of a connected dominating set, and two extensions to Wu and Li's approach: one is based on node degree and the other is based on energy level. Section 3 discusses the proposed power-aware broadcasting and activity scheduling. An example is also included to illustrate di erent activity scheduling methods. Performance evaluation is done in Section 4. In Section 5, we conclude the paper and discuss possible future work. Throughout the paper, we use terms node, host, and vertex interchangeable. In this paper, we h a ve applied Wu and Li's distributed algorithm for broadcasting in a connected dominating set in a given ad hoc wireless network. The connected dominating set is selected based on the node degree and the energy level of each host. In the broadcasting process, only dominating hosts are responsible for retransmitting the broadcast packet. The objective is device a selection scheme (for dominating hosts) so that the overall energy consumption is balanced in the network, and at the same time, a relatively small connected dominating set is generated. A s i m ulation study has been conducted to compare the life span of the network under di erent selection policies. The results have shown that the proposed approach based on energy level is clearly the best in terms of the longer life span of the network. Our future work will perform more in depth simulation under di erent settings.. Although host mobility gives su cient exibility i n c hosing gateway nodes based on their energy levels, such exibility i s v ery limited in an ad hoc wireless networks with static hosts (such as sensor networks). That is, the selection of nodes to form a connected dominating set is limited to a special subset of nodes. Clearly, these nodes tend to bedepleted sooner than the other nodes. Ways to handle this situation will be part of our future work. The broadcasting in literature has been studied mainly for the one-to-all model and we will use this term to refer to broadcasting schemes in which the same packet is retransmitted to all the nodes in the network. All-to-all broadcasting is less frequently used in ad hoc wireless networks. Flooding has been traditionally used for broadcasting where each host transmits (forwards) the broadcast packet once and only once. Flooding is also used for route discovery in source-initiated on-demand routing protocols such as DSR 10] .. Broadcasting was sometimes studied in the context of the address serving in hierarchically clustered networks 11]. The address can besearched and updated by using a variety of algorithms, including ooding, multicast along a spanning tree, and sending a packet directly to each address server. A numberof centralized (where each node is assumed to know the full graph topology) broadcast algorithms were proposed in literature. We are interested here only in distributed approaches.. Ni, Tseng, Chen, and Sheu 13] studied the broadcast storm problem. A straightforward broadcasting by ooding is usually very costly and will result in serious redundancy, contention, and collisions. Several schemes, like probabilistic, counter-based, distance-based, location-based, and cluster-based scheme were proposed to reduce redundant rebroadcasts, and alleviate this storm problem.. In cluster-based broadcasting, nodes are divided into cluster with one of them serving as clusterhead in each cluster (the node with the smallest id in the neighborhood is selected as clusterhead). Each clusterhead has direct links to any of the hosts in its cluster. In the broadcast protocol, the source node forwards the broadcast packet to its clusterhead, which then initiates the construction of a virtual spanning tree of all clusterheads. Gerla and Tsai 6] described a modi ed version of algorithm in which the highest degree node in a neighborhood becomes the clusterhead.. Qayyum, Viennot and Laouiti 14] studied a multipoint relay method for e cient ooding in mobile wireless networks. Gerla, Kwon and Pei 5] proposed a combined clustering and broadcasting algorithm which has no communication overhead for either maintaining cluster structure or updating neighborhoodinformation. The performance of the algorithm depends on two parameters whose best values are in accordance to network density and tra c load, which are generally information not available to hosts.. One simple way to prolong the lifetime of each host is to evenly distributed packet-relaying loads to each node to prevent nodes from being overused. This approach i s u s e d i n L E A CH 9], where a probabilistic approach to randomly select cluster heads in data gathering in sensor networks. Other metrics can be used together with the energy metric for certain routing applications. For example, power and cost are combined into a single metric in order to choose power e cient paths among cost optimal ones. Various combinations are studied by Stojmenovic and Lin 20] and Chang and Tassiulas 1].. Wu, Gao, and Stojmenovic 24] were the rst to propose to use energy metrics in dominatingset-based routing. The selection of a connected dominating set is through a marking process: a node is marked gateway if two of its neighborsare not directly connected. Recently, a modi ed marking process was proposed by a group at MIT 2] . A node is marked gateway if two of its neighborsfail both of the following two conditions: (a) directly connected and (b) connected by one or two gateways. Compared with the marking process by W u and Li, an additional condition (b) is added. This modi ed marking process will generate a smaller set of gateway nodes if nodes do not apply the marking process at the same time. If all nodes apply the marking process at the same time (initially all nodes are non-gateways), condition (b) cannot beusedand this approach is reduced to the marking process. In addition, the modi ed marking process costs more: O( 3 ) with one-hop intermediate gateway ( a n d O( 4 ) w i t h t wo-hop intermediate gateways) at each n o d e vs. O( 2 ) of Wu and Li's marking process, where is the maximum numberof neighbors for a node. In addition, each node in the modi ed marking process needs to know 3-hop neighborhood information while each node in the marking process only require 2-hop neighborhood information. Also, this approach c hanges connected dominating set due to mobility o n l y , not due to energy left at nodes.. Xu, Heidemann, and Estrin 26] discussed the following sensor sleep node schedule. The given 2-D space is partitioned into a set of squares (called cells), such as any node within a square can directly communicate with any nodes in an adjacent square. Therefore, one representative node from each cell is su cient. To prolong the life span of each node, nodes in the cell are rotated to beselected as a representative. The adjacent squares form a 2-D grid and the broadcast process becomes trivial. Note that the selected nodes in 26] make a dominating set, but the size of it far from optimal, and also it depends on the selected size of squares. On the other hand, the dominating set concept used here has smaller size and is chosen without using any parameter.. The notions of saving overall energy consumptions in the networks and/or to prolong life span of each individual node has been discussed in the context of unicasting. Toh 22] discussed general issues related to power-aware (power-e cient) routing. It is argued that power conservation schemes should beapplied to di erent network layers: physical layer and wireless device, data link layer, and network layer (where routing functions are located). At t h e n e t work layer, power-e cient route can beselected based on either minimum total transmission power routing (MTPR) or minimum battery cost routing (MBCR) 17]. MTPR minimizes the total power needed to route packets on the network while MBCR maximizes the lifetime of all nodes. Stojmenovic and Lin 20] described localized power and aware routing algorithms whose performance is close to the performance of non-localized shortest weight path algorithms.

O O O B I O B I 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 B I 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O B I O O O O O O O O O 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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Bagged fuzzy clustering for fuzzy data: an application to a tourism market Segmentation has several strategic and tactical implications in marketing products and services. Despite hard clustering methods having several weaknesses, they remain widely applied in marketing studies. Alternative segmentation methods such as fuzzy methods are rarely used to understand consumer behaviour. In this study, we propose a strategy of analysis, by combining the Bagged Clustering (BC) method and the fuzzy C-means clustering method for fuzzy data (FCM-FD), i.e., the Bagged fuzzy C-means clustering method for fuzzy data (BFCM-FD). The method inherits the advantages of stability and reproducibility from BC and the flexibility from FCM-FD. The method is applied on a sample of 328 Chinese consumers revealing the existence of four segments (Admirers, Enthusiasts, Moderates, and Apathetics) of the perceived images of Western Europe as a tourist destination. The results highlight the heterogeneity in Chinese consumers' place preferences and implications for place marketing are offered. Segmentation is critical for developing customer centric marketing and tourism strategies. Effective segmentation leads to competitive advantage, recognition and exploitation of new market opportunities, selection of the appropriate target market, enhanced differentiation and positioning, and increased profitability [1] . Despite the strategic and tactical benefits of market segmentation, there is much controversy surrounding the most commonly used methods and algorithms to segment consumer markets. Cluster analysis remains the most popular method [2] [3] [4] . The basic idea of cluster analysis is to divide a heterogeneous consumer market into homogeneous sub-groups [5] . This approach is typically representative of data driven segmentation methods [2] . Cluster analysis has been criticized for its overestimation of the validity of the segmentation results [2] and the resulting clusters have been termed "convenient fictions" [6] , a marketing term that refers to the fact that no "natural groupings" could exist, and some information is inevitably lost when objects are grouped. Information loss is not problematic per se, but it can result in the wrong conclusions [7] . Every clustering algorithm has advantages and drawbacks and has to be chosen with awareness of its characteristics and limitations [1, 2] .. Clustering methods are generally split into three groups: non-overlapping (hard), overlapping, and fuzzy algorithms. In hard algorithms, each element to be grouped belongs to a single segment [1] . In overlapping algorithms, an object may belong to more than one cluster [4] . Similar to overlapping algorithms, fuzzy algorithms allow objects to belong to more than one cluster and, in addition, assign to each object a degree of membership to each segment [1, 7] .. Hierarchical (agglomerative) and non-hierarchical (iterative partitioning) methods are two common hard algorithms that permeate the marketing and tourism literature [1, 2, 8] . Ward's method remains popular among agglomerative hierarchical algorithms [1, 2] . However, hierarchical methods have some drawbacks. Hierarchical methods typically become difficult with increasing sample sizes [2] . The application of hierarchical methods is not always justified in market segmentation given that it presupposes an underlying hierarchy among the objects or respondents to be clustered [1] .. Among partitioning methods, k-means remains the most popular in marketing and tourism studies [1, 2] but it suffers from: (1) identifying equally sized clusters, when in reality such patterns rarely exist in empirical data; (2) the clustering solution is dependent on the starting solution, and the possibility of building a marketing strategy based on weak data analysis is high; (3) the outcome of cluster analysis is much dependent on the characteristics of the data set, but such characteristics are not always accounted for; (4) repeated computations typically lead to different grouping of respondents, suggesting that solutions may be unreproducible; (5) the lack of published rules about how large the sample size should be in relation to the number of segmentation variables used leads to deceptive and uncritical partitioning exercises [3, 8, 9] .. More recently, "ensemble methods" [10] , such as the voting approach [11] and Bagged Clustering (BC) [12] , have been successfully applied to enhance the performance of unstable or weak clustering algorithms. The voting algorithm combines partitions sequentially two at a time, obtaining a fuzzy partition of the data. The key idea of the BC is to repeatedly run a partitioning algorithm (like the k-means) on the entire sample, and then to combine the results through a hierarchical algorithm. This ensemble method is able to avoid the problem of local minima of partitioning algorithms and find a partition not affected by the randomness of initialization or the clustering process itself [11, 12] .. Fuzzy procedures allow the assignment of units to each cluster with a membership degree, relaxing the assumption of exclusiveness. A respondent can belong to several clusters without negatively impacting on the managerial usefulness. Conceptually, one consumer's higher statistical probability to belong to one segment does not necessarily mean that s/he only belongs to this segment [13] . For example, a tourist may well desire more than one attribute or benefit from a destination and hence can belong to multiple groups [14] . Among the different fuzzy clustering methods present in the literature, fuzzy C-means (FCM) [15] is the most popular. FCM has several advantages in comparison to hard k-means. In particular, FCM is less affected by local optima, and is computationally more efficient [16, 17] .. In the process of choosing the best algorithm, it is important for the researcher to understand that clustering performance depends strongly on the characteristics of the data to be segmented. In tourism research, information regarding attitudes, emotions, satisfaction, and other aspects that involve personal judgement is commonly captured through qualitative expressions, such as Likert scales. However, this approach has been criticized [18, 19] . Using a Likert scale the researcher tries to capture a human feeling, by definition uncertain, vague, and subjective, through a linguistic expression. Therefore two important drawbacks arise: first, this type of scale entails a source of vagueness and uncertainty in evaluation since it represents subjective knowledge [20, 21] ; second, respondent must automatically convert an opinion on a scale and this conversion can distort the original opinion that had to be captured [22] . One way to overcome these drawbacks is to transform Likert variables into fuzzy numbers [16, 23] . In the tourism field there are relevant applications of this type of transformation [see, e.g., [20] [21] [22] [24] [25] [26] [27] .. In this study we propose a novel clustering method, the Bagged fuzzy Cmeans clustering method for fuzzy data (BFCM-FD), which is an ensemble method that combines BC and fuzzy C-means clustering method for fuzzy data (FCM-FD) to derive market segments. Note that FCM-FD inherits from FCM all the advantages above illustrated, in the case of fuzzy data. This clustering method is illustrated by analysing a sample of Chinese travellers perceptions of the image of Western Europe as a tourist destination.. The contribution of this study is threefold. First, in order to capture the ambiguity and uncertainty arising from the use of a Likert scale we propose the transformation of destination image attributes into fuzzy numbers before conducting the segmentation analysis. Second, we propose the adoption of the novel BFCM-FD that combines the strengths of BC and FCM-FD. The proposed method is less sensitive to the number and type of variables used in the clustering, inheriting this property from the BC method [28] . Furthermore, the method inherits the favourable characteristics of the FCM method mentioned earlier. In particular, the proposed method allows the attribution of a unit to more than one cluster, which is often more realistic than assigning a unit to only one cluster in tourism. Third, image segmentation studies in tourism rely heavily on cluster analysis to understand tourists' perceptions of destinations [29] [30] [31] but the stability and reproducibility of the identified clusters remain questionable. By using BFCM-FD, we obtain clusters which are stable and reproducible.. The paper is organized as follow. In section 2, a review of the literature on destination image and image segmentation, as well as a review of Chinese travellers images of Western Europe. Section 3 describes the method used to collect the data and the survey instrument. Section 4 illustrates the various stages of data analysis, including the transformation of the Likert variables into fuzzy numbers, while section 5 summarizes the results. Section 6 presents both the theoretical and managerial implications, while the paper concludes in section 7 by offering some final remarks. The Chinese outbound market is undoubtedly a growth market for Western Europe. In this study a novel segmentation method, the BFCM-FD, was adopted in order to cluster Chinese visitors by their perceived image of Western Europe as destination. The results suggest that heterogeneity in the perceived image of Western Europe exist and that appropriate marketing strategies for each segment of potential visitors are required and must be implemented. Although, the BFCM-FD method overcomes many of the limitations of traditional hard (both hierarchical and non-hierarchical) algorithms, this study is not without limitations.. First, as many clustering methods available in the literature, the BFCM-FD procedure could be afflicted by outlier sensibility. In particular, FCM-FD algorithm is sensible to the presence of outliers in the data [104] . In order to neutralize and smooth the disruptive effects of possible outliers in the BFCM-FD clustering procedure it would be useful to consider robust fuzzy clustering algorithms for fuzzy data [see, e.g., 95] .. Second, the sample of Chinese visitors was identified from Beijing and the results are pertinent to the outbound market from this city only. Research on the Chinese outbound market [14, 59, 60] suggests that Shanghai and Guangzhou are also important generating markets and this study should be replicated in other locations within China. Third, the list of image at-tributes has mostly cognitive images. Stepchenkova and Li [50] suggest that the Chinese outbound market is driven by cognitive and affective images, with less experienced travellers associating mainly cognitive images with a destination. Hence, it would be worthwhile for future studies to extend the list of attributes for Western Europe to include affective images and also to assess the image of individual countries such as Spain, Italy and France for competitive analysis. Fourth, this study focused on segmenting destination image but there is a need for novel qualitative and quantitative methods to understand the image construct and competitive images of destinations [44, 50] . Quantitative methods such as Bray-Curtis dissimilarity index and Electre II methods may be useful in achieving that [46] .. As a final remark, in the specific case of imprecision associated with the use in the evaluation process of linguistic term-based scales we can distinguish two fuzzy approaches: (a) fuzzy rating scale [80, 105] ; (b) Likert or associated fuzzy conversion scales [80] . Indeed, since nowadays an increasing amount of data arises from human judgements, perceptions and evaluations, it seems necessary to find suitable instruments able to handle and capture the imprecision contained in them. In this study, a fuzzy transformation of the Likert-type variables is proposed, i.e. a fuzzy version of Likert-type scales is employed. In this regards, we remark that an interesting proposal in the tourism context have been suggested by Benítez, et al. [20] . However, in general, robustness and stability of the results obtained from a fuzzy data analysis are still open problems. We will investigate in deep this important topics in our future studies.

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


Land use pattern optimization based on CLUE-S and SWAT models for agricultural non-point source pollution control Improper land use is one major cause of non-point source pollution. Integrated modeling would support the evaluation and optimization of land use for the non-point source pollution control. In this study, the CLUE-S (the Conversion of Land Use and its Effect at Small regional extent) and SWAT (Soil and Water Assessment Tool) models were coupled to simulate pollution loads under different land use scenarios in the upstream watershed of Miyun Reservoir in Beijing, China. The results indicated that changes in land use structure and pattern under different land use scenarios have significantly affected the non-point source pollution load. The increase of orchards and loss of forest cover has led to an increase in the potential pollution loads of nitrogen by 5.27% and phosphorus by 4.03%. However, in the agricultural non-point source pollution control scenario, pollution loads of nitrogen decreased by 13.94% and phosphorus by 9.86%, resulting from the establishment of riparian vegetation buffers and restoring forest on unutilized land and slope arable land. Coupling the hydrological model SWAT and the land use model CLUE-S succeeded in evaluating the land use pattern for agricultural non-point source pollution control. The coupling of two models provides a new approach for land use optimization towards non-point source pollution control. Improper land use structure and management will lead to soil erosion and nutrient loss with surface runoff, resulting in a large area of non-point source pollution in the watershed [1] [2] [3] [4] [5] , causing a loss of nitrogen and phosphorus and water eutrophication. Therefore, domestic and foreign scholars carried out many related researches to seek a reasonable land use structure and pattern so as to control agricultural non-point source pollution [6] [7] [8] [9] .. Due to the temporal and spatial variability in the occurring processes of non-point source pollution, regular monitoring requires a large investment. Consequently, physically based watershed-scale modeling has become useful and popular [10] . The distributed hydrological model SWAT (Soil and Water Assessment Tool) is widely used in evaluating the response of non-point source pollution to land use change, which provides a certain reference for land pattern optimization of a watershed [11, 12] . Bhaduri et al. [13] analyzed the impacts of the dynamic change in land use of a watershed on non-point source pollution from 1973 to 1991. He pointed out that the load of non-point source pollution increased by 15% with the reduction of woodland and the increase in arable land [13] . Sahu and Gu [14] indicated that the load of nitrate can be effectively reduced by about 30% by establishing a watershed vegetation buffer. The study on the Heihe River [7] watershed and the upper watershed of Taihu Lake [15] showed that with the implementation of returning cultivated land to forest as well as water conservation and forest protection projects, non-point source pollution in the watershed would be reduced. However, most researches on the design of land use scenarios mainly adopt qualitative methods, historical inversion, the contrast and extreme land use scenarios design [2, 7, 15] ; these methods find it difficult to involve the factors of spatial land use pattern variation or that under the guidance of a policy. In addition, a single hydrological model or a single land use change model also finds it difficult to analyze the connections between land use change and non-point source pollution variation, not even supporting the optimization of a land use pattern in order to reduce non-point source pollution. Therefore, combining the hydrological model with the land use change model for agricultural non-point source pollution control for land use pattern optimization will be an important direction for future researches [15] .. The dynamic land use simulation model of CLUE-S (the Conversion of Land Use and its Effect at Small regional extent) can carry out a quantitative analysis on the multi-scale land use changes in space, in particular, simulating possible changes under land use scenarios in the future, and taking into account neighborhood factors, driving forces and land suitability related to land use scenario design [16] [17] [18] . This model can also combine with an anti-planning approach, to simulate and predict a non-point source pollution control scenario based on the analysis of security patterns in a regional landscape [19] . The combination of CLUE-S and SWAT can give full play to the advantages of model coupling, which both improves the reasonableness and accuracy of the model for land use scenario simulation and effectively evaluates non-point source pollutions under different scenarios [15] .. Miyun Reservoir is the only surface drinking water source of Beijing, whose water supply accounts for 73% of the total in Beijing. Therefore, its water quality directly determines the drinking water safety of the capital. However, the monitoring data analysis shows that 94% of NH 3 -N, 75% of TN (Total Nitrogen) and 95% of TP (Total Phosphorus) in the upstream watershed of Miyun Reservoir are from non-point source pollution [20] . Therefore, the study on rational land use in the upper watershed of Miyun Reservoir is significant for the protection of water quality.. Dynamic land use simulation model CLUE-S and non-point source pollution model SWAT were coupled in this paper. Non-point source pollution loads under different land use scenarios were evaluated with the coupled models, in order to provide a reference for the land use pattern optimization for agricultural non-point source pollution control in the watershed.

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


Identifying and quantifying metabolites by scoring peaks of GC-MS data Background: Metabolomics is one of most recent omics technologies. It has been applied on fields such as food science, nutrition, drug discovery and systems biology. For this, gas chromatography-mass spectrometry (GC-MS) has been largely applied and many computational tools have been developed to support the analysis of metabolomics data. Among them, AMDIS is perhaps the most used tool for identifying and quantifying metabolites. However, AMDIS generates a high number of false-positives and does not have an interface amenable for high-throughput data analysis. Although additional computational tools have been developed for processing AMDIS results and to perform normalisations and statistical analysis of metabolomics data, there is not yet a single free software or package able to reliably identify and quantify metabolites analysed by GC-MS. Results: Here we introduce a new algorithm, PScore, able to score peaks according to their likelihood of representing metabolites defined in a mass spectral library. We implemented PScore in a R package called MetaBox and evaluated the applicability and potential of MetaBox by comparing its performance against AMDIS results when analysing volatile organic compounds (VOC) from standard mixtures of metabolites and from female and male mice faecal samples. MetaBox reported lower percentages of false positives and false negatives, and was able to report a higher number of potential biomarkers associated to the metabolism of female and male mice. Conclusions: Identification and quantification of metabolites is among the most critical and time-consuming steps in GC-MS metabolome analysis. Here we present an algorithm implemented in a R package, which allows users to construct flexible pipelines and analyse metabolomics data in a high-throughput manner. Identification and quantification of metabolites is among the most critical and time-consuming steps in GC-MS metabolome analysis. The reliability of the biological inferences that can be drawn from metabolomics studies is directly related to the quality of the data upon which they are based. In addition, as the size and number of metabolomics studies conducted by individual laboratories has grown, the time available to analyse each single dataset has reduced. Therefore, to satisfy the criteria of metabolomics studies ideally software must reliably identify and quantify metabolites, and the results must be reported in a format that facilitates further data analysis. Although AMDIS has been widely used in metabolomics, results show that its performance no longer meets the requirements of modern high-throughput analysis of metabolomics experiments. We presented here a new algorithm, PScore, which uses a spectral library to analyse GC-MS samples and score retention times according to their probability of representing a metabolite. We implemented PScore in an R package, MetaBox, and compared its performance against AMDIS when analysing standard mixtures of metabolites and mice faecal samples. PScore greatly reduces the percentage of false positives and false negatives, and it considerably improves the quantification of metabolites analysed by GC-MS. In addition, our new R package MetaBox incorporates functions to generate graphical outputs and reports results in a format accepted by other software, such as Metab and MetaboAnalyst, allowing users to perform further data processing and statistical analyses in a high-throughput way. As an R package, MetaBox allows users to construct flexible pipelines for data analysis and allows pop-up dialog boxes, which facilitate its usage by R beginners.

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