Routing strategy in disconnected mobile ad hoc networks with group mobility Most of the current proposed routing protocols in delay-tolerant network (DTN) are designed based on the entity mobility. In this article, we consider the routing in DTN with group mobility, which is useful in modeling those cooperative activities. The new proposed routing scheme is called group-epidemic routing (G-ER). G-ER is designed on the basis of one DTN protocol called epidemic routing (ER). In G-ER, two strategies related to the unique characteristics of the group mobility have been proposed to greatly improve ER. The first is to treat each group as a single node and exchange packets between groups instead of individual nodes. Thus, the resource-consuming problem of ER could be much alleviated. In the meantime, exchanging packets between two groups could speed up the packet delivery. The second is the buffer sharing inside a group, which is supported by the cooperative nature in group mobility. Moreover, we specifically propose a group dynamic model for group mobility to realize group splitting and merging. The performance of G-ER is studied by extensive simulations and compared with ER and dynamic source routing (DSR). Results show that G-ER outperforms ER and DSR in different network scenarios even with group dynamics. Group mobility has been taken as the basis for the routing scheme design in mobile ad hoc networks due to its realistic meanings. Different from entity mobility, in which nodes move independently among each other, group mobility assumes some nodes move in a group, and they have similar moving behavior. Thus, the topology within a group will keep connected most often. Group mobility could be extracted in many practical scenarios, especially in those cooperative scenarios. For example, a group of soldiers generally move together to execute a common task in the military operation. So far, a number of group mobility models have been proposed, like Reference Point Group Mobility (RPGM) [1] and Community-Based Mobility [2] . Other group mobility models could be found in [3] .. Many routing schemes [4] [5] [6] for group mobility models have been proposed. These routing schemes make use of some features of group structure for the ease of routing.. Since group members inside a group are assumed to be close to each other, these routing schemes aim to send a packet to the group leader of a group rather than to an exact destination node of a group member. Such a design reduces the complexity of route set-up and maintenance. However, these routing schemes could work effectively only when there exists a complete path or route for any source and destination pair. In other words, if such a complete path cannot be found or the network is disconnected, they will fail to work [7] . Actually, the network disconnection will happen in group mobility when each group is with relatively small group radius or group coverage [7] . Consequently, a new routing strategy, called delay-tolerant network (DTN) routing [8] , was proposed to make the packet delivered successfully in such a disconnected network at the cost of longer delay.. DTN routing employs the store-carry-forward approach to deliver packets. Most proposed DTN routing protocols fall into two different types; purposeful movement routing and opportunistic routing. In purposeful movement routing [9] [10] [11] , the node carrying the data packet will move purposely to get closer to the destination or to get connected to the destination. Generally, this will require the location knowledge of the destination. Different from the purposeful movement routing, opportunistic routing assumes all mobile nodes will follow their original moving plans, carrying the packets, and waiting for the opportunity to deliver them to those nodes which will get connected to the destinations. The opportunistic routing could be further classified into three sub-classes; deterministic routing, flooding-based routing, and flooding-controlled-based routing. The deterministic routing [12, 13] chooses the next node to carry the packet based on the known future topology change. This future topology change could be obtained by learning the future nodes' movements. In the flooding-based routing [14] , each packet will be disseminated to every node in the network in hope that those nodes carrying the copies of this packet could meet the destination later. However, with the increasing of the node number in the network, the problem of overhead caused by the flooding or the problem of the resources like buffer size needed for the flooding emerges. Hence, some flooding-controlled-based routing schemes [15] [16] [17] [18] [19] are proposed to reduce the overhead or the resources in need by restricting the number of copies of each packet. In the extreme case, no copy of a packet will be generated. This is generally achieved by delivering the packet to a node which has higher probability to meet the destination [16, 17] .. Besides, some previous studies [20] [21] [22] apply clustering to DTN to improve network performance. Thomas et al. [20, 21] and Dang and Wu [22] consider the scenario in DTN where some nodes under entity mobility may stay close to each other for some time and thus they can form a cluster. Making use of this vicinity among the nodes in one cluster for packet delivery could improve the routing performance. For example, Thomas et al. [20, 21] employ on-demand ad-hoc routing to deliver packets quickly within the cluster; nodes in the same cluster in [22] are required to share their contact probabilities so as to find a better next hop to carry the packets.. So far, those DTN routing schemes introduced above, including the cluster-based DTN schemes, target for entity mobility and they cannot perform effectively in DTN with group mobility. This is because group mobility is different from entity mobility and thus, accordingly some specific mechanisms can be proposed for it to improve routing performance. We will present these specific mechanisms for group mobility while introducing our proposed scheme below.. The objective of this article is to propose a routing scheme which can perform effectively in group mobility scenarios by making full use of the characteristics of the group mobility. After understanding of various DTN routing strategies, we find that the strategy of epidemic routing (ER) [14] well suits the group mobility, and then propose group-epidemic routing (G-ER) for group mobility.. We have proposed two important mechanisms in G-ER, both in the form of cooperation inside the group. The first mechanism is the group-based packet exchange. Similar to [20] [21] [22] , by treating each cluster/group as a single node, G-ER is a two-layer routing, including the inter-group routing and intra-group routing. The strategy of ER is adopted for the inter-group routing to exchange packets between groups, and a table-driven routing is employed for the intra-group routing to handle the packet delivery inside the group. Importantly, we employ the group-based packet exchange to expedite the packet delivery in this two-layer routing: when two nodes from two groups meet each other, other members in these two groups will also take this chance to deliver packets to the neighboring group. In contrast, the packet exchange in all DTN schemes mentioned above takes place only between two contacting nodes, which we refer to as the node-based packet exchange. The second mechanism is the buffer sharing inside a group, which is used to reduce the buffer requirement at one node in G-ER. This buffer sharing could be well supported by the nature of a group, i.e., the cooperation among group members. In addition, we study the performance of G-ER under group dynamics and find that the impact of group dynamics can be reduced by some proper buffer resource allocation in one group. Extensive simulations are conducted to show the advantages of G-ER in different scenarios, even with group dynamics. In this article, we have proposed a new DTN routing scheme called G-ER under group mobility scenario with group dynamics. By making full use of the topology feature of the group mobility, two significant mechanisms in the form of cooperation inside the group are proposed in G-ER. In G-ER, the table-driven routing is employed for the intra-group routing, and ER's strategy with our proposed principle of one inter-group packet copy for one intermediate group is adopted for the inter-group routing. The group-based packet exchange and the buffer sharing are integrated into this two-layer routing, which finally makes G-ER outperform ER and DSR in different scenarios. The main features of G-ER are.. (1) Much less buffer resources are needed for the packet delivery as compared to ER. By treating each group as an individual node and disseminating one copy of one inter-group packet for one group, G-ER becomes much less resource-consuming. Generally, the more stable the group structure is, the more benefits G-ER could bring. (2) G-ER has shorter packet delivery delay than ER because the group-based packet exchange in G-ER increases the opportunities for packets to be sent to other groups. (3) With larger node buffer size and proper buffer assignment in one group, G-ER could be more resilient to the group dynamics.

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


Leader-Following Consensus of Multiple Linear Systems Under Switching Topologies: An Averaging Method The leader-following consensus of multiple linear time invariant (LTI) systems under switching topology is considered. The leader-following consensus problem consists of designing for each agent a distributed protocol to make all agents track a leader vehicle, which has the same LTI dynamics as the agents. The interaction topology describing the information exchange of these agents is time-varying. An averaging method is proposed. Unlike the existing results in the literatures which assume the LTI agents to be neutrally stable, we relax this condition, only making assumption that the LTI agents are stablizable and detectable. Observer-based leader-following consensus is also considered. Multi-agent system is a hot topic in a variety of research communities, such as robotics, sensor networks, artificial intelligence, automatic control and biology. Of particular interest in this field is the consensus problem, since it lays foundations for many consensusrelated problem, including formation, flocking and swarming. We refer to survey papers [17, 19] and references therein for details.. Integrator and double integrator models are the simplest abstraction, upon which a large part of results on consensus of multi-agent systems have been based (see [18, 16, 17, 8, 4, 5] ). To deal with more complex models, a number of recent papers are devoted to consensus of multiple LTI systems [30, 25, 15, 22, 21, 13, 9, 29, 14, 26, 27, 28] . These results keep most of the concepts provided by earlier developments, and provide new design and analysis technique, such as LQR approach, low gain approach, H ∞ approach, parametrization and geometric approach, output regulation approach, and homotopy based approach. However, most of these results [30, 25, 15, 21, 13, 9, 29, 14] mainly focus on fixed interaction topology, rather than time-varying topology. How the switches of the interaction topology and agent dynamics jointly affect the collective behavior of the multi-agent system? Attempts to understand this issue had been hampered by the lack of suitable analysis tools. The results of Scardovi et al. [22] and Ni et al. [15] are mentioned here, because of their contributions to dealing with switching topology in the setup of high-order agent model. However, when dealing with switching topology, [22] and [15] assumed that the system of each agent is neutrally stable; thus it has no positive real parts eigenvalues. This assumption was widely assumed in the literatures when the interaction topology is fixed or switching. Unfortunately, when the agent is stabilizable and detectable rather than neutrally stable, and when the interaction topology is switching, there is no result reported in the literature to investigate the consensus of these agents.. To deal with switching graph topology and to remove the neutral stability condition , we provide a modified averaging approach, which is motivated by [1, 2, 10] . The averaging approach was initially proposed by Krylov and Bogoliubov in celestial mechanics [12] , and was further developed in the work of [3, 11] ; for more details refer to the recent book [20] . Closely related to the averaging theory is the stability of fast time-varying nonautonomous systems [1, 10, 2] , and more specifically the fast switching systems [23, 24] . The modified approach in this paper is motivated by the work of Stilwell et al. [23] , and also the work of [1, 10, 2] . Although this work borrows the idea from [23] , the main difference of this work from [23] is as follows. The synchronization in [23] is achieved under under fast switching condition; that is, synchronization is realized under two time scales: a time scale t for the agent dynamics and a time scale for the switching signal parameterized by t/ε with ε small enough. In our paper, we further establish that the two time scales can be made to be the same and thus the consensus in our paper is not limited to fast switching case. Furthermore, We present an extended averaging approach for consensus: a sequence of averaged systems (rather a single averaged systems) are the indicators of consensus of the the multi-agent systems. This allows to obtain more relax conditions for consensus. At last, We give further investigation on how to render these sequence of averaged systems to achieve consensus, and thus ensure the consensus of the original multi-agent systems. This was not investigated in [22] . The result in our paper shows that if there exists an infinite sequence of uniformly bounded and contiguous time intervals such that during each such interval the interaction graph is jointly connected and if the dwell time for each subgraph is appropriately small, then consensus can be achieved.. In summary, the contributions of this paper are as follows:. • Averaging method is applied to leader-following consensus of multiple LTI systems.. • Results are obtained for a wider class of agent dynamics which is stabilizable and detectable than the existing class of neutrally stable agent dynamics.. • The agent dynamics and the switching signal considered in this paper have the same time scale, rather than having different time scales considered in [23] . Thus the results in our paper are not limited to fast time switching case.. The rest of this paper is organized as follows. Section 2 contains the problem formulation and some preliminary results. Section 3 provides the main result of leader-following consensus, and extensions are made in Section 4 which devotes to observer-based protocols design and analysis. Two illustrated examples are presented in Section 5. Section 6 is a brief conclusion. This paper presents an averaging approach to leader-following consensus problem of multi-agent with linear dynamics, without imposing neutrally stable condition on agent dynamics. The interaction topology is switching. The proposed protocols force the follower agents to follow the independent leader trajectory. The result is extended to observer-based protocols design. Such design can be separated as a two-step procedure: design asymptotically stable distributed observers and asymptotically stable observerstate-feedback protocols.

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


Generic Remeshing of 3D Triangular Meshes with Metric-Dependent Discrete Voronoi Diagrams Abstract-In this paper, we propose a generic framework for 3D surface remeshing. Based on a metric-driven Discrete Voronoi Diagram construction, our output is an optimized 3D triangular mesh with a user-defined vertex budget. Our approach can deal with a wide range of applications, from high-quality mesh generation to shape approximation. By using appropriate metric constraints, the method generates isotropic or anisotropic elements. Based on point sampling, our algorithm combines the robustness and theoretical strength of Delaunay criteria with the efficiency of an entirely discrete geometry processing. Besides the general described framework, we show the experimental results using isotropic, quadric-enhanced isotropic, and anisotropic metrics, which prove the efficiency of our method on large meshes at a low computational cost. W ITH the ever increasing range of applications using sampled 3D geometric models, resampling has become a very important feature for interoperability between those applications. As an example, the accuracy of current 3D scanners has been improved, and they are able to produce very faithful 3D meshes of the scanned model for the price of a large number of vertices. As a consequence, a resampling step is usually carried out before displaying, storing, or using the mesh in another application. Also, the mesh triangle shape factor can be important when considering finite element simulations. In this paper, we propose an adaptive surface mesh-coarsening algorithm, which samples the input surface to a mesh with fewer elements than the original mesh. An extension of this approach also leads to remeshing, when one wants the constructed model to have an arbitrary number of elements. Our approach extends the work by Valette and Chassery [1] to nonuniform and anisotropic Discrete Centroidal Voronoi Diagrams (DCVD). The complexity of our algorithm (in terms of calculations and memory requirements) is low, allowing the processing of large meshes up to several million triangles. Coarsening a mesh consists of resampling the original surface with a lower number of vertices. This field of research has been explored in many ways in recent years. A good review of existing remeshing approaches is given in [2] and coarsening approaches are described more precisely in [3] .. In [4] and [1] , the triangles of the input mesh are clustered and a new coarsened mesh is built according to the clustering. These approaches are efficient when the number of triangles of the output mesh is much lower than the number of triangles of the input mesh. The approach by Cohen-Steiner et al. [4] aims to create approximationefficient meshes, whereas the approach by Valette and Chassery [1] aims to create uniform output triangulations. Note that, in [5] , an extension to the work by Valette and Chassery to adaptive coarsening is proposed. In [6] , similar clustering approaches are used to create base domains on polygonal meshes. These base domains are then combined with parameterization techniques to process quadrangular remeshing of the original model. Note that clustering can have several possible applications aside from remeshing. As an example, in [7] , a hierarchical clustering approach is proposed with a multiresolution radiosity application example. The coarsening of very large meshes (made of millions of vertices) is also an issue when the mesh data structure cannot fit inside the computer memory. As a consequence, out-of-core approaches have been proposed [8] , [9] , [10] , [11] .. Remeshing approaches compute a mesh with a given number of elements or approximation error budget in a single resolution way. Some approaches remesh the original surface in a global parametric space [12] , [13] , [14] , [15] . They provide good results but are limited in practice by the parameterization step, involving heavy calculations and numerical instability. To overcome these problems, methods in [16] and [17] were proposed, involving local parameterization and optimization of the remeshed model. Other works [18] , [19] distribute new vertices directly on the original surface mesh to build a new tessellation that can be further optimized.. In [20] and [21] , the authors propose to remesh the model using geodesic distances: The new vertices are created using geodesic front propagation, and their distribution can be driven by local curvature.. Remeshing approaches allow the construction of meshes with as many vertices as required. Indeed, mesh coarsening is not the main goal of remeshing approaches, as they permit other improvements (in terms of triangle aspect ratio) and shape adapted remeshing (for example, adaption of the sampling according to the local curvature). In this section, we propose to partition the input mesh according to the Delaunay criteria, extending [1] . We will explain several key points, namely, the chosen clusteringmeshing approach, the chosen metrics, and implementation details.

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


Central schemes for the modified Buckley-Leverett equation In this paper, we extend the second and third order classical central schemes for the hyperbolic conservation laws to solve the modified Buckley-Leverett (MBL) equation which is of pseudo-parabolic type. The MBL equation describes two-phase flow in porous media, and it differs from the classical Buckley-Leverett (BL) equation by including a balanced diffusive-dispersive combination. The classical BL equation gives a monotone water saturation profile for any Riemann problem; on the contrast, when the dispersive parameter is large enough, the MBL equation delivers non-monotone water saturation profiles for certain Riemann problems as suggested by the experimental observations. Numerical results in this paper confirm the existence of non-monotone water saturation profiles consisting of constant states separated by shocks. The classical Buckley-Leverett (BL) equation [1] is a simple model for two-phase fluid flow in a porous medium. One application is secondary recovery by water-drive in oil reservoir simulation. In one space dimension the equation has the standard conservation form u t + (f (u)) x = 0 in Q = {(x, t) : x > 0, t > 0}. u(x, 0) = 0 x ∈ (0, ∞) u(0, t) = u B t ∈ [0, ∞) In this content, u : Q → [0, 1] denotes the water saturation (e.g. u = 1 means pure water, and u = 0 means pure oil), u B is a constant which indicates water saturation at x = 0, and M > 0 is the water/oil viscosity ratio. The classical BL Eq. (1.1) is a prototype for conservation laws with convex-concave flux functions. The graph of f(u) and f (u) with M = 2 is given in Fig. 1 . The classical BL Eq. (1.1) has been well studied (see [10] for an introduction). Let ˛ be the solution of f (u) = f (u) u , i.e.,. 3). The entropy solution of the classical BL equation can be classified into two categories: 1 If 0 < u B ≤ ˛, the entropy solution has a single shock at. . 2 If ˛ < u B < 1, the entropy solution contains a rarefaction between u B and ˛ for f (u B ) < x t < f (˛) and a shock at. These two types of solutions are shown in Fig. 2 for M = 2. In either case, the entropy solution of the classical BL Eq. (1.1) is a non-increasing function of x at any given time t > 0. However, the experiments of two-phase flow in porous medium reveal complex infiltration profiles, which may involve overshoot, i.e. profiles may not be monotone [4] . This suggests the need of modification to the classical BL Eq. (1.1).. Hassanizadeh and Gray [5, 6] have included a third order mixed derivatives dispersive term, which models the dynamic effects in the capillary pressure difference between the two phases. Following the linearization and rescaling in [14] [15] [16] where is the diffusion coefficient. van Duijn et al. [15] showed how and determine the type of the solution profile. In particular, for certain Riemann problems, the solution profile of (1.4) is not monotone when is larger than the threshold value * , where * was numerically determined to be 0.61 [15] . The non-monotonicity of the solution profile is consistent with the experimental observations [4] .. The classical BL Eq. (1.1) is hyperbolic, and the numerical schemes for hyperbolic equations have been well developed (e.g. [10, 11, 2, 3, 13, 8] ). The MBL Eq. (1.4), however, is pseudo-parabolic. van Duijn et al. [15] have developed a first order finite difference scheme to solve the MBL Eq. (1.4) . In this paper, we will illustrate how to extend the second and third order central schemes [13, 8, 9] to solve (1.4) numerically. The local discontinuous Galerkin method has been applied to solve equations involving mixed derivatives u xxt term [18, 19] . To the best knowledge of the authors, the central schemes have not been applied to solve equations of this kind. The main advantage of the central schemes is the simplicity. The "direction of the wind" is not required to be identified, and hence the field-by-field decomposition can be avoided.. Unlike the finite domain of dependence for the classical BL Eq. (1.1), the domain of dependence for the MBL Eq. (1.4) is infinite. This naturally raises the question for the choice of computational domain. To answer this question, Wang et al. [17] studied the MBL equation equipped with two types of domains, one is the half line domain x ∈ [0, + ∞), and the other one is finite interval domain x ∈ [0, L]. Wang et al. [17] have shown that the difference between the solutions of these two types of problems decays exponentially with respect to the length of the interval L for practically interesting initial profiles. This provides a theoretical justification for the choice of the computational domain. Therefore, the numerical results in this paper are sought on the finite interval domain x ∈ [0, L] with sufficiently large L. ≈ 0.8165). (a) 0 < uB = 0.7 ≤ ˛, the solution consists of one shock at. the solution consists of a rarefaction between uB and ˛ for f (uB) < x t < f (˛) and a shock at. The organization of this paper is as follows. In Section 2, the second and third order central schemes will be developed for MBL equation in the finite interval domain. We provide a detailed derivation on how to extend the central schemes [13, 8] for conservation laws to solve the MBL Eq. (1.4). The idea of adopting numerical schemes originally designed for hyperbolic equations to pseudoparabolic equations is not restricted to central type schemes only [18, 19] . The numerical results in Section 3 show that the water saturation profile strongly depends on the dispersive parameter value as studied in [15] . For > * , the MBL Eq. (1.4) gives nonmonotone water saturation profiles for certain Riemann problems as suggested by experimental observations [4] . Section 4 gives the conclusion of the paper and the possible future directions. We extended the second and third order classical central schemes originally designed for the hyperbolic systems to solve the MBL equation, which is of pseudo-parabolic type. The numerical solutions for qualitatively different parameter values and initial conditions u B show that the jump locations are consistent with the theoretical calculation and the plateau heights are consistent with the numerically obtained values given in [15] . In particular, when > * , for u B ∈ (u, u), the numerical solutions give non-monotone water saturation profiles, which is consistent with the experimental observations. In addition, the order tests show that the proposed second and third order central schemes achieved the desired accuracies. In [16, 14] , the two-dimensional space extension of the modified Buckley-Leverett equation has been derived. One of the future directions is to develop high order numerical schemes to solve the two-dimensional MBL equation. Central schemes have been used to solve high dimensional hyperbolic problem and dispersive problem [7, 12] , which makes it a good candidate for such a task.

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


Assigning roles to protein mentions: The case of transcription factors Transcription factors (TFs) play a crucial role in gene regulation, and providing structured and curated information about them is important for genome biology. Manual curation of TF related data is time-consuming and always lags behind the actual knowledge available in the biomedical literature. Here we present a machine-learning text mining approach for identification and tagging of protein mentions that play a TF role in a given context to support the curation process. More precisely, the method explicitly identifies those protein mentions in text that refer to their potential TF functions. The prediction features are engineered from the results of shallow parsing and domain-specific processing (recognition of relevant appearing in phrases) and a phrase-based Conditional Random Fields (CRF) model is used to capture the content and context information of candidate entities. The proposed approach for the identification of TF mentions has been tested on a set of evidence sentences from the TRANSFAC and FlyTF databases. It achieved an F-measure of around 51.5% with a precision of 62.5% using 5-fold cross-validation evaluation. The experimental results suggest that the phrase-based CRF model benefits from the flexibility to use correlated domain-specific features that describe the dependencies between TFs and other entities. To the best of our knowledge, this work is one of the first attempts to apply text-mining techniques to the task of assigning semantic roles to protein mentions. Transcription factors (TFs) are proteins that regulate recruitment of RNA polymerase and initiation of transcription [1] , thereby playing a crucial role in regulating gene expression and influencing almost all biological processes in an organism. Because TFs play specific roles in gene expression, they are restricted to specific sub-cellular compartments (i.e. the nucleus), have specific protein structures (e.g. DNA binding domains) and specific functions (activating expression of target genes). These features of TF biology are of critical importance to researchers working on gene expression; yet, the majority of facts about TFs mainly exist in diverse, unstructured formats in the biomedical literature.. There are a number of databases that contain manually-curated data on TFs, such as TRANSFAC [2, 3] , FlyTF [4] , PAZAR [5] , RegulonDB [6] , and ORegAnno [7, 8] , which store information on TFs in structured formats (including normalised TF and target gene names, DNA binding sites, experimental evidence of interactions, literature references etc.). As with all manual curation tasks, provision of such information is time-consuming and always lags behind the actual knowledge available in the biomedical literature. Recently, the regulatory bioinformatics community has initiated joint efforts to increase the number of curators and coverage of structured TF information by organising a community-driven curation process [7, 8] . However, the curation process for each individual curator is only beginning to change. Recent efforts have developed information retrieval and filtering approaches to create a queue of articles to curate [8] and information extraction approaches to identify and map putative TF binding sites [9] . Despite this progress, methods for the identification of TF mentions and textual passages that would support the curation process (or at least improve the ordering within the curation queue ) have not yet been implemented.. In this paper we present an approach for the identification of TF mentions in documents, which can be consequently used to support TF curation tasks. We build the method on top of a TF sentence recogniser developed earlier, which detects sentences likely to contain information relevant to TF biology [10] . Our formulation of the task is to identify proteins that have a special function in a given context, as opposed to the general protein-protein interaction (PPI) recognition task, which identifies (and potentially characterises) interactions between genes. More precisely, we are focused on a specific role of transcription regulation of a target gene that a protein mention plays in a given context. Consequently, we have construed the task as a text-tagging problem that assigns TF tags to protein mentions.. Biomedical text mining research has focused on techniques that allow for automatic extraction of individual entities of a particular class (e.g. protein/gene names [11] , chemical entities [12] , drugs [13] , tissues [14] , etc.) and specific relations among them (e.g. PPI [15, 16] , molecular pathways [17] , etc.). Most of approaches (in particular statistical and machine learning methods) assume that occurrences of entities are independent and typically treat each identification/tagging task in isolation. However, in many cases, considering relations between different entities taking part in a biological function or process could potentially improve overall mining accuracy. If a context surrounding an entity mention is associated with a particular (biological) property and is indicative of a function or role, then this should also influence tagging/recognition of occurrences or roles of other (related) entities in a given context. For instance, in the TF identification task studied here, gene regulation involves interactions and relations between target genes, transcription factors (proteins) and other biological entities (e.g. DNA-binding sites), as modelled for example by the Gene Regulation Ontology [18] , and therefore occurrences of these entities should be taken into account when recognising TF mentions.. Among a large variety of approaches to entity tagging in biomedical text, conditional random fields (CRFs) have been shown as useful for modelling dependences between constituents (e.g. in protein mention detection [19, 20] ). In this paper, we also investigate a CRF model for the identification of TF mentions. However, unlike CRF methods that generally treat a sentence as a word sequence, our model is based on shallow-parsed phrases, with biological entities nested within them used as phrase properties. Thus, the model not only considers linguistic information (from shallow parsing), but also makes use of semantic types assigned to tokens. Furthermore, we integrate local features of individual phrases (e.g. linguistic and biological properties) with context features describing the relations between phrases in a given sentence (e.g. linguistic and semantic properties of the neighbour phrases around the candidate token).. The paper is organised as follows. Section 2 provides a brief analysis of TF contexts available in some relevant databases. The methods designed for phase-based CRF tagging are described in Section 3. Sections 4 and 5 present the results and error analysis, respectively, while Section 6 compares the current method to related work. Finally, Section 7 concludes the paper and gives an outline of topics for future work. In this paper we have proposed a phrase-based CRF model for the identification of transcription factor mentions, which integrates both linguistic features (e.g. phrase types) and domain properties (e.g. mentions of generic or task-specific biological keywords and types). Since many biomedical entities and events are represented via multi-word expressions, the model is built on a phrase rather than sequence structure, which makes it feasible to capture context information surrounding a current candidate by using a set of context features assigned to both the candidate entity and its neighbours. Moreover, phrase normalisation (e.g. morphological, derivational, lemmatisation) was used to provide most representative features.. To the best of our knowledge, this work is one of the first attempts to apply text-mining techniques to the task of assigning TF roles to protein mentions. The approach showed moderate results of an average overall F-measure of 51.5%, with precision of 62.5%. This is a significant improvement compared to the baseline method (F-measure of 39.7%, precision of 25.5%). The experimental results suggest that domain features positively affect both accuracy and coverage of the model. The most useful context information is generally associated with the surrounding tokens within a window size of two to the current candidate.. As this is the first attempt, there is still room for improvement on predication accuracy by augmenting phrases with more suitable properties, such as domain-specific terms describing structure features and function properties of transcription factors and adjectives/adverbs referring to interactions (e.g. direct/indirect). Also, more research is needed for the exploitation of longer distance dependences and global relations between candidate transcription factors and other entities. We plan to investigate dependency parsing that would link non-local entities. Finally, we plan to evaluate the proposed method in a real-world scenario for ORegAnno [7] curation, where the overall 3-step process will be used against a set of abstracts (and potentially full text documents) to (a) filter out relevant documents [9] , (b) identify potential TFs and TGs (including mapping them to referential databases), and (c) present support sentences to curators. The results will be than compared with the real curation queue (created manually as part of the curation process) for a given period of time. Our objective is to develop a system that automatically identifies and tags potential TF mentions in text and extracts relevant evidence sentences to support the annotation of putative transcription factors. We do not aim to tag TFs with molecular functions, but rather to identify proteins that are acting on a target gene in the given context and are therefore likely to be TFs. We approach the problem through two major stages. In the first stage, we use a machine-learning framework to identify TF-related sentences/contexts [10] . In the second stage, potential TFs are tagged in the sentences identified. The tagging approach is based on a Conditional Random Field (CRF) model, which uses shallow-parsed phrases to combine syntactic and semantic features to support identification of TF roles. In this section, we discuss the CRF model and the information that describes the dependencies between different entities involved in the regulation process. We briefly overview the TF sentence identification task first.

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


A hybrid variable neighborhood search algorithm for solving multi-objective flexible job shop problems In this paper, we propose a novel hybrid variable neighborhood search algorithm combining with the genetic algorithm (VNS+GA) for solving the multi-objective flexible job shop scheduling problems (FJSPs) to minimize the makespan, the total workload of all machines, and the workload of the busiest machine. Firstly, a mix of two machine assignment rules and two operation sequencing rules are developed to create high quality initial solutions. Secondly, two adaptive mutation rules are used in the hybrid algorithm to produce effective perturbations in machine assignment component. Thirdly, a speed-up local search method based on public critical blocks theory is proposed to produce perturbation in operation sequencing component. Simulation results based on the well-known benchmarks and statistical performance comparisons are provided. It is concluded that the proposed VNS+GA algorithm is superior to the three existing algorithms, i.e., AL+CGA algorithm, PSO+SA algorithm and PSO+TS algorithm, in terms of searching quality and efficiency. He is now a member of IEEE and CCF. His research is related to the evolutionary optimization methods for discrete events systems, job shop systems, operational research, computer network, peer-to-peer systems and network security. He has (co-)authored around 50 research papers published. He has been serving on editorial boards or reviewers of two international journals. He has been the member of program committees of many international conferences. The job-shop scheduling problem (JSP) is one of the most popular scheduling models existing in practice, which has been proven to be among the hardest combinatorial optimization problems [1, 2] and has got more and more research focus in recent years. The Flexible job-shop problem (FJSP), an extension of the classical JSP, is harder than the latter because the addition of assignment of a suitable machine from a set of candidate machines for each operation.. The FJSP recently has captured the interests of many researchers. The first paper about solving the FJSP was proposed by Brucker and Schlie (Brucker & Schlie, 1990) [3] , which gives a simple FJSP model with only two jobs and each operation performed on each machine with the same processing time. The first author with the hierarchical idea to solve the FJSPs was Brandimarte (Brandimarte, 1993) [4] , who solved the first stage with some existing dispatching rules and the second stage with tabu search heuristic algorithms. Kacem (Kacem, Hammadi & Borne, 2002) [5] solved the two stage problems with the genetic algorithm (GA). Gao (Gao & Gen et al., 2006) [6] used bottleneck shifting method in genetic algorithm for solving the FJSP. Saidi-mehrabad (Saidi-mehrabad, 2007) [7] gave a detailed solution with tabu search method. Li et al. (2009) [8] presented a hybrid particle swarm optimization (PSO) combining with a fast neighborhood structure algorithm for the problem.. The research on the multi-objective FJSP is much less than the mono-objective FJSP. Kacem et al. (2002a Kacem et al. ( , 2002b [5, 9] developed an effective evolutionary algorithm controlled by an assigned model based on the approach of localization (AL). Xia and Wu (2005) [10] presented a practical hierarchical solution approach by making use of PSO to assign operations on machines and simulated annealing (SA) algorithm to schedule operations on each machine. Zhang et al. (2009) [11] developed a hybrid algorithm combining PSO with tabu search (TS) algorithm. Most of the above algorithms solved the multi-objective FJSP problem by transforming it to a mono-objective one through giving each objective a different weight.. In this paper, we propose a novel hybrid variable neighborhood search algorithm combining with the genetic algorithm (VNS+GA) for solving the multi-objective FJSP problems to minimize the makespan, total workload of all machines, and workload of the busiest machine. In the hybrid algorithm, the three objectives are also combined into a single objective by assigning each objective a different weight. GA is used to produce a swarm of candidate solutions, whereas VNS is introduced to obtained more optimal solutions around the given candidate solutions. A mix of two machine assignment rules and two operation sequencing rules are developed to create high quality initial solutions. To produce effective perturbations in the machine assignment module, two adaptive mutation rules are used in the hybrid algorithm. A speed-up local search method based on public critical blocks theory is proposed to produce perturbation in operation sequencing component.. The rest of this paper is organized as follows: In section 2, we briefly describe the problem formulation. Then, the framework of our hybrid algorithm is presented in Section 3. The GA for perturbation in machine assignment component is introduced in Section 4. Section 5 illustrates the VNS approach for local searching in operation sequencing component. Section 6 shows the experimental results compared with other algorithms. Finally, Section 7 gives the conclusion of our works. Flexible job shop scheduling problem is very important in both fields of combinatorial optimization and engineering management. Most literature focus on proposing hybrid algorithms for solving mono-objective FJSPs. The research on the multi-objective FJSP is much less than the mono-objective FJSP. Kacem proposed a hybrid algorithm named AL+CGA combining GA and approach of localization. Xia and Wu presented a hybrid algorithm named PSO+SA which making use of PSO for solving the assignment sub problem and SA for solving the routing sub problem. Zhang et al. developed a hybrid algorithm named PSO+TS for the multi-objective FJSPs with the same three objectives. In this paper, we introduce a novel algorithm named VNS+GA combining VNS and GA for solving the multi-objective FJSPs to minimize the makespan, the total workload, and the workload of the busiest machine. There are mainly three contributions in the hybrid algorithm. Firstly, a mix of two machine assignment rules and two operation sequencing rules are developed in the initialization stage to produce enough high quality initial solutions. Secondly, an adaptive mutation rules are introduced for considering both population diversity and convergence speed in perturbation in the machine assignment component. Thirdly, a speed-up variable neighbor search operator based on public critical block theory was investigated. The new local searching approach makes the search space dwindled deeply and produces high quality neighbor solutions in very short time. Experimental results compared with the three existing algorithms (i.e., AL+CGA algorithm, PSO+SA algorithm and PSO+TS algorithm) show that our hybrid algorithm can either obtain superior solutions or obtain richer non-dominated solutions than the other algorithms, especially for larger scale instances. The future work is to extend the initial solution rules and the public critical block method for solving other combinatorial problems. In addition, we will develop other heuristic algorithms with the public critical block neighborhood structure for solving the multi-objective FJSPs.

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


A globally conforming method for solving flow in discrete fracture networks using the Virtual Element Method A new approach for solving flow in Discrete Fracture Networks (DFN) is developed in this work by means of the Virtual Element Method. Taking advantage of the features of the VEM, we obtain global conformity of all fracture meshes while preserving a fracture-independent meshing process. This new approach is based on a generalization of globally conforming Finite Elements for polygonal meshes that avoids complications arising from the meshing process. The approach is robust enough to treat many DFNs with a large number of fractures with arbitrary positions and orientations, as shown by the simulations. Higher order Virtual Element spaces are also included in the implementation with the corresponding convergence results and accuracy aspects.

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


A generic method to develop simulation models for ambulance systems In this paper, we address the question of generic simulation models and their role in improving emergency care around the world. After reviewing the development of ambulance models and the contexts in which they have been applied, we report the construction of a reusable model for ambulance systems. Further, we describe the associated parameters, data sources, and performance measures, and report on the collection of information, as well as the use of optimisation to configure the service to best effect. Having developed the model, we have validated it using real data from the emergency medical system in a Brazilian city, Belo Horizonte. To illustrate the benefits of standardisation and reusability we apply the model to a UK context by exploring how different rules of engagement would change the performance of the system. Finally, we consider the impact that one might observe if such rules were adopted by the Brazilian system. The reuse of models is a topic of considerable interest in healthcare because, although most care delivery systems are specifically designed for the local context, many share common design elements. As an example, emergency departments share common operational principles but the configuration, management and layout of one department will differ from another. In this paper, we use an example from emergency medicine -ambulance control -as an exemplar with which to explore the question of reuse and standardisation of models.. Ambulance services are attractive to model for a number of reasons. First, the start and end of each task is well defined, tasks are self-contained and take place over short periods of time. Moreover, the processes lend themselves to a logistic analysis well-suited to modelling. This is not the case for all medical services, many of which are open ended, run concurrently with other medical interventions and stretch over long periods of time. Second, as we shall see, although there are many dimensions of uncertainty to modelling an ambulance service, these dimensions can be partitioned with relative ease and changed when moving from one ambulance service to another.. The ability to expand a model by interfacing it to another, even off-the-shelf, model is a third feature of reuse and standardisation. The geographical spread of ambulance services provides an opportunity to explore geographical information systems (GIS) and thus to extend a model's applicability from one city to another. Fourth, the high number of variables and the random nature of demand make the analysis for decision-making a combinatorial problem with a high number of alternatives and renders deterministic methods unattractive.. Finally, setting appropriate metrics is a case of assessing complex trade-offs, rather than applying measures that have been derived from first principles. For instance, an ambulance in front of every house would minimise the response time (the elapsed time from the call to the arrival of an ambulance on the scene), but at prohibitive cost.. To satisfy such demand with a high quality service, it is required a redundant system, with a low utilisation of resource in consequence. Meanwhile, system managers are pressed to operate the system within cost constraints, which implies maximising the utilisation of resource.. For all these reasons, simulation modelling is an attractive way of analysing such scenarios. Section 2 surveys the vast literature on modelling and simulation that has been applied to ambulance services. However, most Discrete Event Simulation (DES) models are built for a specific city in order to analyse a specific aspect of the system, making reuse hard if not impossible.. In this paper, we propose a generic DES modelling for ambulance services. The proposed modelling is comprehensive and emphasises the use of modular approach in order to build generic models. The methodology describes in detail, all stages we usually take during a simulation analysis of an Emergency Medical System (EMS).. As a basis, we have taken a specific model [1, 2] and generalised it to capture features of other systems. Section 3 describes ambulance services in generic terms, the overall structure of the model and the associated parameters, the data sources and collection, and the construction of an optimising loop around the simulation. In section 4 we explain the validation of the model and the results are discussed in section 5, with a short conclusion to clarify the findings (section 6). In this work, we propose a method to build generic simulation models to analyse ambulance service system by simulation and we have applied it to compare two aspects of provision between Brazil and UK. We explain the most important input data and how we should handle them and the main guidelines to build simulation models regardless of the simulation framework being used. We explain the main performance measures under point of view of patients and managers. In addition, we proposed some guidelines to build optimisation for simulation models to check alternatives in order to get good configurations for the system. Furthermore, we built a simulation model using the proposed method and implement it using a commercial simulation framework. The model was validated using real data and results were quite satisfactory. The proposed model seems be comprehensive and easy to use.. We take the advantage of reuse and standardisation to check the impact of rules from UK on Brazilian system in order to investigate likely improvements.. We believe that the guidelines proposed in this paper will be useful for building simulation models more quickly so that the models can be easily reused with minor adjustment. In doing this, we have demonstrated model reuse in two regions which use very different systems and policies. To the best of our knowledge, this is the first time that this has been done.

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


Immunotherapy

with

A

Study

Based

on

Mathematical

Modeling

The

role

of

in

tumor

dynamics

is

illustrated

through

mathematical

modeling,

using

delay

differential

equations

with

a

discrete

time

delay

(a

modified

version

of

the

Kirshner-Panetta

model).

Theoretical

analysis

gives

an

expression

for

the

discrete

time

delay

and

the

length

of

the

time

delay

to

preserve

stability.

Numerical

analysis

shows

that

alone

can

cause

the

tumor

cell

population

to

regress.

The

mechanism

of

the

establishment

and

destruction

of

cancer,

one

of

the

greatest

killer

of

the

world,

is

still

a

puzzle.

Modern

treatments

involve

surgery,

chemotherapy

and

radiotherapy,

but

yet

relapses

occur.

Hence,

the

need

for

a

more

successful

treatment

is

very

obvious.

Developing

schemes

for

immunotherapy

or

its

combination

with

other

therapy

methods

are

the

major

attempts

at

present,

which

aim

at

reducing

the

tumor

mass,

heightening

tumor

immunogenicity

and

removing

the

immunosuppression

induced

in

an

organism

in

the

process

of

tumor

growth.

Recent

progress

in

this

line

has

been

achieved

through

immunotherapy,

which

refers

to

the

use

of

cytokines

(protein

hormones

that

mediate

both

natural

and

specific

immunity)

usually

together

with

adoptive

cellular

immunotherapy

(ACI)

(Rosenberg

and

Lotze,

Schwartzentruber,

Rosenberg

et

al.,

Keilholz

et

al.,

Gause

et

al.,

Hara

et

al.,

Kaempfer

et

al.,

Curti

et

al.,

Rabinowich

et

al.,

The

main

cytokine

responsible

for

lymphocyte

activation,

growth

and

differentiation

is

which

is

mainly

produced

by

T-helper

cells

T-cells)

and

in

relatively

small

quantities

by

cytotoxic

Tlymphocytes

T-cells).

lymphocytes

differentiate

into

T-Helper

and

T-Helper

functional

subjects

due

to

the

immune

response.

acts

in

an

autocrine

manner

on

T-Helper

and

also

induces

the

growth

of

THelper

and

lymphocytes

in

a

paracrine

manner..

The

T-lymphocytes

themselves

are

stimulated

by

the

tumor

to

induce

further

growth.

Thus,

the

complete

biological

assumption

of

adoptive

cellular

immunotherapy

is

that

the

immune

system

is

expanded

in

number

artificially

(ex

vivo)

in

cell

cultures

by

means

of

human

recombinant

This

can

be

done

in

two

ways,

either

by

(i)

a

lymphokine-activated

killer

cell

therapy

(LAKtherapy)

where

the

cells

are

obtained

from

in

vitro

culturing

of

peripheral

blood

leukocytes

removed

from

patients

with

high

concentration

of

or

(ii)

a

tumor

infiltrating

lymphocyte

therapy

(TIL),

where

the

cells

are

obtained

from

lymphocytes

recovered

from

the

patient

tumors,

which

are

then

incubated

with

high

concentrations

of

in

vitro

and

are

comprised

of

activated

natural

killer

(NK)

cells

and

cytotoxic

T-lymphocyte

CTL

cells.

The

tumor

infiltrating

lymphocytes

(TIL)

are

then

put

back

into

the

bloodstream,

along

with

where

they

can

bind

to

and

destroy

the

tumor

cells.

It

has

been

established

clinically

that

immunotherapy

with

has

enhanced

the

cytotoxic

T-lymphocyte

(CTL)

activity

at

different

stages

of

tumor

(Rosenberg

and

Lotze,

Schwartzentruber,

Rosenberg

et

al.,

Keilholz

et

al.,

Also,

there

is

evidence

of

the

restoration

of

the

defective

natural

killer

(NK)

cell

activity

as

well

as

the

enhancement

of

polyclonal

expansion

of

and

T-cells

(Rosenstein

et

al.,

Tartour

et

al.,

Figure

gives

a

schematic

diagram

showing

the

key

players

in

tumorimmune

interactions

rose-hulman.edu

/mathjournal

Interaction

between

tumor

cells

and

an

immune

system

has

been

studied

by

numerous

authors

(Tartour

et

al.,

Kuznetsov

et

al.,

Adam

and

N.

Bellomo,

Kirschner

and

Panetta,

Bodnar

and

Foryś,

Foryś,

Galach,

Kolev,

Zhivkovc

and

Waniewski,

Szymańska,

Matzavinos

et

al.,

Sarkar

and

Banerjee,

Banerjee

and

Sarkar,

Kuznetsov

et

al.

present

a

mathematical

model

of

the

cytotoxic

T-lymphocyte

response

to

the

growth

of

an

immunogenic

tumor.

The

model

exhibits

a

number

of

phenomena

that

are

seen

in

vivo,

including

the

immunostimulation

of

the

tumor

growth,

"sneaking

through"

the

tumor,

and

the

formation

of

a

tumor

"dormant

state".

The

delay

version

of

Kuznetsov's

model

was

studied

by

Galach

where

the

effect

of

the

time

delay

was

taken

into

account

in

order

to

achieve

a

better

compatibility

with

reality.

In

(Foryś,

Marchuk's

model

of

a

general

immune

reaction

is

presented.

Qualitative

behavior

of

solutions

to

the

model

(and

its

simplification),

along

with

many

illustrations

of

the

recovery

process,

oscillations

or

lethal

outcomes

of

a

disease,

is

shown.

The

role

of

interleukins

in

the

immune

process

is

taken

into

account

to

adapt

Marchuk's

model

to

tumor

growth

dynamics.

Szymańska

studied

a

basic

mathematical

model

of

the

immune

response

when

cancer

cells

are

recognized.

The

model

consists

of

six

ordinary

differential

equations

and

is

extended

by

taking

into

account

two

types

of

immunotherapy:

an

active

immunotherapy

and

an

adoptive

immunotherapy.

An

analysis

of

the

corresponding

models

is

made

to

answer

the

question

of

which

of

the

presented

methods

of

immunotherapy

is

better.

The

analysis

is

completed

by

numerical

simulations

which

show

that

the

method

of

adoptive

immunotherapy

seems

better

for

the

patient

at

least

in

some

cases.

A

mathematical

model

describing

the

growth

of

a

solid

tumor

in

the

presence

of

an

immune

system

response

is

presented

by

(Matzavinos

et

al.,

They

focused

upon

the

attack

of

tumor

cells

by

the

so-called

tumor-infiltrating

cytotoxic

lymphocytes

(TICLs),

in

a

small,

multicellular

tumor,

without

necrosis

and

at

some

stage

prior

to

(tumor

induced)

angiogenesis.

Their

study

can

explain

the

complex

heterogeneous

spatio-temporal

dynamics

observed

and

lead

to

a

deeper

understanding

of

the

phenomenon

of

cancer

dormancy

in

the

model,

which

may

be

helpful

in

future

development

of

more

effective

anti-cancer

vaccines..

In

(Sarkar

and

Banerjee,

the

authors

express

the

spontaneous

regression

and

progression

of

a

malignant

tumor

system

as

a

prey-predator-like

system.

Their

model

is

a

three

dimensional

deterministic

system,

consisting

of

tumor

cells,

hunting

predator

cells

and

resting

predator

cells,

which

is

extended

to

a

stochastic

one,

allowing

for

random

fluctuations

around

the

positive

interior

equilibrium.

The

stochastic

stability

properties

of

the

model

are

investigated

both

analytically

and

numerically,

and

the

thresholds

obtained

from

their

study

may

be

helpful

to

control

the

malignant

tumor

growth.

They

also

studied

the

model

by

including

a

discrete

time

delay

in

the

system

(Banerjee

and

Sarkar,

and

concluded

that

the

model

can

provide

an

approximate

estimate

of

timing

(length

of

delay)

and

a

dosage

of

therapy

that

would

best

complement

the

patient's

own

defense

mechanism

versus

the

tumor

cells.

More

work

on

time

delays

in

connection

with

tumor

growth

can

be

found

in

(Byrne,

Bodnar

and

Foryś,

Bodnar

and

Foryś,

Bodnar

and

Foryś,

Kirschner

and

Penetta

studied

the

role

of

in

tumor

dynamics,

particularly,

long-term

tumor

recurrence

and

short

term

oscillations

in

a

mathematical

perspective

(Kirschner

and

Panetta,

The

model

proposed

there

deals

with

three

populations,

namely,

the

activated

immune-system

cells

(commonly

called

the

effector

cells),

such

as

cytotoxic

T-cells,

macrophages

and

natural

killer

cells

that

are

cytotoxic

to

the

tumor

cells,

the

tumor

cells

and

the

concentration

of

The

important

parameters

in

their

study

are

the

antigenicity

of

tumor

(c),

the

treatment

term

that

represents

the

external

source

of

effector

cells

(s

and

the

treatment

term

that

represents

an

external

input

of

into

the

system

(s

Their

results

can

be

summarized

as

follows:

(i)

For

a

non-treatment

case

(s

s

the

immune

system

is

not

able

to

clear

the

tumor

for

low

antigenic

tumors

while

for

highly

antigenic

tumors,

reduction

to

a

small

dormant

tumor

is

the

best

case

scenario.

(ii)

The

effect

of

adoptive

cellular

immunotherapy

(ACI)

therapy

(s

s

alone

can

yield

a

tumor

free

state

for

tumors

of

almost

any

antigenicity,

provided

the

treatment

concentration

is

above

a

given

critical

level.

But

for

tumors

with

small

antigenicity,

an

early

treatment

is

needed,

while

the

tumor

is

small,

so

that

the

tumor

can

be

controlled.

(iii)

The

treatment

with

alone

(s

s

states

that

if

administration

is

low,

there

is

no

tumor-free

state.

However,

if

the

input

is

high,

the

tumor

can

be

cleared

but

the

immune

system

grows

without

bounds

causing

problems

such

as

a

capillary

leak

syndrome.

(iv)

Finally,

it

is

the

combined

treatment

with

ACI

and

(s

s

that

gives

the

combined

effects

obtained

from

the

monotherapy

regime.

For

any

antigenicity,

there

is

a

region

of

tumor

clearance.

These

results

indicate

that

a

treatment

with

ACI

may

be

a

better

option

either

as

a

monotherapy

or

in

conjunction

with

In

this

paper,

a

modification

of

the

model

studied

by

Kirschner

and

Panetta

is

done,

by

adding

a

discrete

time

delay

which

exists

when

activated

T-cells

produce

The

modified

model

is

discussed

in

Section

Section

deals

with

the

qualitative

analysis

of

the

model.

In

Section

the

numerical

results

are

discussed,

and

Section

is

the

conclusion..

Immunotherapy

with

A

study

based

on

mathematical

modeling

The

aim

of

this

paper

was

to

see

the

effect

of

time

delay

during

immunotherapy

with

The

effect

of

immunotherapy

with

on

the

modified

model

was

explored

and

circumstances

under

which

the

tumor

can

be

eliminated

are

described.

The

model

represented

by

a

set

of

delay

differential

equations

contains

treatment

terms

s

and

s

that

represent

an

external

source

of

the

effector

cells

by

adoptive

cellular

immunotherapy

(ACI)

and

an

external

input

of

into

the

system,

respectively.

However,

the

effects

of

on

the

tumor-immune

dynamics

with

time

delay

are

the

main

focus.

It

is

shown

that

treatment

with

alone

can

offer

a

satisfactory

outcome.

When

there

is

an

external

input

of

the

concentration

of

and

the

effector

cells

are

stimulated

after

hours,

during

which

the

production

reaches

its

peak

value

to

generate

more

effector

cells,

a

tumor

with

medium

to

high

antigenicity

shows

regression

and

the

concentration

of

stabilizes.

Unlike

in

(Kirschner

and

Panetta,

the

immune

system

also

stabilizes,

indicating

that

side

effects

like

the

capillary

leak

syndrome

do

not

arise

here.

In

other

words,

a

patient

does

not

need

to

endure

very

many

side

effects

before

the

therapy

successfully

clears

the

tumor.

In

(Rosenberg

et

al.,

the

effectiveness

of

the

high

dose

bolus

treatment

with

is

studied,

where

many

patients

are

in

complete

remission

for

to

months.

Hence,

this

model

predicts

that

it

is

indeed

possible

to

treat

a

patient

cancer

free

with

immunotherapy

with

alone..

Finally,

it

can

be

said

that

the

above

finding

sheds

some

light

on

immunotherapy

with

and

can

be

helpful

to

medical

practitioners,

experimental

scientists

and

others

to

control

this

killer

disease

of

cancer.

An

extension

along

this

line

of

work

will

be

to

examine

the

effect

of

other

cytokines

such

as

interferon

−γ,

which

are

involved

in

the

cellular

dynamics

of

the

immune

system

response

to

tumor

invasion

and

how

these

cytokines

affect

the

dynamics

of

the

system.

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