Approximating rank-width and clique-width quickly Rank-width was defined by Oum and Seymour [2006. Approximating clique-width and branchwidth. J. Combin. Theory Ser. B 96, 4, 514-528] to investigate clique-width. They constructed an algorithm that either outputs a rank-decomposition of width at most f (k) for some function f or confirms that rank-width is larger than k in time O(|V | 9 log |V |) for an input graph G = (V, E) and a fixed k. We develop three separate algorithms of this kind with faster running time. We construct an O(|V | 4 )-time algorithm with f (k) = 3k + 1 by constructing a subroutine for the previous algorithm; we avoid generic algorithms minimizing submodular functions used by Oum and Seymour. Another one is an O(|V | 3 )-time algorithm with f (k) = 24k by giving a reduction from graphs to binary matroids; then we use an approximation algorithm for matroid branch-width by Hliněný [2005. A parametrized algorithm for matroid branch-width. SIAM J. Comput. 35, 2, 259-277]. Finally we construct an O(|V | 3 )-time algorithm with f (k) = 3k − 1 by combining the ideas of above two cited papers.Corollary 1.1. Let k be a fixed positive integer. There is an O(|V (G)| 3 )-time algorithm that either outputs an (8 k −1)-expression of an input graph G or confirms that the clique-width of G is larger than k.Courcelle and Oum [2007] showed that, for each k, there is a formula of modulo-2 counting monadic second-order logic (C 2 MS logic) expressing that the rank-width is at most k. C 2 MS logic is an extension of first order logic, which allows set variables denoting sets of objects (in our case, sets of vertices) and the set predicate Graph complexity measures such as tree-width and branch-width are important for algorithmic purposes and for understanding the structure of families of graphs. One of them is the clique-width, defined by Courcelle and Olariu [2000] . We discuss its definition in the next section. Many NP-hard graph problems are solvable in polynomial time if a tree-like decomposition corresponding to clique-width, called. Paper. Running time f (k) Remark Oum and Seymour O(n 9 log n) 3k + 1 Works for any symmetric submodular [2006] functions with some conditions. Section 3 O(n 4 ) 3k + 1 Provides a subroutine for [Oum and Seymour 2006] a k-expression, is given as an input in addition to the adjacency list of the input graph. (In fact, the clique-width is the minimum k so that there is a k-expression of G.) In general, every graph problem expressible in monadic second-order logic with quantifications over vertices and vertex sets (MS 1 -logic) can be solved in linear time if the input graph is given with a k-expression ]. However, problems such as deciding whether the graph is Hamiltonian [Wanke 1994] and finding the chromatic number [Kobler and Rotics 2003] are not expressible in monadic second-order logic but have nevertheless polynomial-time algorithms on graphs of bounded clique-width if the input graph is given with a k-expression. Therefore we hope to have, for each fixed k, a polynomial-time algorithm to find a k-expression of an input graph if the input graph has clique-width at most k. This problem is still open when k > 3. Corneil et al. [2000] solved this problem when k = 3.. Instead, Oum and Seymour [2006] found an "approximation" algorithm that either outputs a (2 3k+2 − 1)-expression or confirms that the clique-width of G is larger than k. This can be combined with algorithms requiring a k-expression and therefore those algorithms no longer have to require a k-expression as an input to be polynomial-time algorithms. To obtain this approximation algorithm, they defined another graph width parameter, called the rank-width and showed that rank-width is at most clique-width and clique-width is at most 2 1+rank-width − 1. In addition, they showed a polynomial-time algorithm to find a rank-decomposition of width 3k + 1 or to confirm that the rank-width is larger than k. (Rank-width is defined as the minimum possible width of all rank-decompositions. We will discuss its definition in the next section.). In this paper we improve their results; we present three separate algorithms with faster running time that, for fixed k, output a rank-decomposition of width at most f (k) for some function f or confirm that the rank-width is larger than k. We summarize them in Table I .. The following is one of the consequences.

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


Optimal Indexes for Sparse Bit Vectors We consider the problem of supporting rank and select operations on a bit vector of length m with n 1-bits. The problem is considered in the succinct index model, where the bit vector is stored in "read-only" memory and an additional data structure, called the index is created during pre-processing to help answer the above queries. We give asymptotically optimal density-sensitive trade-offs, involving both m and n, that relate the size of the index to the number of accesses to the bit vector (and processing time) needed to answer the above queries. The results are particularly interesting for the case where n = o(m). We consider the problem of representing a bit vector S [1. .m] of length m, and supporting the following operations, for x ∈ {0, 1}:. -rank x (S, i) returns the number of occurrences of x in the prefix S [1. .i], -select x (S, i) returns the position of the ith occurrence of x in S.. Such a data structure is called a fully indexable dictionary (FID) [25] . We consider this problem in the context of systematic encodings, also known as the succinct index model. In this model, the bit vector S is not directly accessible to the data structure as "bits in memory": instead, when answering a query, the data structure can inspect parts of S through an access operation, which may be relatively expensive. In order to reduce the number of access operations, we augment S with an index, or a data structure that contains pre-computed information specific to S. To answer a query, the data structure performs a combination of access operations and "local" computations using the index as well as results of the access operations. We consider three measures of the performance of the data structure:. (i) the size of the index, also termed the redundancy, (ii) the number of access operations, (iii) the amount of "local" computation.. (We do not include preprocessing time, or access operations performed during preprocessing.) We provide new and tight density-sensitive lower and upper bounds for this problem, where the above parameters depend both upon the length m and the weight n of the bit vector, where the weight is the number of 1s in S. One can, without loss of generality, assume that n ≤ m/2; our primary interest is bit vectors of relatively small weight, i.e., the case n = o(m).. We also mention the non-systematic model, as our succinct indices will in fact consist of a number of non-systematic FIDs. In this model, the string S is explicitly given as input. The algorithm is responsible for storing S in an information-theoretic minimum amount of space, according to one of a number of possible measures of the "information content" of S. In this setting, the redundancy is the space usage of the data structure above and beyond the information-theoretic minimum amount needed to store S. Representing a bit vector to support rank x and select x is one of the most fundamental operations in the field of space-efficient data structures [24] . For example, solutions for this problem (such as FIDs) are used in text indexing [6, 13, 14] and representing semi-structured data [5, 9] . Considering systematic data structures for this problem was initiated by the desire to prove lower bounds on index size [8] . However, the algorithmic advantages of systematic data structures were recognized in the works of [7, 12, 26] , and the succinct index model was fully formalized (from an upper bound perspective) in [1] . By decoupling the representation of S from the set of operations that are being supported, it is noted in [1] that a succinct index offers many advantages including optimal compressibility of the data being indexed and easy integration of different indices over the same data. Furthermore, a succinct index can also be used in cases when the data being indexed is never explicitly stored, but computed on demand (for example, see [16] ). Finally, technological trends, in the form of increased use of remote data storage and service based computing [20] , have also made the case for studying systematic data structures stronger.. Finally, the case that we emphasize here, namely bit vectors of length m with weight o(m), are frequently encountered as the characteristic vectors of sparse sets that occur in practical applications, see e.g. [15, 19] . In addition, many space-efficient data structures often need to represent sequences that have few 1s by construction [9, 13] .

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Induction in Algebra: A First Case Study Abstract-Many a concrete theorem of abstract algebra admits a short and elegant proof by contradiction but with Zorn's Lemma (ZL). A few of these theorems have recently turned out to follow in a direct and elementary way from the Principle of Open Induction distinguished by Raoult. The ideal objects characteristic of any invocation of ZL are eliminated, and it is made possible to pass from classical to intuitionistic logic. If the theorem has finite input data, then a finite partial order carries the required instance of induction, which thus is constructively provable. A typical example is the well-known theorem "every nonconstant coefficient of an invertible polynomial is nilpotent". Many a concrete theorem of abstract algebra admits a short and elegant proof by contradiction but with Zorn's Lemma (ZL). A few of these theorems have recently turned out to follow in a direct and elementary way from the Principle of Open Induction (OI) distinguished by Raoult [1] . A proof of the latter kind may be extracted from a proof of the former sort. If the theorem has finite input data, then a finite partial order carries the required instance of induction, which thusunlike OI in general-is provable by fairly elementary means.. This approach is intended as a contribution to a partial realisation of Hilbert's Programme in algebra [2] , and was motivated by related work in infinite combinatorics [3] , [4] and by the rise of dynamical algebra [5] , [6] and formal topology [7] , [8] . The ideal objects characteristic of any invocation of ZL are eliminated, and it is made possible to work with finite methods only, e.g. to pass from classical to intuitionistic logic.. A typical example, which we study in this paper, is the wellknown theorem "every nonconstant coefficient of an invertible polynomial is nilpotent". This theorem can be reduced to the case, which in turn is readily settled, of polynomials over an integral domain. The reduction is usually done by a universal quantification over prime ideals, which are ideal objects in Hilbert's sense. One in fact invokes the contrapositive KL below of a variant of Krull's Lemma, which contrapositive can notably be deduced from ZL by a proof by contradiction.. Along this reduction proof via KL one virtually loses the computational information contained in the hypothesis of the theorem. In particular the proof fails to provide an algorithm for computing an exponent under which the nilpotent indeed vanishes. All this notwithstanding, we can extract a proof that is based on induction over a finite partial order; and the tree one can grow in an obvious way alongside the induction encodes an algorithm which computes the exponent.. This may be little surprising if one takes into account that the theorem has already seen constructive proofs before [9] . However, the point rather is that our constructive proof is gained from a given classical one, the one by reduction mentioned above. Further sources for this instance of extraction are a polynomial trick due to Gauß that has played a role in related situations [10] , [11] , as well as a direct deduction of KL from OI, which we thus do first.

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Robust airline schedule design in a dynamic scheduling environment Creative Commons Attribution-NonCommercial-NoDerivs License Detailed TermsIn the past decade, major airlines in the U.S. have moved from banked hub-and-spoke operations to de-banked hub-and-spoke operations to lower operating costs. In [1] , it is shown that dynamic airline scheduling, an approach that makes minor adjustments to flight schedules in the booking period by re-fleeting and re-timing flight legs, can significantly improve utilization of capacity and hence increase profit. In this paper, we develop robust schedule design models and algorithms to generate schedules that facilitate the application of dynamic scheduling in de-banked hub-and-spoke operations. Such schedule design approaches are robust in the sense that the schedules produced can more easily be manipulated in response to demand variability when embedded in a dynamic scheduling environment. In our robust schedule design model, we maximize the number of potentially connecting itineraries weighted by their respective revenues. We provide two equivalent formulations of the robust schedule design model and develop a decomposition-based solution approach involving a variable reduction technique and a variant of column generation. We demonstrate, through experiments using data from a major U.S. airline, that the schedule generated can improve profitability when dynamic scheduling is applied. It is also observed that the greater the demand variability, the more profit our robust schedules achieve when compared to existing ones. Since 2001, the airline industry in the U.S. has been negatively impacted by terrorist attacks, soaring fuel cost, stiff competition, and a weak economy. In order to reduce operating costs, major airlines have decided to de-bank their banked schedules in their hub-and-spoke networks. A hub-and-spoke network is one in which, one or more, typically large, stations (or airports) are designated as hub stations and flights are scheduled between hub stations and the other stations, namely, spoke stations. A banked schedule refers to the practice where a set of aircraft arrive at the hub station from spoke stations in a relatively short period of time, park at the gates to allow passengers to deplane and connect to the next flights in their itineraries, and finally depart the hub station in a relatively short period of time. The set of inbound flights and outbound flights operated by these aircraft form a bank at the hub station. Airlines often schedule a series of banks at the hub station to capture time-of-day demand. Because flight arrivals and departures occur in a relatively short period to allow shorter passenger connection times, banked schedules generate negative, sometimes serious, economic impacts including demand peaks for various resources and increased schedule vulnerability in bad weather. In contrast, in de-banked operations, flight arrivals and departures at the hub are smoothed, eliminating the demand peaks for resources and reducing operating costs dramatically. American [1] has shown that in a de-banked hub-and spoke network, dynamic scheduling, an approach that alters the flight schedule slightly according to observed actual demand and updated forecasts for future demand in the booking period, that is, the time from schedule publication until flight departure, can dramatically improve airline profitability. To date, two types of dynamic scheduling mechanisms (or schedule adjustment mechanisms) are studied in the literature: one is flight leg re-fleeting and the other is flight leg re-timing. Flight leg re-fleeting changes the fleet type assigned to a flight leg with higher than planned demand to a larger aircraft type, and the fleet type assigned to a flight leg with lower than planned demand to a smaller aircraft type while still maintaining aircraft flow balance. Representative literature describing flight leg re-fleeting can be found in [6] , [7] , and [8] . In flight leg re-timing, flight departure and arrival times of a flight leg are altered to create new connecting itineraries through the hub to serve markets with higher than expected demands. Later, [9, 10] present further experiments with dynamic scheduling under different scenarios, using data from a major European airline.. The success of dynamic scheduling not only relies on improved demand forecast quality, but also depends on the amount of re-optimization flexibility in the original schedule. One certainly can design a schedule where there is little or no room for dynamic scheduling. Hence, an important and challenging research question is how to design the flight schedule to maximize future dynamic scheduling impacts. In this paper, we address this question by designing robust schedule design models to produce schedules with improved capability to respond to demand uncertainty through dynamic scheduling. The result is that the schedules produced can better utilize the capacity and hence, capture more revenue.. Research aimed at improving schedule robustness in light of demand variability in a dynamic environment is rather limited. Focusing on models and solution approaches for the dynamic re-fleeting problem, [8] proposes to study the interaction between an original schedule and subsequent dynamic re-fleeting decisions. To our knowledge, the results of this study have not been reported to date. In a loosely related paper, [11] argues that suitably distributed aircraft capacity is critical to the successful implementation of dynamic re-fleeting procedures, and propose a scenario aggregation-based approach to determine an optimal fleet composition that facilitates dynamic re-fleeting.. Expanding on the observations of [6] that flight re-fleeting opportunities can be abundant in hub-and-spoke networks, we identify metrics to measure opportunities for flight re-timing. We focus on the magnitude of "infeasibility" for infeasible connecting itineraries, defined as connecting itineraries whose connection times are either less than the minimum required or more than the maximum allowed. When flights are re-timed in a dynamic scheduling environment to alter connecting times for itineraries, an infeasible connecting itinerary that violates the minimum (or maximum) connection time requirement by 5 minutes is easier to transform into a feasible itinerary than one that violates the minimum (or maximum) connection time requirement by 30 minutes.. In our schedule design model, we modify an existing debanked schedule and generate a flight schedule in which the number of feasible and slightly infeasible connecting itineraries weighted by their respective revenues is maximized, while meeting two major conditions: 1) there is no banking (or peaking) in aircraft departures and arrivals at the hub, and 2) key connecting itineraries through hubs are not disrupted in the modified de-banked schedule. We present two alternate formulations of the robust model, each with different computational properties. To solve our models, we develop a decompositionbased approach involving a variable reduction technique and a variant of column generation. The schedule generated by the robust model is then simulated in a dynamic scheduling environment to evaluate its performance relative to the existing debanked schedule.. The contributions of this paper include the following:. • We develop a novel approach to build flexibility into the original schedule to facilitate the application of dynamic scheduling;. • We present a mathematical model and two equivalent reformulations to achieve robust schedules. We explore their computational properties and devise new solution algorithms; and. • We demonstrate with data from a major U.S. airline that our approach is capable of generating schedules that when combined with dynamic scheduling outperform the existing schedules.. We organize the remainder of this paper as follows. In Section 2, we present two alternative formulations of our robust schedule design model. We detail our solution algorithm in Section 3. In Section 4, we report the computational and dynamic scheduling results for our case study. Finally, In Section 5, we conclude our discussion and outline possible future research directions.

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Higher order numerical methods for solving fractional differential equations Abstract In this paper we introduce higher order numerical methods for solving fractional differential equations. We use two approaches to this problem. The first approach is based on a direct discretisation of the fractional differential operator: we obtain a numerical method for solving a linear fractional differential equation with order 0 < α < 1. The order of convergence of the numerical method is O(h 3−α ). Our second approach is based on discretisation of the integral form of the fractional differential equation and we obtain a fractional Adams-type method for a nonlinear fractional differential equation of any order α > 0. The order of convergence of the numerical method is O(h 3 ) for α ≥ 1 and O(h 1+2α ) for 0 < α ≤ 1 for sufficiently smooth solutions. Numerical examples are given to show that the numerical results are consistent with the theoretical results. We consider numerical methods for solving the fractional differential equation where n = α is the smallest integer ≥ α. Existence and uniqueness of solutions for (1.1) -(1.2) have been studied, for example, in Podlubny [21] , Diethelm [8] , Diethelm and Ford [10] . Numerical methods for solving fractional differential equations have been considered by many authors and we mention here a few key contributions. Lubich [18] wrote the fractional differential equation in the form of an Abel-Volterra integral equation and used the convolution quadrature method to approximate the fractional integral and obtained approximate solutions of the fractional differential equation. Diethelm [7] wrote the fractional Riemann-Liouville derivative by using the Hadamard finite-part integral and approximated the integral by using a quadrature formula and obtained an implicit numerical algorithm for solving a linear fractional differential equation. Diethelm and Luchko [13] used the observation that a fractional differential equation has an exact solution, which can be expressed as a Mittag-Leffler type function. Then they used convolution quadrature and discretised operational calculus to produce an approximation to this Mittag-Leffler function. Blank [1] applied a collocation method to approximate the fractional differential equation. Podlubny [21] used the Grünwald and Letnikov method to approximate the fractional derivative and defined an implicit finite difference method for solving (1.1)-(1.2) and proved that the order of convergence is O(h), where h is the step size. Gorenflo [17] introduced a second order O(h 2 ) difference method for solving (1.1)-(1.2), but the conditions to achieve the desired accuracy are restrictive. In [11] , the authors approximated the integral in (1.5) by using a piecewise linear interpolation polynomial and introduced a fractional Adams-type predictor-corrector method for solving (1.1)-(1.2), proving that the order of convergence of the numerical method is min{2, 1 + α} for 0 < α ≤ 2 if C 0 D α t y ∈ C 2 [0, T ]. Deng [3] modified the method in [11] and introduced a new predictor-corrector method for solving (1.1)-(1.2) and the convergence order is proved to be min{2, 1 + 2α} for α ∈ (0, 1]. In [22] , the authors introduced a so-called Jacobi-predictor-corrector approach to solve (1.1)-(1.2) which is based on the polynomial interpolation and the Gauss-Lobatto quadrature with respect to some Jacobi-weight function and the computational cost is O(N), N = 1/h and any desired convergence order can be obtained. In [2] , a high order numerical method for solving (1.1)-(1.2) is obtained where a quadratic interpolation polynomial was used to approximate the integral. Ford, Morgado and Rebelo recently (see [16] ) used a nonpolynomial collocation method to achieve good convergence properties without assuming any smoothness of the solution. There are also several works that are related to the fixed memory principle and the nested memory concept for solving (1.1)-(1.2), see, e.g., [15] , [12] , [3] , [4] , [5] , etc.. Two approaches are used in this paper to develop new numerical methods for solving (1.1)-(1.2). The first approach is based on a direct discretisation of the fractional differential operator in the form proposed by Diethelm [6] . In [7] , Diethelm considered the following linear fractional differential equation, with 0 < α < 1, C 0 D α t y(t) = β y(t) + f (t), 0 ≤ t ≤ 1, (1.3) y(0) = y 0 , (1.4) where β < 0, f is a given function on the interval [0, 1]. Diethelm [7] used a firstdegree compound quadrature formula to approximate the Hadamard finite-part integral in the equivalent form of (1.3)-(1.4) and defined a numerical method for solving (1.3)-(1.4) and proved that the order of convergence of the numerical method is O(h 2−α ), 0 < α < 1. Here we approximate the Hadamard finite-part integral by using the second-degree compound quadrature formula and obtain an asymptotic expansion of the error for solving (1.3)-(1.4), which implies that the order of convergence of the numerical method is O(h 3−α ), 0 < α < 1. Moreover, a high order finite difference method (O(h 3−α ), 0 < α < 2) for approximating the Riemann-Liouville fractional derivative is given, which may be applied to construct high order numerical methods for solving time-space-fractional partial differential equations. Our second approach for solving the fractional differential equation (1.1)-(1.2) is based on the discretisation of the integral in the equivalent form of (1.1)-(1.2), see [11] . It is well-known that (1.1)-(1.2) is equivalent to the Volterra integral equation. We use piecewise quadratic interpolation polynomials to approximate the integral in (1.5) and introduce a high order fractional Adams method for solving (1.5) and prove that the order of convergence of the numerical method is min{3, 1 + 2α} for. This method has higher convergence order than the method in [3] . It is easier to implement our numerical algorithm compared with the method in [22] where the Jacobi-Gauss-Lobatto nodes must be calculated at each time level. Our method is simpler than the method in [2] in the sense that we are using a predictor-corrector method and therefore we do not need to solve the nonlinear system at each time level.. The paper is organised as follows: in Section 2, we consider how we can extend the Diethelm method for solving a linear fractional differential equation. In Section 3, we consider the fractional Adams method for solving a nonlinear fractional differential equation. Finally in Section 4, we consider some numerical examples.

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


Towards Security in Nano-communication: Challenges and Opportunities Incredible improvements in the field of nano-technologies have enabled nano-scale machines that promise new solutions for several applications in biomedical, industry and military fields. Some of these applications require or might exploit the potential advantages of communication and hence cooperative behavior of these nano-scale machines to achieve a common and challenging objective that exceeds the capabilities of a single device. Extensions to known wireless communication mechanisms as well as completely novel approaches have been investigated. Examples include RF radio communication in the terahertz band or molecular communication based on transmitter molecules. Yet, one question has not been considered so far and that is nano-communication security, i.e., how we can protect such systems from manipulation by malicious parties? Our objective in this paper is to provide some first insights into this new field and to highlight some of the open research challenges. We start from a discussion of classical security objectives and their relevance in nano-networking. Looking at the well-understood field of sensor networks, we derive requirements and investigate if and how available solutions can be applied to nano-communication. Our main observation is that, especially for molecular communication, existing security and cryptographic solutions might not be applicable. In this context, we coin the new term biochemical cryptography that might open a completely new research direction and lead to significant improvements in the field of molecular communication. We point out similarities with typical network architectures where they exist but also highlight completely new challenges where existing solutions do not apply. Nano-technology has made significant developments and progresses well into what has very recently believed being science fiction. The research field of nano-technology is becoming a key area in science based on multi-disciplinary collaborations among medicine, engineering, physics, biology, computer science, and others. It turned out that many of the envisioned applications for nano-technology require or might exploit the potential advantages of communication and hence cooperative behavior of these nano-scale machines to achieve a common objective that exceeds the capabilities of a single device.. At this point, the term nano-networks is defined as a set of nano-scale devices, i.e., nano-machines, communicating with each other and sharing information to realize a common objective. Nano-networks allow nano-machines to communicate and share any kind of information required by wide range of applications including biomedical engineering, biological and chemical defense technologies, and environmental monitoring.. • acoustic communication, e.g., ultrasonic communication that is based on what is currently successfully used for imaging methods,. • nano-mechanical communication that is based on physical contact between sender and receiver, and. • molecular communication that can further be categorized into short-range communication using calcium signaling, medium-range communication using molecular motors, and long-range communication using pheromones. Other options include, e.g., information transport using flagellated bacteria.. The motivation behind nano-machines and nano-scale communications and networks has also originated from and been inspired by biological systems and processes [1, 3] . In fact, nano-networks are significant and novel artifacts of bioinspiration in terms of both their architectural elements, e.g., nano-machines, and their principle communication mechanism, i.e., molecular communication [5] . Indeed, many biological entities in organisms behave like nanomachines as they have similar structures, i.e., cells, and similar interaction mechanism and vital processes, e.g., cellular signaling [6] . Within cells of living organisms, molecular motors such as dynein or myosin [7] realize intracellular communication through chemical energy transformation. Similarly, cells often communicate with each other through exchange of biochemical transmitters over the surface or the diffusion of soluble molecules that bind to specific receptor molecules on other cells [6, 8, 9] .. Depending on the application, a multitude of different nano-devices will be used. Thus, more than one communication channel needs to be considered for efficient information dissemination. Applications described by Akyildiz et al. [1] range from biomedical (e.g., drug delivery and glucose level monitoring) to industrial (e.g., food and water control) and environmental (e.g., air pollution control) services.. Assuming wide-spread use of nano-devices and communication, it is only logical to assume malicious actors trying to negatively affect nano-communication in the same way as it happens today in the Internet. Given the criticality of the envisioned application domains and the close embedding of nano-machines into our environment, food, or even our body, manipulation of such processes could have disastrous consequences, far beyond what an Internet attack would be able to achieve.. Examples of such attacks may include. • Disruption of medical applications, e.g. drug delivery, in order to harm or kill persons using specific substances or radio communication;. • Jamming communication in a denial-of-service attack to prevent alarms in industrial applications, e.g., when water is intoxicated;. • Modifying operation of nano-machines in environmental applications.. Security and robustness are therefore extremely relevant in this field. With this article, which extends earlier work presented in [10] , we aim to draw attention to security as a major challenge for nano-communication in a new era of Cyber Physical Systems (CPS). We will therefore evaluate the typical security objectives and solutions for applicability in nano-communication. The objective is not only to establish nano-communication security as a field of research but also to highlight some of the completely novel challenges. As a key paradigm, we coin the term biochemical cryptography as a primitive that may be used for efficiently securing biologically based information channels.. The key contributions of this paper can therefore be summarized as follows:. • We introduce nano-communication security as a new research field within the nano-domain (Section 3).. • We analyze attacker models and compare challenges that are known from sensor network security with those in nano-communication (Section 4). This includes a discussion of related problems from key management, cryptographic primitives, to access control and intrusion detection.. • We give some directions for future research towards security in nano-communication (Section 5). With this paper, we are directing attention to the security issues involved in the recent research trend towards nano-communication. All the benefits of enabling nanomachine communication can only be leveraged if this communication can be protected from malicious parties by ensuring confidentially, integrity, and availability. In this paper, we provided a first discussion of security of nanocommunication looking at threats and different forms of attackers. As we have pointed out, there are certain similarities with wireless sensor networks where security has intensively been investigated. Studying these similarities more deeply should be a first step towards secure nanocommunication. However, we also argue that for the most advanced bio-inspired nano-machines that use molecular communication, existing security solutions might not be applicable at all and completely new solutions have to be found. This creates a new field for security research that we termed biochemical cryptography where security is implemented based on molecular and biological processes. We envision that this approach can lead to a new form of high-speed and energy-preserving security mechanisms that can protect the nano-machines of the future from malicious attacks in a much better form than established cryptographic mechanisms could do.

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


Unique Sink Orientations of Grids We introduce unique sink orientations of grids as digraph models for many well-studied problems, including linear programming over products of simplices, generalized linear complementarity problems over P-matrices (PGLCP), and simple stochastic games.We investigate the combinatorial structure of such orientations and develop randomized algorithms for finding the sink. We show that the orientations arising from PGLCP satisfy the Holt-Klee condition known to hold for polytope digraphs, and we give the first expected linear-time algorithms for solving PGLCP with a fixed number of blocks.

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User acceptance of mobile TV services Mobile digital television technology facilitates broadcast TV on a mobile phone as well as interactive add-on services provided on top of the selected TV channel. In this paper we describe the results of a six-month field trial where 27 users were evaluating commercially available mobile TV services and 10 different pilot services. Mobile TV found a role in the everyday lives of the users as an extension to ordinary TV. The users appreciated easy and continuous access to TV contents. The results highlight that short usage situations typical to mobile TV use are hindering the adoption of new add-on services. The adoption can be supported by using content, appearance or functionality familiar from other media. The main problems with add-on services were related to knowing about the mere existence of these services and their contents as well as understanding the concept of services available only during a certain TV show. The mobile phone has evolved into a multipurpose platform for many different applications. Recent technical developments have enhanced the application possibilities with mobile TV. A mobile phone equipped with a DVB-H (Digital Video Broadcasting Handheld) receiver can receive real-time mobile TV broadcasts. Mobile broadcast TV requires dedicated broadcasting stations, and therefore mobile broadcast TV is currently available only locally, in major cities. Mobile TV integrates the major mass medium -TV -and the most personal medium -the mobile phone. This combination forms an interesting platform for interactive add-on services. The services can be provided connected to certain TV programmes, facilitating situationallyrelevant content. Users are familiar with the user interface of a mobile phone, so the add-on services could be easy to adopt.. The aim of the study described in this paper was to support the mobile TV developer community in developing successful mobile television services. We provided the developer companies with a common user panel and a common field test environment where service developers could put their pilot services to be evaluated in real everyday use and as a part of a mobile television service entity. We gathered user feedback both from individual services and the gradually developing service entity. The research focus was especially on interactive add-on services that have not been studied much thus far. The aim was to study user acceptance of the services to identify characteristics of successful services. In our study we were focused on the mobile service entity consisting of mobile TV channels and add-on services. During the half-year evaluation period, mobile TV usage was established with about half of the respondents using mobile TV at least once a week. Similar to earlier studies [1, 3, 12] , the main usage situations took place at home and when commuting. In our study, the panellists saw mobile TV as an extension to ordinary TV that facilitated continuing watching TV when leaving home and starting watching before coming home. The panellists thought the best feature of mobile TV was that it freed them to move instead of being bound in front of the primary TV. Mobile TV could be watched early in the morning and late in the evening without disturbing the rest of the family. Mobile TV was also a good tool to take a break or kill time when commuting. Setting up the device and getting to the desired channel took time, so usage sessions had to be sufficiently long, macro breaks as described by Cui et al. [1] .. The technical quality of sound and image in DVB-H broadcasting received very positive feedback. Even though the users were informed about the limited coverage of the DVB-H broadcast, coverage was mentioned first when asked about problems in use. The panellists did not like the uncertainty regarding where mobile TV was available and where not, especially as the coverage could change over time,. Similar to other studies [8, 11, 13, 16] , news was mentioned as the most interesting content, even if our panellists saw the value of mobile TV in entertainment rather than in useful information. The panellists saw news in a wide sense, including domestic news, international news, local news, sports news and entertainment news. The panellists would have liked to access more personal content such as information from their own sports club. Topical content that facilitated being the first to know e.g. local news was appreciated by the panellists. The requirements for topical and personal content have been identified in earlier studies as well [5, 12] . In addition to topical and personal content, our study indicates high interest in local content such as event information, local politics, information from authorities and traffic information. This kind of information was appreciated in local teletext, and the panellists said that they would like to have more, and even more local, information.. Familiar add-on services such as commercial teletext services were well accepted as the panellists liked the familiar content, familiar appearance and familiar interaction method. It was a positive surprise to the panellists that these services offered some better functionalities than conventional teletext. It has to be kept in mind that only four of our 27 panellists were familiar with mobile Internet, so web browsing was not a self-evident alternative to them. The good acceptance of teletext supports the finding by Hübel et al. [2] : "Anchors" from other media create a familiar environment where users can gradually adopt new features. The findings also support the findings by Oksman et al. [13] : people are often drawn to new services with the help of established brands and channels.. In our study the panellists were informed about add-on services to be evaluated. Still, the concept of interactive services available only during certain time slots as they were connected to certain TV or radio programmes was new and sometimes confusing to the panellists. Some panellists said that they did not find the services to be evaluated. In the final interviews, the panellists said that they did not like complex add-on services. Usage sessions were typically short breaks. During those short usage sessions the panellists did not have time or interest to become acquainted with complex functionalities or totally new services, and they therefore appreciated services whose functionality was simple or familiar from other media. Further studies will be needed to discover how users become used to the concept of mobile TV add-on services and how they could be supported in getting information about available services and their characteristics.. With the new TV channels and video-on-demand services the users were missing a better overview of the offerings. Even if using the service just to kill time, purposeless browsing was not how the panellists wanted to access the content. Gaining an overview of the content was much easier if the service was familiar from other media. The panellists said that familiar video content would have helped to assess e.g. the length of the video offerings. Here there also seems to be need for the familiar anchors proposed by Hübel et al. [2] .. Except for teletext services, the piloted interactive services were not found especially interesting. However, based on their experience with the pilot services, the panellists realized that addon services can be made easily available on mobile TV channels. The panellists said that "the services will certainly be easy to use for those who need them." When asked about suggestions for additional services, the users mentioned ways to affect the broadcast content, additional information on the ongoing programme, buying music as well as information on local attractions and events as potentially interesting content.. The users stated that paying per viewing was the preferred payment policy. Their opinions changed during the trial, as prior to the trial, half of them preferred a monthly fee. In the final interviews it became evident that mobile TV had taken its place in the everyday life of the panellists as one additional TV set. Thus the panellists thought that they should receive the content with the same payment policy as conventional TV.. Based on our study, mobile TV broadcasting content already seems to be interesting and attractive to the users. Mobile phones are personal devices that are typically carried all the time with the user. The devices are increasingly equipped with positioning devices providing location data to services. Users are also used to interacting with the device. This creates potential to provide the users with more topical, more local and more personal content than on other media, regarding both TV broadcast and add-on services. These kinds of services would change mobile TV from an additional TV set to a medium in its own right.

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


On the convergence of uncertain sequences Uncertain variables are measurable functions from uncertainty spaces to the set of real numbers. In this paper, a new kind of convergence, convergence uniformly almost surely (convergence uniformly a.s.), is presented. Then, relations between convergence uniformly almost surely and convergence almost surely (convergence a.s.), convergence in measure, convergence in mean, and convergence in distribution are discussed. This paper is mainly to discuss some limit theorems of uncertain variables based on continuous uncertain measure. Then some sufficient and necessary conditions for convergence of uncertain sequences are proposed. Furthermore, the relationships between them are as shown in Table 1:

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Knowledge organization landscape: A content analysis of introductory courses This paper presents the results of a study examining the subject content of knowledge organization courses taught in ALA-accredited LIS programs. Close to 2,000 course readings of introductory-level knowledge organization courses from 34 Library and Information Science (LIS) schools in the U.S. and Canada were analyzed and indexed. Results indicate that traditional bibliographic methods and practices remain at the core of knowledge organization courses. Findings also show that metadata has become a central component of course content and new topics from information architecture to markup languages and semantic web are becoming part of introductory-level knowledge organization education. Undeniably, knowledge organization lies at the very heart of library and information science. As Library and Information Science (LIS) rapidly evolves and the digital dimension becomes increasingly pervasive, the role and scope of the knowledge organization curriculum is also evolving. This paper presents the results of a study examining the subject content of knowledge organization courses taught in ALA-accredited LIS programs. The study aims at gaining an understanding of what content is covered in introductory-level knowledge organization courses in LIS schools. The overall goal is to help understand whether introductory knowledge organization education is responding to the evolving areas of expertise required of today's information professionals. The study is intended to offer elements of discussion on the design requirements of knowledge organization courses and, in general, on requisites knowledge organization education should possess to educate future LIS professionals to meet the demands of the twenty-first century workplace. 1 Correspondence to: M. Cristina Pattuelli This paper presents the results of a study examining subject content of knowledge organization courses taught in ALA-accredited LIS programs. Close to 2,000 course readings of introductory-level knowledge organization courses from 59 syllabi were analyzed and indexed. Results indicate that traditional bibliographic methods and practices remain at the core of knowledge organization courses. Findings also show that metadata has become a central component of course content. New topics from different traditions and practices have also made it in to the curriculum. It is not uncommon for topics like information architecture and semantic web to be present alongside subject cataloguing and bibliographic classification schemes. The breadth of the content scope with its array of new and emerging topics relevant to different types of information environments found in introductory-level knowledge organization education seems to reflect a field in evolution.. Knowledge organization education faces challenges similar to those that LIS education programs in general are facing: redefining its role and restructuring the curriculum to respond to a changing profession. Core competences need to evolve in response to the changes taking place in professional practices and the new areas of expertise needed for today's library and information work environment. This study offers a snapshot of the state of introductory knowledge organization education that provides context for a broader discussion of the characteristics that knowledge organization education needs to meet the challenges of a profession and a discipline in flux. Replication of this study over time would offer an opportunity to identify trends and monitor patterns of change. More research is needed to gain a deeper and more comprehensive view of knowledge organization education that should include the various instructional perspectives and approaches to knowledge organization teaching and learning and contribute to the "construction of knowledge organization as a field of learning" [35] . Results indicate that traditional bibliographic methods and systems are at the core of course content. These results are largely aligned with the literature that identifies traditional knowledge organization areas as the most prominent in knowledge organization courses. This study confirms the findings of previous studies that have also pointed out that a broad range of cataloguing topics are addressed in these courses. A rich bibliographic universe emerges encompassing different types of formats and standards as well as materials and practices. The topic of metadata appears to have increased its presence and depth beyond that reported by Hsieh-Yee [20] . Metadata makes up a considerable portion of course content with a total of 218 occurrences (11%), 174 occurrences (8.8%) of metadata (general) and 44 occurrences (2.2%) of metadata standards.. In general, the spectrum of topics addressed in course readings is far broader than traditional cataloguing classes. Topics from different fields and traditions are represented including both established and emerging knowledge organization systems such as thesauri (39 occurrences or 2%), folksonomies (35 occurrences or 1.8%) and ontologies (27 occurrences or 1.4%).. On the other end of the spectrum, a traditional knowledge organization topic such as abstracting appears to be infrequently represented with a rate of 0.4% and 8 occurrences confirming Morgan & Bawden's findings [30] . Conversely, the topic of indexing is well represented with 89 occurrences (4.5%) confirming its centrality in the field.. An interesting finding is the presence of the emerging topic personal information management represented by 9 occurrences (0.5%). The topic broadens the context of knowledge organization outside the traditional institutional boundaries.. The results show that a growing segment of course content is devoted to topics that have direct implications for electronic resources and digital libraries in particular, including metadata (11%), information retrieval (8.7%), and knowledge representation (0.9%). In fact, digital libraries are often addressed as a standalone topic (2%). Other subject areas potentially relevant to networked electronic environments are knowledge representation (3.6%), web 2.0 (2.8%), semantic web (2.4%), and information architecture (0.5%). The knowledge requirements identified in the literature review as essential to future digital library professionals seem to be well represented in the study's results, including metadata and markup languages, which were deemed to be among the most important and desired information technology knowledge for digital librarianship by Smith and Rasmussen [34] .. Issues of system design and usability are also represented prominently including information retrieval (5.4%), and information architecture (0.5%). The user perspective is another dimension increasingly addressed through various approaches including information seeking (1.6%), user behaviour (0.4%), and human-computer interaction (0.2%).. It is important to note that a substantial portion of course content is devoted to theoretical topics including information theory (4%), history of information organization (2.7%), and information organization theory (2.5%) contributing to a more balanced approach between theory and applications.. Course readings were also computed and a core of 15 most frequently assigned readings (those occurring more than 10 times) was identified. Table 3 Most frequently assigned course readings. As table 3 shows, the top 15 readings cover a wide spectrum of topics. The Anglo-American Cataloguing Rules (AACR2) manual is ranked highest with 40 occurrences while the textbook The Organization of Information by Arlene Taylor is the main source of the most frequently assigned readings.. Overall, results indicate a profile of organization courses grounded in traditional bibliographic practices, but inclusive of methods and techniques aimed at electronic resources (e.g., metadata, markup languages, encoding standards, etc.), and applicable to different types of information systems and environments (e.g., digital libraries and archives). This finding suggests that organization courses are starting to move beyond institutional boundaries toward a more unified idea of information systems and services.. The broad scope of the topics, although present with varied rates of frequency, appears to reflect the evolving state of a field that is growing more complex and multifaceted. Frequency of readings provided the primary metric for determining the content of knowledge organization courses. Figure 1 shows the extent of the subject areas and offers a bird's-eye view of the entire readings content space. As the chart indicates, traditional bibliographic subject areas are the most extensively covered. Bibliographic control represents the broadest area with a rate of 23% followed by subject access and vocabulary control (18%) and classification (14%). Metadata (11%) and information retrieval (9%) are the top fourth and fifth subject areas covered. Tabulation of article topics is presented in table 3. At a more granular level, scope and frequency of topics is illustrated in figure 2. The dominant topic is bibliographic formats and standards (181 occurrences or 9.2%). This topic is indeed representative of a variety of tools ranging from Anglo-American Cataloguing Rules (AACR2) to RDA (Resource Description and Access). This topic is covered even more extensively if we consider it together with the related topic data models (42 occurrences or 2.1%) which primarily refers to FRBR (Functional Requirements for Bibliographic Records). The complete list of topics is shown in table 4. A collection of syllabi of knowledge organization courses was conducted during spring 2008 for the population of all the 57 ALA-accredited LIS schools in North America and Canada. All programs offered at least one course on knowledge organization. Syllabi were acquired from websites when available, and through direct solicitation via email to instructors and school administrative offices. A total of 63 syllabi from 36 schools (63%) were collected. Four syllabi could not be included because class readings were not listed. As a consequence, two schools could not provide data for the study and were removed from consideration. The collection of syllabi proved to be more challenging than anticipated mostly due to the insufficient information found in several schools' websites that made it difficult to identify even basic course information including instructor's name and number of sections taught. As mentioned earlier, introductory-level organization courses are identified by a wide variety of titles that can be confusing and often require additional verification.. A content analysis of 59 syllabi was performed with the primary goal of determining the range and the frequency of topics addressed in the courses. A total of 1,992 class readings were identified of which 1,976 were used as sources of data. Sixteen lacked even minimal bibliographic information and were therefore deemed not useable for the study. Bibliographic data were entered in a spreadsheet, normalized, and mapped onto corresponding individual class sessions, course titles, and relative schools. Ranging from printed book chapters to online articles, the class readings served as units of analysis. Each reading was analyzed based on content and context (e.g., corresponding course sessions and neighbour readings within the session) and later indexed. One index term was assigned to each reading. Where a reading addressed multiple topics, the most general and comprehensive term was chosen. For example, a reading on thesauri, ontologies, and topic maps was indexed as controlled vocabularies. A total of 43 index terms were applied [See Table 1 ]. Later, index terms were grouped in 15 general categories to assist in the identification of subject areas [See Table 2 ]. The indexing process was inductive and iterative. To enforce consistency, each reading was indexed by two coders independently. Discrepancies were reconciled through iterative negotiation and terms were normalized, whenever possible, using the ASIST thesaurus [33] . Table 2 List of Subject Areas

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Analyzing Midpoint Subdivision Midpoint subdivision generalizes the Lane-Riesenfeld algorithm for uniform tensor product splines and can also be applied to non regular meshes. For example, midpoint subdivision of degree 2 is a specific Doo-Sabin algorithm and midpoint subdivision of degree 3 is a specific Catmull-Clark algorithm. In 2001, Zorin and Schröder were able to prove C 1 -continuity for midpoint subdivision surfaces analytically up to degree 9. Here, we develop general analysis tools to show that the limiting surfaces under midpoint subdivision of any degree ≥ 2 are C 1 -continuous at their extraordinary points. The midpoint subdivision schemes form a class of subdivision schemes for arbitrary two-manifold meshes. The midpoint subdivision scheme of degree n ∈ N is given by the operator. where R and A are the refinement and averaging operators, respectively. The midpoint subdivision schemes of degree 2, 3 and 4 are specific instances of the well-known Doo-Sabin, Catmull-Clark and Qu algorithms [DS78, CC78, Qu90] .. The valence m of a vertex or a face is the number of incident or surrounding edges. An inner vertex or face is called regular if m = 4 and irregular or extraordinary otherwise. After subdividing a mesh by M n , the mesh has no irregular vertices or faces if n is even or odd, respectively. Subdividing the mesh further does not increase the number of extraordinary vertices and faces and extraordinary elements become more and more isolated.. Therefore, and since midpoint subdivision generalizes the Lane-Riesenfeld algorithm, midpoint subdivision surfaces are spline surfaces except for finitely many extraordinary points. At these points, the smoothness analysis is complicated. Using Reif's C 1 -criterion [Rei95, Theorem 3.6] and interval arithmetic, Zorin and Schröder [ZS01] showed C 1 -smoothness for degrees n = 2, . . . , 9.. Naturally, this numeric approach is limited to a finite number of degrees. Here, we develop a geometric framework that allows us to prove C 1 -continuity of midpoint subdivision surfaces of all degrees. Moreover, we think that this framework may conceptually be useful for other classes of (simple) subdivision schemes and that it provides -for the first time -an analysis toolbox for a complete class of subdivision schemes.. In Section 2, we discuss the basic topological dependencies between the vertices of a mesh before and after a subdivision step. These dependencies correspond to a certain block structure of the subdivision matrix with a block possessing a strictly positive power. This particular block represents the subdivision operator restricted to a certain central part of the mesh, which we call a core mesh. In Section 3, definitions and properties of symmetric meshes and symmetric subdivision schemes are introduced. For symmetric meshes, in Section 4, we define a partial order based on particular coordinate systems. In Section 5, we show that subdividing specific symmetric grid-like core meshes results, in the limit, under normalization in a symmetric mesh whose regular vertices do not coincide with the center and show that it is an eigenvector of the subdivision matrix restricted to core meshes. In Section 6, we use the partial ordering introduced in Section 4 to compare the eigenvector constructed in Section 5 to any other eigenvector and show its subdominance. Hence, in Sections 5 and 6, we restrict the analysis to core meshes for which the subdivision matrix has a strictly positive power. Then, in Section 7, we extend the analysis to larger meshes using the particular block structure of the subdivision matrix. In Section 8, we show that subdominant eigenvectors define a regular surjective characteristic map, which concludes the proof that generic midpoint subdivision surfaces of any degree n(≥ 2) are C 1 -continuous. This result is stated in Theorem (8.4) and the entire paper consists of its proof which is composed of 19 lemmata, theorems and corollaries whose ramified interdependencies are depicted in Figure (1.2) .

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The unscented filter as an alternative to the EKF for nonlinear state estimation: a simulation case study The Kalman filter has been widely used for estimation and tracking of linear systems since its formulation in 1960 due to its simplicity and robustness. In many chemical engineering applications the extended Kalman filter (EKF) is often used to deal with certain classes of nonlinear systems. In spite of that, designing an EKF for highly nonlinear processes is not a trivial task, particularly those involving highly exothermic reactions. In this work we compared the performance of a new technique, the unscented filter, with that of the extended Kalman filter. The unscented filter produced better results without performing potentially ill-conditioned numerical calculations and linearly approximating the evolution of the state vector covariance. In many engineering areas the extended Kalman filter (EKF) is widely used for state estimation and tracking. Numerous successful applications of this tool have been reported in the literature. Nonetheless, when one applies an EKF to a complex system, a few implementation and numerical problems may arise. One of them is the computation of the state transition matrix which calls for calculation of the Jacobian matrix and its matrix exponential. Besides being a computationally expensive operation, there is no universal and robust numerical way to carry it out (Moler & Van Loan, 1978) .. Moreover, the linearization at each time step can introduce large errors and even cause divergence of the filter (Wan & van der Merwe, 2000) . These concerns are especially acute in complex industrial set-ups (Wilson, Agarwal, & Rippin, 1998) . Although higher order Kalman filters exist, they are more difficult to implement and prone to instability. Grewal and Andrews (1993) introduced measures to improve numerical stability of the EKF while Mostov (1996) proposed a way to stabilize higher order EKF. In some applications (Chang & Hwang, 1998a,b) , however, when suboptimal filtering is justified, the original EKF algorithm can be modified in order to make it more robust in a nonlinear dynamic environment.. In his work, Schei (1997) proposed an improvement for the EKF in which using a central difference method it is possible to perturb the system and determine covariances without explicit calculation of the Jacobian. Julier, Uhlmann, and Durrant-Whyte (1995) argued that with a fixed number of parameters it should be easier to approximate a Gaussian distribution than to approximate an arbitrary nonlinear function and introduced a new generalization of the Kalman filter, the unscented filter (UF), which permits the direct propagation of means and covariances through the nonlinear system equations. The main difference between the UF and the method developed by Schei (1997) is that the unscented filter approximates the underlying distribution.. In a striking review of new contributions in the field of state estimation, Nørgaard, Poulsen, and Ravn (2000) compared the two above mentioned filters and proposed a third formulation whose performance is argued to be superior to the filter described in (Schei, 1997) and similar to the one of the UF.. Despite the fact that these techniques apparently surpass the EKF, there have been no references in the literature to their application in the field of chemical engineering. In this work we apply the extended Kalman filter and the unscented filter to a highly nonlinear simulated CSTR in a system state estimation framework and compare their performance. In this paper, we have assessed the use of the unscented filter in a typical chemical engineering application and found out that this estimation tool is able to provide superior accuracy in comparison to the ones produced by the EKF. The absence of model linearization step and, consequently, errors induced by it, allows the UF to be used in a wider range of operating conditions as well as in situations where the differentiability of the system model cannot be assured. Furthermore, the derivative free design of the UF makes its implementation significantly simpler than the one of the EKF.

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