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.

In this paper we propose task swapping networks for task reassignments by using task swappings in distributed systems. Some classes of task reassignments are achieved by using iterative local task swappings between software agents in distributed systems. We use group-theoretic methods to find a minimum-length sequence of adjacent task swappings needed from a source task assignment to a target task assignment in a task swapping network of several well-known topologies.

Nonparametric estimation of the conditional distribution of a response given high-dimensional features is a challenging problem. It is important to allow not only the mean but also the variance and shape of the response density to change flexibly with features, which are massive-dimensional. We propose a multiscale dictionary learning model, which expresses the conditional response density as a convex combination of dictionary densities, with the densities used and their weights dependent on the path through a tree decomposition of the feature space. A fast graph partitioning algorithm is applied to obtain the tree decomposition, with Bayesian methods then used to adaptively prune and average over different sub-trees in a soft probabilistic manner. The algorithm scales efficiently to approximately one million features. State of the art predictive performance is demonstrated for toy examples and two neuroscience applications including up to a million features.

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.

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.

Screening is the problem of finding a superset of the set of non-zero entries in an unknown p-dimensional vector \beta* given n noisy observations. Naturally, we want this superset to be as small as possible. We propose a novel framework for screening, which we refer to as Multiple Grouping (MuG), that groups variables, performs variable selection over the groups, and repeats this process multiple number of times to estimate a sequence of sets that contains the non-zero entries in \beta*. Screening is done by taking an intersection of all these estimated sets. The MuG framework can be used in conjunction with any group based variable selection algorithm. In the high-dimensional setting, where p >> n, we show that when MuG is used with the group Lasso estimator, screening can be consistently performed without using any tuning parameter. Our numerical simulations clearly show the merits of using the MuG framework in practice.

Reconstructing transcriptional regulatory networks is an important task in functional genomics. Data obtained from experiments that perturb genes by knockouts or RNA interference contain useful information for addressing this reconstruction problem. However, such data can be limited in size and/or are expensive to acquire. On the other hand, observational data of the organism in steady state (e.g. wild-type) are more readily available, but their informational content is inadequate for the task at hand. We develop a computational approach to appropriately utilize both data sources for estimating a regulatory network. The proposed approach is based on a three-step algorithm to estimate the underlying directed but cyclic network, that uses as input both perturbation screens and steady state gene expression data. In the first step, the algorithm determines causal orderings of the genes that are consistent with the perturbation data, by combining an exhaustive search method with a fast heuristic that in turn couples a Monte Carlo technique with a fast search algorithm. In the second step, for each obtained causal ordering, a regulatory network is estimated using a penalized likelihood based method, while in the third step a consensus network is constructed from the highest scored ones. Extensive computational experiments show that the algorithm performs well in reconstructing the underlying network and clearly outperforms competing approaches that rely only on a single data source. Further, it is established that the algorithm produces a consistent estimate of the regulatory network.

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.

An undirected graphical model is a joint probability distribution defined on an undirected graph G*, where the vertices in the graph index a collection of random variables and the edges encode conditional independence relationships among random variables. The undirected graphical model selection (UGMS) problem is to estimate the graph G* given observations drawn from the undirected graphical model. This paper proposes a framework for decomposing the UGMS problem into multiple subproblems over clusters and subsets of the separators in a junction tree. The junction tree is constructed using a graph that contains a superset of the edges in G*. We highlight three main properties of using junction trees for UGMS. First, different regularization parameters or different UGMS algorithms can be used to learn different parts of the graph. This is possible since the subproblems we identify can be solved independently of each other. Second, under certain conditions, a junction tree based UGMS algorithm can produce consistent results with fewer observations than the usual requirements of existing algorithms. Third, both our theoretical and experimental results show that the junction tree framework does a significantly better job at finding the weakest edges in a graph than existing methods. This property is a consequence of both the first and second properties. Finally, we note that our framework is independent of the choice of the UGMS algorithm and can be used as a wrapper around standard UGMS algorithms for more accurate graph estimation.

Finite mixtures of regression models offer a flexible framework for investigating heterogeneity in data with functional dependencies. These models can be conveniently used for unsupervised learning on data with clear regression relationships. We extend such models by imposing an eigen-decomposition on the multivariate error covariance matrix. By constraining parts of this decomposition, we obtain families of parsimonious mixtures of regressions and mixtures of regressions with concomitant variables. These families of models account for correlations between multiple responses. An expectation-maximization algorithm is presented for parameter estimation and performance is illustrated on simulated and real data.