Discovery of communities in complex networks is a fundamental data analysis task in various domains. Generative models are a promising class of techniques for identifying modular properties from networks, which has been actively discussed recently. However, most of them cannot preserve the degree sequence of networks, which will distort the community detection results. Rather than using a blockmodel as most current works do, here we generalize a configuration model, namely, a null model of modularity, to solve this problem. Towards decomposing and combining sub-graphs according to the soft community memberships, our model incorporates the ability to describe community structures, something the original model does not have. Also, it has the property, as with the original model, that it fixes the expected degree sequence to be the same as that of the observed network. We combine both the community property and degree sequence preserving into a single unified model, which gives better community results compared with other models. Thereafter, we learn the model using a technique of nonnegative matrix factorization and determine the number of communities by applying consensus clustering. We test this approach both on synthetic benchmarks and on real-world networks, and compare it with two similar methods. The experimental results demonstrate the superior performance of our method over competing methods in detecting both disjoint and overlapping communities.

The evolution from non-deterministic to weighted automata represents a shift from qual- itative to quantitative methods in computer science. The trend calls for a language able to reconcile quantitative reasoning with formal logic and set theory, which have for so many years supported qualitative reasoning. Such a lingua franca should be typed, poly- morphic, diagrammatic, calculational and easy to blend with conventional notation.
This paper puts forward typed linear algebra as a candidate notation for such a unifying role. This notation, which emerges from regarding matrices as morphisms of suitable categories, is put at work in describing weighted automata as coalgebras in such categories.
Some attention is paid to the interface between the index-free (categorial) language of matrix algebra and the corresponding index-wise, set-theoretic notation.

Coalgebras provide a uniform framework for studying dynamical systems, including several types of automata. In this article, we make use of the coalgebraic view on systems to investigate, in a uniform way, under which conditions calculi that are sound and complete with respect to behavioral equivalence can be extended to a coarser coalgebraic language equivalence, which arises from a generalized powerset construction that determinizes coalgebras. We show that soundness and completeness are established by proving that expressions modulo axioms of a calculus form the rational fixpoint of the given type functor. Our main result is that the rational fixpoint of the functor FT, where T is a monad describing the branching of the systems (e.g., non-determinism, weights, probability, etc.), has as a quotient the rational fixpoint of the determinized type functor F, a lifting of F to the category of T-algebras. We apply our framework to the concrete example of weighted automata, for which we present a new sound and complete calculus for weighted language equivalence. As a special case, we obtain nondeterministic automata in which we recover Rabinovich’s sound and complete calculus for language equivalence.

One-person solitaire-like games are explored with a view to using them in teaching algorithmic problem solving. The key to understanding solutions to such games is the identification of invariant properties of polynomial arithmetic. We demonstrate this via three case studies: solitaire itself, tiling problems and a novel class of one-person games. The known classification of states of the game of (peg) solitaire into 16 equivalence classes is used to introduce the relevance of polynomial arithmetic. Then we give a novel algebraic formulation of the solution to a class of tiling problems. Finally, we introduce an infinite class of challenging one-person games, which we call “replacement-set games”, inspired by earlier work by Chen and Backhouse on the relation between cyclotomic polynomials and generalisations of the seven-trees-in-one type isomorphism. We present an algorithm to solve arbitrary instances of replacement-set games and we show various ways of constructing infinite (solvable) classes of replacement-set games.

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Gossip, or epidemic, protocols have emerged as a highly scalable and resilient approach to implement several application level services such as reliable multicast, data aggregation, publish-subscribe, among others. All these protocols organize nodes in an unstructured random overlay network. In many cases, it is interesting to bias the random overlay in order to optimize some efficiency criteria, for instance, to reduce the stretch of the overlay routing. In this paper we propose X-BOT, a new protocol that allows to bias the topology of an unstructured gossip overlay network. X-BOT is completely decentralized and, unlike previous approaches, preserves several key properties of the original (non-biased) overlay (most notably, the node degree and consequently, the overlay connectivity). Experimental results show that X-BOT can generate more efficient overlays than previous approaches.

Problem statements often resort to superlatives such as in eg. “. . . the smallest such number”, “. . . the best approximation”, “. . . the longest such list” which lead to specifications made of two parts: one defining a broad class of solutions (the easy part) and the other requesting the optimal such solution (the hard part).
This paper introduces a binary relational combinator which mirrors this linguistic structure and exploits its potential for calculating programs by optimization. This applies in particular to specifications written in the form of Galois connections, in which one of the adjoints delivers the optimal solution being sought.
The framework encompasses re-factoring of results previously developed by Bird and de Moor for greedy and dynamic programming, in a way which makes them less technically involved and therefore easier to understand and play with.

In this paper we propose a framework for defining and discovering optimal association rules involving a numerical attribute A in the consequent. The consequent has the form of interval conditions A, A≥ x or A ∈ I where I is an interval or a set of intervals of the form [x_l,x_u. The optimality is with respect to leverage, one well known association rule interest measure. The generated rules are called Maximal Leverage Rules MLR and are generated from Distribution Rules. The principle for finding the MLR is related to the Kolmogorov-Smirnov goodness of fit statistical test. We propose different methods for MLR generation, taking into account leverage optimallity and readability. We theoretically demonstrate the optimality of the main exact methods, and measure the leverage loss of approximate methods. We show empirically that the discovery process is scalable.

This paper revisits the idea of slicing programs based on their axiomatic semantics, rather than using criteria based on control/data dependencies. We show how the forward propagation of preconditions and the backward propagation of post conditions can be combined in a new slicing algorithm that is more precise than the existing specification-based algorithms. The algorithm is based on (i) a precise test for removable statements, and (ii) the construction of a slice graph, a program control flow graph extended with semantic labels. It improves on previous approaches in two aspects: it does not fail to identify removable commands; and it produces the smallest possible slice that can be obtained (in a sense that will be made precise). The paper also reviews in detail, through examples, the ideas behind the use of preconditions and post conditions for slicing programs.

Aggregation of data values plays an important role on distributed computations, in particular, over peer-to-peer and sensor networks, as it can provide a summary of some global system property and direct the actions of self-adaptive distributed algorithms. Examples include using estimates of the network size to dimension distributed hash tables or estimates of the average system load to direct load balancing. Distributed aggregation using nonidempotent functions, like sums, is not trivial as it is not easy to prevent a given value from being accounted for multiple times; this is especially the case if no centralized algorithms or global identifiers can be used. This paper introduces Extrema Propagation, a probabilistic technique for distributed estimation of the sum of positive real numbers. The technique relies on the exchange of duplicate insensitive messages and can be applied in flood and/or epidemic settings, where multipath routing occurs; it is tolerant of message loss; it is fast, as the number of message exchange steps can be made just slightly above the theoretical minimum; and it is fully distributed, with no single point of failure and the result produced at every node.

Existing bidirectional languages are either state-based or operation-based, depending on whether they represent updates as mere states or as sequences of edit operations.In-between both worlds are delta-based frameworks, where updates are represented using alignment relationships between states.In this paper, we formalize delta lenses over inductive types using dependent type theory and develop a point-free delta lens language with an explicit separation of shape and data.In contrast with the already known issue of data alignment, we identify the new problem of shape alignment and solve it by lifting standard recursion patterns such as folds and unfolds to delta lenses that use alignment to infer meaningful shape updates.

Recent approaches to component-based software engineering employ coordinat- ing connectors to compose components into software systems. For maximum flexibility and reuse, such connectors can themselves be composed, resulting in an expressive calculus of connectors whose semantics encompasses complex combinations of synchronisation, mutual exclusion, non-deterministic choice and state-dependent behaviour. A more expressive notion of connector includes also context-dependent behaviour, namely, whenever the choices a connector can take change non-monotonically as the context, given by the pending activity on its ports, changes. Context dependency can express notions of priority and inhibition. Capturing context-dependent behaviour in formal models is non-trivial, as it is unclear how to propagate context information through composition. In this paper we present an intuitive automata-based formal model of context- dependent connectors, and argue that it is superior to previous attempts at such a model for the coordination language Reo.