Protean graphs with a variety of ranking schemes Abstract. We introduce a new class of random graph models for complex realworld networks, based on the protean graph model by Luczak and Pra lat. Our generalized protean graph models have two distinguishing features. First, they are not growth models, but instead are based on the assumption that a "steady state" of large but finite size has been reached. Second, the models assume that the vertices are ranked according to a given ranking scheme, and the rank of a vertex determines the probability that that vertex receives a link in a given time step. Precisely, the link probability is proportional to the rank raised to the power −α, where the attachment strength α is a tunable parameter. We show that the model leads to a power law degree distribution with exponent 1 + 1/α for ranking schemes based on a given prestige label, or on the degree of a vertex. We also study a scheme where each vertex receives an initial rank chosen randomly according to a biased distribution. In this case, the degree distribution depends on the distribution of the initial rank. For one particular choice of parameters we obtain a power law with an exponent that depends both on α and on a parameter determining the initial rank distribution. There is considerable interest in using random graphs to model complex realworld networks in order to gain insight into their properties (see for example [1] or [3] ). Most prevalent models are based on the principle of preferential attachment: new vertices link to existing vertices with a probability that is proportional to the degree of the existing vertex. The preferential attachment principle has been successful in explaining the power law degree distribution that has been observed in many real-life networks. On the other hand, it is hard to adapt the principle to incorporate more diverse criteria that make a vertex attractive to receive a link, such as innate popularity or initial advantage (see [2] ). Moreover, most models are growth models, where the graphs grow larger over time. In many real-world networks, such as protein-protein interaction networks, social networks, and even the World Wide Web, a more realistic assumption seems to be that the network will eventually reach a "steady state" where the size stays approximately constant, but vertices keep appearing and disappearing over time.. In [7] , Luczak and Pra lat introduced a random graph model called the protean graph P n (d, α) , where the model is controlled by two parameters: initial degree d ∈ N and attachment strength 0 < α < 1). The major feature of this model is that the link probability, that is, the probability that a vertex receives a link in a given time step, is based on a ranking of the vertices. More precisely, each vertex v has a rank r(v, t) at time t, and its link probability is proportional to r (v, t) −α . In the original protean graph model, vertices were ranked according to age, leading to a model where the old get richer. In the paper it was proven that the degrees in P n (d, α) are distributed according to a power law with exponent 1 + 1/α. This implies that the attachment strength α can be used to tune the exponent of the power law: In order to establish the right attachment strength to model a given real-life network where the number of vertices of degree k is approximately k −γ , the attachment strength should be chosen to be α = 1/(γ − 1).. In [7] , the behaviour of the protean graph model near the connectivity threshold is studied, where d = d(n) is allowed to grow with n. The second author of this paper showed also in [9] that the protean graph P n (d, α) asymptotically almost surely (aas) has one giant component, containing a positive fraction of all vertices. The diameter of this component is equal to Θ(log n). In [10] , the recovery time of certain connectivity properties was studied. Suppose that the protean graph aas possesses property P , but at some particular time instance, the graph looses property P . Then the following natural question can be asked: how much time does it take for the protean graph to regain its typical property P ? Since P holds aas and after O(n log n) steps each vertex from the original graph is deleted aas, the recovery time is aas bounded from above by O(n log n). It has been shown, however, that the recovery time for connectivity is smaller than the above universal bound implied by the coupon collector problem.. In this paper, we extend the idea of the protean graph to include variations where vertices are ranked according to other criteria than age. The general approach of using a link probability based on a ranking of the vertices according to degree or an externally determined prestige label was first proposed by Fortunato, Flammini and Menczer in [4] . The specific model used by Fortunato et al . was a growth model, where one new vertex is added in every time step, and no vertices disappear. The occurrence of a power law with exponent 1 + 1/α was postulated based on simulations. The authors of this paper provided rigorous proofs and extended their results in [6] . A growth model based on the original protean graph, where vertices are ranked by age, was proposed in [12] . Here new vertices are added at a faster rate than old vertices are deleted. A prelimary version of this paper appeared in [11] .. As we will show, the protean graph model leads to power law graphs for a variety of different ranking schemes. The ranking scheme of the original protean graph from [7, 9] ranks vertices by age (the old get richer ); as we already mentioned, this leads to a power law with exponent 1 + 1/α. As a contrast, here we also consider the case where vertices are ranked inversely according to age (the young get richer ). As suspected, the young are not young long enough to accumulate a lot of wealth, and we find that in the resulting graph, aas all vertices have degree bounded by log 2 n. We also study a ranking scheme where each vertex receives an independently chosen prestige label, and vertices are ranked according to their prestige label.. Here we do obtain a power law, with the same exponent. In order to allow for a non-uniform distribution of "prestige" over the vertices, we considered also a scheme based on random initial rank. Here, each vertex is assigned an initial rank according to a given distribution. We consider distributions of the following form. Let R i be the initial rank of a vertex born at time i.. Thus, when s = 1 the initial rank is chosen according to the uniform distribution. In this case, the behaviour is very similar to that of ranking by by prestige label: vertices with initial rank R i exhibit behaviour as if they had received fitness R i /n. When s > 1, so the initial rank of new vertices is biased towards the lower ranks (highly ranked vertices tend to be older). In this case, the behaviour is similar to that of ranking by age, and we obtain a power law degree distribution with exponent 1 + 1/α. If 0 < s < 1, so the initial rank is biased towards the higher ranks (young vertices tend to be ranked high), the behaviour is more complex, and depends on both s and α. If 0 < s ≤ 1 − α, the behaviour is like ranking by inverse age, and we have a "flat" degree distribution with maximum degree bounded by log 2 n. If 1 − α < s < 1, then we do obtain a power law, but with exponent 1 + s/(s + α − 1).. These results suggest a broader explanation for the power law degree distributions often observed in real-life networks such as the web graph, protein interaction networks, and social networks, even when they have reached a stage where their size does not grow significantly. The distribution of new links in such networks can be seen as governed by a rank-based attachment scheme, based on a ranking scheme that can be derived from a number of different factors such as age, degree, or fitness. The exponent of the power law is independent of these factors, but is rather a consequence of the attachment strength. In addition, rank-based attachment accentuates the difference between higher ranked vertices: the difference in link probability between the vertices ranked 1 and 2 is much larger than that between the vertices ranked 100 and 101. This again corresponds to our intuition of what constitutes a credible mechanism for link attachment.

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


A new framework for efficient password-based authenticated key exchange Protocols for password-based authenticated key exchange (PAKE) allow two users who share only a short, low-entropy password to agree on a cryptographically strong session key. The challenge in designing such protocols is that they must be immune to off-line dictionary attacks in which an eavesdropping adversary exhaustively enumerates the dictionary of likely passwords in an attempt to match a password to the set of observed transcripts.To date, few general frameworks for constructing PAKE protocols in the standard model are known. Here, we abstract and generalize a protocol by Jiang and Gong to give a new methodology for realizing PAKE without random oracles, in the common reference string model. In addition to giving a new approach to the problem, the resulting construction offers several advantages over prior work. We also describe an extension of our protocol that is secure within the universal composability (UC) framework and, when instantiated using El Gamal encryption, is more efficient than a previous protocol of Canetti et al.

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An optimal bandwidth allocation and data droppage scheme for differentiated services in a wireless network Abstract-We present an optimal proportional bandwidth allocation and data droppage scheme to provide differentiated services (DiffServ) for streaming multimedia data in a single-hop wireless network. Our resource allocation scheme finds the optimal bandwidth allocation and data drop rates under minimum quality-of-service (QoS) constraints. It combines the desirable attributes of relative DiffServ and absolute DiffServ approaches. In contrast to relative DiffServ approach, our scheme guarantees the minimum amount of bandwidth provided to each user without dropping any data at the base-station, when the network has sufficient resources. If the network does not have sufficient resources to provide minimum bandwidth guarantees without data droppage to all users, the proportional data dropper finds the optimal data drop rates within acceptable levels of QoS and thus avoids the inflexibility of absolute DiffServ approach. We formulate the optimal bandwidth allocation and data droppage as constrained non-linear optimization problems and solve these using efficient techniques. We demonstrate through simulations that our scheme exhibits the desirable features of the absolute and relative DiffServ approaches.Index Terms-Bandwidth allocation, data droppage, quality-of-service (QoS), differentiated services (DiffServ), wireless network. oday's wireless networks must be able to provide different levels of quality-of-service (QoS) to mobile users. This diversity in the service provided to mobile users stems from the fact that users have subscribed to different service classes, have different portable devices with different playout capabilities, and are accessing various types of multimedia data such as audio, video and images. Providing differentiated services to mobile users in a wireless network is a challenging problem which needs to take into account the constraints and heterogeneities of the wireless network along with the diverse QoS requirements of users. The random time-varying fading effect of the wireless channel makes the provision of diverse services more complex by requiring that the resource allocation scheme for service differentiation should be able to dynamically adjust to the time varying nature of the wireless channel. In this paper we provide a cross-layer optimized optimal bandwidth allocation and data droppage scheme, implemented at the base-station, to provide differentiated services for multimedia data in a single-hop mobile wireless network. Our scheme adapts to the random variations in channel capacity and in the user's bandwidth requirements and finds the optimal bandwidth allocation and data droppage rate for differentiated services under minimum QoS constraints. Our service differentiation scheme combines the desirable features of the absolute and relative DiffServ approaches. Our scheme finds the optimal separation between the bandwidth allocations to the users under minimum bandwidth constraints, whenever the network has sufficient resources to provide minimum bandwidth guarantees, without any data droppage, at the base-station to all the users. If the minimum bandwidth requirement of users can not be provided, we provide an optimal mechanism for dropping the data at the base station according to the DiffServ class weights. The data droppage scheme provides a mechanism for graceful degradation of video quality by finding the optimal values of the data drop rates according to the various service classes.. We formulate the optimal bandwidth allocation and data droppage problems as non-linear optimization problems, discuss their efficient solution techniques and evaluate our scheme against weighted proportional fair scheduling (WPFS) with simulations.. We make the following practical assumptions in this paper. We assume that all of the multimedia data is available at the basestation before its playout deadline. This is realistic because the wired backhaul network has sufficient resources to transmit multimedia data to the base-station before its playout deadline at the mobile terminal. We assume that the mobile users can tolerate a fixed maximum playout delay. Since for streaming multimedia data the playout delay depends on how much bandwidth is allocated to the user, we assume that the users provide a minimum bandwidth request corresponding to their maximum playout deadline and buffer capacity. We do not consider queuing delay at the base-station, since it is reasonable to assume that the base-station has sufficient memory to store all the multimedia data.. The proposed resource allocation with service differentiation scheme has the following novel features and advantages over the existing schemes:. First, the proposed scheme combines the desirable features of the absolute and relative DiffServ schemes as follows. Under high load conditions, a relative DiffServ scheme keeps the service classes separated by the same relative distance even if the minimum acceptable QoS requirements of certain connections are being violated. This is especially undesirable for streaming multimedia applications which require minimum bandwidth guarantees for acceptable quality-of-presentation. On the other hand an absolute DiffServ scheme is also undesirable since it may be infeasible to provide absolute service guarantees especially in a wireless network with limited and time-varying resources. In addition, absolute DiffServ provides an inflexible admission control mechanism. Under absolute DiffServ, a request may be denied because the system can not provide absolute service guarantees, however, if the distances between the service classes are readjusted, new users may be admitted to the system. Our scheme provides optimal service class separation while ensuring minimum QoS guarantees to all the users.. Second, the proposed scheme provides a flexible admission control mechanism. A relative service differentiation scheme does not provide an admission control mechanism whereas the absolute service differentiation scheme provides an inflexible admission control. Our scheme allows the base-station to admit new users while keeping the different service classes separated and their degradation within acceptable bounds.. Third, the granularity of service differentiation in our scheme is per-flow basis. The traditional DiffServ mechanism provides only aggregate based granularity of service differentiation. Our scheme gives better and fine-grained control of resource allocation than the traditional DiffServ model. As a consequence, the accounting and billing can be done on per flow basis whereas in the traditional DiffServ scheme it is done on aggregate basis [1] .. Fourth, the proposed scheme involves very little signaling overhead between mobile users and the base-station. The only parameters needed by the base station to solve the optimization problem are the DiffServ class weights, minimum bandwidth requirement, maximum data drop rate and the predicted channel capacity of all the users.. Finally, the proposed resource allocation scheme suits many adaptive multimedia applications such as multilayered encoded video, where users can tolerate certain degradation in the quality of service. It allows the users to specify the maximum degradation in QoS acceptable to them.. The paper is organized as follows. In Section II we discuss the related work in the area of providing differentiated services. Section III formulates the cross-layer optimized optimal bandwidth allocation and data droppage problem for providing differentiated services in a wireless network. Section IV discusses the implementation of our solution techniques and the simulation environment for evaluation. In section V we present the simulation results of our proposed solution and show its desirable features. Finally, we conclude the paper in Section VI. In this paper we have proposed an optimal proportional bandwidth allocator and an optimal proportional data dropper under minimum QoS constraints. Our scheme finds the best possible service class separation between users while satisfying the minimum QoS guarantees. Our scheme combines the desirable features of absolute DiffServ and the relative DiffServ approaches. We show the desirable features of our scheme by using extensive simulations. In [1] the authors compare different service differentiation schemes such as absolute DiffServ, relative DiffServ, and Proportional DiffServ (Prop-DiffServ). The authors state that the absolute DiffServ approach can offer absolute assurances, which are mainly useful for unelastic applications. The relative DiffServ provides a mechanism for the users to select a service class that best matches the quality-cost tradeoff. The authors propose the Prop-DiffServ model as a special case of relative DiffServ. This model allows the network operator to control the quality spacing between classes independent of class loads. The authors also describe a packet scheduling and buffer management mechanism for approximating the Prop-DiffServ model. However, this model is completely independent of class loads which may not be desirable when the minimum QoS guarantees of the users are not being met. The authors in [2] present a bandwidth allocation mechanism for differentiated services on streaming servers. This mechanism aims to deliver high bit rate streams to high priority requests without over-compromising low priority requests. The authors formulate the bandwidth allocation problem as optimization of a harmonic utility function of stream quality factors and derive optimal streaming bit rates for requests of different classes under various server load conditions. However, this scheme is not applicable to transmission of multimedia data over wireless networks. The authors in [3] address the problem of providing concurrently a wide range of end-to-end throughput and delay assurances in wireless ad hoc networks. Their proposed solution is based on the neighborhood proportional delay differentiation (NPDD) service model. Using game theoretic concepts, the authors model dynamic class selection (DCS) applications in an NPDD network as selfish players in non-cooperative game. In [4] , the authors propose a stateless network model which uses distributed control algorithms to deliver service differentiation in wireless ad hoc network. However the previous two schemes address the problem in a wireless ad hoc network which is different from the problem considered in this paper.. Our work differs considerably from the previous work in the area of service differentiation as follows. Our bandwidth allocation scheme provides optimal bandwidth allocation for proportional bandwidth allocation under minimum bandwidth constraints. If the network can not provide minimum bandwidth guarantees to all mobile users, we provide a mechanism of dropping data at the base-station by finding the optimal data drop rates for proportional data droppage at the base-station.

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


Comparing tag scheme variations using an abstract machine generator In this paper we study, in the context of a WAM-based abstract machine for Prolog, how variations in the encoding of type information in tagged words and in their associated basic operations impact performance and memory usage. We use a high-level language to specify encodings and the associated operations. An automatic generator constructs both the abstract machine using this encoding and the associated Prolog-to-bytecode compiler. Annotations in this language make it possible to impose constraints on the final representation of tagged words, such as the effectively addressable space (fixing, for example, the word size of the target processor / architecture), the layout of the tag and value bits inside the tagged word, and how the basic operations are implemented. We evaluate a large number of combinations of the different parameters in two scenarios: a) trying to obtain an optimal general-purpose abstract machine and b) automatically generating a specially-tuned abstract machine for a particular program. We conclude that we are able to automatically generate code featuring all the optimizations present in a hand-written, highly-optimized abstract machine and we can also obtain emulators with larger addressable space and better performance. Dynamically typed languages, where the type of an expression may not be completely known at compile time, have experienced increased popularity in recent years. These languages offer a number of advantages over statically typed ones: the source code of the 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. PPDP'08, July 15-17, 2008 programs tend to be more compact (e.g., type declarations are not present and castings are unneeded), faster to develop, and easier to reuse.. In statically typed languages with prescriptive types the type of each expression is to be declared in the source code. This makes it possible to generate tighter data encodings and remove all type checks at compile time, which in general results in faster execution times and reduced memory usage and, hopefully, in the static detection of more programming errors. At the same time, extra redundancy is added in the cases where types can be inferred, and calls for a more rigorous (or strict) developing methodology. Additionally, some program and data structures which are natural for dynamically typed languages need to be adapted significantly to be cast into common, well-known type systems.. It is interesting to note that recent advances in program analysis can potentially reconcile to a large extent this apparent dichotomy by inferring automatically the properties needed to perform the optimizations brought about by static typing and by using such properties to perform non-trivial error and property checking which subsumes traditional type-based static checking (10; 5; 14; 6) . Also, even in the cases where types and other information cannot be statically inferred, performance of dynamic languages can be quite competitive, since modern compilers and abstract machines have evolved significantly and offer a high degree of optimization.. However, the same high degree of specialization and optimization that brings about the performance of modern compilers and abstract machines implies significant complexity in their design which in turn makes it very difficult to explore a large design space of modifications in order to obtain significant further advances, at least "by hand.". In this paper we explore, in the context of a state-of-the-art WAM-based (18; 1) implementation of Prolog, how a number of variations in the way the core data structures of an abstract machine are implemented impact performance and memory usage. Our objective is to draw general conclusions about which are the best optimization options. We use a Prolog-inspired high-level language to specify encodings, the associated operations, and in general to generate complete abstract machines using these variations. This language has a type and property system which, while quite flexible, is decidable at compile time, so that very efficient low-level code (C, in our case) can be generated.

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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O 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


Subjective Quality Evaluation via Paired Comparison: Application to Scalable Video Coding Abstract-Scalable video coding is a powerful solution for content delivery in many interactive multimedia services due to its adaptability to varying terminal and network constraints. In order to successfully exploit such adaptability, it is necessary to understand users' preference among various scalability options and consequently develop an optimal bit rate adaptation strategy. In this paper, we present a study of subjective quality assessment of scalable video coding, which investigates the influence of the combination of scalability options on perceived quality with the goal of providing guidelines for an adaptive strategy that selects the optimal combination for a given bandwidth constraint. In particular, the study is based on paired comparison of stimuli that is suitable for our goal due to its simplicity and easiness. We propose a new method, called Paired Evaluation via Analysis of Reliability (PEAR), which analyzes paired comparison results and produces not only quality scores but also intuitive measures of confidence of the scores for significance analysis. Results and analysis of extensive subjective tests for two different scalable video codecs and high definition contents are described, from which general consistent conclusions are drawn. The video and subjective data used in the paper are publicly available to the research community. 1 In this paper, we have presented a subjective quality evaluation study of scalable video coding for adaptive content delivery. The evaluation was performed via a paired comparison methodology, for which we have proposed the new PEAR method that converts comparison results to quality scores and facilitates performing intuitive significance analysis of the scores. It was demonstrated that the proposed paired comparison test methodology can be effectively used for comparing different scalability options and developing guidelines for an adaptive strategy of exploiting scalability in comparison to the conventional SSCQS method. The analysis of the test results showed that the priority between the spatial resolution and frame rate depends on the bit rate condition and content type, which was considerably consistent in the two codecs under test. For low bit rate conditions, the spatial resolution was important for perceived quality, whereas for higher bit rate conditions, a high frame rate was preferable.. While we applied the proposed paired comparison methodology for evaluation of scalable video coding, it can also be used to solve diverse multimedia quality evaluation problems. Particularly, it is suitable for online crowdsourcing from which many subjective data can be collected more easily when compared to MOS-based methodologies such as SSCQS. The rating procedure of paired comparison is simple so that training of subjects can be performed easily. In addition, the reliability of each subject's ratings can be judged independently in our methodology, where as other subjective data are required for outlier detection in MOS-based methodologies, as shown in Section V-E.. It will be necessary to perform further validation of the conclusions made in our work by using more diverse contents. In the future, it would be desirable to develop an adaptive decision strategy of scalability options for resource-constrained networks by taking into account the drawn observations in this paper as guidelines. Previously, there have been some work of proposing such strategies (e.g., [8] , [23] ), which are not usually based on thorough subjective evaluation across all three scalability dimensions. Moreover, it is useful to develop objective quality measures of video sequences generated by scalable video coding based on the results reported here, which can be used in adaptive strategies for real-time automatic quality measurement and monitoring of delivered content.

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


Localization dynamics in a binary two-dimensional cellular automaton: the Diffusion Rule We study a two-dimensional cellular automaton (CA), called Diffusion Rule (DR), which exhibits diffusion-like dynamics of propagating patterns. In computational experiments we discover a wide range of mobile and stationary localizations (gliders, oscillators, glider guns, puffer trains, etc), analyze spatio-temporal dynamics of collisions between localizations, and discuss possible applications in unconventional computing. In our previous studies on minimal cellular automaton (CA) models of reactiondiffusion chemical system we constructed [4] a binary-cell-state eight-cell neighborhood 2D CA model of a quasi-chemical system with one substrate, state 0, and one reagent, state 1. In that model chemical reactions were represented by semi-totalistic transition rules. Every cell switches from state 0 to state 1 depending whether sum of neighbors in state 1 belongs to some specified interval or not. A cell remains in state 1 if sum of neighbors in state 1 belongs to another specified interval.. From 1296 cell-state transition rules, we selected a set of rules with complex behavior [4] . Amongst the complex rules, namely in G-class of morphological classification [4] , we located so-called Diffusion Rule. CA governed by this rule often exhibits slowly non-uniformly growing patterns, resembling diffusive patterns in chemical systems with non-trivial coefficients of diffusion, or reaction-dependent diffusion coefficients, so the name of the rule.. The rule simulates sub-excitable [36] medium-like mode of perturbation propagation -cell in state 0 takes state 1 if there are exactly two neighbors in state 1, otherwise the cell remains in state 0, and, conditional inhibitioncell in state 1 remains in state 1 if there are exactly seven neighbors in state 1, otherwise the cell switches to state 1.. In present paper we are trying to answer the following questions. Is there a reaction-diffusion binary-state CA that express complex dynamic? Can we demonstrate that CA exhibits non-stationary growth of reaction-diffusion patterns? Do stationary or mobile generators of localizations, glider guns, exist in binary-state reaction-diffusion CA? Can the reaction-diffusion CA simulate an effective procedure and therefore be universal?. CA with space-time dynamics similar to that in spatially extended chemical systems are studied from early days of CA theory and applications [35] , however most rules discovered so far lack minimality (some of the rules employ dozens of cell-states). Methods of selecting the rules also widely vary depending on theoretical frameworks, e.g. probabilistic spaces [20, 38] and genetic algorithms [14, 32] . Therefore, we envisage a strong need for a systematic analysis of propagating patterns like those observed in the Diffusion Rule. The propagating patterns are of upmost importance in modern computer science because such patterns play a vital role in developing novel and emerging computing paradigms and architectures, particularly collision-based computing [1, 3, 23] .. We must mention that various authors have already obtained pioneering results in the studied rule. Magnier et al. discovered three primary gliders [33] . David Eppstein found four gliders known, already incorporated in our framework, and four new gliders which were novel for us (Fig. 4 (q) (t) and (u)). 1 The glider traveling along diagonals of the lattice (Fig. 4 (v) ) was firstly recorded by Amling in 2002 (see Eppstein's web site). Finally, a glider gun and three puffer trains were discovered by Wótowicz. Diffusion Rule CA is just one of many complex CA 3 exhibiting mobile localizations. Other famous examples include semi-totalistic rules as the Game of Life [17, 10 ], Brain's-brain and Critters rules [34] , High Life [9] , Life 1133 [22] , Life Without Death [18] , and Life variant B35/S236. 4 Other variant is with Larger than Life [16] and the Beehive and Spiral rules hexagonal CA [39, 5, 6] , more recent candidates were proposed by George Maydwell with Hexagonal Life and Hexagonal Long Life rules.. 5 Amongst 3D binary state CA supporting gliders Life 4555 and Life 5766 by Carter Bays [7, 8] are most widely known. In 1D there are Rule 110 [13, 37, 30, 26] and Rule 54 [11, 21, 25] CA, which support an impressive range of mobile localizations.. Our paper is structured as follows. In Sect. 2 we introduce basic concepts of CA model under investigation. Section 3 introduces results of statistical analysis of the Diffusion Rule using mean field theory. In Sect. 4 we present basic structures discovered in the Diffusion Rule CA. Section 5 compiles a catalogs of non-trivial interactions between mobile localizations, which could be used to designing basic elements of collision-based computers. In Sect. 6 we highlight our achievements in analysis of the Diffusion Rule and prospects for future studies. Findings discussed in the paper are based on computational experiments with the Diffusion Rule CA and, particularly, exhaustive search of mobile and stationary localizations emerged in spatio-temporal dynamics of the automaton. Amongst known 2D CA supporting localizations, the Diffusion Rule CA is the minimal model because cell-state transitions depend not on intervals of 'cell sensitivity' but on singletons, i.e. transition 0 → 1 occurs if there is exactly two neighbors in state 1, and transition 1 → 1 if there exactly seven neighbors in state 1. Moreover, we are not aware of any other CA which exhibits so large variety of mobile localizations (gliders) and high diversity of outcomes of collisions between mobile and/or stationary localizations. Despite of trying to undertake exhaustive study of localization dynamics we nevertheless missed several important points that could form objectives of future studies.. A simple but interesting physical simulation was made setting a reaction like luminescence. Using packages of both diagonal lines of 50 cells everyone. The luminescence phenomenon was obtained over the evolution in densities of cells in small intervals as illustrated the Fig. 26 . The final state is dominated by blinkers or oscillators. This simulations are developed by the group of researchers iGEMMéxico at the MIT.

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


Towards an evidence-based decision making healthcare system management: Modelling patient pathways to improve clinical outcomes The concept of patient flow modelling has attracted managers, commissioners and clinicians to better understand the operational and clinical functions of the healthcare system. Understanding major drivers could reduce inefficiencies, improve patient experience, and most importantly lead to a better outcome for patients, carers and taxpayers. In this context, we study individual clinical pathways of chronic obstructive pulmonary disease (COPD) patients, a source of concern for major stakeholders. In this study, a random effects continuationratio logit model is applied to capture the individual clinical pathways of patients leading to multiple readmissions. Data on COPD patients were extracted from the national English Hospital Episodes Statistics dataset. Individual patient pathways from initial admission through to more than four readmissions are captured. We notice that as patients are frequently readmitted, males are more likely to be in the higher risk group than females. Furthermore, the number of previous readmissions has a direct impact on the propensity of experiencing a further readmission. This method could easily be implemented as a decision support tool to determine disease specific (e.g. stroke, congestive heart failure) probabilities of multiple readmissions. Therefore, this could be a valuable tool for clinicians (health care managers, policy makers, etc.) for informed decision making in the management of diseases, which ultimately contributes to improved measures for hospital performance management. Advances in medicine, a well-informed patient population, and demographic changes (e.g. an ageing population) mean that the demand on health and social care services will continue to rise. This makes it more important for us to find the most efficient and effective ways of delivering the best outcomes for people who need care and support. Furthermore, given the increasing demand and capacity constraints, most countries including the United Kingdom (UK) have forced their health organisations to work under intense pressure. This means that without affecting the quality of the existing service deliveries, providers (i.e. hospitals) and purchasers will have to find ways of providing 'better health at lower cost'. Therefore, it is important to strike a good balance between the need for new capacity and ways of making better use of existing capacity. In many cases this may mean service re-design to ensure that patients receive the right care at the right time and in the right place.. Current UK Government policy, as set out in the 2011 Health and Social Care Bill, establishes outcomes as the measure by which the National Health Service (NHS) will be judged [1, 2]. As well as adapting to the shift in focus from process to outcomes, the NHS also faces an unprecedented resource challenge: net savings of £20 billion must be achieved over the coming 4-5 years, representing a productivity challenge of around 4% a year [3] . Since 2000, productivity in the NHS (useful outputs divided by resources) has fallen by around 1% per year [4] . The key challenge for the NHS, with its budget constrained system, is to deliver maximum patient benefit, measured as useful outcomes per pound spent. Health expenditure is estimated to cost the UK economy £120 billion/year [5] . However, in anticipation of tough times ahead, providers and purchasers are not only interested in the effectiveness of the intervention but whether the intervention is cost effective. Achieving an understanding of how best to increase value in the delivery of health care is therefore critical.. Related to this, the concept of patient flow modelling have enabled managers, commissioners and clinicians to better understand the operational and clinical functions of the health system. Understanding major drivers could reduce inefficiencies, improve patient experience, and most importantly lead to a better outcome for patients, carers and taxpayers.. The medical condition with which the patient is confronted may require a number of different interactions between services or departments, such as xrays, tests and investigations, surgical operations, etc. At each stage of the care process patients are associated with an activity and resource use, such as the departments visited and the amount of time required to deliver care (e.g. length of stay). These studies have been devoted to two types of modelling, namely conceptual patient pathways and physical patient pathways. Conceptual patient pathways research has been undertaken to diagnose issues related to length of stay (LoS), i.e. the conceptual (or virtual) phases that a patient goes through before discharge. Here, the interest is in determining the probability of a patient being discharged from a particular conceptual phase, giving that he/she has been in care for x number of days. Previous research has been devoted to the use of markov models [6, 7, 8, 9] and compartmental modelling [10, 11] . For instance, Faddy and McClean [6] applied a stochastic network approach to LoS modelling. In their model, a patient's stay in a geriatric department is viewed as transitions through a set of ordered phases, where the conceptual phases could correspond to the increase in disease severity, or some loosely defined stages, for instance, "short stay", "medium stay" and "long stay". However, any phase found empirically by fitting the model to a dataset may not have such a practical interpretation. Under this model, the distribution of LoS is a Coxian phase-type distribution with the least number of phases that provides adequate fit, and the estimation of model parameters is by maximum likelihood. Using a subset of data used in [8] , the authors show that a model with four phases provides a good fit to the empirical LoS distribution.. However, incorporating individual patient pathways (instead of explaining the LoS distribution with virtual phases) within a modelling framework is an emerging field and so far little research has aimed at quantitatively modelling physical patient pathways.. Patient pathways can be viewed from two perspectives; operational and clinical. Though these are the traditional perspectives, common characteristics of both include an entrance, an exit, a path connecting both entrance and exit, and the random nature of the health care elements. The randomness is embodied in two features. First, for a given health care service, not all of the elements in a patient flow network may be applicable to all patients. Second, the time patients spend at each phase and the time patients spend in the overall network also implies a degree of randomness. These are the subject specific random effects. Patient pathways, thus, summarize the individual patient clinical (disease progression) and operational (movement) experience during the process of care.. Two papers on this subject were found to be highly relevant. The first developed a stochastic model (semi-Markov processes) [12] to capture individual patient's experience during a visit to the local family practice clinic. This estimated the transition probabilities between the paths (waiting room, nurse aide station, examining room, lab/x-ray, and discharge) visited by the patient. The second developed a multinomial logit model [13] to capture the individual patient's pathway in the process of care, where patient frailties are modelled as random effects. The approach identified interesting pathways such as those that resulted in a high probability of death (survival), pathways incurring the least (highest) cost of care or pathways with the least (highest) length of stay. Patient specific discharge probabilities from the healthcare system were also predicted.. In [13] it was assumed that the movement of babies from one level of care to the other until discharge is multinomial. In reality, these movements can be considered as an improvement in their condition (or vice versa). Hence, it is plausible to assume that the outcome from previous activity (e.g. care, treatment) is likely to effect the next. In line with our previous work, we introduce a continuation ratio random effects model to investigate readmission progression and the differential effect of gender on these progressions. In an earlier study, regional disparities were detected in multiple readmissions of COPD in the UK [14] . Note that the leading causes of emergency readmission are congestive heart failure and COPD [15] . As a result, these two disease categories are widely studied in the context of emergency readmissions. We therefore focus on COPD and extract data based on individual patient pathways from initial admission to hospital through to more than four emergency readmissions, i.e., tracking individual patient readmissions longitudinally over the full care cycle and effectively focusing on chronically ill patients. These are known to be frequent users of our services and highly costly.. In the literature, the definition of readmission varies according to the purpose of the study, generally from 30 to 90 days [16, 17] , but some studies have used readmissions following certain surgeries, for shorter (14 days) [18] or longer time window (1 year) [19] . So, if a patient is readmitted within the chosen time window, then it is regarded as a quality issue otherwise it is just an unplanned admission. The chosen time windows are generally subjective. Therefore, we have used an approach [20] that objectively defined the time window for COPD patients as 36 days. In the present study, based on this time window, we classify patients into high risk and low risk readmission groups, depending on whether a patient comes back to the hospital before or after a threshold of 36 days.. The current study has two objectives. First, to introduce a random effects continuation-ratio logit model, suitable for detecting stage wise transitions, to patient pathways modelling. Second, we aim at advancing our knowledge with regard to the application of modelling techniques to patient pathways. By doing so, the aim is to widen the remit of applications of modelling techniques in health care management and assess the pertinence of the insights gained from such exercises. Therefore, given the importance of modelling patient pathways (patient readmissions in particular), our research can be of great interest to providers and commissioners of care in England and other countries. For instance, better understanding the pathways with the least and highest cost of care could enable healthcare providers to allocate resources (staff, equipment) more efficiently and effectively, which may lead to improvement in services and cost-effectiveness of care pathways. Furthermore, our results could enable senior decision makers to adopt more pro-active and evidence-based methods in the commissioning decision making process, such as re-designing care pathway to improve clinical outcomes and reduce costs, or identifying bottlenecks of services.. In the next section, we present the National Hospital Episodes Statistics (HES) data with relevant data analysis; Section 3.1 briefly summarises the generalized linear random effects models for patient pathways and the estimation of model parameters; section 3.2 and 3.2.1 describes the continuation ratio logit model and the results, respectively; section 3.3 extends our modelling approach to examine gender disparity with the results illustrated in section 3.3.1, the discussion and conclusion are in section 4 and 5, respectively. Under new government plans NHS hospitals will face financial penalties if patients are readmitted as an emergency within 30 days of being discharged. Hospitals in England will be paid for initial treatment but not paid again if a patient is brought back in with a related problem.. There is an acknowledgment of a lack of robust analysis of routine data to inform models that measures outcomes (i.e. readmissions), cost and effectiveness. Substantial and often unwarranted variations exist across the NHS and other health systems both in terms of inputs to care and the useful outputs (quality, or outcomes) of care. In this context, it is important that clinicians, hospital managers and commissioners have a better understanding of "individual" patient pathways from initial admission to subsequent readmissions (longitudinal cycle of care).. To truly understand the operational and clinical functions of the healthcare system, patient centred outcomes (e.g. readmissions) must be aggregated around the patient rather than discrete services. It is the longitudinal aspect of providing care that matters and so far very little research has aimed at tracking individual patient pathways that are modelled within an advanced statistical framework.. The majority of published papers can be grouped into two categories: 1) risk factors and prediction models [30, 31] ; and 2) whether readmission is an indicator of poor process of care (quality of care) [32, 33, 34, 35, 36, 37, 38] . Our research aims at advancing our knowledge in this newly emerging field of modelling care pathways, hence does not belong to either categories. Our primary objective is to showcase this new approach as an additional decision making tool that can be complementary to other techniques.. It is accepted that clinical factors explain variations better than using administrative data. However, in the absence of such data, we have developed a framework that incorporates patient history of readmissions with frailty modelled as random effects, an important concept often neglected in this area of research. Using the national HES dataset, we demonstrate the use of clinical pathway to model probability of progression to multiple readmissions. The models show differences in case-mix. Individual profiles (pathways) of multiple readmissions is a novel approach that has been modelled to capture patient to patient heterogeneity, ensuring that individual patients progression to multiple readmission is incorporated into the model. In the majority of studies, this heterogeneity is not accounted for due to its complexity and the lack of availability of data. Though we have only considered COPD patients, this model could easily be adapted to other disease categories. This method could easily be implemented as a software toolkit to determine disease specific (e.g. COPD, stroke, congestive heart failure, etc) probabilities of multiple readmissions. Therefore, this could be a valuable tool for clinicians (health care managers, policy makers, etc.) for informed decision making in the management of diseases, which ultimately contributes to improved measures for hospital performance management.. We have presented models that capture patients pathways, but an elegant way will be to jointly model length of stay (for each readmission patients stay in hospital for a period of time) and clinical flow paths for improvement in the process of care and better planning. Therefore, future work will be devoted to the joint analysis of patients pathways and length of stay. We will develop a method for the joint modelling of mixtures of ordinal (multiple readmissions) and continuous (i.e. LOS) outcomes, since models for this type of problem are new to health services research in general and LOS modelling in particular.. In conclusion, we demonstrated that the random effects continuation ratio logit model can be used to capture COPD patients progression to multiple readmissions as a function of initial admission, previous readmissions and predictors (e.g. IMD, age, gender). This model is very useful in detecting the most critical threshold at which multiple readmissions are more probable, thereby informing decision making in the management of COPD. The recession and the banking crisis forced the UK government to cut funding to public services. During 2010-11, the National Health Service will need to save £20bn over the next 4-5 years, and thus every service provider and purchaser is faced with the challenge of making the best use of their resources and showing value for money at every opportunity. One of the most effective ways of doing this is to truly understand service provision and thus make informed decision in the face of uncertainties, e.g. is our services improving patient outcomes, is it effective, and are there any unknown patterns and trends in the use of our services?. The recent Transparency in Outcomes [28] paper clearly stresses the importance of measuring the outcomes of care as well as structure and process in order to evidence and drive up quality. Providers and purchasers seek to ensure that their funds are used effectively to address the underlying determinants of patients in their local population. They need to constantly identify where developments and changes need to occur and predict the outcomes of services to improve both patient outcomes and practice in relation to the organisation and delivery of health care.. Given that healthcare outcomes (readmissions in particular) are at the heart of the UK Government's (and other countries) initiative towards improving patient satisfaction and safety, it is important that robust and effective methodologies are developed to better understand the behaviour of those patients who are frequently readmitted, that is, focusing on the main drivers associated with patients progression to multiple readmissions. From the point of view of individual patients, hospital managers and primary care trusts, the identification of these risk factors is of considerable importance.. In essence, the four models profile COPD patients based on readmission groups and relate group membership to characteristics, demographics and prior use of medical services. For example, in all the models, it can be noticed that the propensity to experience a second readmission is higher for those who had a first readmission. Therefore, this model is very useful in detecting the most critical threshold at which multiple readmissions are more probable. Clinicians should note that a first readmission signifies a problem in the process of care and if care is not taken this may be the beginning of many subsequent readmissions.. Exploring how gender may impact the diagnosis, treatment and surveillance of COPD is beginning to be popular [27] . This is made possible by the complex questions surrounding how differences in male/female biology may interact with gender differences in environmental, societal, cultural and behavioural determinants of health to influence outcomes. Our results suggest a critical point in readmission progression to be those patients with a second readmission. However, the result of gender disparity means that female patients are worse off at this critical point. Therefore, clinicians should especially note female patients on a second readmission as they are more prone to more readmissions beyond the second readmission.. Note that pathways capture both the operational and clinical experience of patients within the health system. By representing these in a model, patients experience can be studied to detect points at which clinical decisions were taken and the outcome of such decisions. It also offers an opportunity to make adjustments when necessary to improve the clinical outcome.. Rapid patient discharge to free beds for incoming patients is a controversial debate in the UK. Some argue that patients may have been discharged too soon, raising the issue that patients are being discharged 'sicker and quicker' [29] . As a result, early discharges may generate high levels of readmissions, which could possibly be seen as patients being discharged inappropriately. However, results suggest that the LOS effect on readmission progression is minimal in this study population. In this respect, other measures different from keeping patients unnecessarily longer in hospital and which may result in the reduction of emergency readmissions, increase patient and staff satisfaction, reduce waiting lists, increase the performance of the hospital, and given the economic conditions in the UK, cost savings need to be developed.. Almost all public organisations including the NHS in England are data rich, but starving for information. This suggests a potential to bring together data sources to routinely evaluate outcomes. Given this vast amount of data, the current study has led to some important insights concerning COPD patient readmissions progression and their behaviour in the health care system. However, it has only added to our thirst to learn more about this important element of the management of specific disease categories. The results of this research have already paved the way to the investigation of more issues regarding the management of healthcare services. For example, it would be very interesting to know the effects of management policies, changes to admission policies, integration of services, and restructuring of delivery structures on the performance of these systems.. Our research has the potential to have numerous benefits for providers and purchasers of health and social care, such as: 1) the availability of techniques to support strategic and business planning through effective evaluation of patient readmissions; 2) the transferable skills in advanced data analytics using large and complex datasets; 3) the health outcomes for the local population through more timely and effective interventions (reduction in waiting lists, mitigating financial risks and hence cost savings); 4) developing a holistic understanding of how the local population accesses and uses health service; 5) identification of patterns and pathways of service usage previously unrecognized; 6) understanding how information is applied in making strategic decisions, particularly in the health sector based around emergency readmissions; and 7) practical involvement in how information informs commissioning decisions. The generalized continuation ratio logit model is applied to the HES data set summarised in section 2. Multiple readmissions play a key role in measuring disease severity [21] . The HES is a large data set, where no amount of data exploration will bring out the enormous information embedded in the data. Here, the progression to multiple readmissions as a function of initial admission and series of readmissions is modelled, hence the patient flow is clinical rather than operational.. Individual patient pathways from current readmission through to at least four previous readmissions is captured within this model. In this context, current can be defined as the patient being observed at any stage of progression. Suppose a patient is on their 2nd readmission, this could be their current and 1st can be their previous readmission. Here, the focus is to determine the probability of being readmitted for a third time. Likewise, if we observe a patient to be in their sixth readmission, this is recognized as a patient who has experienced four or more readmissions. Hence, four or more readmissions is the current readmission, and we look into the past history of readmissions to determine the probability for their next readmission. We present the model based results in the following order by group of patients according to the number of readmissions.. Model I: Group of patients having only current readmission (1st readmission) Model II: Group of patients having a current readmission (2nd readmission) and a previous readmission (1st readmission), i.e, at most two readmissions Model III: Group of patients having a current readmission (3rd readmission) and two previous readmissions (1st and 2nd readmission), i.e, at most three readmissions Model IV: Group of patients having a current readmission (4th readmission) and three previous readmission (1st, 2nd and 3rd readmission), i.e, at most four readmissions. In other words, we want to determine the probability of a patient belonging to any of the lower group advancing to a higher group as a function of patients characteristics, such as gender, age, readmission history, total length of stay in hospital prior to discharge, number of previous readmissions, Charlson co-morbidity index, index of multiple deprivation(IMD), ethnicity, reasons for discharge and discharge destinations.. The Charlson index of comorbidity [25] is a measure of patient severity, which is based on ICD-10 diagnosis codes, where various weights are attached to the presence of conditions, such as congestive heart failure and cancer. The IMD [26] is a weighted index based on seven factors of deprivation, which can be recognized and measured separately, and are related to: income; employment; health and disability; education, skills and training; barriers to housing and services; living environment and crime. The English Indices of Multiple Deprivation identifies the most deprived areas across the country. They combine the seven indicators into a single deprivation score for each small area in England. Charlson comorbidity index and IMD are not available in the HES dataset and a number of steps had to be taken to incorporate this information.. The Charlson co-morbidity index is only statistically significant (see Table 3 ) for patients having more than four readmissions (Model IV). Patients belonging to this group are suffering more from other opportunistic infections as a result of COPD (and or related diseases contributing to multiple readmissions for COPD).. Methods of discharge are as follows: discharged on clinical advice or with clinical consent (clinical); self discharged or discharged by a relative or advocate (selfadv); discharged by a mental health review tribunal (tribunal); and death. Note that death records from this dataset has been removed because interest lies in modeling readmissions, as deceased patients cannot be readmitted. Destination of discharge are as follows: the usual place of residence including no fixed abode (home); Penal establishments (penal); NHS other hospital provider or nursing/residential homes (NHS); local authority residential accommodation (local); and non-NHS run hospital, nursing or residential homes (nonhs).. There are no significant age effects on having only a first readmission. However, significant age effects can be seen in other readmission groups. There is a slight increase in the number of readmissions as COPD patients become older, making older patients more prone to multiple readmissions. The same phenomenon could be observed for length of stay (LOS), where multiple readmissions is associated with prolonged hospital stay. The index of multiple deprivation (IMD) increases with multiple readmissions, making people who are highly deprived to be more likely to have multiple readmissions. IMD, however, is lower for the group of patient with three previous readmissions. There is a significant decrease in the number of new admissions as readmission progresses after adjusting for death on admission. Progress in readmissions results in increased readmission, for example patients with only one readmission before the current are less likely to progress to multiple readmissions. Across the groups it is less likely for any patient to be readmitted as low risk, that is most patients across the group are more likely to be readmitted as high risk patients as readmission progresses. This might be true since multiple readmissions are clinically related to advancement in the medical condition leading to more frequent visits to hospitals.. The majority of patients in each of the groups are White and people of Asian origin. Surprisingly, gender doesn't seem to be playing any significant role in multiple readmissions. Since smoking is the main causal agent of COPD, gender might not significantly play a role in choosing a "good" smoker. Though, female smokers may be at greater risk of developing COPD, possibly due to sex differences in the metabolism of cigarette smoke [27] , nothing is known on how gender influences multiple COPD readmissions. The model presented above might not be adequate to capture the gender difference in multiple COPD readmissions. Therefore, in the next section, we investigate gender bias in COPD readmission progression, since it has been shown that gender difference in the diagnosis, treatment and management of COPD is an important research area that is still lagging behind in the epidemiological study of COPD [27] .. As in section 3.2.1, we present the results according to the number of readmissions. Model I referred to the group of patients having only current readmission (1st readmission), Model II the group of patients having a current readmission (2nd readmission) and a previous readmission (1st readmission), i.e, at most two readmissions, and so on. In this section we further examine to see if these results will be different if the fourth group is split into two, that is, an additional group with four readmissions and at least five readmissions. Note that in section 3.2.1 we modelled individual patient pathways from current readmission through to at least four previous readmissions and if a patient had 6 previous readmissions this was considered to be at least four readmission. This section develops series of methods based around the continuation ratio random effects model to investigate readmission progression and the effect of predictors (e.g. gender) on these progressions. The objective is to capture the sequential readmission of individual patients by tracking them longitudinally from their initial admission to subsequent readmissions (see Figure 1) , and determine the probability of experiencing further readmission. All patients having more than four readmissions are grouped. The justification is that we do not observe many patients having more than five readmissions. Note that each readmission is classified as high risk (within 36 days) or low risk group (greater than 36 days), hence a binary outcome at each readmission.. The next section 3.1 illustrates the generalized linear random effects model for patient pathways and an estimation method based on Gaussian quadrature.

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 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 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