In this paper we discuss four problems regarding Markov equivalences for subclasses of loopless mixed graphs. We classify these four problems as finding conditions for internal Markov equivalence, which is Markov equivalence within a subclass, for external Markov equivalence, which is Markov equivalence between subclasses, for representational Markov equivalence, which is the possibility of a graph from a subclass being Markov equivalent to a graph from another subclass, and finding algorithms to generate a graph from a certain subclass that is Markov equivalent to a given graph. We particularly focus on the class of maximal ancestral graphs and its subclasses, namely regression graphs, bidirected graphs, undirected graphs, and directed acyclic graphs, and present novel results for representational Markov equivalence and algorithms.

We introduce matrix and its block to the Dung's theory of argumentation framework. It is showed that each argumentation framework has a matrix representation, and the indirect attack relation and indirect defence relation can be characterized by computing the matrix. This provide a powerful mathematics way to determine the "controversial arguments" in an argumentation framework. Also, we introduce several kinds of blocks based on the matrix, and various prudent semantics of argumentation frameworks can all be determined by computing and comparing the matrices and their blocks which we have defined. In contrast with traditional method of directed graph, the matrix method has an excellent advantage: computability(even can be realized on computer easily). So, there is an intensive perspective to import the theory of matrix to the research of argumentation frameworks and its related areas.

Using an interactive theorem prover to reason about programs involves a sequence of interactions where the user challenges the theorem prover with conjectures. Invariably, many of the conjectures posed are in fact false, and users often spend considerable effort examining the theorem prover's output before realizing this. We present a synergistic integration of testing with theorem proving, implemented in the ACL2 Sedan (ACL2s), for automatically generating concrete counterexamples. Our method uses the full power of the theorem prover and associated libraries to simplify conjectures; this simplification can transform conjectures for which finding counterexamples is hard into conjectures where finding counterexamples is trivial. In fact, our approach even leads to better theorem proving, e.g. if testing shows that a generalization step leads to a false conjecture, we force the theorem prover to backtrack, allowing it to pursue more fruitful options that may yield a proof. The focus of the paper is on the engineering of a synergistic integration of testing with interactive theorem proving; this includes extending ACL2 with new functionality that we expect to be of general interest. We also discuss our experience in using ACL2s to teach freshman students how to reason about their programs.

We introduce a new regression framework, Gaussian process regression networks (GPRN), which combines the structural properties of Bayesian neural networks with the non-parametric flexibility of Gaussian processes. This model accommodates input dependent signal and noise correlations between multiple response variables, input dependent length-scales and amplitudes, and heavy-tailed predictive distributions. We derive both efficient Markov chain Monte Carlo and variational Bayes inference procedures for this model. We apply GPRN as a multiple output regression and multivariate volatility model, demonstrating substantially improved performance over eight popular multiple output (multi-task) Gaussian process models and three multivariate volatility models on benchmark datasets, including a 1000 dimensional gene expression dataset.

A pivotal problem in Bayesian nonparametrics is the construction of prior distributions on the space M(V) of probability measures on a given domain V. In principle, such distributions on the infinite-dimensional space M(V) can be constructed from their finite-dimensional marginals---the most prominent example being the construction of the Dirichlet process from finite-dimensional Dirichlet distributions. This approach is both intuitive and applicable to the construction of arbitrary distributions on M(V), but also hamstrung by a number of technical difficulties. We show how these difficulties can be resolved if the domain V is a Polish topological space, and give a representation theorem directly applicable to the construction of any probability distribution on M(V) whose first moment measure is well-defined. The proof draws on a projective limit theorem of Bochner, and on properties of set functions on Polish spaces to establish countable additivity of the resulting random probabilities.

This paper deals with the arrow of complexification of engineering. We claim that the complexification of engineering consists in (a) that shift throughout which engineering becomes a science; thus it ceases to be a (mere) praxis or profession; (b) becoming a science, engineering can be considered as one of the sciences of complexity. In reality, the complexification of engineering is the process by which engineering can be studied, achieved and understood in terms of knowledge, and not of goods and services any longer. Complex engineered systems and bio-inspired engineering are so far the two expressions of a complex engineering.

Clustering with fast algorithms large samples of high dimensional data is an important challenge in computational statistics. Borrowing ideas from MacQueen (1967) who introduced a sequential version of the $k$-means algorithm, a new class of recursive stochastic gradient algorithms designed for the $k$-medians loss criterion is proposed. By their recursive nature, these algorithms are very fast and are well adapted to deal with large samples of data that are allowed to arrive sequentially. It is proved that the stochastic gradient algorithm converges almost surely to the set of stationary points of the underlying loss criterion. A particular attention is paid to the averaged versions, which are known to have better performances, and a data-driven procedure that allows automatic selection of the value of the descent step is proposed. The performance of the averaged sequential estimator is compared on a simulation study, both in terms of computation speed and accuracy of the estimations, with more classical partitioning techniques such as $k$-means, trimmed $k$-means and PAM (partitioning around medoids). Finally, this new online clustering technique is illustrated on determining television audience profiles with a sample of more than 5000 individual television audiences measured every minute over a period of 24 hours.

The success of an agent mediated e-market system lies in the underlying reputation management system to improve the quality of services in an information asymmetric e-market. Reputation provides an operatable metric for establishing trustworthiness between mutually unknown online entities. Reputation systems encourage honest behaviour and discourage malicious behaviour of participating agents in the e-market. A dynamic reputation model would provide virtually instantaneous knowledge about the changing e-market environment and would utilise Internets' capacity for continuous interactivity for reputation computation. This paper proposes a dynamic reputation framework using reinforcement learning and fuzzy set theory that ensures judicious use of information sharing for inter-agent cooperation. This framework is sensitive to the changing parameters of e-market like the value of transaction and the varying experience of agents with the purpose of improving inbuilt defense mechanism of the reputation system against various attacks so that e-market reaches an equilibrium state and dishonest agents are weeded out of the market.

We introduce matrix and its block to the Dung's theory of argumentation frameworks. It is showed that each argumentation framework has a matrix representation, and the common extension-based semantics of argumentation framework can be characterized by blocks of matrix and their relations. In contrast with traditional method of directed graph, the matrix way has the advantage of computability. Therefore, it has an extensive perspective to bring the theory of matrix into the research of argumentation frameworks and related areas.

Standard compressive sensing results state that to exactly recover an s sparse signal in R^p, one requires O(s. log(p)) measurements. While this bound is extremely useful in practice, often real world signals are not only sparse, but also exhibit structure in the sparsity pattern. We focus on group-structured patterns in this paper. Under this model, groups of signal coefficients are active (or inactive) together. The groups are predefined, but the particular set of groups that are active (i.e., in the signal support) must be learned from measurements. We show that exploiting knowledge of groups can further reduce the number of measurements required for exact signal recovery, and derive universal bounds for the number of measurements needed. The bound is universal in the sense that it only depends on the number of groups under consideration, and not the particulars of the groups (e.g., compositions, sizes, extents, overlaps, etc.). Experiments show that our result holds for a variety of overlapping group configurations.