Observer-Based Synchronization for a Class of Unknown Chaos Systems with Adaptive Fuzzy-Neural Network SUMMARY This investigation applies the adaptive fuzzy-neural observer (AFNO) to synchronize a class of unknown chaotic systems via scalar transmitting signal only. The proposed method can be used in synchronization if nonlinear chaotic systems can be transformed into the canonical form of Lur'e system type by the differential geometric method. In this approach, the adaptive fuzzy-neural network (FNN) in AFNO is adopted on line to model the nonlinear term in the transmitter. Additionally, the master's unknown states can be reconstructed from one transmitted state using observer design in the slave end. Synchronization is achieved when all states are observed. The utilized scheme can adaptively estimate the transmitter states on line, even if the transmitter is changed into another chaos system. On the other hand, the robustness of AFNO can be guaranteed with respect to the modeling error, and external bounded disturbance. Simulation results confirm that the AFNO design is valid for the application of chaos synchronization. The synchronization of chaotic systems has been extensively studied and given its potential application to security communications. Synchronization means that the master and slave have identical states as time goes to infinity. Pecora and Carroll first considered the synchronization of chaotic systems [18] , in which the drive-response concept is introduced to achieve synchronization by a scalar transmitted signal. Perfectly identical parameters cannot be achieved in real applications. Therefore, the nonlinear robust control [22] , [23] concept is employed to chaos, synchronization with previous known states within the margin of synchronization error. An adaptive recurrent neural controller can be utilized to synchronize with respect to unknown systems nizing using a scale transmitted signal. Message-free synchronization has been developed to permit communication with masking message in chaotic signals [14] . Messages can be extracted with message-free synchronization. Moreover, Boutayeb [3] proposed a scheme which is provided to synchronize and extract message simultaneously. Nevertheless, these systems do not consider the robustness of the state observer with respect to parameters mismatch [3] , [8] , [16] . Adaptive sliding observer design [2] , [7] can handle parameters mismatch. Furthermore, a robust observer [13] is designed for synchronization using the Takagi-Sugeno fuzzy model and the LMI approach. Millerioux and Daafouz recently introduced the input-independent global chaos synchronization [15] . In this method, the added message does not affect the synchronization if the observer gain is appropriately designed. Other studies consider nonlinear observer designs for chaos synchronization [1] , [17] . However, by the methods of previous descriptions, the chaotic systems should be known previously before synchronization design. Recently, the system identification approaches [5] , [6] , [9] have been introduced for a scale signal identification and chaos synchronization respectively. In [6] , the system identification concepts are applied to approximate the chaos signal. The proposed identification scheme assumes a Lur'e type system as a reference model. This allows us to separate the identification process into two parts, adjusting alternatively the parameters of the linear and the nonlinear part. For modeling the linear system, the autoregressive moving average (ARMA) approach is utilized. On the other hand, the genetic algorithm is applied to optimize the break points parameters of nonlinear static functions to approximate nonlinear mapping. However, this approach is based on off-line identification, and it is not an on-line tuning scheme. Furthermore, the order in linear part identification should be by trial and error. The identification results just imitate the transmission signal and the other states in the master end cannot be achieved to synchronize simultaneously. In addition, the simulation results of this approach seem not very well. According to [5] , the recursive identification is applied for chaos synchronization when the slave has exactly identical structure to the master system, but its parameters are unknown. It is shown that the unknown slave system parameters can be found by the concepts of adaptive synchronization. In other words, when the unknown slave system parameters are found, the synchronization is achieved. However, the structures in the master and slave ends should be known previously and exactly the same, although the pa-rameters in the slave end can be estimated by recursive identification. The discussion of robustness is not included too. More recently, an alternative indirect Takagi-Sugeno fuzzy model based adaptive fuzzy observer design has been applied to chaos synchronization under assumptions that states are unmeasurable and parameters are unknown [9] . The adaptive law is designed to estimate the unknown parameters in the T-S fuzzy model of the slave end. When the unknown parameters are estimated correctly, the synchronization is achieved. However, the form of the T-S fuzzy model should be known first, and then the adaptive fuzzy observer is designed by the T-S fuzzy model. In addition, the discussion of robustness is not included.. This investigation achieves synchronization with respect to a class of unknown master chaotic systems by introducing the concepts of AFNO [11] , Brunowsky canonical form [16] and Lur'e systems [21] . The proposed system includes a chaotic master with canonical form and the slave with AFNO. The AFNO combines a FNN and a linear observer. In this design, the slave should synchronize with the master by a scale transmitted signal. This approach employs adaptive FNN to model the nonlinear term of the master end. The output of the adaptive FNN, robust input and a transmitted state are sent to the linear observer to estimate the states of the slave. The master and slave achieve synchronization when all states are estimated at the slave. Additionally, the adaptive laws are needed to update the weights of the FNN, when the reconstructed and transmitted states differ from each other.. The benefits of provided AFNO for synchronization can be stated as follows. AFNO is first applied to chaotic synchronization with only one transmitted signal. Since AFNO is on line learning at the slave, the synchronization can be achieved respect to a switched unknown chaotic system with the Lur' e type. Additionally, the adaptability for parameters change or even system switched in the mater and the robustness for modeling error and external bounded disturbance are also given. AFNO also has FNN's inherent properties of fault-tolerance, parallelism learning, linguistic information and logic control. By comparing with [5], [6], [9] , our presentation provides the on-line, robust and adaptive synchronization for a class of chaos systems. The form of nonlinear functions in the master end cannot be known in previous due to soft computing with FNN for fitting it in the slave end.. The paper is organized as follows. Section 2 describes the overall structure of adaptive synchronization with the AFNO design. Section 3 then introduces the AFNO design. Next, Sect. 4 includes the simulation results, including two examples to demonstrate the effectiveness of this application. Conclusions are finally are made in Sect. 5. This work has applied AFNO for synchronization with respect to a class of unknown chaos systems via a scalar transmitted signal only. Once the nonlinear chaotic systems could be transformed into the canonical form of Lur'e system type by the differential geometric method, the AFNO method can be utilized for synchronization.. In this approach, the nonlinear term in the master end was modeled by the adaptive fuzzy-neural network (FNN) in AFNO

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One-reversal counter machines and multihead automata: Revisited Abstract. Among the many models of language acceptors that have been studied in the literature are multihead finite automata (finite automata with multiple one-way input heads) and 1-reversal counter machines (finite automata with multiple counters, where each counter can only "reverse" once, i.e., once a counter decrements, it can no longer increment). The devices can be deterministic or nondeterministic and can be augmented with a pushdown stack. We investigate the relative computational power of these machines. Our results (where C1 and C2 are classes of machines) are of the following types:1. Machines in C1 and C2 are incomparable. 2. Machines in C1 are strictly weaker than machines in C2. In obtaining results of these types, we use counting and "cut-and-paste" arguments as well as an interesting technique that shows that if a language were accepted by a device in a given class, then all recursively enumerable languages would be decidable. A deterministic pushdown automaton (DPDA) is a deterministic finite automaton (DFA) augmented with a pushdown stack. The nondeterministic versions are called NPDA and NFA, respectively. It is well-known that a DPDA is weaker than an NPDA, and the latter machines accept exactly the context-free languages. A special case of a pushdown stack is one where the stack alphabet has only two symbols, one of which is used only to mark the bottom of the stack and cannot be modified. Such a stack is called a counter. Thus, we can think of a counter as a memory unit that holds a non-negative integer (initially zero), which can be incremented by 1, decremented by 1, left unchanged and tested for zero. A DFA (NFA) augmented with multiple (at least two) counters is equivalent to a Turing machine [12] . However, if we restrict the counters to be reversal-bounded, the equivalence no longer holds. Here, reversal-bounded means that the number of alternations between non-decreasing mode and nonincreasing mode each counter makes during the computation is at most r for some given positive integer r. An NFA augmented with such counters is called a (reversal-bounded) counter machine (NCM). The deterministic version is called a DCM. It was shown in [7] that an NCM can accept only a language whose Parikh map is semilinear. Closure and decidable properties for NCM and DCM were also investigated in [7] . For related results, see [2, 3, 4, 5, 8, 10] . We note that a counter making r-reversals can be simulated by r+1 2 counters each of which makes 1 reversal. Hence, we may assume that the counters in a DCM and NCM are 1-reversal.. An NFA with multiple one-way input heads is called an NMHFA. The deterministic version is called DMHFA. These devices were first studied in [13] , where it was reported that for any integer k ≥ 1, a DMHFA (resp., NMHFA) with k + 1 head is more powerful than one with only k heads. The proof in [13] was incomplete and was later completed in [15] . Stateless version of this hierarchy was later shown in [9] .. A DPDA (resp. NPDA) can be generalized by augmenting it with multiple reversal-bounded counters -we will call it a DPCM (resp. NPCM), or by equipping it with multiple input heads -we will call it DMHPDA (resp. NMHPDA).. As for the classes of 1-reversal (pushdown) counter machines (DCM, NCM, DPCM, NPCM), our primary interest lies in the following questions:. 1. whether a pushdown stack or non-determinism strictly strengthens 1-reversal counter machines, and 2. whether there is a trade-off, that is, whether an NCM can simulate a DPCM, and vice-versa.. We exhibit two languages which are in the symmetric difference of NCM and DPCM to answer the above questions negatively (Corollary 2). It is of particular interest for applications to determine whether a given language is in DCM (or in DPCM) or not. This is because these deterministic classes possess desirable properties about decidability which are not shared by their non-deterministic counterparts such as the decidability of equivalence between a DCM and a DPCM (Corollary 5.4 in [7] ) or between two DPDAs [14] . A typical tool to prove that a language is not in a given class is the pumping lemma, and actually pumping lemmas are available for DFA(= NFA), DPDA, and NPDA [6, 16, 17] . We propose another type of tool (Lemma 4), which reduces a language that is accepted by a DPCM with k-counters into its sub-language that is accepted by a DPCM with at most k − 1 counters. Then, using the pumping lemma for DPDA [16] , the reduction enables us to prove the existence of a language in NCM which cannot be accepted by any DPCM (Corollary 1).. In order to prove the incomparability between DPCM and NCM, we will also propose a language which is accepted by a DPCM but cannot be accepted by any NCM. A technique used toward this end deserves special mention: on the supposition that an NCM accepted this language, we could design an algorithm to decide the halting problem for Turing machines (Theorem 2).

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Finding paths in graphs avoiding forbidden transitions Let v be a vertex of a graph G; a transition graph T(v) of v is a graph whose vertices are the edges incident with v. We consider graphs G with prescribed transition systems T = {T(v)|v ∈ V(G)}. A path P in G is called T-compatible, if each pair uv, vw of consecutive edges of P form an edge in T(v). Let A be a given class of graphs (closed under isomorphism). We study the computational complexity of finding T-compatible paths between two given vertices of a graph for a specified transition system T ⊆ A. Our main result is that a dichotomy holds (subject to the assumption P ≠ NP). That is, for a considered class A, the problem is either (1) NP-complete, or (2) it can be solved in linear time. We give a criterion--based on vertex induced subgraphs--which decides whether (1) or (2) holds for any given class A. A transition in a graph is a pair of adjacent edges. We consider the problem of finding paths between two given vertices avoiding forbidden transitions (or equivalently, paths that use only allowed transitions); such paths are called compatible. For a vertex v, the set of allowed transitions define a graph T (v) on the set of edges incident with v; the graph T (v) is called the transition graph of v.. If, for example, all transition graphs are cliques, then the compatible-pathproblem is trivial, since every path is compatible. It is natural to ask for the computational complexity of the compatible-path-problem with respect to a given class A of transition graphs. We give a complete answer to this question showing that-with respect to a given class A-the problem is either (1) NP-complete, or (2) can be solved in linear time (both cases exclude each other if P = NP holds). We supply a 'forbidden induced subgraph'-criterion which decides whether (1) or (2) prevails. For the linear time cases we present algorithms which not only decide existence but actually find a compatible path (if one exists) in linear time.. In the final section we give an application of our linear time results to the problem of finding alternating paths in edge-colored graphs and extend a result by Bang-Jensen and Gutin [1] .. Our work is closely related to [10] , where the complexity of finding compatible 2-factors is studied. Compatible paths and cycles have been intensively studied in the context of eulerian graphs (see [5] for a survey on this topic).

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Parity Forwarding For Multiple-Relay Networks Abstract-This paper proposes a relaying strategy for networks with multiple relays where each relay forwards parities of decoded codewords. This parity-forwarding scheme can be thought of as a generalization of Cover and El Gamal's wellknown decode-and-forward strategy for the classic three-terminal relay channel to networks with multiple relays. As compared to previous multiple-relay decode-and-forward strategies, the parity-forwarding scheme is more flexible and can achieve a higher rate. The proposed strategy can be easily applied to networks with complex topologies. We show that relay networks can be degraded in more than one way, and parity-forwarding is capacity achieving for a new form of degraded relay networks. A fundamental understanding of the role of relays in a network is crucial in the design of efficient network protocols for future wireless systems. Although the capacity of the simplest, yet the most fundamental, three-terminal relay channel [1] is still unknown, recent surge of interest in relay networks has resulted in not only new achievable rates for multiple-relay networks [2] , [3] , but also novel network protocols derived from the information theoretical insights [4] , which improve previous protocols [5] .. This paper generalizes Cover and El Gamal's decode-andforward strategy [6, Theorem 1] for a single-relay network to a network with multiple relays. This generalization is simple yet flexible when applied to large networks with complex topologies. In particular, we show that a relay network can be degraded in more than one way and parity-forwarding protocols can be used to achieve the capacity of a new class of degraded networks with two relays.. The three-terminal relay channel was originally introduced in [1] . Key results for the single-relay channel were derived by Cover and El Gamal in their classic work [6] , where two fundamental relay strategies, decode-and-forward [6, Theorem 1] and compress-and-forward [6, Theorem 6] , are devised. Several coding strategies for networks with multiple-relays have since been proposed [4] , [7] , [3] , [8] , [9] , [10] , [2] , [11] . In [2] , an achievable rate is derived using successive interference cancelation at each relay. In [7] , an improved rate is derived using a decode-and-forward scheme based on Carleial's coding strategy for the generalized multipleaccess channel with feedback (named 'regular encoding' in [3] ) which achieves the capacity of a certain class of degraded multiple-relay networks. In the latter scheme, each source message is repeatedly sent by the source and all the relays that have decoded the message so far. The destination decodes a message only after all relays have decoded the message and have participated in the cooperative transmission. One drawback of this scheme is that the achievable rate is bounded by the condition that all relays must decode the source message successfully. This can be restrictive in cases where the sourcerelay channel is poor. This paper proposes a new parityforwarding scheme for the relay network in which each relay has the ability to facilitate transmission between any two communicating nodes in the network (and not just communication by the source.) This additional flexibility results in a higher overall transmission rates for a general relay network as compared to [7] .. This paper focuses on decode-and-forward-like strategies in a relay network and does not explore the possibility of compress-and-forward. Compress-and-forward for relay networks has been considered in [3] , where the relay nodes are divided into two groups: the decode-and-forward nodes and the compress-and-forward nodes. In addition, [3] also considers the possibility that a compress-and-forward node may partially decode the other relay's message to enhance its estimation of the source message. We note that compress-and-forward can be layered on top of the parity-forwarding scheme proposed in this paper to further enhance the overall transmission rate, although this is not explored in detail here.. We name our proposed scheme "parity-forwarding" because binning for the relay channel may be interpreted as parity generation. In Cover and El Gamal's decode-and-forward strategy [6, Theorem 1] , the relay transmits a bin index of the source message to facilitate the decoding of the source message at the destination. In a linear coding context, binning can be realized by identifying parity bits (or syndrome) as the bin index [12] . This interpretation also facilitates practical code constructions for the relay channel as shown in our previous work [13] .. The parity-forwarding strategy proposed in this paper bears a resemblance to network coding [14] . In both schemes, the intermediate nodes forward parities to efficiently help a pair of terminals communicate.. In this paper, directed acyclic graphs are used to visualize relay protocols. Each parity-forwarding scheme can be associated with a graph, which can also be interpreted as a routing scheme. To obtain the best overall transmission rate, all routing possibilities should be considered.. Throughout the paper, we use the random variable X to denote the symbol transmitted by the source and Y as the symbol received by the destination. Random variables X k and Y k denote the transmitted and received symbols at the k'th relay. The source message in block i is denoted by w i ; s

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The bits and flops of the n-hop multilateration primitive for node localization problems The recent advances in MEMS, embedded systems and wireless communication technologies are making the realization and deployment of networked wireless microsensors a tangible task. Vital to the success of wireless microsensor networks is the ability of microsensors to "collectively perform sensing and computation". In this paper, we study one of the fundamental challenges in sensor networks, node localization. The collaborative multilateration presented here, enables ad-hoc deployed sensor nodes to accurately estimate their locations by using known beacon locations that are several hops away and distance measurements to neighboring nodes. To prevent error accumulation in the network, node locations are computed by setting up and solving a global non-linear optimization problem. The solution is presented in two computation models, centralized and a fully distributed approximation of the centralized model. Our simulation results show that using the fully distributed model, resource constrained sensor nodes can collectively solve a large non-linear optimization problem that none of the nodes can solve individually. This approach results in significant savings in computation and communication, that allows fine-grained localization to run on a low cost sensor node we have developed. Precise knowledge of node location in ad-hoc deployed microsensor networks yields a wide variety of profound advantages. Knowledge of location can be used to report the geographical origin of events, to assist in target tracking, geographic aware routing [10] , to administer the sensor network and evaluate its coverage [11] . These together with security and smart environment applications such as the Smart Kindergarten [18] are only a few of the applications where location aware nodes are required.. In many situations, wireless sensor nodes are expected to be deployed in an ad-hoc fashion (i.e air-dropped over an area). With ad-hoc deployment however, one cannot accurately predict or plan a-priori the location of each sensor. Based on this and the fact that direct line-of-sight with beacons is not always feasible, we seek to develop an algorithm that can perform precise localization of sensor nodes with indirect line-of-sight by utilizing location information and distance measurements over multiple hops. To achieve this goal, nodes use their ranging sensors to measure distances to their neighbors and share their measurement and location information with their neighbors to collectively estimate their locations.. In this paper we present collaborative multilateration that we also refer to as the n-hop multilateration primitive. Collaborative multilateration consists of a set of mechanisms that enables nodes found several hops away from location aware beacon nodes collaborate with each other to estimate their locations with high accuracy. This multihop capability waives the line-of-sight to beacons requirement making fine-grained localization possible while requiring very few beacon nodes. Position estimates are obtained by setting up a global non-linear optimization problem and solving it using iterative least squares. Collaborative multilateration is presented in two computation models, centralized and distributed. These can be used in a wide variety of network setups from fully centralized where all the computation takes place at a base station, to locally centralized (i.e computation takes place at a set of cluster heads) to fully distributed where computation takes place at every node.. The fully distributed computation model presented here is an approximation of its centralized counterpart and has several properties favorable to sensor networks. It offers a significant reduction in computation requirements thus allowing the execution of collaborative multilateration on resource constrained sensor nodes such as the Medusa MK-2 node described in this paper. Using this mechanism, resourceconstrained nodes can collaborate with each other to jointly estimate their locations, a task that none of the nodes can perform individually because of their computation and memory limitations. The use of a fully distributed computation model is also tolerant to node failures, and distributes the communication cost evenly across the sensor nodes and does not require any additional supporting mechanisms such as leader election and multihop routing that would be required for a fully centralized implementation.. The algorithms presented in this paper are validated on a combined ns-2 and MATLAB simulation testbed, using the measured parameters of our experimental sensor nodes. The remainder of this paper is organized as follows. Next section briefly describes the related work. Section 3 provides some preliminary information and overview of our approach. Section 4 describes the initial setup configuration for collaborative multilateration. Section 5 explains centralized and distributed computation models. Our simulation results are presented in section 6 and section 7 concludes the paper. In this paper we have described collaborative multilateration for node localization problems. We have shown that using this three phase approach nodes that are indirectly connected to beacon nodes can estimate their locations with similar accuracies at the single hop multilateration. Also, with our distributed approach colonies of constrained sensor nodes can collectively solve a global optimization problem that an individual node cannot solve. The use of a global gradient for computing a global optimum locally reinforces a distributed computation model with other potential applications in sensor networks. In addition to the distributed computation model the collaborative multilateration appears to be an attractive choice for assisting infrastructure based localization systems to better handle obstructions. In this paper we have developed the computational part of collaborative multilateration. The remaining challenge is to study its feasibility with respect to the physical effects. To this end, as part of our future work we plan to study the interaction of our algorithms with the physical world using our sensor network testbed of Medusa MK-2 nodes. Node localization has been the topic of active research and many systems have made their appearance in the past few years. A detailed survey of such systems is provided by Hightower and Boriello in [7] . Despite these efforts, very few systems are actually ad-hoc. Even fewer methods are have been proposed that offer a fully distributed operation. Doherty's [3] convex position estimation approach for instance describes a method for localizing ad-hoc nodes based only on connectivity. This method is based on semi-definite programming and requires rigorous centralized computation so it is not always suitable for many ad-hoc setups.. Some forms of ad-hoc localization also exist in the domain of mobile robotics [8, 13] . The localization problem in mobile robotics is similar to the ad-hoc localization problem investigated in sensor networks. One main difference however is that mobile robots have additional odometric measurements that can help with estimating the initial robot positions, something that is not available in sensor networks. Furthermore, localization studies in the sensor network community also consider scalability communication and power consumption issues that are not studied by the robotics community.. The AHLoS system we proposed in [16] uses iterative multilateration which relies on a small set of nodes initially configured as beacons to estimating node locations in an ad-hoc setup. This work identified two main problems: 1) without relatively large beacon densities, the iterative multilateration may get stuck in regions of the network that are relatively sparse, and 2) error propagation becomes an issue in large networks. The collaborative multilateration algorithms presented in this paper address these two issues.. In parallel to our work some other ad-hoc node localization approaches have been independently proposed in [12] and [15] . In both these approaches anchor node location information is propagated in the network. Nodes with unknown location note the shortest hop distance to each of the anchor nodes a multiply this an average hop distance to get an approximate distance to each of the anchor nodes. With this information nodes perform a multilateration to get an initial estimate of their locations. To obtain better estimates, the authors of [15] also use a further refinement phase that uses least squares to refine node positions based on local computation. The authors claim that their approaches are independent of ranging technologies and can deliver localization accuracy within one third of the communication range.. Despite the similarities, the work presented here has several fundamental differences from the aforementioned approaches. We provide a mechanism for limiting error propagation by computing in the context of over-constrained node configurations (the collaborative subtrees). At the same time, we provide a fully distributed computation model and we demonstrate its scalability. Our algorithms are targeted for a fine-grained ad-hoc localization system that we are currently developing.

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Serialized asynchronous links for NoC Abstract As multiprocessor system-on-chip solutions increase there are benefits to provide a scalable on chip communication architecture. One promising approach is Network-on-Chip (NoC). The growth of research into NoC has led to a number of viable architectures, examples [1] [2] [3] [4] [5] . Typically the NoC consists of network interfaces which allow a core to interface to the network, switches which are responsible for routing the packet and links which connect the switches together. Numerous NoC architectures adopt a synchronous approach and more recently there have been studies of asynchronous NoC [6, 7] which highlight some of the problems with synchronous NoC such as global clock power consumption, clock skew and electromagnetic interference. An asynchronous point-to-point link that can be used for communication has been investigated in [8] . This scheme uses clock pausing techniques to pass data from the synchronous to asynchronous domains. Power in synchronous design can be reduced by lowering the clock speed, but to maintain the throughput the data width would need to be increased by the same factor. Interconnect cost, in terms of the number of wires required between switches, could grow to be considerable in NoC if the data width is increased since each switch is effectively connected by a point-to-point * The authors would like to acknowledge the Engineering and Physical Sciences Research Council (EPSRC) for funding under grant no. EP/C512804. link to a neighboring switch and the high cost of parallel links has been shown in [9] which compares fully parallel and bit-serial buffered wires. It is expected with further scaling down of technology the number of point-to-point links between the switches of a NoC will grow as more and more cores are integrated into a system. This paper proposes the application of serialization as a means of reducing the number of wires between NoC switches. Byte-level serialization of the data is performed as opposed to a fully bit-serial single wire link. Furthermore, the serialization is employed in the asynchronous domain to remove the need for high frequency global clocking of the serial links which would be required in a synchronous design. The paper is organised as follows, section II provides the motivation, section III describes the asynchronous link and circuits, section IV discusses word-level acknowledgement for increasing the performance, section V is the experimental results and finally VI the concluding remarks.

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Highly dynamic Destination-Sequenced Distance-Vector routing (DSDV) for mobile computers An ad-hoc network is the cooperative engagement of a collection of Mobile Hosts without the required intervention of any centralized Access Point. In this paper we present an innovative design for the operation of such ad-hoc networks. The basic idea of the design is to operate each Mobile Host as a specialized router, which periodically advertises its view of the interconnection topology with other Mobile Hosts within the network. This amounts to a new sort of routing protocol. We have investigated modifications to the basic Bellman-Ford routing mechanisms, as specified by RIP [5], to make it suitable for a dynamic and self-starting network mechanism as is required by users wishing to utilize ad hoc networks. Our modifications address some of the previous objections to the use of Bellman-Ford, related to the poor looping properties of such algorithms in the face of broken links and the resulting time dependent nature of the interconnection topology describing the links between the Mobile Hosts. Finally, we describe the ways in which the basic network-layer routing can be modified to provide MAC-layer support for ad-hoc networks.

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Computation of nonclassical shocks using a spacetime discontinuous galerkin method We present a numerical study for two systems of conservation laws using a spacetime discontinuous Galerkin (SDG) method with causal spacetime triangulations and the piecewise constant Galerkin basis. The SDG method is consistent with the weak formulation of conservation laws, and, in the case of strictly hyperbolic systems, also with the Lax entropy condition. Convergence of the method was shown for a special class of hyperbolic systems (Temple systems).The initial data we consider lead to nonclassical shocks. The first part of our study is for the Keyfitz-Kranzer system. We compute the SDG solutions approximating overcompressive and singular shocks, and note that our results are consistent with those obtained by [Sanders, and Sever 2003] using a finite difference scheme. The second system we consider is an approximation of a three-phase flow in the petroleum reservoirs. Numerical solutions for this system were computed by [Schecter, Plohr, and Marchesin 2004] using the Dafermos regularization and a technique for numerical solving of ordinary differential equations. We compute the SDG approximation to a solution containing a transitional shock.We note that even though convergence of the SDG method was shown so far only for Temple systems, numerical examples herewith show that it can be successfully used in approximating solutions of more general conservation laws. Conservation laws describe various phenomena involving advective transport or wave motion, as gas dynamics, elastodynamics, biomechanics, chromatography, oil recovery, etc. The study of these partial differential equations is very challenging because they poses some special features that are not seen elsewhere in the PDE theory. Solutions may become discontinuous after a finite time even for smooth initial data and one has to define weak solutions. Weak solutions are not necessarily unique, and to distinguish a physically meaningful solution additional conditions are needed (see [Lax 1973 ], [Serre 1999] , [Dafermos 2000]) .. The development of numerical methods for conservation laws involves an interplay between physical modeling, mathematical theory and numerical analysis. Finite difference methods (for eg., [Lax, and Wendroff 1964] , [Glimm 1965 ], [Osher 1984] ) and finite volume methods (for eg., [LeVeque 2002] ) are the most studied and widely used numerical methods for conservation laws. In finite difference methods, the solution is approximated pointwise at the grid points, while the finite volume methods are based on the integral form of conservation laws instead, and one is approximating the cell average of the exact solution. Discontinuous Galerkin methods (see [Cockburn, Karniadakis, and Shu 2000] ) use an element-wise representation of a solution and enforce the conservation law locally. The Runge-Kutta DG methods ( [Cockburn 2001] ) are based on a finite element discretization of a spatial domain and a special Runge-Kutta type discretization is used to propagate the solution in time.. In this paper we consider a DG method based on spacetime discretizations.

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Bisimulation and Cocongruence for Probabilistic Systems We introduce a new notion of bisimulation, called event bisimulation on labelled Markov processes (LMPs) and compare it with the, now standard, notion of probabilistic bisimulation, originally due to Larsen and Skou. Event bisimulation uses a sub σ-algebra as the basic carrier of information rather than an equivalence relation. The resulting notion is thus based on measurable subsets rather than on points: hence the name. Event bisimulation applies smoothly for general measure spaces; bisimulation, on the other hand, is known only to work satisfactorily for analytic spaces. We prove the logical characterization theorem for event bisimulation without having to invoke any of the subtle aspects of analytic spaces that feature prominently in the corresponding proof for ordinary bisimulation. These complexities only arise when we show that on analytic spaces the two concepts co-incide.We show that the concept of event bisimulation arises naturally from taking the co-congruence point of view for probabilistic systems. We show that the theory can be given a pleasing categorical treatment in line with general coalgebraic principles. As an easy application of these ideas we develop a notion of "almost sure" bisimulation; the theory comes almost "for free" once we modify Giry's monad appropriately. The main point of this paper is to argue that one should work with probabilistic cocongruence rather than with probabilistic bisimulation. The theory works smoothly for LMPs on general measure spaces: one need not work with analytic spaces. The proof of the logical characterization of cocongruence is much simpler and more general than the proof of the logical characterization of bisimulation. One only needs to invoke the theory of analytic spaces to show that cocongruence and bisimulation coincide: which they indeed do on analytic spaces. Indeed, it seems to us that bisimulation defined categorically is a historical anomaly. In the discrete case bisimulation and cocongruence coincide and one can argue that it makes no difference. However transition systems are coalgebras and cospans should fit the theory better than spans; as indeed is our experience in the probabilistic case. It would be interesting to reformulate the general theory in terms of cocongruences.. In the case of probabilistic systems it has been argued that one should use metrics rather than equivalence relations [DGJP99, DGJP04] . In the present context a pressing problem is to understand the metric analogue of the theory of probabilistic cocongruence.

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Dynamic hyperparameter optimization for bayesian topical trend analysis This paper presents a new Bayesian topical trend analysis. We regard the parameters of topic Dirichlet priors in latent Dirichlet allocation as a function of document timestamps and optimize the parameters by a gradient-based algorithm. Since our method gives similar hyperparameters to the documents having similar timestamps, topic assignment in collapsed Gibbs sampling is affected by timestamp similarities. We compute TFIDF-based document similarities by using a result of collapsed Gibbs sampling and evaluate our proposal by link detection task of Topic Detection and Tracking. Bayesian approach is an outstanding trend in data mining. Especially, latent Dirichlet allocation (LDA) [4] leads to challenges in various fields [5] [7] [8] [14] . In this paper, we focus on topical trend analysis and propose a new approach, called Latent dYNnamically-parameterized Dirichlet Allocation (LYNDA), by regarding the parameters of topic Dirichlet priors in LDA as a function of document timestamps. In LYNDA, a topic multinomial for each document is drawn from a Dirichlet prior whose parameters are an instantiation of a per-topic function defined over document timestamps. However, if topic Dirichlet priors are markedly different among documents, we cannot fully take advantage of Bayesian approach, because too different per-document topic multinomials result in overfitting to word co-occurrence patterns local to each document. Therefore, we regard the parameters of topic Dirichlet priors as a smooth function of continuous timestamps. Consequently, documents having similar timestamps are generated based on similar Dirichlet priors and exhibit similar topic mixture.. LYNDA has an advantage in its simplicity. We can use collapsed Gibbs sampling (CGS) for LDA [6] as is and can estimate hyperparameters in the course of CGS by using an existing gradient-based method such as L-BFGS [11] [9] .. CGS for LDA provides a topic assignment to all word tokens and induces predictive word probabilities conditional on each document [16] . Since document similarities can be computed based on these probabilities, we compare LYNDA with competing methods by link detection task of Topic Detection and Tracking (TDT), where better document similarity leads to a better result. Note that our approach may be applied to other probabilistic models where Dirichlet priors are prepared for timestamped data. In this paper, we give a new approach for using document timestamps in LDA-based document modeling. We clarify when our approach succeeds by discussing the correlation between timestamp similarities and document similarities by comparing the results of various competing methods. However, we reveal differences between the methods only with respect to link detection task. Further investigation will be required to confirm the efficiency of our approach. Figure 3 : TDT-topics where our approach fails. Based on Figure 1 , we can conclude that hyperparameter estimation improves LDA, because both LYNDA and Hy- Figure 2 : TDT-topics where our approach succeeds.. pLDA work better than LDA. However, there seem no significant differences between LYNDA and HypLDA. The differences will later be revealed by inspecting several TDT-topics separately. Further, Figure 1 shows that TOT results in a weak performance. However, if we inspect TDT-topics separately, we will know that TOT is comparable with LYNDA under a specific condition, and nevertheless that LYNDA is more robust with respect to overfitting to timestamp data. In each of Figures 2 and 3 , we select four TDT-topics and clarify detailed differences. Figure 2 presents the results for the TDT-topics where LYNDA succeeds, and Figure 3 for the TDT-topics where LYNDA fails. Each scatter graph is tagged with a TDT-topic ID and includes markers each of which corresponds to a pair of a false alarms probability (horizontal axis) and a miss probability (vertical axis). One cross marker is given for TFIDF, and 30 markers are for other methods, because we have 30 results of CGS except for TFIDF. The line graph on the left side of each scatter graph shows the number of on-topic documents at each date ranging from December 1 in 2000 to January 31 in 2001, where horizontal grids are put at unit interval.. First, we compare LYNDA with HypLDA and LDA. Fig-ures 2 and 3 provide the following observations. In these figures, we give the TDT-topics whose on-topic documents exhibit a distribution with one distinguished peak along time axis. However, smaller peaks are also observed. When the height of smaller peaks is far less than that of the largest peak, LYNDA succeeds (e.g. 40007 and 41026 in Figure 2 ). However, even when the height of smaller peaks is considerably less than that of the largest peak, LYNDA fails as long as some smaller peaks are placed far from the largest peak (e.g. 40026 and 41025 in Figure 3 ). When the height of smaller peaks is comparable with that of the largest peak, LYNDA fails (e.g. 40003 and 41014 in Figure 3 ). However, even when the height of smaller peaks is comparable with that of the largest peak, LYNDA succeeds as long as smaller peaks are located near the largest peak (e.g. 40004 and 40038 in Figure 2 ). Based on these observations, we can draw a claim: For a pair of documents having similar timestamps, LYNDA works. Second, to compare LYNDA with TOT2 and TOT5, we observe from Figure 2 that TOT achieves the results better than or comparable with LYNDA for many of the presented TDT-topics, e.g. 40007 and 41026. That is, TOT also works for a pair of documents having similar timestamps. However, recall that Figure 1 shows weaker results for TOT, where NDCs are averaged over all TDT-topics. This means that TOT gives poor results for the TDT-topics which are not included in Figure 2, We can combine these two claims as follows: While TOT excessively favors the TDT-topics whose on-topic documents show a concentrated timestamp distribution, LYNDA receives such TDT-topics with moderate favor. In this sense, LYNDA helps us to prevent from overfitting to timestamp data. We use TDT4 dataset [1] for our link detection evaluation. This dataset is accompanied with the on-topic document sets for 40 topics of TDT 2002 competition and those for 40 topics of TDT 2003 competition. From now, we say "TDTtopic" to indicate the topics prepared for these TDT competitions. While an off-topic document set is also prepared for each TDT-topic, we regard all documents other than ontopic documents as off-topic to make evaluation reliable by using as many documents as possible. The entire dataset is used both to train probabilistic models and to compute document similarities. A similar strategy is taken when LDAbased models are evaluated in ad-hoc retrieval tasks [16] . If we split the dataset into a training and a test sets, we will face a difficulty in constructing new on-topic document sets based on this split, because distributions of on-topic documents along time axis may be heavily modified. The dataset consists of J = 96, 259 documents, W = 196, 131 unique unstemmed words, and 17,638,946 word tokens after removing stop words. We use the dates as document timestamps.. Our baseline method is TFIDF, because it is widely known that TFIDF is effective in TDT tasks [2] [12] . We define the weight of word w in document j as njw{log(J/Jw) + σ log(n jw /n j )}, where J w is the document frequency of word w, n jw is the term frequency of word w in document j, and n j is the length of document j. When σ = 0, we obtain the conventional TFIDF. While our weighting schema looks ad-hoc, only this could give results better than the conventional TFIDF. We set σ = 0.4 and regard this as our baseline TFIDF, because other values give comparable or weaker results. We adopt cosine measure for document similarity.. When we use a result of CGS, the above weighting schema is modified as njw{log(J/Jw)+ρ log p(w|j)+σ log(njw/nj)}, where p(w|j) denotes the predictive probability of word w given document j. Based on preliminary experiments, we set ρ = 0.2 and σ = 0.2. For LDA and HypLDA, we have p(w|j). . For TOT, we have p(w|j). where a normalization is required. In Section 2, we discuss that TOT suffers unbounded increase of the likelihood of per-topic Beta distributions. Therefore, for all Beta parameters a k , b k , we put two types of limits: a k , b k ≤ 2 and a k , b k ≤ 5. Correspondingly, we present evaluation results under the tags TOT2 and TOT5. Since the peak of Beta density is higher for larger parameters, TOT5 is more affected by timestamp data. We use these two limits, because smaller limits make TOT indistinguishable from LDA, and larger limits heavily degrade the overall performance. Finally, for LYNDA,. . We compare LYNDA with five methods: TFIDF, LDA with fixed hyperparameters (α k = 0.5 for all k, β = 0.01), HypLDA, TOT2, and TOT5. The number of topics K is set to 100. While we tested K = 50 and 200, we only obtained worse results for K = 50 and comparable results for K = 200. We prepare 30 results of CGS from different random initializations. The number of iterations of CGS is 500 for LDA, TOT2, and TOT5. In the course of CGS for HypLDA and LYNDA, we estimate hyperparameters by L-BFGS once for every 10 iterations. HypLDA and LYNDA require 1,000 iterations, because convergence is slow due to the incorporation of hyperparameter estimation.. Our evaluation is conducted as follows. Assume that the number of on-topic documents for a TDT-topic t is T t . By computing the similarities between each on-topic document and all documents, we have similarities for Tt × J document pairs. Among these pairs, we call Tt × Tt pairs of two on-topic documents "correct" and the rest "incorrect." We would like to approximate this ideal split by devising a document similarity and then by setting a similarity threshold to obtain a split. We introduce two functions of similarity threshold η. Rt(η) is the number of correct pairs whose similarities are larger than η. A t (η) is the number of incorrect pairs whose similarities are larger than η. Now we can define two evaluation measures: miss probability P

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


How to involve structural modeling for cartographic object recognition tasks in high-resolution satellite images? With the new generation of satellite systems, very high resolution satellite images will be available daily at a high delivery rate. The exploitation of such a huge amount of data will be made possible by the design of high performance analysis algorithms for decision making systems. In particular, the detection and recognition of complex man-made objects is a new challenge coming with this new level of resolution. In this study, we develop a system that recognizes such structured and compact objects like bridges or roundabouts. The original contribution of this work is the use of structural shape attributes in an appearance based statistical learning method framework leading to valuable recognition and false alarm rates. This hybrid structural/statistical approach aims to construct an intermediate step between the low-level image characteristics and high-level semantic concepts. The new satellite systems like PLEIADES or QuickBird will provide satellite images up to 70 cm per pixel spatial resolution with a high delivery rate. Thus, new challenges for automatic interpretation of these valuable images are coming up. Much work has been done so far about the segmentation/recognition of textured areas like urban ones at low resolution. The detection of transport networks like roads or rivers considered as lineic structure networks in images has also been intensely studied and efficient algorithms have been proposed so far like in (Tupin et al., 1998; Mayer et al. , 2006) . However, few results have been presented for the recognition of complex, cartographic structures like bridges or roundabouts. These versatile objects do not lend themselves to classical statistical approaches for which a set of quantitative measures about the intensity distribution within a normalized window feeds a global statistical classifier used to discriminate between different objects. In the case of roundabouts for instance, the spatial configurations of object's parts are so versatile that a global statistical approach is not applicable. While the decomposition of the objects into parts is almost unavoidable, a purely structural part-based approach (Erus and Lomenie , 2005) , is not appropriate to be applied on a real detection task, mainly due to the difficulty of segmenting the target objects to well-defined primitive shapes.. We propose in this study a hybrid approach based on learning the spatial configuration of structural primitives constituting an object, according to their statistical distribution in a labeled training set. Our method is evaluated on a cartographic object recognition task defined in the framework of a national program called Technovision that aims to assess the state of the art in object recognition (project ROBIN). For that academic-industrial joint study, The French Space Agency (CNES) prepared a database of satellite images containing cartographic objects. The recognition task consists of classifying images of size 100x100 pixels into one of the categories, like bridges, roundabouts, crossroads or isolated buildings.. In the object category recognition domain, the need for more structural analysis is progressively growing. In particular, low-level as well as high-level spatial relationships of object components are used as part of the object model definitions (Ferrari et al. , 2008) . However, the handling of such spatial relationships is not obvious since symbolic/linguistic reasoning is more or less involved (Erus and Lomenie , 2005) and the concept of spatial ontology is not straightforwardly usable in current image processing lines (Hudelot , 2005) . However preliminary examples of the use of spatial relations in a recognition task can be found for example in Colliot et al. (2006); Cao (2009) . In this study, we explored the use of high-level structural and spatial characteristics of man-made objects on satellite images in a statistical classification framework. Our method is based on recent appearance-based approaches, but is differentiated from other methods by the integration of structural primitives and their geometric and spatial attributes. We believe that the continuous technological developments in satellite imagery that makes available higher resolution images justify our quest for a structural approach, which is also applicable on practical real problems.. We obtained promising results that might be improved by the addition of intensity and textural features, which are completely ignored in this study, in order to focus exclusively on the structural aspects of target object categories. The obtained classifiers, and the primitives selected by our method, aim to construct an intermediate step between the low-level image characteristics and high-level semantic concepts.. The exploration and use of more explicit spatial relations, as in the center, around, between, between object parts is an important perspective of our studies. Fig. 9 . The 3 best ranked, and the 3 worst ranked roundabout images in SMC RA , (a). All detected primitives, (b). Selected primitives, (c). represented by a gray level corresponding to their membership score. We tested our method on the cartographic objects base of CNES consisting of 962 images belonging to 10 categories. From these images, 72 are roundabouts and 99 are bridges. The image set is divided into a training set and a test set, each containing approximatively half of the objects in each category. A codebook for the roundabouts (SMC RA ) and a codebook for bridges (SMC BR ) are constructed independently using the training images, considering the images belonging to the target category as positive, and all other images as negative. For each image in the testing set, membership scores to both classifiers are calculated and they are classified accordingly. In Table 2 the classification results for the optimal decision threshold (corresponding to the highest f-measure value) are given.. We obtained an f-measure similar to that obtained using the Adaboost classifier (Erus and Lomenie , 2007) for the classification of roundabouts. However the f-measure of the classifier for bridges is 25% higher. Among the 49 images having the best scores in SMC BR we get 31 bridges instead of 24 bridges in our previous study. Table 2 The classification results obtained using an optimal threshold (TP=true positive, FP=false positive, FN=false negative, TN=true negative, P=precision, R=recall).. We applied random sub-sampling as a cross-validation strategy in order to test the robustness of the method. The data is split into two sets containing equal number of randomly selected positive and negative samples in all categories. The method is applied by using these two sets as training and testing sets. We repeated the random sub-sampling 100 times and calculated the mean and standard deviation (std ) of the AUC for both object categories. We obtained a mean AUC of 0.9466 with std 0.0342 for the roundabouts, and a mean AUC of 0.838 with std 0.0251 for the bridges.. A qualitative analysis of the results is also performed by examining the categories that obtained high scores for each classifier, and observing the selected primitives for target objects with highest and lowest scores. As shown in Table 3, the categories isolated buildings and crossroads obtained high scores in SMC RA . These are the categories which are the most similar to roundabouts structurally, and this result is mainly due to the small size of some of the roundabouts in the image base that does not allow to extract properly the geometric primitives. With higher resolution images we expect that the number of misclassified images would reduce significantly.. In SMC BR the non-bridge objects that obtained highest scores all belong to 17 hal-00497809, version 1 -6 Jul 2010. Object category Roundabout Isolated building Crossroad Number of objects 30 4 2 Table 3 Number of objects that obtained the highest 36 scores in SMC RA grouped by their categories.. linear object categories (Table 4 ). These objects have all similar parts with bridges in different spatial configurations. Our model represents the spatial configuration of parts of objects implicitly using statistics of their geometric and spatial characteristics. The classification errors indicate the limits of this implicit modeling approach.

O O O O O O O B I O O O B I O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 cooperative coevolutionary genetic algorithm for learning bayesian network structures We propose a cooperative coevolutionary genetic algorithm for learning Bayesian network structures from fully observable data sets. Since this problem can be decomposed into two dependent subproblems, that is to find an ordering of the nodes and an optimal connectivity matrix, our algorithm uses two subpopulations, each one representing a subtask. We describe the empirical results obtained with simulations of the Alarm and Insurance networks. We show that our algorithm outperforms the deterministic algorithm K2. Bayesian networks are graphical models for representing and reasoning under uncertainty [13] . They provide a means of expressing any joint probability distribution, and in many cases can do so very concisely. The core of a Bayesian network is a directed acyclic graph, whose nodes represent the random variables, and whose edges specify the conditional independence assumptions between the random variables. After construction, a Bayesian network constitutes an efficient tool for performing probabilistic inference.. A Bayesian network can be either constructed "by hand" or learned from direct empirical observations. Manual network construction is usually impractical since the amount Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. GECCO '11, July 12-16, 2011 of knowledge required is just too large. An alternative is to learn the network from a set of samples generated from the probability distribution we wish to model.. The task of learning Bayesian network structures from a fully observable data set can be formulated as an optimization problem [4, 7] . It is proved that this problem is NP-Hard [3] . The number of possible structures is superexponential in the number of nodes [15] . In this way, structure learning methods usually resort to search heuristics.. An interesting point about the structure learning task is that it can be decomposed into two dependent subtasks: 1) to find an optimal ordering of the nodes, and 2) to find an optimal connectivity matrix. In this paper, we present a method for learning Bayesian network structures from a fully observable data set that explores this idea. It is based on cooperative coevolutionary genetic algorithms where each subtask is represented by a subpopulation.. Besides this introductory section, the rest of this paper is organized as follows. In the next section, we introduce Bayesian networks and the structure learning problem. In Section 3, we present our cooperative coevolutionary genetic algorithm for learning Bayesian network structures as well as particular choices concerning the genetic operators. In Section 4, we describe the empirical results obtained with simulations of the Alarm and Insurance networks. We show that our solution outperforms the deterministic algorithm K2. In Section 5, we review the literature related to our work. Finally, we conclude in Section 6. We proposed a cooperative coevolutionary genetic algorithm for learning Bayesian network structures from fully observable data sets. Our proposed representation exploits the fact that this learning problem can be decomposed into two dependent subtasks, that is to find an optimal ordering of the nodes and an optimal connectivity matrix. We compared the performance of our solution with the deterministic algorithm K2 using six data sets generated from two traditional Bayesian networks, namely the Alarm network and the Insurance network. The results showed that our solution obtained better average scores for all data sets.. There are several exciting directions for future research work. First, we note that our algorithm does not restrict the number of parents that a node may have. However, the number of entries in a conditional probability table grows exponentially with the number of parents of the underlying node. Thus, the statistical cost of adding a parent to a node can be very large. An interesting extension of our algorithm is to explicitly penalize complete solutions that have nodes with an excessive number parents. This would seriously improve the computational efficiency of CCGA.. Furthermore, we intend to extend CCGA to deal with partially observable data sets. The problem of learning Bayesian network structures from incomplete data is more difficult than learning them from fully observable data sets. The major issue is that the BDe score no longer exists in closed form since it involves sufficient statistics that are not known when the data are incomplete. An interesting approach to circumvent this problem is to use CCGA with a third subpopulation that evolves the missing values. This would allow us to use the original BDe score together with the power of CCGA to find good network structures.. Finally, our novel representation can be of value to other graph-related problems, e.g., the TSP. Thus, we intend to investigate extensions of our algorithm to these problems. For each data set, we ran both algorithms 100 times. In each run, we stored the best structure found by CCGA. The results related to the Alarm network and the Insurance network are respectively shown in Table 3 and 4. Besides standard descriptive statistics, these tables also contain pvalues from one-tailed t-tests, where the alternative hypothesis is that the mean of the scores resulting from CCGA is greater than the mean of the scores resulting from K2. Below the name of each data set is the score of the original DAG. We note that such scores are not necessarily the highest ones: the data sets being of finite sizes may not represent all the (in)dependencies within the original structure. However, since the BDe score is consistent, the scores of the original structures quickly become the highest ones when the number of samples increases. The convergence of CCGA, averaged over 100 runs, is shown in Figure 5 and 6.. As can be seen from Table 3 , CCGA slightly outperforms the K2 algorithm in all data sets from the Alarm network. Although some maximum and/or minimum values resulting from the K2 algorithm are higher, the average scores resulting from CCGA are greater than the average scores from K2. The p-values show that the differences between the average scores are statistically significant. From Table 4 , we can see that the performance of CCGA on data sets from the Insurance network is even better. Both the average and the extreme scores from CCGA are greater than those resulting from K2. Again, the p-values confirm that the differences between the average scores are statistically significant.. About the convergence of CCGA, Figure 5 shows that for data sets from the Alarm network, the average score resulting from CCGA becomes greater than the average score resulting from the K2 algorithm after, approximately, 230 generations. This value is around 150 for data sets from the Insurance network ( Figure 6 ). We can see the result of our elitism-preserving approach in the fact that the average scores resulting from CCGA are monotonically increasing.. About the computational time spent by the algorithms, K2 was usually two orders of magnitude faster than CCGA (measured in seconds). However, we note that there is a lot of room for optimization in our CCGA implementation. First, we do not exploit parallelism. CCGA is highly suitable for parallel computation since the subpopulations evolve independently of each other in each generation (lines 8 to 13, Algorithm 1). Furthermore, differently from the K2 algorithm, we do not exploit the score decomposability property of the BDe score. Since the best individual of each subpopulation is used to create several complete solutions, we expect a lot of them to be very similar to each other. Thus, we can improve the performance of CCGA by using local scores together with standard bookkeeping techniques. We leave these code optimizations as future work. Genetic algorithms have become a popular method for learning Bayesian network structures. One of the pioneering work was done by Larrañaga et al. [10] . They propose a genetic algorithm where a DAG is represented by a connectivity matrix, which is stored as the concatenation of its columns. Since this approach violates the acyclicity constraint, the authors use a repair operator that randomly eliminates edges that produce cycles. The authors also use the proposed algorithm assuming a predefined ordering between the nodes, thus removing the necessity of the repair operator. Few years later, Larrañaga et al. [9] propose a hybrid genetic algorithm that searches for an optimal ordering of the nodes that is passed on to the K2 algorithm. The authors study the behaviour of the proposed algorithm with respect to different combinations of crossover and mutation operators. However, it is not clear whether their approach outperforms the K2 algorithm with random orderings.. Cooperative coevolution has also been used for learning Bayesian network structures. Wong et al. [18] propose a hybrid method that combines characteristics of constrainedbased and score-based approaches. The proposed algorithm has two main phases. First, it performs conditional independence tests to reduce the size of the search space. Thereafter, it uses a cooperative coevolutionary genetic algorithm to find a near-optimal network structure in the reduced search space. This genetic algorithm uses a different representation than the one proposed in this paper. In detail, it divides the network learning problem of n variables into n sub-problems, the goal of which is to find the "optimal" parent set for the underlying node. To avoid cycles in complete solutions, the authors propose a feedback mechanism that uses the node ordering implied by a complete solution x to produce constraints for each subpopulation such that new complete solutions will conform with that ordering. x is later updated with results from newer complete solutions. A major drawback with this approach is that, for any update, x will conform to the same ordering. This is equivalent to use a fixed, predefined ordering. The authors propose a Original score CCGA K2. Original score CCGA K2. Original score CCGA K2 Figure 6 : Convergence of CCGA, averaged over 100 runs, on data sets from the Insurance network.. solution to this issue, which is to associate every directed edge with a degree of belief. When the current degree of belief is less than a fixed threshold, the belief factor, this suggests that the ordering imposed by the underlying edge may be wrong. Hence, a new ordering different than the original one can be used. We note that this solution brings back the original problem, namely the existence of cycles.. We can see our algorithm as an evolution of the previous genetic algorithms for learning Bayesian network structures from fully observable data sets. First, it does not require a predefined ordering of nodes because it coevolves multiple orderings. Furthermore, connectivity matrices are represented by strictly upper triangular matrices, thus ensuring that complete solutions do not violate the acyclicity constraint. Consequently, repair operators are not necessary. We compared the performance of our method, using the parameters shown in Table 2 , with the deterministic algorithm K2 [4] . The K2 algorithm can be seen as a greedy heuristic. It starts by assuming that each node has no parents. Hence, for a given node, it incrementally adds the parent whose addition most increases the score of the resulting structure. It stops adding parents when the addition of a single parent cannot increase the overall score. This algorithm has a major drawback, which is to require a predefined ordering of the nodes. In our experiments, we used random permutations as input to K2. This algorithm also requires an upper-bound on the number of parents that a node may have. We set this value to ten. This is a reasonable value since none of the structures used in our experiments have a node with ten or more parents. Our implementation of the K2 algorithm is based on the Bayes Net Toolbox [11] .. We used two well-known Bayesian networks in our experiments, namely Alarm and Insurance. The Alarm network [1] was constructed for monitoring patients in intensive care. It has 37 nodes and 46 edges. Its structure can be seen in Figure 3 . The Insurance network [2] was constructed for evaluating car insurance risks. It contains 27 nodes and 52 edges. Its structure can be seen in Figure 4 . For each Bayesian network, we generated three data sets containing, respectively, 1000, 3000, and 5000 instances.

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