We study an economic decision problem where the actors are two firms and the Antitrust Authority whose main task is to monitor and prevent firms' potential anti-competitive behaviour and its effect on the market. The Antitrust Authority's decision process is modelled using a Bayesian network where both the relational structure and the parameters of the model are estimated from a data set provided by the Authority itself. A number of economic variables that influence this decision process are also included in the model. We analyse how monitoring by the Antitrust Authority affects firms' strategies about cooperation. Firms' strategies are modelled as a repeated prisoner's dilemma using object-oriented Bayesian networks. We show how the integration of firms' decision process and external market information can be modelled in this way. Various decision scenarios and strategies are illustrated.

Nonnegative Matrix Factorization (NMF) has been a popular representation method for pattern classification problem. It tries to decompose a nonnegative matrix of data samples as the product of a nonnegative basic matrix and a nonnegative coefficient matrix, and the coefficient matrix is used as the new representation. However, traditional NMF methods ignore the class labels of the data samples. In this paper, we proposed a supervised novel NMF algorithm to improve the discriminative ability of the new representation. Using the class labels, we separate all the data sample pairs into within-class pairs and between-class pairs. To improve the discriminate ability of the new NMF representations, we hope that the maximum distance of the within-class pairs in the new NMF space could be minimized, while the minimum distance of the between-class pairs pairs could be maximized. With this criterion, we construct an objective function and optimize it with regard to basic and coefficient matrices and slack variables alternatively, resulting in a iterative algorithm.

A distributed system is defined as a collection of independent computers or processors that are connected by an arbitrary interconnection network [36, 42]. The objective of a task assignment [36, 39] in a distributed system is to find an optimal or suboptimal assignment of tasks to processors (or agents), while satisfying temporal and spatial constraints imposed on the system. A task assignment is either preemptive or non-preemptive [32]. If a task assignment is preemptive, a task reassignment is allowed in such a way that tasks are transferred between processors (or agents) during their execution for improving the system performance [32, 37]. Recent advances in software agent technology [25, 27, 34] in distributed systems allow software entities to observe their environment, and cooperate with other entities if necessary to accomplish their goals. Task migration between software agents intends to improve the system throughput in a distributed system in which the loads incurred by tasks vary over time [27]. A task reassignment can be achieved by iterative local task swappings, where a task swapping involves task migrations between a pair of agents as a method of local task reassignment [7]. A subclass of task assignment (or reassignment) problems involves an equal number of tasks and agents, finding a bijective task assignment between tasks and agents in such a way that the total task assignment (or reassignment) benefit is maximized [45]. Those bijective task assignment problems and their variants appear in a wide variety of areas in computer science and mathematics [5, 6, 44, 45].

In this paper we discuss various problems, associated to temporal phenomena. These problems include persistence and change, the integration of objects and processes, and truth-makers for temporal propositions. We propose an approach which interprets persistence as a phenomenon emanating from the activity of the mind, and which, additionally, postulates that persistence, finally, rests on personal identity. The General Formal Ontology (GFO) is a top level ontology being developed at the University of Leipzig. Top level ontologies can be roughly divided into 3D-ontologies, and 4D-ontologies. GFO is the only top level ontology, used in applications, which is a 4D-ontology admitting additionally 3D objects. Objects and processes are integrated in a natural way.

Massive datasets are becoming an ubiquitous byproduct of modern scientific and industrial applications. These data present statistical and computational challenges because many previously developed analysis approaches do not scaleup sufficiently. Challenges arise because of the ultra high-dimensionality and relatively low sample size. Parsimonious models for such big data assume that the density in the ambient space concentrates around a lower-dimensional (possibly nonlinear) subspace. A plethora of methods are emerging to estimate such lower-dimensional subspaces [25, 2]. 1 We are interested in using such lower-dimensional embeddings to obtain estimates of the conditional distribution of some target variable(s). This conditional density estimation setting arises in a number of important application areas, including neuroscience, genetics, and video processing. For example, one might desire automated estimation of a predictive density for a neurologic phenotype of interest, such as intelligence, on the basis of available data for a patient including neuroimaging.

Linear Dynamical System (LDS) is an elegant mathematical framework for modeling and learning multivariate time series. However, in general, it is difficult to set the dimension of its hidden state space. A small number of hidden states may not be able to model the complexities of a time series, while a large number of hidden states can lead to overfitting. In this paper, we study methods that impose an $\ell_1$ regularization on the transition matrix of an LDS model to alleviate the problem of choosing the optimal number of hidden states. We incorporate a generalized gradient descent method into the Maximum a Posteriori (MAP) framework and use Expectation Maximization (EM) to iteratively achieve sparsity on the transition matrix of an LDS model. We show that our Sparse Linear Dynamical System (SLDS) improves the predictive performance when compared to ordinary LDS on a multivariate clinical time series dataset.

High-dimensional, large-sample astrophysical databases of galaxy clusters, such as the Chandra Deep Field South COMBO-17 database, provide measurements on many variables for thousands of galaxies and a range of redshifts. Current understanding of galaxy formation and evolution rests sensitively on relationships between different astrophysical variables; hence an ability to detect and verify associations or correlations between variables is important in astrophysical research. In this paper, we apply a recently defined statistical measure called the distance correlation coefficient which can be used to identify new associations and correlations between astrophysical variables. The distance correlation coefficient applies to variables of any dimension; it can be used to determine smaller sets of variables that provide equivalent astrophysical information; it is zero only when variables are independent; and it is capable of detecting nonlinear associations that are undetectable by the classical Pearson correlation coefficient. Hence, the distance correlation coefficient provides more information than the Pearson coefficient. We analyze numerous pairs of variables in the COMBO-17 database with the distance correlation method and with the maximal information coefficient. We show that the Pearson coefficient can be estimated with higher accuracy from the corresponding distance correlation coefficient than from the maximal information coefficient. For given values of the Pearson coefficient, the distance correlation method has a greater ability than the maximal information coefficient to resolve astrophysical data into highly concentrated V-shapes, which enhances classification and pattern identification. These results are observed over a range of redshifts beyond the local universe and for galaxies from elliptical to spiral.

Model-based clustering has become increasingly popular during the last decade. Parametric mixture models are used in model-based clustering; however, such models generally do not exploit covariates. Incorporating a regression structure can yield important insight when there is a regression relationship between some variables. Methodologies that deal with such data include finite mixtures of regressions (FMR; [7, 13]) and finite mixtures of regressions with concomitant variables (FMRC; [22]), supported by the popular flexmix package [13]. Multivariate correlated responses can be naturally integrated into such models. However, flexmix currently does not account for correlated response variables for both FMR and FMRC. FMR models that deal with correlated response variables have recently been proposed [19, 9].

Recently, deep architectures, such as recurrent and recursive neural networks have been successfully applied to various natural language processing tasks. Inspired by bidirectional recurrent neural networks which use representations that summarize the past and future around an instance, we propose a novel architecture that aims to capture the structural information around an input, and use it to label instances. We apply our method to the task of opinion expression extraction, where we employ the binary parse tree of a sentence as the structure, and word vector representations as the initial representation of a single token. We conduct preliminary experiments to investigate its performance and compare it to the sequential approach.

Recent research in off-the-grid compressed sensing (CS) has demonstrated that, under certain conditions, one can successfully recover a spectrally sparse signal from a few time-domain samples even though the dictionary is continuous. In particular, atomic norm minimization was proposed in \cite{tang2012csotg} to recover $1$-dimensional spectrally sparse signal. However, in spite of existing research efforts \cite{chi2013compressive}, it was still an open problem how to formulate an equivalent positive semidefinite program for atomic norm minimization in recovering signals with $d$-dimensional ($d\geq 2$) off-the-grid frequencies. In this paper, we settle this problem by proposing equivalent semidefinite programming formulations of atomic norm minimization to recover signals with $d$-dimensional ($d\geq 2$) off-the-grid frequencies.