Optimal Placement of Valves in a Water Distribution Network with CLP(FD) This paper presents a new application of logic programming to a real-life problem in hydraulic engineering. The work is developed as a collaboration of computer scientists and hydraulic engineers, and applies Constraint Logic Programming to solve a hard combinatorial problem. This application deals with one aspect of the design of a water distribution network, i.e., the valve isolation system design.We take the formulation of the problem by Giustolisi and Savić (2008) and show how, thanks to constraint propagation, we can get better solutions than the best solution known in the literature for the Apulian distribution network.We believe that the area of the so-called hydroinformatics can benefit from the techniques developed in Constraint Logic Programming and possibly from other areas of logic programming, such as Answer Set Programming. An aqueduct is a complex system that includes a main component to transport water and a water distribution component, that brings the water to the users. The water distribution network can be thought of as a labelled graph, in which pipes are represented as undirected edges. In the network, there is at least one special node that is the source of the water (node 0 in Figure 1) ; users are then connected to the edges of the water distribution network. Each user has a demand (in litres per seconds) that is quantified by the hydraulic engineer through the available data. In particular, such a demand is frequently expressed as a daily average value. Each edge of the graph is labelled with the total demand of the users linked to it. For example, in Figure 1 , the edge connecting nodes 2 and 5 (let us name it e 2,5 ) has a demand of 15l /s (that may be due, e.g., to five clients each requesting 3l /s on average). When designing a water distribution network, one of the steps is designing the isolation system: in case a pipe has to be repaired (e.g., because of a break), a part of the network has to be disconnected from the rest of the network, in order to allow workers to fix the broken pipe. The isolation system consists of a set of isolation valves, that are placed in the pipes of the network. Once closed, the isolation valve blocks the flow of water through the valve itself. In common practice, a valve is usually placed in a pipe near one of the two endpoints; this means that in each pipe at most two valves can be placed. If in some pipe there are two valves, this means that this single pipe can be isolated by closing both the valves. In the example of Figure 1 , the edge e 2,3 connecting nodes 2 and 3 has two valves, so in case this pipe is damaged, valves v 2,3 and v 3,2 will be closed, isolating only e 2,3 .. However, placing two valves in each pipe is often not a viable option, because each valve has a cost; the cost is not only due to the manufacturing and physical placing of the valve, but also to the fact that the pipe is more fragile and deteriorates more quickly near valves. In case there are not two valves in each pipe (as it is usually the case in real distribution networks), the isolation of a pipe implies the closure of more than two valves and thus the isolation of more than one pipe. In this case, more users other than those connected to the broken pipe will remain without service during pipe substitution. Suppose that the pipe e 3,4 connecting nodes 3 and 4 is damaged. In order to de-water it, workers have to close valves v 3,2 and v 5,4 ; as a result edge e 5,4 will be de-watered as well, and the clients that take water from it will have no service as well. Valves partition the network in the so-called sectors, that are, intuitively, those parts of the distribution network enclosed by some set of valves: edges e 3,4 and e 4,5 are in the same sector, so they cannot be de-watered independently one from the other.. The usual measure of the disruption in the service is the undelivered demand, i.e., the demand (in litres per second) that is not fulfilled during the repair operations; in the case there is need to de-water edge e 3,4 , the disruption is the demand of the edges e 3,4 and e 4,5 , i.e., 7 + 6 = 13l /s. However, notice that the undelivered demand does not always coincide with the sector the damaged pipe belongs to. For example, pipe e 2,5 belongs to the sector consisting of the edges e 1,2 and e 2,5 , that is surrounded by valves v 1,2 , v 2,3 , v 5,4 , and v 5,6 ; however by closing these four valves, we will de-water a larger part of the network: edges e 2,3 , e 3,4 , and e 4,5 will be de-watered even though they are not in the same sector of the broken pipe. This effect is called unintended isolation (Jun and Loganathan 2007) .. The design of the isolation system consists of placing in the distribution network a given number of valves such that, in case of damage, the disruption is "minimal". Of course, the level of disruption depends on which pipe has to be fixed. In Figure 1 we have four sectors: if e 2,3 is damaged, the undelivered demand during repair is 3l /s, if one of {e 3,4 , e 4,5 } is broken, the undelivered demand is 13l /s, if the broken pipe is e 1,6 or e 5,6 the undelivered demand is 3 + 8 = 11l /s, while for sector {e 1,2 , e 2,5 } the undelivered demand is 36l /s, corresponding to the demand of {e 1,2 , e 2,5 , e 2,3 , e 3,4 , e 4,5 }. A usual measure (Giustolisi and Savić 2010) is to take the worst case, and assign to the placement shown in Figure 1 (characterised by 6 valves) the effect of the maximal possible disruption: 36l /s. Giustolisi and Savić (2010) address the design of an isolation valve system as a two-objective problem: one objective is minimizing the number of valves in the isolation system, and the other is the minimization of the (maximum) undelivered demand. They adopt a genetic algorithm that is able to provide near-Pareto-optimal solutions, and apply it to the Apulian distribution network. The genetic algorithm provides good solutions in a very short time, but it is incomplete, so it does not provide, in general, Pareto-optimal solutions, but only solutions that are hopefully near to the Pareto front. The real optimal Pareto front remains unknown.. We believe that a complete search algorithm could provide better solutions, although at the cost of a higher computation time. Since the problem should be solved during the design of the valve system, there is no need to have a solution in real-time, and an algorithm providing a provably Pareto-optimal solution may be preferable with respect to incomplete algorithms, even with higher computation times.. In this paper, we address the same two-objective problem studied by Giustolisi and Savić (2010) as a sequence of single-objective ones; this is always possible when one of the objectives is integer (Van Wassenhove and Gelders 1980; Gervet et al. 1999; Gavanelli 2002) . Given the number of valves, we model the design of the isolation valve system as a two-player game, and solve it with a minimax approach (Russell and Norvig 2003) . As the game has an exponential number of moves, we reduce the search space by pruning redundant branches of the search tree, implementing the minimax algorithm in Constraint Logic Programming (CLP) (Jaffar and Maher 1994) on Finite Domains (CLP(FD)) (Marriot and Stuckey 1998; Frühwirth and Abdennadher 2003; Dechter 2003) , in particular we used ECL i PS e (Apt and Wallace 2006) . Our algorithm is complete, so it is able to find the optimal solutions and prove optimality; we show improvements on the best solutions known in the literature, up to 10% of the objective function value.. The rest of the paper is organized as follows. In the next section, we give a formal description of the problem, then we propose the minimax interpretation in Section 3. We give a CLP(FD) model in Section 4, then we detail some implementation issues in Section 5. Section 6 is devoted to experimental results. We discuss related work in Section 7 and then we conclude. We presented a new application, taken from the hydraulic domain, for logic programming. We proposed an algorithm based on CLP(FD), and found solutions better than the best solutions known in the literature. The computation time can be high when the number of valves is high, but in many cases it is still acceptable since it is applied during the design of a water distribution network.. The model can be improved in various directions. Taking cue from the findings of Creaco et al. (2010) , the variable "weighted average demand shortfall", based on the likelihood (or, more in general, on the probability relative to a prefixed time interval) of failures occurring within the segments as a result of mechanical factors could be used. In fact it has been observed that this variable is superior to the variable "maximum demand shortfall". Weighted average demand shortfall takes into account the entire network and not only the largest segment in terms of demand shortfall; moreover, it guarantees that unique solutions will be found for a pre-established number or cost of the valves in the network.. The current implementation runs on an open source Prolog, but very fast commercial ones, such as SICStus or B-Prolog (Zhou 2011) may provide a strong speedup; in the future we plan to port the implementation on other Prolog systems. In fact, there exist a library for graph algorithms also in SICStus, while in B-Prolog the table mode (Warren 1992; Zhou et al. 2008 ) lets one easily implement efficient graph predicates. Unluckily, the syntax of ECL i PS e and SICStus/B-Prolog is different, although similar; for example, although both ECL i PS e (Schimpf 2002 ) and B-Prolog (Zhou 2011 ) support logical loops, they adopt a different syntax.. From the computational viewpoint, other techniques could be adopted in order to reduce the computation time. For example, we could apply restarts (Gomes et al. 1997) , or try better heuristics to select the next variable to be assigned; from general ones, like, for example, dom/wdeg (Boussemart et al. 2004) , to specific ones.. When the number of valves is very high, we could directly apply incomplete methods, that try to get quickly good solutions sacrificing the proof of optimality. One very promising approach would be to use Large Neighbourhood Search, that has been implemented in Prolog in previous works (Dal Palù et al. 2010) , A very interesting line of research would be to develop an Answer Set Program-ming model. ASP is often faster than CLP(FD) when the domains of the variables do not contain many values (Dovier et al. 2005; Mancini et al. 2008 ); we plan to develop an ASP application in the near future. In the literature of hydraulic engineering, two main problems related to the isolation valves in a pipe network have been faced, that is a) the identification of the segments and undesired disconnections that occur after a set of isolation valves has been closed and b) the (near) optimal location of the set of isolation valves.. As far as the first topic concerns, in the literature there are a number of studies regarding segment identification and the undesired disconnections that occur following the closure of a set of isolation valves. In particular, the methods proposed by Jun and Loganathan (2007) and Kao and Li (2007) are based on a dual representation of the network, with segments treated as nodes and valves as links. The methods proposed by Creaco et al. (2010) and Giustolisi and Savić (2010) use topological incidence matrices to identify the segments.. As far as the second topic concerns, recently, Giustolisi and Savić (2010) have presented a method for the near-optimal placement of isolation valves based on a multi-objective genetic algorithm. Given that the placement of isolation valves is the result of a compromise between the need to reduce the costs tied to purchasing and installing the valves and the simultaneous need to assure high system reliability in the event of routine or non-routine maintenance, Giustolisi and Savić (2010) use the number of valves to be installed-as a surrogate for cost-and the maximum demand shortfall (the demand shortfall represents the unsupplied water demand after isolating a segment) in the different (disconnected) segments of the network as the objective functions to be minimised. Creaco et al. (2010) instead propose a different couple of objective functions, that is total cost of the set of valves, the cost of each valve being calculated as a function of the pipe diameter, and the weighted average unsupplied demand associated with the segments. Also in (Creaco et al. 2010 ) the optimization is solved through a multi-objective genetic algorithm. All of these works use incomplete algorithms, that cannot ensure that the found solution is the real optimum; to the best of our knowledge, this work presents the first complete algorithm to address the valve placement problem.. The valve placement problem has some similarities with the graph partitioning problem, in which the goal is to partition a graph into (almost) equal-size parts by removing the minimal number of edges or (in the weighted edges case) such that the total weight of the edges which connect different parts is minimized. In general, graph partitioning is NP-hard (Garey and Johnson 1990) . Most works in the literature deal with heuristics or approximation algorithms.. One of the first works in the area is by Kernigan and Lin (1970) , that propose a greedy algorithm which outputs a graph bisection. Starting from an initial solution (which can be suggested by some criterion or also be found randomly), each step of the algorithm evaluates the improvement in the objective function that would be obtained moving a vertex from one partition to the other and takes the best choice. Iteration goes on until convergence to a local optimum is reached. The bisection can be applied recursively to partition further. Fiduccia and Mattheyses (1982) improve the algorithm so that the asymptotic behaviour of the algorithm is linear rather than quadratic.. A different approach is based on the spectral analysis of the graph. A graph can be represented by its incidence matrix: a square matrix N × N (if N is the number of vertices) whose (i, j ) element is 1 if there is an edge from vertex i to vertex j and 0 otherwise. Its representation as a Laplacian matrix is obtained as the (matricial) difference between the diagonal matrix which has in position (i, i) the degree of the node i, and the incidence matrix. The set of the eigenvalues of the Laplacian is the graph spectrum (Chung (1994) gives an extended tractation of the subject). Since it was shown (Fiedler 1973 ) that the second smallest eigenvalue of the Laplacian associated to a graph contains information about its connectivity, various partitioning heuristics were proposed relying on the eigenvectors (Hendrickson and Leland 1995a; Spielman and Teng 1996) . In comparison with other heuristics, spectral methods provide good quality partitions at an increased computational cost (necessary to compute the matrix eigenvalues).. Various kinds of heuristics can be used in multilevel schemes, which reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph. Hendrickson and Leland (1995b) employ spectral methods to partition the smaller graph, and use a variant of the Kernighan-Lin algorithm to periodically refine the partitions. Karypis and Kumar (1998) adopt a coarsening heuristic for which the size of the partition of the coarse graph is within a small factor of the size of the final partition.. The special case of planar graphs (i.e. graphs which can be drawn without intersecting edges) is of particular interest for our application since it is often the case for water supply networks. Finding the optimal solution is NP-hard also for the planar case, however the planar separator theorem (Lipton and Tarjan 1979) states that a bisection in which the biggest set contains at most two thirds of the vertices and whose separator contains O ( √ n) vertices can be found in linear time. Other related problems are the multicut problems (Pichler et al. 2010) , in which the aim is to find the minimal set of edges (or nodes) such that given pairs of nodes are no longer connected. In our case, instead, the aim is to disconnect a possibly small part of the network while keeping connected all the rest.. The algorithms for graph partitioning or solving multicut problems are clearly not directly applicable to the valve placement problem, also because of the issue of unintended isolation mentioned in Section 1. However, it would be interesting to hybridise our algorithm with some of the techniques available for such problems; we plan to study the feasibility of such approaches in future work.

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Topology-preserving simplification of 2D nonmanifold meshes with embedded structures Abstract Mesh simplification has received tremendous attention over the years. Most of the previous work in this area deals with a proper choice of error measures to guide the simplification. Preserving the topological characteristics of the mesh and possibly of data attached to the mesh is a more recent topic and the subject of this paper. We introduce a new topology-preserving simplification algorithm for triangular meshes, possibly nonmanifold, with embedded polylines. In this context, embedded means that the edges of the polylines are also edges of the mesh. The paper introduces a robust test to detect if the collapse of an edge in the mesh modifies either the topology of the mesh or the topology of the embedded polylines. This validity test is derived using combinatorial topology results. More precisely, we define a so-called extended complex from the input mesh and the embedded polylines.We show that if an edge collapse of the mesh preserves the topology of this extended complex, then it also preserves both the topology of the mesh and the embedded polylines. Our validity test can be used for any 2-complex mesh, including nonmanifold triangular meshes, and can be combined with any previously introduced error measure. Implementation of this validity test is described. We demonstrate the power and versatility of our method with scientific data sets from neuroscience, geology, and CAD/CAM models from mechanical engineering. We assume the reader is familiar with mesh simplification techniques in general. Most of the previous works on mesh simplification are devoted to the development of a specific scalar error measure, taking into account the geometry of the mesh and possibly the values of data attached to the mesh. A more recent topic in mesh simplification is the preservation of topological characteristics of the mesh and of data attached to the mesh. In this paper a new topologypreserving simplification algorithm is introduced for triangular meshes, possibly nonmanifold, in which polylines are embedded. In this context embedded means that the edges of the polylines are also edges of the mesh. The mesh is simplified by repeated edge collapses, following the classical scheme introduced in previous works. For each edge of the mesh, the cost of its collapse is computed and inserted in an ordered heap of edges. The algorithm iteratively pops the edge collapse, introducing the low-est error in the simplified mesh, checks for the validity of the collapse (i.e., geometry, topology, or attribute consistency), and, if this operation is accepted, updates both the mesh and the heap. Since the polylines form a subset of the edges of the mesh, edge collapses modify both the mesh and the set of polylines embedded in the mesh. The main contribution of this paper is a robust validity algorithm that detects whether or not an edge collapse preserves the topology of the mesh as well as the topology of the embedded polylines. To this end we define a so-called extended complex that implicitly encodes both topologies. Thereafter edge collapses that preserve the topology of this extended complex are detected. We show that these edge collapses preserve also both the topologies of the mesh and the embedded polylines. As we will see in this introduction, the preservation of these topological characteristics is crucial in several applications.. Many application areas may produce meshes with embedded polylines. This work has been motivated by three applications, for which the topology of the mesh and the topology of the embedded polylines must be preserved throughout the simplification. This paper has introduced a new topology-preserving simplification algorithm, based on edge collapse, for nonmanifold triangular meshes with embedded polylines. The topology of the polylines as well as the mesh is preserved throughout the simplification using a unified and robust validity algorithm to select edges that can be collapsed. Our algorithm is based on powerful combinatorial topology results and can be applied to general triangular meshes, including nonmanifold meshes. The idea of the extended complex, encoding implicitly the topologies of the mesh and the polylines in a unified way, is at the heart of our results. One of the most appealing feature of this idea is its possible extension to 3-complexes. We are currently working on this in order to generalize this concept to tetrahedral meshes with embedded 2D and 1D structures. Research on surface simplification in computer graphics and scientific visualization has led to a substantial number of methods within the last 12 years. An exhaustive description of this field is beyond the scope of this paper, and one can refer to the many surveys [2, 10, 24] available. In the remainder of this section we only review the methods relevant to our work.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Associative memory of phase-coded spatiotemporal patterns in leaky Integrate and Fire networks We study the collective dynamics of a Leaky Integrate and Fire network in which precise relative phase relationship of spikes among neurons are stored, as attractors of the dynamics, and selectively replayed at different time scales. Using an STDP-based learning process, we store in the connectivity several phase-coded spike patterns, and we find that, depending on the excitability of the network, different working regimes are possible, with transient or persistent replay activity induced by a brief signal. We introduce an order parameter to evaluate the similarity between stored and recalled phase-coded pattern, and measure the storage capacity. Modulation of spiking thresholds during replay changes the frequency of the collective oscillation or the number of spikes per cycle, keeping preserved the phases relationship. This allows a coding scheme in which phase, rate and frequency are dissociable. Robustness with respect to noise and heterogeneity of neurons parameters is studied, showing that, since dynamics is a retrieval process, neurons preserve stable precise phase relationship among units, keeping a unique frequency of oscillation, even in noisy conditions and with heterogeneity of internal parameters of the units.It has been hypothesized that, in many areas of the brain, having different brain functionality, repeatable precise spatiotemporal patterns of spikes play a crucial role in coding and storage of information. Temporally structured replay of spatiotemporal patterns have been observed to occur during sleep, both in the cortex and hippocampus [1] [2] [3] [4] , and it has been hypothesized that this replay may subserve memory consolidation. The sequential reactivation of hippocampal place cells, corresponding to previously experienced behavioral trajectories, has been observed also in the awake state (awake replay) [6] [7] [8] [9] , namely during periods of relative immobility. Awake replay may reflect trajectories through either the current environment or previously, spatially remote, visited environments. A possible interpretation is that spatiotemporal patterns, stored in the plastic synaptic connections of hippocampus, are retrieved when a cue activates the emergence of a stored pattern, allowing these patterns to be replayed and then consolidated in distributed circuits beyond the hippocampus [9] . Crosscorrelogram analysis revealed that in prefrontal cortex the time scale of reactivation of firing patterns during post-behavioral sleep was compressed five-to eightfold relative to waking state [3, 5] , a similar compression effect may also be seen in primary visual cortex [2] . Internally generated spatiotemporal patterns have also been observed in the rat hippocampus during the delay period of a memory task, showing that the emergence of consistent pattern of activity may be a way to maintain important information during a delay in a task [10] .Among repeating patterns of spikes a central role is played by phase-coded patterns [11] [12] [13] 15] , i.e. patterns with precise relative phases of the spikes of neurons participating to a collective oscillation, or precise phases of spikes relatively to the ongoing oscillation.First experimental evidence of the importance of spike phases in neural coding was observed in experiments on theta phase precession in rat's place cells [17, 19] , showing that spike phase is correlated with rat's position. Recently, the functional role of oscillations in the hippocampal-entorinal cortex circuit for path-integration has been deeply investigated [3, [16] [17] [18] [19] 28] , showing that place cells and grid cells form a map in which precise phase relationship among units plays a central role. In particular it has been shown [21, 23, 24] that both spatial tuning and phase-precession properties of place cells can arise when one has interference among oscillatory cells with precise phase relationship and velocity-modulated frequency.Further evidence of phase coding comes from the experiments on spike-phase coding of natural stimuli in auditory and visual primary cortex [12, 13] , and from experiments on short-term memory of multiple objects in prefrontal cortices of monkeys [11] .These experimental works support the hypothesis that collective oscillations may underlie a phase dependent neural coding and an associative memory behavior which is able to recognize the phase coded patterns.The importance of precise timing relationships among neurons, which may carry information to be stored, is supported also by the evidence that precise timing of few milliseconds is able to change the sign of synaptic plasticity. The dependence of synaptic modification on the precise timing and order of pre-and post-synaptic spiking has been demonstrated in a variety of neural circuits of different species. Many experiments show that a synapse can be potentiated or depressed depending on the precise relative timing of the pre-and post-synaptic spikes. This timing dependence of magnitude and sign of plasticity, observed in several types of cortical [39, 40, 47] and hip-

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


A new algorithm for wavelet-based heart rate variability analysis One of the most promising non-invasive markers of the activity of the autonomic nervous system is Heart Rate Variability (HRV). HRV analysis toolkits often provide spectral analysis techniques using the Fourier transform, which assumes that the heart rate series is stationary. To overcome this issue, the Short Time Fourier Transform is often used (STFT). However, the wavelet transform is thought to be a more suitable tool for analyzing non-stationary signals than the STFT. Given the lack of support for wavelet-based analysis in HRV toolkits, such analysis must be implemented by the researcher. This has made this technique underutilized. This paper presents a new algorithm to perform HRV power spectrum analysis based on the Maximal Overlap Discrete Wavelet Packet Transform (MODWPT). The algorithm calculates the power in any spectral band with a given tolerance for the band's boundaries. The MODWPT decomposition tree is pruned to avoid calculating unnecessary wavelet coefficients, thereby optimizing execution time. The center of energy shift correction is applied to achieve optimum alignment of the wavelet coefficients. This algorithm has been implemented in RHRV, an opensource package for HRV analysis. To the best of our knowledge, RHRV is the first HRV toolkit with support for wavelet-based spectral analysis. Heart Rate Variability (HRV) refers to the variation over time of the intervals between consecutive heartbeats. Since the heart rhythm is modulated by the autonomic nervous system (ANS), HRV is thought to reflect the activity of the sympathetic and parasympathetic branches of the ANS. The continuous modulation of the ANS results in continuous variations in heart rate. One of the most powerful HRV analysis techniques is based on the spectral analysis of the time series obtained from the distances between each pair of consecutive heartbeats. The HRV power spectrum is a useful tool as a predictor of multiple pathologies [1] , [2] .. Akselrod et al. [3] described three components in the HRV power spectrum with physiological relevance: the very low frequency (VLF) component (frequencies below 0.03 Hz), which is modulated by the renin-angiotensin system; the low frequency (LF) component (0.03-0.15 Hz), which is thought to be of both sympathetic and parasympathetic nature; and the high frequency (HF) component (0.18-0.4 Hz), which is related to the parasympathetic system. At present, there is no absolute consensus on the precise limits of the boundaries of these three bands. In the literature we can find authors who use slightly different bands' boundaries [4] .. There exist several HRV spectral analysis techniques. These techniques may be classified as nonparametric and parametric [5] . The main advantage of the nonparametric methods is the simplicity and speed of the algorithm used (The Fast Fourier Transform). The main advantage of the parametric methods is that they give smoother spectral components. However, parametric methods present problems regarding to correct model order selection. Although these techniques are widely used, they have no temporal resolution. This severely limits their ability to analyze non-stationary signals and transient phenomena. To alleviate this limitation temporal windows are often used, so that small segments of the whole signal are analyzed. Among these techniques we may highlight the Short Time Fourier Transform (STFT) [6] . However, timefrequency resolution of the STFT depends on the spread of the window used. Thus, the STFT has fixed time-frequency resolution: high frequency resolution implies poor time resolution and vice versa. Conversely to Fourier, the wavelet transform performs time-frequency analysis and it is recognized as a powerful tool to study non-stationary signals [7] .. HRV analysis toolkits such as Kubios HRV [8] or aHRV [9] only enable HRV spectral analysis based on the Fourier transform or parametric methods. To the best of our knowledge, the only option for using the wavelet transform in HRV analysis is to manually implement the algorithms, probably with the support of some general wavelet library. This is tedious, and prone to error. Although some researchers have done this [10] , [11] , many more (especially those with a medical background) choose to use Fourier-based tools, even when they know that the signal being analyzed is non-stationary. A query in the PubMed database with the terms "heart rate variability Fourier transform" returns 660 articles, while a query with the terms "heart rate variability wavelet transform" only returns 145 articles. The lack of tools for carrying out HRV analysis using the wavelet transform has made this potentially superior analysis technique underutilized in comparison with the Fourier transform.. In this paper we present an algorithm to perform HRV power spectrum analysis based on the Maximal Overlap Discrete Wavelet Packet Transform (MODWPT). The algorithm calculates the spectrogram in any frequency band, allowing a certain tolerance for the position of the band's boundaries. The algorithm has been validated over simulated and real RR series. Its capability for identifying fast changes in the RR series' spectral components has been compared with the STFT and a windowed version of the Burg method, showing that these techniques miss some transient changes that are successfully identified by the wavelet transform. We have implemented the algorithm in RHRV, an open-source package for HRV analysis publicly available on the Internet. A previous version of this algorithm was published in [12] .. Section 2 starts with a brief review of the wavelet transform, with particular attention to the MODWPT, and then introduces our algorithm to perform HRV power spectrum analysis. Section 2.5 provides a short description of the implementation of the algorithm in the RHRV package. Section 3 presents a comparison between our algorithm, the STFT and the windowed Burg method over simulated and real RR series. Finally, the results of this paper are discussed and some conclusions are given. We have presented an algorithm to perform HRV power spectrum analysis based on the MODWPT. The computational load of the our algorithm is comparable to the load of widely used STFT-based algorithms. The algorithm has been validated over simulated RR series with known spectral components. We have shown that the STFT and the windowed Burg method miss some quick changes that are successfully identified by the MODWPT. These results suggest that wavelet-based analysis is a better tool to analyze fast transient phenomena in the RR time series than other techniques based on windowing.. In order to obtain optimal temporal resolution, we should avoid descending to deep levels of the PMODWPT decomposition tree. In RHRV, a warning is generated if the band cover needed for the analysis requires expanding more than log 2 (N/(L − 1) + 1) levels, N being the number of samples of the signal and L the filter length. A careful selection of the frequency bands to be analyzed provides some control over the depth of the tree. For example, if the RR time series is sampled at 4 Hz, and we want to obtain the power in the band [0.27, 0.5] Hz with a tolerance in the position of the band's boundaries of 0.01, our algorithm will need to descend seven levels on 13 the tree. However, to calculate the power in [0.26, 0.5] Hz with the same tolerance our algorithm only needs to descend three levels. In this way, we obtain a good estimate of the power in the band [0.27, 0.5] Hz without compromising the temporal resolution of the results. A corollary of the phenomenon described in the previous paragraph is that, in order to achieve optimum temporal resolution (and therefore maximize the chance of identifying fast transient phenomena), the spectral bands used in HRV analysis with wavelets will probably have to differ from those traditionally associated with VLF, LF and HF. This opens the question of what may be the pathophysiological significance of spectral bands different from those which have already been widely studied in the literature.. The mother wavelet used in HRV analysis also influences the time-frequency resolution because it determines the filter shape. Further study on how the mother wavelet influences the results of the HRV analysis is required. For example, our initial tests suggest that shorter wavelets have greater time resolution than the larger wavelets, whereas the latter have a better filtering behavior than the first ones.. When performing a wavelet analysis, a careful choice of the bands is needed to avoid heavy computations, as well as a choice of the mother wavelet. When using STFT analysis we also have to choose the frequency bands (although we have more flexibility in the choice), as well as the window size, window displacement and zero padding size. Overall, more parameter choices need to be made when using the STFT. Furthermore, the selection of the STFT parameters is complex, not only because of the computation efficiency, but also because the use of a certain window size influences the temporal resolution and the frequency bands available to the analysis. To address this issue, some authors use different windows for each frequency band. This makes the analysis process heavy. Moreover, the results obtained in each of the bands are not comparable since they have been obtained using different windows. The need for tuning a lower number of knobs, and the possibility of using the same parameters in the analysis of all the HRV frequency bands are two additional advantages of using wavelets in HRV studies.. The algorithm described in this paper has been implemented in the RHRV package for the R environment in its 3.0 version. To the best of our knowledge, RHRV is the first HRV analysis toolkit that supports wavelet-based spectral analysis of the RR time series. This software can be freely downloaded from [25] . The availability of this package will enable researchers to carry out HRV power spectrum analysis based on the wavelet transform in a simple manner (see Listing 2) . We hope that this will help increase the number of HRV studies that use the higher temporal resolution wavelet-based techniques.

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


Role-based access control for publish/subscribe middleware architectures Research into publish/subscribe messaging has so far done little to propose architectures for the support of access control, yet this will be an increasingly critical requirement as systems move to Internet-scale. This paper discusses the general requirements of publish/subscribe systems with access control. We then present our specific integration of OASIS role-based access control into the Hermes publish/subscribe middleware platform. Our system supports many advanced features, such as the ability to work within a network where nodes are attributed different levels of trust, and employs a variety of access restriction methods which balance expressiveness with the content-based routing optimisations available. We illustrate our achievements by discussing an application scenario in which our system will be of particular use. The Opera Research Group at the University of Cambridge has worked in both publish/subscribe (pub/sub) middleware [1, 7] , and in Role-Based Access Control (RBAC) [3, 8] . We believe that combining these two technologies would be a useful contribution to pub/sub system research.. Publish/subscribe technology has to date focused on event filtering, efficient event routing, delivery semantics, and event composition. Access control has been largely neglected. Access control is an important requirement when customers are expected to pay for publish/subscribe services. A simplistic approach would be to run the entire pub/sub system over a secure network infrastructure (for example using Netscape's Secure Socket Layers SSL). However, this does not allow access control policy to be expressed on a subscription or publication basis, and it lacks differential treatment of various nodes in the network by assuming complete trust. It would not be practical for Internet-scale applications with nodes of varying reliability and trust. Further, this approach does not allow the policy governing the privileges of nodes to evolve based on experience.. To address these issues, we have extended our pub/sub system to support a form of role-based access control, and use roles as the basis for security-oriented filtering of both publication and subscription of events within the network. We also support the efficient, dynamic update of pub/sub RBAC policy.. To our knowledge, this paper presents the first complete architecture for policy-based access control in publish/subscribe research.. This paper is organised as follows. Section 2 describes the aims and contributions of our research. Section 3 introduces the fundamental pub/sub and RBAC concepts used. We describe a general architecture for pub/sub access control in Section 4. We extend this architecture to include trust management for brokers in Section 5. Details of our implementation using the specific OASIS [3] and Hermes [7] technologies are presented in Section 6. Some common types of access control policy, based on what we expect to be useful applications, are presented in Section 7. Section 8 describes some of the future research directions we shall pursue. We discuss research closely related to our work in Section 9. Finally, Section 10 concludes this paper, summarising our research contributions. We have presented a general architecture for integrating role-based access control into publish/subscribe messaging systems. We demonstrated our approach through an implementation that combines the Hermes pub/sub system and OASIS RBAC. We discussed likely application scenarios and then related our work to other current research. Our architecture is expressive and powerful; it supports optimisation of access control checks by the pub/sub infrastructure where possible, as well as the management of networks in which intermediate nodes are not all equally trustworthy. We found two pieces of recent research which were directly related to our work. In [10] , Wang et al. present a number of considerations for access control in general publish/subscribe systems. As discussed in Sect. 2, their paper also discusses the need to be placed within a continuum from totally secure, accountable systems, to systems with efficient broadcasting and routing of events largely powered by a lack of need for security-related accounting.. A similar introduction is presented in [6] . Miklós devotes significant attention to specifying maximum and minimum security restrictions by assuming an ordering of events. We feel this approach is too restrictive, and unnecessarily prescriptive. Another problem with his work is the apparent lack of implementation details. Our approach provides a more expressive policy language with which to control security. After we have completed privilege negotiation we can compile down any restrictions into the event filters of the pub/sub system itself, enabling their enforcement to be managed efficiently. This section provides a quick overview of the technology used within our research, including the Hermes publish/-subscribe middleware, and the OASIS role-based access control system. It introduces fundamental concepts that will be used throughout the paper. In this section, we present the enhanced implementation of Hermes that includes the role-based access control mechanisms introduced in this paper. Since our proposed architecture makes few assumptions about the internal implementation of the publish/subscribe middleware that it is deployed on, only small parts of the current Hermes system required modification. The major changes were the addition of new parameters to the event broker API and the integration of OASIS with local event brokers for carrying out policy-based access control decisions. An authoritative replica of the subscription and advertisement policy is conveniently stored at the rendezvous node (cf. Section 3.1.1) for this event type. This allows any local event broker to access policy via Hermes' peer-to-peer overlay network in a simple and scalable way. In addition, local brokers maintain a policy cache to reduce network load. Other types of policy are kept in a centralised repository. Figure 7 shows the public API of a Hermes event broker after OASIS integration. For simplicity of exposition, we do not show the exceptions thrown by the calls in case of failure or rejection. All API calls require a client to authenticate itself when invoking a function by providing a set of credentials (creds), which will effectively communicate this client's role in the system (publisher, subscriber, or typeowner). The identity and credentials are then passed to the OASIS implementation that performs a policy check in order to determine whether the particular operation should be executed by the local event broker. The connect calls are governed by the broker-client connection policy. If a client is not authorised to connect to a particular broker, it will not be able to invoke any further API calls and thus consume resources at the broker. The addEventType/removeEventType functions are invoked by an event type owner to manage event types according to the type management policy.

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


Testing spatial autocorrelation in weighted networks: the modes permutation test Abstract In a weighted spatial network, as specified by an exchange matrix, the variances of the spatial values are inversely proportional to the size of the regions. Spatial values are no more exchangeable under independence, thus weakening the rationale for ordinary permutation and bootstrap tests of spatial autocorrelation. We propose an alternative permutation test for spatial autocorrelation, based upon exchangeable spatial modes, constructed as linear orthogonal combinations of spatial values. The coefficients obtain as eigenvectors of the standardized exchange matrix appearing in spectral clustering and generalize to the weighted case the concept of spatial filtering for connectivity matrices. Also, two proposals aimed at transforming an accessibility matrix into an exchange matrix with a priori fixed margins are presented. Two examples (inter-regional migratory flows and binary adjacency networks) illustrate the formalism, rooted in the theory of spectral decomposition for reversible Markov chains. Real spatial networks are irregular and subject to aggregation. They are bound to exhibit regions differing in sizes or weights. This paper proposes a weighted analysis of Moran's I, in the possibly most general setup provided by the exchange matrix formalism, rooted in the theory of reversible Markov chains and gravity flows of geographers.. Besides providing a rationale for overcoming the heteroscedasticity problem in the direct application of permutation or bootstrap autocorrelation tests, the concept of spatial modes we have elaborated upon arguably generalizes the concept of spectrally based spatial filtering (e.g. Griffith 2003 ) to a weighted setting and helps integrating other network-related issues in a unified setting: typically, the first nontrivial raw coordinate c 1 of Sect. 2.2 has been known for some time to provide the optimal solution to the spectral clustering problem, partitioning a weighted graph into two balanced components (e.g. Chung 1997; von Luxburg 2007; Bavaud 2010) .. Finally, local variance (4) can be generalized to local inertias 1 2 P ij e ij D ij (where D represents a squared Euclidean distance between regions) and to local covariances 1 2 P ij e ij ðx i À x j Þðy i À y j Þ, whose future study may hopefully enrich formal issues and applications in spatial autocorrelation.

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


Communication and team situation awareness in the OR: Implications for augmentative information display Team Situation Awareness (TSA) is one of the critical factors in effective Operating Room (OR) teamwork and can impact patient safety and quality of care. While previous research showed a relationship between situation awareness, as measured by communication events, and team performance, the implications for developing technology to augment and facilitate TSA were not examined. This research aims to further study situation-related communications in the cardiac OR in order to uncover potential degradation in TSA which may lead to adverse events. The communication loop construct-the full cycle of information flow between the participants in the sequence-was used to assess susceptibility to breakdown. Previous research and the findings here suggest that communication loops that are open, nondirected, or with delayed closure, can be susceptible to information loss. These were quantitatively related to communication indicators of TSA such as questions, replies, and announcements. Taken together, both qualitative and quantitative analyses suggest that a high proportion of TSA-related communication (63%) can be characterized as susceptible to information loss. The findings were then used to derive requirements and design a TSA augmentative display. The design principles and potential benefits of such a display are outlined and discussed. Patient safety and medical errors are internationally recognized as a critical problem [1, 2] . While many factors have been associated with medical errors and adverse events, this paper addresses information sharing and team situation awareness as critical factors in effective Operating Room (OR) teamwork and patient safety. The research approach was to focus on communication as an essential process in building and maintaining situation awareness, and in view of its susceptibility to breakdown, explore a possible solution to augment and facilitate these processes.. Teamwork is characteristic to many healthcare contexts and to the OR in particular [3, 4] . The OR is a critical and complex work environment consisting of people, devices and tools, actions and events. Effective teamwork in the OR is critical to patient safety because healthcare workers interact with each other in order to achieve successfully and safely a common goal [5] [6] [7] [8] . To accomplish the common goal, all members of the surgery team must perform their roles and tasks with full and continuous comprehension and awareness of the dynamic situation. To do this they rely on continuous coordination, communication, and information sharing with their team mates [9] [10] [11] [12] [13] 7] . Accurate information sharing among people and technology is essential to effectively coordinate the interdependent activities as part of the teamwork process [13] [14] [15] [16] . The process by which people acquire information (whether from devices and displays or shared with other people), understand it, and utilize it to comprehend and be aware of the dynamic situation is often referred to as Situation Awareness (SA). The objective of the data analysis was to identify situation-related communications that were susceptible to breakdown. To achieve this objective, the analytic approach progressed in two steps: (1) identifying situation-related communications; (2) within the sub-set of situation-related communications, identifying those that were susceptible to breakdown and information loss. Identification of such communications would imply the potential for TSA degradation and justify the need for a TSA display. Once that need was empirically demonstrated, the communication data was subsequently used to derive the information requirements for a TSA display.

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


Root Isolation of Zero-dimensional Polynomial Systems with Linear Univariate Representation In this paper, a linear univariate representation for the roots of a zero-dimensional polynomial equation system is presented, where the roots of the equation system are represented as linear combinations of roots of several univariate polynomial equations. The main advantage of this representation is that the precision of the roots can be easily controlled. In fact, based on the linear univariate representation, we can give the exact precisions needed for isolating the roots of the univariate equations in order to obtain the roots of the equation system to a given precision. As a consequence, a root isolation algorithm for a zero-dimensional polynomial equation system can be easily derived from its linear univariate representation. Solving polynomial equation systems is a basic problem in the field of computational science and has important engineering applications. In most cases, we consider zero-dimensional polynomial systems. We will discuss how to solve this kind of systems in this paper. In particular, we will consider how to isolate the complex roots for such a system.. One of the basic methods to solve polynomial equation systems is based on the concept of separating elements, which can be traced back to Kronecker (14) and has been studied extensively in the past twenty years (1; 2; 4; 8; 9; 10; 11; 12; 13; 15; 19; 20; 24) . The idea of the method is to introduce a new variable t = i c i x i which is a linear combination of the variables to be solved such that t = i c i x i takes different values when evaluated at different roots of the polynomial equation system P = 0. In such a case, we say that t is a separating element for P = 0. If t = i c i x i is a separating element for P = 0, the roots of P = 0 have the following rational univariate representation (RUR):. f (t) = 0, x i = R i (t), i = 1, ..., n, where f ∈ Q[t] and R i (t) are rational functions in t. As a consequence, solving multi-variate equation systems is reduced to solving a univariate equation f (t) = 0 and to substituting the roots of f (t) = 0 into rational functions R i (t). Along this line, better complexity bounds and effective software packages for solving polynomial equations such as the Maple package RootFinding by Rouillier (20) and the Magma package Kronecker by Giusti, Lecerf, and Salvy (11) are given.. The above approaches still have the following problem: for an isolation interval [a, b] of a real root α of f (u) = 0, to determine the isolation interval of x i = R i (α) under a given precision is not a trivial task. In this paper, we propose a new representation for the roots of a polynomial system which will remedy this drawback. In the ISSAC paper (3), based on ideas similar to separating elements, a local generic position method is introduced to solve bivariate polynomial systems and experimental results show that the method is quite efficient for solving equation systems with multiple roots. In this paper, we extend the method to solve general zero-dimensional polynomial systems. A local generic position for a polynomial equation system P = 0 is also a linear combination of the variables to be solved: t = i c i x i which satisfies two conditions. First, t k = k i=1 c i x i is a separating element of P k = (P) ∩ Q[x 1 , . . . , x k ] for k = 2, . . . , n, and the roots of P k = 0 have a one-to-one correspondence with the roots of a univariate equation T k (t k ) = 0. Second, for a root ξ = (ξ 1 , . . . , ξ k ) of P k = 0 represented by a root η of T k (t k ) = 0, all the roots η j of T k+1 (t k+1 ) = 0 corresponding to the roots of P k+1 = 0, say ξ j = (ξ, ξ k+1,j ), "lifted" from ξ are projected into a fixed square neighborhood of η. This "local" property is illustrated in Figure 1 . We prove that if t n = n i=1 c i x i is a local generic position for P, then the roots of P = 0 can be be represented as special linear combinations of the roots of univariate equations T k (t k ) = 0, k = 1, . . . , n:. where s j are certain positive rational numbers and the α j+1 matching α j are in certain square neighborhood of α j to be defined in Section 2. Such a representation is called a linear univariate representation (LUR for short) of the polynomial system. The main advantage of the LUR representation is that the precision of the roots can be easily controlled. For RUR, computing solutions with a given precision is not a trivial task as we mentioned before. It is not easy to know with which precision to isolate the roots of f (t) = 0 is enough in order for the roots of the system x i = R i (t) to satisfy a given precision. For LUR, precision control becomes very easy. We can give an explicit formula for the precision of the roots of T i (x) = 0 in order to obtain the roots of the system with a given precision. So we can obtain the solutions of the system by refining the roots of T i (x) = 0 at most once. Another advantage of LUR is that when we isolate the roots of T i+1 (x) = 0, we need only to consider a fixed neighborhood of each root of T i (x) = 0.. We propose an algorithm to compute an LUR for a zero-dimensional polynomial system. The key ingredients of the algorithm are to estimate the root bounds of P = 0 and to estimate the separating bounds for the roots of P k+1 = 0 lifted from a root of P k = 0. We adopt a computational approach to estimate such bounds in order to obtain tight bound values. For the root bounds of P = 0, we use Gröbner basis computation to obtain the generating polynomial of the principal ideal (P) ∩ Q[x i ] and use this polynomial to estimate the root bound for the x i coordinates of the roots of P = 0. The separating bounds for P k = 0 are obtained from the isolating boxes for the roots of the T k (x) = 0. These bounds in turn will be used to compute the isolating boxes for the roots of P k+1 = 0. Hence, the algorithm to compute an LUR also gives a set of isolating boxes for the roots of P = 0.. In Section 2, we give the definition of LUR and the main result of the paper. In Section 3, we present an algorithm to compute an LUR of a zero-dimensional polynomial system as well as a set of isolation boxes of the roots of the equation system. In Section 4, we provide some illustrative examples. We conclude the paper in Section 5. Now, we can give the full algorithm based on LUR. Algorithm 1. The input is a zero dimensional polynomial system P = {P 1 , . . . , P t } in Q[x 1 , . . . , x n ] and a positive rational number ǫ. The output is an LUR for P and a set of ǫ-isolation boxes for the roots of P = 0. S1 Compute a Gröbner basis G of P with the graded reverse lexicographic order and a monomial basis B for linear space A = Q[x 1 , . . . , x n ]/(P) over Q. S2 Compute T 1 (x) as defined in (17) with the method given in Section 3.2; compute a set of ǫ-isolation boxes B 1 for the complex roots of T 1 (x) = 0; set. . . , n − 1, do steps S4-S9; output the set of boxes (19) . S4 Compute r i+1 with the method in Lemma 8. Select a rational number s i such that condition (7) is valid. S5 Compute T i+1 (x) as defined in (17) Remark 18. From Lemma 9, the roots of T i+1 (x) = 0 are in the rectangle I Ii . So, we need only to isolate the roots of T i (x) = 0 inside these rectangles. This property is very useful in practice, see Figure 1 for an illustration.

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


Modal Knowledge and Game Semirings The aim of algebraic logic is to compact series of small steps of general logical inference into larger (in)equational steps. Algebraic structures that have proved very useful in this context are modal semirings and modal Kleene algebras. We show that they can also model knowledge and belief logics as well as games without additional effort; many of the standard logical properties are theorems rather than axioms in this setting. As examples of the first area we treat the classical puzzles of the Wise Men and the Muddy Children. Moreover, we show possibilities for handling knowledge update and revision algebraically. For the area of games, we generalise the well-known connection between game logic and dynamic logic to the setting of modal semirings and link it to predicate transformer semantics, in particular to demonic refinement algebra. We think that our study provides evidence that modal semirings are able to handle a wide variety of (multi-)modal logics in a uniform algebraic fashion. The aim of algebraic logic is to compact series of small steps of general logical inference into larger (in)equational steps. Moreover, it attempts to replace tedious model-theoretic argumentation, in particular, elementwise argumentation, by more abstract and compact reasoning.. During the recent years it has turned out that variants of semirings (e.g. [2] ) are very useful algebraic structures for this. They may be seen as abstract representations of (state) transition systems and axiomatise the fundamental operations of choice and sequential composition in such systems. Semirings with an idempotent choice operator have a natural approximation order that corresponds to implication (or inclusion); hence implicational inference can be replaced by inequational reasoning. Adding finite and infinite iteration leads to Kleene algebras [3] and omega algebras [4] .. An essential extension of these basic structures is provided by modal semirings, as studied extensively in [5, 6] . They are based on the concept of tests [7] that algebraically represent state predicates. Modal semirings add diamond and box operators and are more general than Kripke structures: the access between possible worlds can be described not only by relations, but, e.g., by sets of computation paths or even by computation trees. Kleene and omega algebras with This paper is a significantly extended and revised version of [1] . modal operators can be used to give algebraic semantics of PDL, LTL and CTL; as shown in [8] , the subclass of left Boolean quantales can even handle full CTL * and the propositional µ-calculus. Many further applications have been developed.. In the present paper we show that modal semirings can also model knowledge and belief logics (e.g. [9] ) as well as games (e.g. [10] ) without additional effort; many of the standard logical properties there are theorems rather than axioms in this setting. As examples of the first area we treat the classical puzzles of the Wise Men and the Muddy Children and show possibilities for handling knowledge update and revision algebraically. The algebraic treatment offers a more concise way of reasoning than classical natural deduction proofs. Moreover, since the algebraic treatment is completely first-order, it offers the possibility of using off-the shelf fully automatic theorem provers without a need for specially tailoring them towards modal/epistemic logic. For the area of games, we generalise the wellknown connection between game logic and dynamic logic to the setting of modal semirings and link it to predicate transformer semantics, in particular to demonic refinement algebra [11] .. The character of this paper is that of a feasibility study, not that of a re-development of existing particular modal logics in a new setting. Nevertheless, a surprising result seems to be that the relatively simple axiomatisation of modal semirings and modal Kleene algebras achieves many of the standard properties of such logics in an easy and uniform way. Our framework is intended for defining the semantics of new, special-purpose modal logics as they arise, e.g., with multi-agent systems. Using it will provide the advantage that many standard modal properties such as axioms M and K as well as certain induction rules hold automatically and do not need to be reproved or added as axioms separately for each new logic.. The paper is organised as follows. Part I deals with an algebraisation of knowledge/belief logics. These are briefly recapitulated in Section 2 and illustrated with a variant of the Wise Men Puzzle. Section 3 defines several variants of modal (left) semirings and Kleene algebras and lists the most essential properties of the box and diamond operators. They are applied in Section 4 to represent the usual knowledge/belief operators for multiagent systems algebraically. The laws these inherit from the general algebraic framework are used in Section 5 for a concise solution of the Wise Men Puzzle. Section 6 reuses parts of the solution to treat the Muddy Children Puzzle. In Section 7 we show further use of the algebra in modelling certain aspects like knowledge/belief revision (e.g. [12] ) and preference relations between possible worlds and their upgrade (e.g. [13] ).. Part II treats games and predicate transformers. Section 8 gives a brief recapitulation of games and their algebra, in particular, of their representation by predicate transformers. These are analysed in a general fashion in Section 9, and a connection to Parikh's iteration operators for games is set up. Section 10 considers predicate transformers as elements of a left i-semiring which is extended to a modal one. It relates the box and diamond operators there to the enabledness and termination operators of demonic refinement algebra [14] . Section 11 provides a brief conclusion and outlook.

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Performance evaluation of data aggregation for cluster-based wireless sensor network In wireless sensor network, data fusion is considered an essential process for preserving sensor energy. Periodic data sampling leads to enormous collection of raw facts, the transmission of which would rapidly deplete the sensor power. In this paper, we have performed data aggregation on the basis of entropy of the sensors. The entropy is computed from the proposed local and global probability models. The models provide assistance in extracting high precision data from the sensor nodes. We have also proposed an energy efficient method for clustering the nodes in the network. Initially, sensors sensing the same category of data are placed within a distinct cluster. The remaining unclustered sensors estimate their divergence with respect to the clustered neighbors and ultimately join the least-divergent cluster. The overall performance of our proposed methods is evaluated using NS-2 simulator in terms of convergence rate, aggregation cycles, average packet drops, transmission cost and network lifetime. Finally, the simulation results establish the validity and efficiency of our approach. The wireless sensor network (WSN) [1] has started receiving huge research incentives for its omnipresence in several applications, including environmental monitoring, wildlife exploration, medical supervision and battlefield surveillance. The sensor network is formed with small electronic devices possessing self-configuring capability that are either randomly deployed or manually positioned in huge bulk [2] . It performs activities in several dimensions, for instance identifying the neighborhood, presence of targets or monitoring environmental factors (motion, temperature, humidity, sound and other physical variables). However, owing to limited battery power, the sensor networks demand energy efficient resolutions to enhance the performance of sensor network.. Energy consumption problem, being the most visible challenge, is considered central to the sensor research theme. The processing of data, memory accesses and input/output operations, all consume sensor energy. However, the major power drain occurs due to wireless communication [3] . Therefore, attempts require to be carried out to perform as much in-network processing as possible within a sensor or a group of sensors (cluster). This is achieved by performing aggregation and filtration of raw data before transmitting them to destined targets. As a result of which redundancy in the recorded sensory samples is eliminated, thereby reducing the transmission cost and network overloading. Moreover, decrease in the effective number of packet transmissions also leads to minimized chances of network congestion, thereby saving the excess energy consumption in the network. For instance, if the radio electronics requires 50nJ/bit and amplifier circuitry needs 10pJ/bit/m 2 for communication, then power used in transmitting 1 bit of information to the processing center situated 1 km away, consumes 1.005 × 10 4 nJ per unit time (watts). However, energy used in data processing for aggregation is 5 nJ/bit/signal, which implies that execution of almost 2010 instructions compensates the energy used for one transmission in unit time. Therefore, it is quite recommendable to apply aggregation techniques. Previous researches have already proven the fact that in-network processing cost is much less than the communication cost [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] . The proliferation of sensor network has created the urge of exploring novel ideas for data aggregation. However, the aggregation schemes would require efficient clustering protocols to well-implement its functioning. Hence, in this paper we have contributed a divergence-measure based clustering protocol along with entropy based data aggregation, to the ongoing sensor network research. The remainder of this paper is organized as follows: a brief review of previous research carried out in the related field is included in section 2. Our proposed clustering technique based on divergence measure is provided in section 3. In section 4, the proposed fuzzy-entropy based aggregation scheme has been elaborated. Analysis of network diagram is presented in section 5. Section 6 shows the performance evaluation of our proposed method. Finally, the paper is concluded in section 7 along with directions for further scope. The energy consumption in wireless sensor network has created enormous awareness among the researchers for increasing the network lifetime. The sensor network is considered to have prospective results in terms of dynamism and diversity in everyday applications. Several resource efficient protocols have been introduced by researchers in order to limit the sensor energy usage, at the same time maintaining a sufficient degree of reliability and throughput.. Several methods of data aggregation depend on the topology of the sensor network [15] . For instance, a tree-based data aggregation protocol constructs a simple topology based on a parent and child association [16] . However, large transmission delays and poor rate of aggregation makes it unsuitable for the dynamic applications. Further, we have centralized aggregation protocol [17] , in which aggregation is done only at the sink (data processing center). As a result, such protocols lead to heavy workload and unnecessary packet drops. There are other clustering schemes based on static [18] [19] [20] and dynamic cluster aggregation [21] [22] [23] . In case of static environment, the clusters are formed in the initial stage and the aggregation is carried out by the cluster heads. The clusters once formed remain unchanged throughout the network lifespan. This procedure is suitable for area monitoring (recording earthquake, temperature, humidity, etc.), but not supported over wide range of applications, like-forest fire supervision, wildlife monitoring, target tracking, etc. Therefore most of the research awareness can be found in dynamic cluster aggregation schemes, where clusters are formed dynamically and updated on sensing environmental parameters followed by aggregation at the cluster head. The clusters formed in this case, are also known as adaptive clusters.. An energy aware algorithm has been provided in [4] for constructing an aggregation tree prior to data transmission. The algorithm seems to reflect the influence of both the energy and distance parameters to construct the tree. In another research [5] , the authors have performed aggregation by considering entropy of correlated data transmitted by the source nodes. This procedure reduces the amount of redundant data forwarded to the sink. Furthermore, the estimation of joint entropy of the correlated data set helps in maximizing information integrity. Another interesting aggregation protocol is developed in [6] on the basis of wavelet-entropy. Initially, multi-scale wavelet transforms are used to spread signals in multi-scale range, after which information is aggregated using waveletentropy discriminance theorem. Simulation results indicate that the proposed method is capable to extend the lifetime of networks to a much greater degree than Low-Energy Adaptive Clustering Hierarchy (LEACH) protocol [7] . In [8] the authors have put forward a novel approach that focusses on data aggregation with significantly reduced aggregation latency. Collision-free schedule is generated by a distributed algorithm for performing data aggregation in wireless sensor network. The time latency of aggregation schedule is minimized using greedy strategy.. In a recent research [9] , an aggregation scheme called smart aggregation is developed for continuous monitoration in sensor networks. The proposed technique maintains a tolerable deviation (a bounded error) in the aggregated data while utilizing the spatio-temporal correlation of data. In another subsequent work [10] , data aggregation techniques are designed on the basis of statistical information extraction. The applied methods exhibits bounded message overhead and robustness against link failures. The expectation-maximization (EM) algorithm is used in order to accomplish accurate estimation of distribution parameters of sensory data. The experimental outcome confirms reduced network communication cost even in large scale sensor networks. In a latest publication [11] , the corresponding authors have presented α-local spatial clustering algorithm along with data aggregation mechanism. The contribution was mainly made for environmental surveillance applications in high density sensor networks. The aggregation algorithm constructs a dominating set by exploiting the spatial correlation between data measured by different sensors. The dominating set is further considered as network backbone to execute data aggregation on the basis of information summarization of the dominator nodes. Another research in [12] proposed cooperative information aggregation (CIA) mechanisms to handle observation noise and communication errors initially found in the sampled data. Moreover, the authors have designed an aggregation hard decision estimator (AHDE) and an Aggregation Maximum-Likelihood Estimator (AMLE). Simulation shows the effectiveness of CIA schemes to be suitably applied to environments prone to observation noise.. In this paper, we have proposed a dynamic clustering and aggregation strategy that aggregates data at the sensor node and cluster head as well. With the use of entropy and information theory, we attempt to reduce the transmission and processing cost, but maintaining the relevance of the aggregated data. For the evaluation of the performance of our proposed strategy, we make a comparative analysis with two well-known clustering protocols: Hybrid Energy-Efficient Distributed Clustering (HEED) [13] and an inference clustering protocol based of Belief Propagation (BP) [14] . HEED is a distributed clustering approach that operates in energy efficient manner and helps in prolonging network lifetime. It is scalable over large network sizes and performs load balancing within clusters. However, frequent computation of communications cost and broadcasting among neighbors degrades its performance. As a strong counterpart, BP clustering method offers energy effective solutions based on belief calculations with potential functions. Though BP performs better than HEED in terms of clustering the network and packet delivery performance, but long-length messages induce larger overheads in message passing. This makes transmission cost higher in case of BP. Previous simulations have shown a marginal difference in network lifetimes contributed by these protocols.

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