Achieving pervasive awareness through artwork Aesthetics and ludic aspects of pervasive awareness applications make the awareness system more attractive and aesthetically pleasing to its users. The same objective can be achieved by adding pervasive awareness features to an aesthetic object such as an artwork. In this article we describe how an artwork can be transformed to an pervasive awareness application by adding awareness features into the artwork. Art in public space such as installation arts have a good opportunity to convey messages to its spectators apart from providing aesthetically pleasant experience to the users. The concept of pervasive computing promotes the idea of integrating computing in everyday objects and activities. In this way it makes scope for providing pervasive awareness in a certain context to its users. New media art especially artworks using computing technology placed in a public place can be a media to support pervasive awareness. In this paper we would like to present Open Digital Canvas, an artwork, placed in a working space and discuss the possibilities to make the artwork informative for its spectators by incorporating pervasive awareness features in it. Art Installations has a special advantage of supporting ubiquitous computing along with provision of aesthetics and pleasant experience for its users. In this article we have shown how an artwork can be configured and upgraded to support pervasive awareness in a workplace setting. Feeling connectedness is an important issue; the increasing popularity of social networking applications like myspace, facebook, wayn and so on reveals peoples need towards feeling connectedness. We believe that implementing different prototypes of pervasive awareness applications in workplace will reveal the importance of feeling connectedness among the employees.

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Modeling media access in embedded two-flow topologies of multi-hop wireless networks In this paper, we decompose a large-or small-scale multi-hop wireless network into embedded subgraphs, each consisting of four nodes and two flow pairs. We systematically study all twelve possible topologies that arise according to whether the different nodes are in radio range of each other. We show that under both a random spatial distribution of nodes and random waypoint mobility with shortest-path routing, a critical and highly probable scenario is a class in which the channel state shared by the two flows is not only incomplete (i.e., the graph is not fully connected), but there is also asymmetry in the state between the two flows. We develop an accurate analytical model validated by simulations to characterize the long-term unfairness that naturally arises when CSMA with twoor four-way handshake is employed as a random access protocol. Moreover, we show that another key class of topologies consists of incomplete but symmetric shared state. We show via modeling and simulations that in this case, the system achieves long-term fairness, yet endures significant durations in which one flow dominates channel access with many repeated transmissions before relinquishing the channel. The model predicts the time-scales of this unfairness as a function of system parameters such as the maximum retransmission limit. To better understand the performance characteristics of large-or small-scale multi-hop wireless networks, we begin with the basic building blocks of pairs of contending one-hop flows. If all four nodes of the two flows are within radio range, or if the two senders are within radio range, a CSMA protocol with two-or fourway handshake obtains fair performance that can be accurately predicted using existing models [4] .. Unfortunately, all remaining two-flow topologies encounter performance problems, including severe long-term unfairness and shortterm unfairness on timescales of up to seconds. While the existence of some problematic topologies is well known (see [2, 11, 12, 17] for example), this paper is the first to systematically and comprehensively identify and study via analytical modeling and simulations all twelve possible configurations of two flows in a random access environment. We compute the likelihood of each scenario occurring in a random topology, develop models that accurately predict each flow's short-and long-term performance in each scenario where senders are not in range, and predict the impact of key system parameters such as the maximum retransmission limit.. In particular, our contributions are as follows. First, we enumerate the twelve distinct scenarios and classify them into three groups based on their geometric properties: Senders Connected (SC), Asymmetric Incomplete State (AIS), and Symmetric Incomplete State (SIS). We develop a spatial model that predicts the likelihood of the scenarios and groups when nodes are placed randomly. Moreover, we use simulations with random waypoint mobility and routing protocols to further characterize scenario likelihood. We show that the problematic AIS and SIS groups should not be viewed as rare "corner cases," but rather characterize topologies that occur with high frequency.. Second, we perform an extensive set of simulations to characterize the short-and long-term performance in each of the twelve scenarios. The experiments quantify the severe long-term unfairness of the AIS class and the seconds time-scale short-term unfairness of the SIS class. We describe the MAC mechanisms that lead to each class' performance limits. Moreover, we show how random waypoint mobility allows flows to alternate among classes, resulting in improved long-term performance but velocity-controlled epochs of poor performance in the AIS and SIS classes.. Third, we develop an accurate analytical model for the AIS class. We begin with a general "decoupling model" of IEEE 802.11 which provides key temporal embedding points that are critical for development of a Markov model for topologies in which nodes are not fully connected and performance is asymmetric. We generalize the model to incorporate flows that are not continuously backlogged and use simulations to validate the model's accuracy.. Finally, we develop a model to characterize the short-term unfairness that arises in the SIS class. Because this class achieves long-term fairness, the steady state distribution is not of interest. Instead, we derive an expression for the expected time for the system to switch between one flow dominating and the other flow dominating. The model incorporates effects of key system parameters such as the maximum retransmission limit on the timescales of unfairness. Simulation results indicate that the model is able to accurately predict transition times ranging from 10's of msec to 1 sec, with the range accounted for by both the maximum retransmission limit and whether or not RTS/CTS is used.. The reminder of this paper is organized as follows. In Section 2 we identify the twelve topologies for the flow pairs, classify them into three groups, and conduct a spatial analysis to determine their likelihood in a random network. In Section 3, we study via simulations the impact of protocols on the fairness of the three classes and describe the protocol-driven origins of this behavior. In Section 4 and Section 5, we model the AIS and SIS classes respectively. Finally, in Section 6 we discuss related work and in Section 7 we conclude. We have systematically and comprehensively investigated the foundational scenarios of multi-hop wireless networks. We identified all possible topologies consisting of four nodes and two flows, classified them into three geometric groups, and computed their likelihood under random node placement. In each case, we showed how fundamental properties of two-and four-way handshake CSMA protocols yield short-term unfairness in one group, and long-term unfairness in another. Because these problematic scenarios are highly likely to occur in a random graph, we developed an analytical model that can accurately predict the performance in each of these scenarios. For example, we are able to precisely predict each flow's throughput in scenarios with long-term unfairness and the time scale that flows alternate domination in scenarios with shortterm unfairness. Problematic Topologies. Variants of some of the scenarios we investigated are known to incur poor performance. Among them are the classic hidden terminal and exposed terminal problems examined in [2, 12, 18] . Likewise, AIS scenarios are described in [2, 3, 11, 12, 20] . Yet no prior studies comprehensively analyze all scenarios within a single analytical framework nor predict scenario likelihood in a random graph.. Modeling Throughput. The fully connected topology and Senders Connected (SC) group can be accurately modeled using [4] and hence we do not consider them here. In contrast, we model topologies in which senders are disconnected, which leads us to develop new modeling techniques for both the AIS and SIS groups.. In [15, 16] , a queuing analysis of Scenario 11 in Figure 1 is developed under (unrealistic) assumptions that (i) the time between retransmissions (i.e. the backoff delay) is negligible, and (ii) the maximum number of retransmissions allowed for each packet is unlimited. Consequently, the model matches simulations well only under light traffic conditions and with very large packets transmitted at low data rate. In contrast, our analysis incorporates all details of 802.11 DCF, applies to both saturated and non-saturated conditions, incorporates variable packet sizes, and shows the significant impact of the maximum retransmission limit and access method (two-or four-way handshake). In [10] the authors present a throughput analysis that incorporates topology dependent relations, and report preliminary results for the ring topology neglecting the impact of the binary exponential backoff.. Modeling Short-Term Unfairness. While a number of studies have analyzed short-term unfairness due to various aspects of the wireless medium ranging from channel errors to contention, (see [1, 5, 6] for example), none accurately characterize the time scale in which 802.11 stations alternate domination in SIS scenarios. In particular, in our analysis of the SIS group, we model short-term unfairness of IEEE 802.11 with and without RTS/CTS, derive the behavior of the flows from the collision probability, analyze the transient behavior of the system, and accurately predict the timescale of this unfairness as a function of key system parameters.. Receiver Oriented Media Access. A number of receiver-based access mechanisms, in which channel contention is initiated by the receiver, not the sender, have been proposed to improve fairness and performance in various scenarios [2, 8, 19] . The Request-forRequest-to-Send (RRTS) solution is an example receiver-oriented mechanism originally proposed in MACAW [2] : whenever a station receives an RTS to which it cannot respond (due to deferral), it contends during the next contention period on behalf of the sender, reserving the channel by means of an additional control packet called RRTS. The RRTS message solicits the sender to immediately send a new RTS. We have investigated the effectiveness of this solution in both the AIS and SIS group, implementing the RRTS packet exchange in the ns simulator. We have found that this solution has a fundamental limitation in the fact that it requires the receiver of a flow to correctly decode the RTS packet sent by the sender. Unfortunately, this occurs extremely rarely when a transmission attempt is not successful. Consider the scenarios of the AIS group: the RTS packet sent by A typically arrives at a during a transmission of flow B, or it is destroyed by a new packet sent by B before it is fully received by a. Simulation results confirm that the RRTS mechanism does not help in the scenarios of the AIS group.. In the SIS group, the RRTS mechanism is also not useful in scenarios 8 and 9, because during a collision event both RTS packets are destroyed at the receivers. The only exception is scenario 10: in this case, the two flows are connected only through the receivers; the receiver of a flow is not in range of the transmitter of the other flow, and correctly receives the RTS sent by the sender. This scenario leads to short-term unfairness, and can be analyzed in a similar way as described in Section 5. Figure 22 shows that the RRTS mechanism partially mitigates the observed unfairness. Notice that the occurrence probability of Scenario 10 is only about 10%, as reported in Figure 5 .

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A Polynomial Time Algorithm for Obtaining a Minimum Vertex Ranking Spanning Tree in Outerplanar Graphs The minimum vertex ranking spanning tree problem is to find a spanning tree of G whose vertex ranking is minimum. This problem is NP-hard and no polynomial time algorithm for solving it is known for non-trivial classes of graphs other than the class of interval graphs. This paper proposes a polynomial time algorithm for solving the minimum vertex ranking spanning tree problem on outerplanar graphs. In this paper, we proposed a polynomial time algorithm for solving the minimum vertex ranking spanning tree problem, when an input graph is an outerplanar graph. Our algorithm solves this problem on an outerplanar graph using dynamic programming. It would be interesting to know whether our time complexity can be improved. In order to improve this, we should reduce the number of subgraphs G[x, y : z, w]), x, y, z, w = 1, · · · , n, each of which is required to compute a MVRST in it. However, for computing a MVRST in G using dynamic programming, we need each value of MVRSTs in G[x, y : z, w])'s. Thus, we think that it is difficult to reduce the time complexity as far as we use dynamic programming. We might need some other methods not using dynamic programming. We are also interested in whether other classes of graphs in which the minimum vertex ranking spanning tree problem is polynomially solvable, exists or not using dynamic programming. Our algorithm finds an MVRST in G by finding MVRSTs in subgraphs on G induced by the l consecutive vertices on the boundary of the exterior face. In order to find the value of an MVRST in G using formula (2) , it is necessary to find the value of MVRSTs in subgraphs G [v, u] G[v, u] is used as the input data of the algorithm and we can continue to compute the value of an MVRST of G [v, u] recursively. We, of course, do not use a dummy edge to construct an MVRST on the calculation of formula (2) .. However, for the realization of the above idea, our algorithm solves the MVRST problem by a bottom up manner, that is, the algorithm find MVRSTs of subgraphs induced by k, 2 ≤ k ≤ n, in the order of increasing number of vertices without explicitly using recursion.. We first find, for ) is set to be 3 so that the condition that v is assigned the largest rank is satisfied. When v is i (i + 2, respectively), we must assign rank 3 to v and 1,2 to i + 1, i + 2(i, respectively).. We is set to be 3 as (v, i), (i, i + 1) (or (i, i + 1), (i + 1, v)) are a spanning tree and we must assign ranks 1, 2 to i, i + 1, respectively, and then rank 3 to v.. In the following, we similarly compute the value of MVRSTs in subgraphs induced by l (4 ≤ l ≤ n) vertices under the condition that v is assigned the largest rank. In formula (2), the value of an MVRST in G is computed from MVRSTs in subgraphs G [v, u] Fig. 3 (a) ). Moreover, when a half-cycle subgraph is divided into two subgraphs, the other type of structure of subgraphs is generated. This type of subgraph G[x, y : z, w] is induced by two vertex sets {x, · · · , y}, {z, · · · , w} (See Fig. 3 (b) ). Consequently, it is necessary to consider the following two types of structure of subgraphs induced by l vertices. . For example, in Fig. 3 (x, w) or (y, z) , we regard G[x, y : z, w] as a biconnected outerplanar graph whose boundary of the exterior face is x, x + 1, · · ·, y, z, z + 1, · · ·, w. Let us assume that, for a vertex u (x < u < y or z < u < w), two subgraphs obtained by

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Efficient estimation of neural weights by polynomial approximation Abstract-It has been known for some years that the uniformdensity problem for forward neural networks has a positive answer: Any real-valued, continuous function on a compact subset of R R R d can be uniformly approximated by a sigmoidal neural network with one hidden layer. We design here algorithms for efficient uniform approximation by a certain class of neural networks with one hidden layer which we call nearly exponential. This class contains, e.g., all networks with the activation functions A RTIFICIAL forward neural networks are nonlinear parametric expressions representing multivariate numerical functions. In connection with such paradigms there arise mainly three problems: a density problem, a complexity problem, and an algorithmic problem. The density problem deals with the following question: which functions can be approximated and, in particular, can all members of a certain class of functions be approximated in a suitable sense. This problem was satisfactorily solved in the late 1980's [7] , [15] , and [16] . Any continuous function on any compact subset of can be uniformly approximated arbitrarily closely by a neural network with one hidden layer. Moreover, the proof given in [16] provides an intimate connection between forward neural networks and polynomials. This observation suggested to consider the remaining two problems, too, from this point of view.. Manuscript received April 17, 1997; revised January 10, 1999 . The author is with the Fakultät für Mathematik und Informatik, Universität Passau, 94030 Passau, Germany.. Communicated by P. Moulin, Associate Editor for Nonparametric Estimation, Classification, and Neural Networks.. Publisher Item Identifier S 0018-9448(99)04736-7.. In fact, more recently the complexity problem which deals with the relationship between the size of an expression (i.e., the number of neurons) and its approximation capacity was solved [32] , [26] , [25] for two classes of activation functions, both including the popular logistic function and none of them the Heaviside step function. The constructions in these papers provide answers of Jackson's type to the question: How closely can a continuous or -times differentiable function be uniformly approximated by a network with one hidden layer of a given size? or, in other words, how many hidden units are sufficient to approximate such a function uniformly with an error not exceeding ? The order of approximation of a parametric functional expression describes the asymptotic behavior of the maximum approximation error with respect to a given class of functions as the number of parameters in the expression tends to infinity. It was shown that neural networks based on the logistic and many other activation functions approximate any -times differentiable function with a Lipschitz-continuous th derivative of the order , being the size of the input layer and the number of hidden neurons; cf. Comment III-C a).. It remains to exploit the efficiency promised in the solution of the complexity problem. The proofs given in [32] , [26] , and [25] are based on polynomial approximation. Moreover, they are constructive so that algorithms for approximation can be derived from them. It is the main purpose of this paper to turn the method of proof introduced in [32] into algorithms for direct and effective uniform approximation. The most popular method of neural-network training today is backpropagation, i.e., gradient search in combination with the chain rule of multivariate differential calculus. However, this method is slow since it proceeds iteratively although some progress has been made in the past; cf. [4] , [19] , [36] , [1] , and [30] . Moreover, it may get stuck in a local minimum, cf. [24] . The algorithms proposed here are noniterative, thereby avoiding these disadvantages. Furthermore, they need no starting point and no learning parameters. We note finally that Chen [5] designed another efficient, noniterative algorithm but for a different, more complex network architecture.

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Classical communication and non-classical fidelity of quantum teleportation Abstract In quantum teleportation, the role of entanglement has been much discussed. It is known that entanglement is necessary for achieving non-classical teleportation fidelity. Here we focus on the amount of classical communication that is necessary to obtain non-classical fidelity in teleportation. We quantify the amount of classical communication that is sufficient for achieving nonclassical fidelity for two independent 1-bit and single 2-bits noisy classical channels. It is shown that on average 0.208 bits of classical communication is sufficient to get non-classical fidelity. We also find the necessary amount of classical communication in case of isotropic transformation. Finally we study how the amount of sufficient classical communication increases with weakening of entanglement used in the teleportation process. Quantum information theory, the generalization of classical information theory governed by the rules of quantum mechanics, has been a subject of much recent interest. It is now known that various interesting communication schemes, like teleportation [1, 2, 3] and dense coding [4, 5, 6] , are possible when the laws of quantum mechanics are invoked in information processing. It was customary to ignore the classical communication cost in different quantum information processes like entanglement distillation [7, 8, 9] . The motivation was that classical communication is free whereas entanglement is expensive. However, as emphasized in [10] , in dense coding process classical communication cost is of primary interest and one can not ignore it. On the other hand in quantum teleportation protocol classical communication is one of the required resource other than entanglement. An unknown qubit can be teleportated perfectly by using a maximally entangled state and 2 bits of classical communication. Naturally, accuracy of the teleportation process decreases if noise is introduced in the quantum as well as classical channel. A lot of works has been devoted to study teleportation process in presence of noisy quantum channel [11, 12, 13, 14] , but very little is discussed about the efficiency of teleportation in case where classical channel is noisy. So it is also important to study quantum teleportation in presence of noisy classical channel.. Suppose there are two spatially separated fellows, say Alice and Bob. Alice is holding a spin-1 2 system in state |φ , where the state of the system |φ is unknown to her. Now challenge for them is to prepare the state |φ at Bob's location. Bennett et.al. have shown that this seemingly impossible task can be done in quantum mechanical framework, which is known as quantum teleportation [1] . To be successful in this challenge, Alice and Bob must share two different types of resources namely entanglement and classical communication.. In general they will not succeed in perfectly reproducing the state |φ at Bob's location, but will prepare some other state, denoted by |φ ′ if it is pure, or by χ (density matrix) if it is mixed. The measure of success -the "score" obtained can be quantified by | φ|φ ′ | 2 or equivalently by Tr(χ|φ φ|). Suppose now that this process is repeated many times, each time Alice gets an unknown particle uniformly distributed on the unit sphere. The final score of the process -the average of the scores obtained in the different runs -is called the fidelity of the transmission [11] . If Alice and Bob cannot communicate at all, Bob could try to guess the state, according to some particular scheme ( one of such scheme is that Bob will always prepare a particle in some state). The fidelity of any such guess scheme will be always 1 2 [11, 15] . If Alice and Bob use no entanglement but classical communications then they can raise the fidelity value beyond 1 2 . Alice measures her state and sends the result to Bob, who makes his best guess of the state based on this information. The success of sending the state |φ is calculated as. , where p(i||φ ) = φ|A i |φ is the probability of Alice obtaining the result corresponding to the positive operator A i out of n possible outcomes of the positive operator valued measure (POVM) {A i } [16, 17] , where n i=1 A i = 1 2 , with 1 2 denoting the identity operator; and |α i be the Bob's guess, given outcome i. When the input state is completely unknown, the average of the success over a uniform distribution of all states on the Bloch sphere is taken to obtain the fidelity of the teleportation process [18, 19] . It has been shown that the fidelity in this case becomes. , here dΩ denote the haar measure over the set of pure states on the Bloch sphere and the subindex 'cl' denotes that only classical communication has been used as teleportation resource. This value we call classical fidelity of teleportation process. In [11] , Popescu showed that if Alice performed a two outcomes projective measurement in any basis (say σ z ) and communicated her measurement result to Bob, who prepared the particle either in σ z -up or σ z -down state depending on Alice's measurement result, then optimal classical fidelity (i.e. 3 ) can be achieved. If in any teleportation scheme the value of the teleportation fidelity becomes greater than 2 3 , then one can conclude that some quantum entanglement must have been used in the process. When 2 bits of classical communication and maximally entangled state (e.g. singlet) are used in teleportation protocol the value of teleportation fidelity becomes unity, which reflects complete accuracy of the process. If the degree of entanglement used in the teleportation process is weakened in the form of Werner state. 2 , then teleportation fidelity takes the value F = 1+α 2 [11] . The parameter (1−α) in the Werner state W α quantifies the amounts of white noise (i.e. 12 2 ⊗ 12 2 ) present in the state W α along with the singlet state. It is known that the state W α is entangled for α > 2 ) one can infer that to achieve the fidelity greater than the classical value the Werner state has to be necessarily entangled. Interestingly it has been shown that any two-qubit entangled state is good for teleportation [20] . In this paper we pose the following question: how much classical communication is necessary to achieve non-classical fidelity in quantum teleportation process when there is no restriction on entanglement? Interestingly we have found that:. (a) If two independent 1-bit noisy classical channels are used then on average (0.255 + ǫ) bits of classical communication (with ǫ > 0) is sufficient to make the teleportation fidelity non-classical.. (b) In case of 2-bits noisy classical channel, on average (0.208 + ǫ) bits of classical communication (with ǫ > 0) is sufficient to make the teleportation fidelity non-classical. We also argue that (0.208 + ǫ) bits of classical communication is necessary if the quantum state transforms isotropically under teleportation process.. (c) We have shown how the amount of classical communication increases when the entanglement, used in the teleportation process, is weakened.. The paper is organized in the following way. First, in section-2 and section-3 we study teleportation process with 1-bit noisy classical channel and 2-bits noisy classical channel respectively. Then in section-4 we discuss about necessary amount of classical communication required to get non classical fidelity when state transforms isotropically. In section-5 we find how the amount of classical communication increases to get non classical fidelity when entangled channel is weakened in Werner form. Our result shows that in quantum teleportation, there is a threshold amount of classical communication that is required for achieving non classical fidelity. The optimal amount of classical communication that is necessary for achieving non-classical fidelity in quantum teleportation still remains an open problem. We only provide sufficient amount in two cases. In case of isotropic state transformation, we find the necessary amount of classical communication to reach quantum fidelity. We also show that the sufficient amount of classical communications increase with weakening of the singlet state to Werner state. It remains interesting to study the necessary amount of classical communication for a general entangled state used as teleportation resources.

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


Designing Chaotic Mathematical Circuits for Solving Practical Problems We introduce the paradigm of chaotic mathematical circuitry which shows some similarity to the paradigm of electronic circuitry, especially in the frame of chaotic attractors for solving practical problems (generating hyperchaos; developing chaos based pseudo random number generator (CPRNG) and chaotic multistream PRNG; secure communication via synchronization). They can also be used in cryptography, generic algorithms in optimization, control, etc. Our purpose is to build up an analogue to the paradigm of electric circuitry, which is the design of electronic circuits: the paradigm of chaotic mathematical circuitry, in order to easily improve the performance of well known chaotic attractors for application purposes (chaotic cryptography, evolutionary and genetic algorithms in optimization, control, etc). However, some differences occur in the analogy: Mathematical circuits are generic rather than specific like electric circuits.. An electronic circuit is composed of individual electronic components, such as resistors, transistors, capacitors, inductors and diodes, connected by conductive wires through which electric current can flow. The combination of components and wires allows various simple and complex operations to be performed: Signals can be amplified, computations can be accomplished, and data can be moved from one place to another. Very complex systems can be analyzed using various sophisticated methods [1−3] . We introduce in the same way mathematical circuits which are composed of individual components (generators, couplers, samplers, mixers, reducers and cascaders, etc.) connected through streams of data. The combination of such mathematical components leads to several new applications such as improving the performance of well known chaotic attractors (Chua, Lorenz, Rössler, etc.) for application purposes.. From a mathematical point of view, at least in order to implement applications of chaotic behaviors, all these chaotic attractors have the same structure: Given initial values and a set of parameters, they provide three streams of data symbolized by three arrows. On the contrary, the electric realization of their equation leads to very different electric circuits. In fact, mathematical circuits capture the essential of dynamics of chaotic attractors.. In Section 2, we present several symbols of generators (both continuous and discrete) used in the paradigm of mathematical circuits, and we compare mathematical cir- Following the worldwide tradition of using Chua s circuits for various purposes, we have introduced the paradigm of chaotic mathematical circuitry which shows some similarity to the paradigm of electronic circuitrythe design of electronic circuits. This new paradigm allows, for instance, building new chaotic and random number generators. However, there are some differences in the analogy: Mathematical circuits are generic rather than specific like electric circuits. In fact, they capture the essential of dynamics of chaotic attractors.. We have presented the symbols of generators (both continuous and discrete) used in the paradigm of mathematical circuits, and compared mathematical circuits with the electric ones.. We considered others circuit elements (couplers, sampler, mixer, reducer and cascader) in practical problems: generating hyperchaos; developing chaos based pseudo random number generators (CPRNGs), chaotic multistream pseudo random number generators (Cms-PRNGs) and secure communication via synchronization.. Alongside electronic circuits, the new theory of mathematical circuits allows many new applications in chaotic cryptography [29] , genetic algorithms in optimization and in control [30] , etc. Due to the versatility of the new components we introduce, the combined operation of these chaotic mathematical circuits remains largely unexplored.

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


Lattice-Boltzmann simulations of the thermally driven 2D square cavity at high Rayleigh numbers The thermal lattice Boltzmann equation (TLBE) with multiple-relaxationtimes (MRT) collision model is used to simulate the steady thermal convective flows in the two-dimensional square cavity with differentially heated vertical walls at high Rayleigh numbers. The MRT-TLBE consists of two sets of distribution functions, i.e., a D2Q9 model for the mass-momentum equations and a D2Q5 model for the temperature equation. The dimensionless flow parameters are the following: the Prandtl number Pr = 0.71 and the Rayleigh number Ra = 10 6 , 10 7 , and 10 8 . The D2Q9+D2Q5 MRT-TLBE is shown to be second-order accurate and to be capable of yielding results of benchmark quality, including various Nusselt numbers and local hydrodynamic intensities. The results obtained by using the MRT-TLBE agree well with existing benchmark data obtained by other methods. There has been a systematic effort to construct the lattice Boltzmann equation (LBE) for thermal hydrodynamics since the inception of the lat-tice Boltzmann method (LBM). From early on, it was realized that, while the LBE with energy conservation can lead to the correct macroscopic equations (cf., e.g., [1] ), the energy-conserving lattice Boltzmann (LB) models are plagued with severe numerical instability [2] , hence they are of little practical use.. It was found that in addition to being prone to numerical instabilities, energy-conserving LBE is also plagued with spurious couplings between energy and shear modes of the linearized evolution operator [2] . To remove this spurious coupling between energy and shear modes, the energy-conservation law must be separated from the mass and momentum conservation laws and there exist at least two approaches to accomplish this goal. The first approach is to use two sets of distribution functions, one for the mass-momentum conservations and the other for the energy conservation (cf., e.g., [3, 4] ); and the second is a hybrid approach with the LBE for the mass-momentum conservations and a finite-difference (FD) scheme for the temperature equation [2, 5] . Both these approaches effectively remove the spurious energy-shear mode coupling. However, the hybrid thermal LBE encounters a new problem -it is difficult to realize the temperature boundary conditions which are consistent with the LB boundary conditions for mass-momentum equations. Consequently, the approach of dual distributions becomes the prevailing one.. In this work we will use the thermal lattice Boltzmann equation (TLBE) with dual distributions and the multiple-relaxation-time collision model to simulate internal thermal flows in two-dimensions (2D). The TLBE consists of a D2Q9 MRT-LBE [6, 7] for the mass-momentum conservations and a D2Q5 MRT-LBE [8, 9, 10, 11, 12] for the advection-diffusion equation for the temperature. The TLBE with D2Q9 and D2Q5 LB models has been validated for its accuracy and stability [4] . In particular, we will use the D2Q9+D2Q5 TLBE to simulate the thermally driven convective flow in the 2D square cavity with differentially heated vertical walls [13, 14] . This flow has been used to validate various numerical methods including pseudo-spectral (PS) [15] , finite difference (FD) [14, 16] , finite element (FE) [17, 18] , finite volume (FV) [19, 20] , and control volume (CV) [21] methods. In fact, the 2D square cavity with differentially heated vertical walls has become a standard benchmark problem for incompressible thermal flows. One of the primary purpose of the present work is to reproduce benchmark quality results for the thermally driven steady 2D cavity flow at high Rayleigh numbers (Ra = 10 6 , 10 7 , and 10 8 ) by using the MRT-TLBE model we have developed [4] .. The remainder of the paper is organized as follows. Section 2 provides a detailed description of the D2Q9+D2Q5 MRT-TLBE for thermal flows [4] , including specifically the details of the MRT-TLBE and the corresponding macroscopic hydrodynamic equations, and the implementation of the TLBE algorithm. Section 3 discusses the flow configuration of the 2D square cavity with differentially heated vertical walls. We pay a special attention to the boundary conditions in the flow and their LB implementations. Section 4 describes the numerical procedures for post-processing, which are used to measure various quantities in the simulations. Section 5 presents our numerical results. We first present a study on the effect of a parameter in the MRT-TLBE which determines the heat diffusivity κ; we also conduct a convergence study of the flow fields, Nusselt numbers, and some local hydrodynamic intensities; we then compare our results with existing benchmark data. Finally, Section 6 concludes the paper with a summary. In this work we use the multiple-relaxation-time lattice Boltzmann model with dual distributions [4] to simulate thermal flows in the two-dimensional square cavity with differentially heated vertical walls. The MRT-TLBE uses the D2Q9 model and D2Q5 model for mass-momentum and temperature conservations, respectively. The D2Q9+D2Q5 MRT-LB model essentially solves the thermal fluid system with the Boussinesq approximation. The flow parameters are the Prandtl number Pr = 0.71 (for air) and the Rayleigh number Ra = 10 6 , 10 7 , and 10 8 . The Mach number is fixed to be Ma = 0.1 in our simulations. With the given Rayleigh numbers, the flow is steady. We now summarize our observations in this work as the following. First, we emphasize that the MRT collision model is imperative to achieve accurate boundary conditions and numerical stability. We would also like to point out that the LBGK model fails in both these aspects. Second, with the given flow conditions, we have shown that the MRT-TLBE model is second-order accurate for flow fields with L 2 -norm, global quantities, such as Nusselt numbers, and local hydrodynamic intensities as well as their positions, with L ∞ -norm. Third, our results demonstrate that the MRT-LB model can reproduce numerical results of benchmark quality for internal incompressible thermal flows. Our results agree well with existing benchmark data obtained by using traditional methods. Finally, the LB algorithm has been implemented on GPU, and can achieve a speed of 560 million millions site-updates per second with double precision (1080 millions site-updates per second with single precision), which allows us to complete the simulations on a mesh as large as 2043 2 within 15 hours. The LB algorithm has been implemented on both CPU and GPU. With a mesh of size N 2 = 2043 2 , the LB code running on an Intel Core-I7 CPU and on a Quadro-6000 GPU can achieve about, respectively, 12 and 1080 millions site updates per second in single precision and 9 and 560 millions per second in double precision. For a smaller mesh size of 256 2 , the speed on the Quadro-6000 GPU is 396 and 617 millions site updates per second in single and double precision, respective. The GPU allows us to obtain the results of steady-state with a mesh size as large as 2043 2 within 15 hours.. The simulations are conducted with the following formula to determine the parameter a, which is obtained by using κ = ν/ Pr, the special value of σ κ given by Eq. (19) , and the upper bound of ν given by Eq. (32):. with the condition −4 < a < 1 for thermal stability -The lower bound −4 corresponds to a positivity of κ in Eq (21) and the upper bound +1. corresponds to stability limit of the checkers-board mode. In our simulations, the Mach number Ma is fixed at 0.1 unless otherwise specified, and Pr = 0.71, the equality usually holds. Thus, with the Rayleigh number Ra and the resolution N given, the parameter a is determined, and so are the heat diffusivity κ and the viscosity (ν = Pr κ), the value of ν is also checked against the stability criterion of Eq. (33).

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


Kriging metamodeling in simulation: A review This article reviews Kriging (also called spatial correlation modeling). It presents the basic Kriging assumptions and formulas-contrasting Kriging and classic linear regression metamodels. Furthermore, it extends Kriging to random simulation, and discusses bootstrapping to estimate the variance of the Kriging predictor. Besides classic one-shot statistical designs such as Latin Hypercube Sampling, it reviews sequentialized and customized designs for sensitivity analysis and optimization. It ends with topics for future research. Metamodels are also known as response surfaces, surrogates, emulators, auxiliary models, etc. By definition, a metamodel is an approximation of the Input/Output (I/O) function that is implied by the underlying simulation model. Metamodels are fitted to the I/O data produced by the experiment with the simulation model. This simulation model may be either deterministic or random (stochastic). Note that simulation is applied in many different disciplines, so the terminology varies widely; therefore, this article gives several terms for the same concept.. Examples of deterministic simulation are models of airplanes, automobiles, TV sets, and computer chips-applied in Computer Aided Engineering (CAE) and Computer Aided Design (CAD) at Boeing, General Motors, Philips, etc.. Detailed examples are the helicopter test example in [4] , the vehicle safety example in [18] , and the other examples in [30, 47] .. Deterministic simulations give the same output for the same input. However, deterministic simulations may show numerical inaccuracies; i.e., a minor (infinitesimal) change in the input produces a major change in the output. A well-known mathematical example is the inversion of a matrix that is nearly singular (ill-conditioned). Simulation examples are discussed in [12, 15, 16, 50] . These inaccuracies may make deterministic simulation related to random simulation.. Random simulations use Pseudo-Random Numbers (PRNs) inside their models, so simulations of the same input combination give different outputs (unless, the PRN streams are identical; i.e., the PRN seeds are identical). Examples are models of logistic and telecommunication systems. Details are given in textbooks on discrete-event simulation, such as [1, 32] . This article covers both deterministic and random simulation! Most publications on metamodels focus on low-order polynomial regression. This type of metamodel may be used for the explanation of the underlying simulation model's behavior, and for prediction of the expected simulation output for combinations of input values that have not yet been simulated (inputs are also called factors; combinations are also called points or scenarios). The final goals of metamodeling may be Validation and Verification (V&V) of the simulation model, sensitivity or what-if analysis of that model, and optimization of the simulated system; see [25, 27, 32] . This article focuses on Kriging metamodels. Typically, Kriging models are fitted to data that are obtained for larger experimental areas than the areas used in loworder polynomial regression; i.e., Kriging models are global (rather than local). These models are used for prediction; the final goals are sensitivity analysis and optimization.. Kriging was originally developed in geostatistics (also known as spatial statistics) by the South African mining engineer called Krige (who is still alive). The mathematics were further developed by Matheron; see his 1963 article [39] . A classic geostatistics textbook is Cressie's 1993 book [9] . More recent are the references 17 through 21 in [38] .. Later on, Kriging models were applied to the I/O data of deterministic simulation models. These models have kdimensional input where k is a given positive integer (whereas geostatistics considers only two-dimensional input); see Sacks et al.'s classic 1989 article [43] . More recent publications are [24, 44, 49] .. Only in 2003, Van Beers and Kleijnen [51] started with the application of Kriging to random simulation models. Although Kriging in random simulation is still rare, the track record that Kriging achieved in deterministic simulation holds great promise for Kriging in random simulation.. Note: Searching for 'Kriging' via Google on August 20, 2007 gave 661,000 hits, which illustrates the popularity of this mathematical method. Searching within these pages for 'Operations Research' gave 134,000 hits.. The goal of this article is to review the basics of Kriging, and some recent extensions. These basics may convince analysts in deterministic or random simulation of the potential usefulness of Kriging. Furthermore, the review of recent extensions may also interest those analysts who are already familiar with Kriging in simulation.. The rest of this article is organized as follows. Section 2 compares Kriging with linear regression, and covers the basic assumptions and formulas of Kriging. Section 3 presents some relatively new results, including Kriging in random simulation and estimating the variance of the Kriging predictor through bootstrapping. Section 4 includes oneshot and sequential statistical designs for Kriging metamodels, distinguishing between sensitivity analysis and optimization. Section 5 presents conclusions and topics for future research.

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


The branching problem in generalized power solutions to differential equations Generalized power asymptotic expansions of solutions to differential equations that depend on parameters are investigated. The changing nature of these expansions as the parameters of the model cross critical values is discussed. An algorithm to identify these critical values and generate the generalized power series for distinct families of solutions is presented, and as an application the singular behavior of a cosmological model with a nonlinear dissipative fluid is obtained. This algorithm has been implemented in the computer algebra system Maple. Quite frequently physical models depend on parameters and the predictions of these models, when confronted with observations, yield constraints that fix the parameters or disqualify the model. Hence, for models described in terms of a set of differential equations, it becomes of prime importance to investigate the dependence of solutions on the parameters. Now, when exact solutions to these equations are not available, or even when they are available but they have a complex implicit or parametric form, it may become useful to obtain asymptotic expansions of these solutions. And when solutions do not admit power series expansions with integer or rational exponents (Pusieux series), we are led to consider series with more general terms like "generalized" powers with real exponents [1] or exp-log terms [2] . Though the algebraic issues of generalized power series have already been investigated (cf. [3] ), for applications the main problem lies in the dependence of the exponents on the parameters, as the ordering of terms and even the nature of the asymptotic expansion may change as these parameters reach some critical values.. In this paper, we will discuss the problems involved in the determination of the critical values of the parameters and an algorithm to calculate the coefficients and exponents of the generalized power series in the regions of the parameter space where real solutions admit such an expansion.. Several critical steps in the search for solutions in the form of generalized power expansions involve calculations with large number of terms and this number grows very fast with the size of the ODE, making hand calculation inconvenient. On the other hand, as many of the steps in these calculations have a systematic nature, use of computer algebra systems appears ideally suited. For this purpose, we have developed a set of routines in Maple (for a brief review of a previous implementation, see Ref. [4] ).. The plan of this paper is as follows. In section 2, we present the basics of generalized power expansions of solutions to a class of nonlinear ODES. In section 3, we review the problem of branching of these solutions as parameters cross critical values. The algorithm used to find these solutions is presented in section 4 and it is applied to an example equation arising from a cosmological model in section 5. Finally, the conclusions are stated in section 6. We have shown some problems that occur when dealing with generalized power expansions of solutions to nonlinear ordinary differential equations that depend on parameters, and we have sketched an algorithm that allows identifying critical values of the parameters and obtaining the series for the distinct families of solutions by an iterative process.. As an example, we have applied this algorithm to obtain two term truncations of the series expansions of solutions to a cosmological model filled with a nonlinear causal viscous fluid. Thus, it is shown as feasible to deal with the case branching that occurs in series solutions to nonlinear ordinary differential equations relevant to physical applications. It deserves to be investigated how the complexity of the algorithm increases with the order of iteration, and whether this growth puts an effective limit to practical calculations. In such a case, it would be interesting to know whether more efficient algorithms could be devised. Also, it would be interesting to know whether expansions of solutions as shown in this paper can give information about the integrability of the equation.

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


Effective analytic functions One approach for computations with special functions in computer algebra is the systematic use of analytic functions whenever possible. This naturally leads to problems of how to answer questions about analytic functions in a fully e ective way. Such questions comprise the determination of the radius of convergence or the evaluation of the analytic continuation of the function at the endpoint of a broken like path. In this paper, we propose a rst de nition for the notion of an e ective analytic function and we show how to e ectively solve several types of di erential equations in this context. We will limit ourselves to functions in one variable. An important problem in computer algebra is how to compute with special functions which are more complicated than polynomials. A systematic approach to this problem is to recognize that most interesting special functions are analytic, so they are completely determined by their power series expansions at a point.. Of course, the concept of special function is a bit vague. One may for instance study expressions which are built up from a nite number of classical special functions, like exp, log or erf. But one may also study larger classes of special functions , such as the solutions to systems of algebraic di erential equations with constant coe cients. Let us assume that we have xed a class F of such special functions or expressions for the sequel of this introduction.. In order to develop a satisfactory computational theory for the functions or expressions in F, one may distinguish the following main subproblems: How to test whether f 2 F locally represents the zero power series? How to evaluate f 2 F safely and e ciently at any point where f may be de ned?. The rst subproblem is called the zero-test problem and it has been studied before in several works Ris75, DL84, DL89, Kho91, Sha89, Sha93, PG97, SvdH01, vdH02b] . For large classes of special functions, it turns out that the zero-test problem for power series can be reduced to the zero-test problem for constants (see also vdH01b] for a discussion of this latter problem).. In this paper, we will focus on the second subproblem, while leaving aside the e ciency considerations and restricting our attention to functions in one variable. By safe evaluation of f 2F at z, we mean that we want an algorithm which computes an approximation f~2 (Z+i Z)2 Z for f(z) with jf~? f(z)j < " for any " 22 Z . If such an algorithm exists, then we say that f(z) is an e ective complex number. By any point where the expression may be de ned , we mean that we do not merely plan to study f near the point where a power series expansion was given, but that we also want to study all possible analytic continuations of f.. In other words, the aim of this paper is to develop an e ective complex analysis for computations with analytic functions in a class F which we wish to be as large as possible.. Such computations mainly consist of safe evaluations, bound computations for convergence radii and absolute values of functions on closed disks, and analytic continuation. Part of the philosophy behind this paper also occurs in BB85, CC90] , but without the joint emphasis on e ectiveness at all stages and usefulness from the implementation point of view. In previous papers vdH99, vdH01a], we have also studied in detail the fast and safe evaluation of holonomic functions. When studying solutions to non-linear di erential equations, one must carefully avoid undecidable problems:. Theorem 1. DL89] Given a power series f = P f n z n with rational coe cients, which is the unique solution of an algebraic di erential equation. with rational coe cients and rational initial conditions, one cannot in general decide whether the radius of convergence (f) of f is < 1 or > 1.. What we will show in this paper, is that whenever we know that an analytic function f = P f n z n as in the above theorem may be continued analytically along an e ective broken line path , then the value f( ) of f at the endpoint of is e ective (theorem 11). We will also show that we may e ectively solve any monic linear di erential equation, without introducing singularities which were not already present in the coe cients (theorem 10).. In order to prove these results, we will carefully introduce the concept of an e ective analytic function in section 2. The idea is that such a function f is given locally at the origin and that we require algorithms for Computing coe cients of the power series expansion; Computing a lower bound for the radius of convergence;. Computing an upper bound for jf j on any closed disk of radius < .. Analytic continuation. But we will also require additional conditions, which will ensure that the computed bounds are good enough from a more global point of view. In section 3, we will show that all analytic functions, which are constructed from the e ective complex numbers and the identity function using +; ?; ; /; R ;exp and log, are e ective. In section 4, we will study the resolution of di erential equations.. It is convenient to specify the actual algorithms for computations with e ective analytic functions in an object oriented language with abstract data types (like C++). E ective types and functions will be indicated through the use of a sans serif font. We will not detail memory management issues and assume that the garbage collector takes care of this. The Columbus program is a concrete implementation of some of the ideas in this paper vdH02a], although this program works with double precision instead of e ective complex numbers.. 2. Effective analytic functions 2.1. E ective numbers and power series A complex number z 2 C is said to be e ective, if there exists an algorithm which takes a positive number 0 < " 2 2 Z on input and which returns an approximation z 2 (Z + i Z) 2 Z for z with jz ? zj < ". We will also denote the approximation by z = z <" . In practice, we will represent z by an abstract data structure Complex with a method approximate which implements the above approximation algorithm. The asymptotic complexity of an e ective complex number z 2Complex is the asymptotic complexity of its approximation algorithm.. We have a natural subtype Real Complex of e ective real numbers. Recall, however, that there is no algorithm in order to decide whether an e ective complex number is real.. In the sequel, we will use the notations R > = fx 2 R: x > 0g and R > = fx 2 R: x > 0g.. Let R be a weakly e ective ring, in the sense that all elements of R can be represented by explicit data structures and that we have algorithms for the ring operations 0; 1; +; ?. and . If we also have an e ective zero test, then we say that R is an e ective ring.. An e ective series over R is a series f 2 R z]], such that there exists an algorithm in order to compute the n-th coe cient of f. E ective series over R are represented by instances of the abstract data type Series(R), which has a method expand: N!R z], which computes the truncation f 0 + + f n?1 z n?1 2 R z] of f at order n as a function of n 2 N.. The asymptotic complexity of f is the asymptotic complexity of this expansion algorithm. In particular, we have an algorithm to compute the n-th coe cient f n of an e ective series. A survey of e cient methods to compute with e ective series can be found in vdH02c].. When f is an e ective series in Series(Complex), then we denote by f 2C z]] the actual series which is represented by f. If f is the germ of analytic function, then we will denote by (f ) the radius of convergence of f and by jf j r the maximum of jf j on the closed disk B r = fz 2 C: jzj 6 rg of radius r, for each r < (f ).

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


What if there were desktop access to the computer science literature? What if there were an electronic computer science library? Consider the possibilities of having your favorite publications available within finger's reach. Consider Project Envision, an ongoing effort to build a user-centered database from the computer science literature. This paper describes the project's lirst year progress, stressing the underlying motivation, user-centered development, and the overall design. Project Envision is developing an archive for computer science, using literature provided by the ACM and other sources. Through interviews and the study of existing publications, we are identifying document features that should be managed to allow users to more efficiently carry out tasks they desire, including those where information retrieval is an embedded application. We hope to develop methods so that authors can prepare documents that can be easily converted into archival form with descriptive markup that facilitates automatic handling of key objects. Document conversion efforts will allow us to develop an archive of sufficien t size to enable evaluation 2SuperCard is a trademark of Silicm Beach Software by faculty, students, and staff. Our distributed expert-system based information retrieval system, CODER, and the graphof-objects database engine, LEND, should enable flexible access to relevant data.. As efforts proceed, and we gain experience with the problems and successes of electronic libraries, larger efforts will no doubt be launched. Of particular interest, and of urgent importance for our nation's future progress, is construction of a national electronic archive. What if that could be in place by the turn of the century?

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Synthetic hybrid indicators based on scientific collaboration to quantify and evaluate individual research results Abstract: Governmental initiatives around scientific policy have progressively raised collaboration to priority status. In this context, a need has arisen to broaden the traditional approach to the analysis and study of research results by descending to the group or even the individual scale and supplementing the output-, productivity-, visibility-and impact-based focus with new measures that emphasize collaboration from the vantage of structural analysis. To this end, the present paper proposes new hybrid indicators for the analysis and evaluation of individual research results, popularity and prestige, that combine bibliometric and structural aspects. A case study was conducted of the nine most productive departments in Carlos III University of Madrid. The findings showed hybridization to be a tool sensitive to traditional indicators, but also to the new demands of modern science as a self-organized system of interaction among individuals, furnishing information on researchers' environments and the behavior and attitudes adopted within those environments. In the last few decades, scientific collaboration has been a core area of study for many researchers. Most of the literature has focused on the analysis of international and national output, scientific domains or research institutions, while studies addressing smaller units such as departments or research groups are less common (Bordons, Zulueta, Cabrero, & Barrigón, 1995; Bordons & Zulueta, 1997; Molina, Muñoz, & Losego, 2000; Molina, Muñoz, & Domenech, 2002; Zulueta, Cabrero, & Bordons, 1999; .. Science is a collective activity and collaboration, as an intrinsic feature, is more a need than a choice (Beaver & Rosen, 1978; Beaver & Rosen, 1979) . For this reason, any number of initiatives have been undertaken to encourage, stimulate and enhance collaboration among researchers, while many a policy has been adopted to improve the connections between science and technology through intersectoral scientific collaboration (universities, health systems, private enterprise, and so on).. The message conveyed by governments and bodies that finance research is increasingly explicit: collaboration and association are requisite to research investment, the funding that ensures the quality of the work performed and the savings inherent in equipment and competence sharing. Recent examples are to be found in the latest tenders organized on the European (VII Research Framework Programme (European Union, 2006) Consequently, scientific collaboration, which is apparently organized and controlled by the scientists themselves, is conditioned by science policy initiatives that have progressively made it a priority (Melin & Persson, 1996) .. In this context, a need has arisen to broaden the traditional approach to the analysis and study of research results, descending to the group or even the individual scale and supplementing the output-, productivity-, visibility-and impact based focus with new measures that emphasize collaboration from the vantage of structural analysis (Acedo et al., 2006; Bonaccorsi & Daraio, 2003; Börner et al., 2005; Calero et al., 2006; Cohen, 1991; Colman, Dhillon, & Coulthard, 1995; García-Aracil, Gutiérrez Gracia, & Pérez-Martín, 2006; Genest & Thibault, 2001 ; Kretschmer, 1997; Lee, 2003; Moed et al., 1998; Noyons, Moed, & van Raan, 1999; Qurashi, 1993; Rey-Rocha, Martín-Sempere, & Garzón-García, 2002; Rey-Rocha, Garzón-García, & Martín-Sempere, 2006; Seglen & Aksnes, 2000; van Leeuwen & Moed, 2005) . The formulation of new convergence indicators has revealed the patterns of ties between actors as an invaluable aid to understanding networking on the individual scale. New formulas for characterizing researchers constitute valid and effective analysis and evaluation tools for identifying excellent authors, understood to be not only the most productive or visible, but also those able to combine those qualities with the effort involved in collective work. They are regarded to be excellent because their individual worth and capacity (number of articles published or citations) is enhanced by the merit deriving from joint work, with which they generate new, high quality scientific, technical and/or technological knowledge and guarantee the availability of new resources for further research.. This has made it possible to rank individual scientists and determine the differences revealed by indicators that distinguish among central professors, the most prestigious authors and the ones who act as intermediaries, reflecting the collaboration strategies deployed by the various actors to achieve recognition and impress their ideas on their colleagues.. Another interesting finding was that researchers' collaboration modus operandi is independent of their output or visibility.. These tools, then, are sensitive to traditional indicators, but also to the new demands of modern science as a self-organized system of interaction among individuals, furnishing information on researchers' environments and their behavior and attitudes within those environments (always collaborating with the same colleagues and keeping to the same lines of research, or changing scientific partners in pursuit of new challenges, for instance). In this new panorama, it does not suffice to "have" (published papers or citations): one must "be" from the perspective of the phrase so adeptly coined by Björneborn, connecto ergo sum (Björneborn, 2004) .. As noted earlier, the scientific environment may influence individual behavior, particularly if such behavior affects research funding. Despite the exceptions described above that may put upward pressure on its value, the clustering coefficient is sufficiently robust to reduce the possible inflationary effects of adaptations in researcher behavior to accommodate new funding requirements. This is because the coefficient is based not only on the number of an actor's collaborative actions, but also on the degree of cohesion of the resulting relationships.. The new popularity and prestige indicators broaden the range of indicators used to quantify individual researcher development. Information can naturally be obtained on known indicators, and the differences between two authors with the same number of papers and citations can be readily quantified (using the H-index). In much the same way, the combination of such indicators via the clustering coefficient can be used to distinguish between or qualify the positions of authors with the same number of papers or citations based on their collaboration practices.. The future enlargement of this type of analysis to broader domains or the comparison between micro-domains addressing similar subject matters will lead to an understanding of the relationships between UC3M author popularity and prestige on the international arena. The effect of endogamic sub-structures as well as and network size and density will also be ascertained and a more detailed and precise view of the evolution and scope of the results will be obtained. Nonetheless, the complexity of such studies conducted at the individual level in meso-or macro-aggregates should not be underestimated. The standardization of authors' names is the primary obstacle to analyzing such networks, for the number of authors may range from several thousand to several tens of thousands, depending on the domain and period analyzed. An initial analysis of the behavior and evolution of the new indicators, popularity and prestige, yields suggestive results. By combining bibliometric and structural indicators, an author's rank in a list based on either measure can be qualified. It is interesting to note, for instance, that the actors ranking highest in terms of collaborative output, citations or clustering coefficient lack the characteristics necessary to be ranked equally highly in terms of popularity and prestige.. The Spearman correlation values (Table 11) show the results of comparing three simple indicators (number of papers, number of citations and clustering coefficient) to the two hybrid indicators (popularity and prestige). The low correlation among variables confirms the lack of uniformity in authors' positions under the various indicators used. In other words, since an author's predominant position in terms of a simple indicator (production, visibility or collaboration) does not guarantee a comparable position in terms of popularity or prestige, these hybrid indicators, with respect to their predecessors, furnish novel and non-redundant information. High correlation among authors' positions was observed in the Materials Science Department only, and was more significant between number of documents and popularity than between citations and prestige.. Moreover, the number of nodes in the co-authorship networks differed from one discipline to another, however, due to the variety and specialized nature of the research problems addressed and the number of years the network was in place. In addition, the mean number of co-authors per paper depended largely on whether the article was theoretical or experimental. Theory papers tended to have a smaller number of co-authors, while the number of collaborating researchers was larger in experimental science. Lastly, in co-authorship networks the clustering coefficient was sometimes affected by the existence in the network of subgroups of only a few authors who collaborated intensely and tended to form cliques or circles. Consequently, special network parameters may better characterize their degree of clustering. In short, the new indicators emphasize not only the importance of the values furnished by traditional bibliometric indicators, but also the need for authors to have a prominent position from a structural standpoint. The Physics Department may be a good example of actors' behavior and show that a well-structured research environment may be much more beneficial than a larger number of co-authored papers or citations. Therefore, much has to be gained from the differentiation proposed, whereby authors are evaluated based not only on absolute volume but also their importance in the network. The latter is defined in terms of their ability to draw and shape working teams in which everyone collaborates with everyone else (distributed network), as opposed to groups in which the main node manages collaboration and keeps the various participating partners isolated (star network).. While the analysis was limited to the nine most productive departments in a specific institution, the results obtained are valid at the micro level addressed. Clustering coefficient values may vary depending on the size of the network, certainly. And the individual results for the professors analyzed may (and, when the time comes, should) be transferred to higher levels of aggregation (providing they are compatible), as suggested in the future lines of research discussed in the following section. But at the same time, the evaluation of all researchers in a common context, namely their department, affords sufficient guarantees for a valid comparison.. Nonetheless, certain reservations and exceptions must be borne in mind. The clustering coefficient values, like those of any other general or individual structural indicator, are impacted by the choice of the time period. A wide window for a given aggregate guarantees a larger number of papers and relationships, and vice versa. Moreover, the existence of different collaboration and citation cultures in different scientific fields, and even in different institutions, is an obstacle to inter-aggregate comparison. Taken alone, the prestige and popularity indicators are scantly useful for evaluating something as multidimensional as an individual's research merit. Nonetheless, they do make a valuable contribution when combined with other measures. Tables 2-10 give a number of individual indicators, both structural and bibliometric, for the main authors in each of the departments analyzed to create a context as widely informative as possible. The data include author position, output (ndoc), number of observed citations, normalized impact factor (NIF) for output, nodal degree and betweenness centrality, the clustering coefficient and the new hybrid indicators, popularity and prestige. Most bibliometric indicators are formulated on the national scale. Data are gathered on system actors, analyses are conducted on national collaboration, or the numbers of citations obtained by the articles published in a country, region or subject area are tallied. Analyses involving indicators that examine national science systems with data disaggregated by centre or even department are less frequent but nonetheless necessary, for such analyses explore the internal dynamics of national systems in detail. Moreover, to achieve the objectives proposed, indicators must be designed to calibrate individuals' degree of collaboration.. In this context, the use of units of measure deriving from structural analysis acquires particular relevance. Nonetheless, despite their long history and internationally accepted use, network theory and analysis constitute an approach seldom used in Information Science theory or methodology (Otte & Rousseau, 2002) . Fortunately, this trend is changing and network theory and its analysis may signify a quantitative and qualitative leap in the representation and analysis of the structure of all manner of scientific domains, be they defined in terms of geography, subject matter or institution (Vargas-Quesada & Moya-Anegón, 2007) .. In this regard, scientific collaboration networks obtained from co-authorship data are particularly useful for analyses such as addressed here. The advantages of this approach are: (i) these networks describe the characteristics of "academic society" and can reveal the structure of scientific knowledge; (ii) they contain all the necessary components to be regarded to be small worlds: the mean inter nodal distance is small, the clustering coefficient is high and the degree distribution of its nodes fits a power-law distribution; (iii) they are constantly expanding due to the addition of new authors to the databases, ensuring the existence of new nodes that explain the dynamic evolution of this type of networks; (iv) the time when nodes and ties are added to the network, a determining factor for managing their dynamics, can be controlled.. Co-authorship networks are ideal for the intents and purposes of this study. Generated from bibliometric information, they are a source of new information in the form of structural indicators. Such structural information is valuable for the analysis of both the network as a whole and of each of its component actors. The following chapters contain a detailed description of the methodology used to formulate such social networks and introduce the hybrid indicators resulting from the combination of bibliometric and structural analysis.

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