Motivation: This paper introduces the software EMMIX-GENE that has been developed for the specific purpose of a model-based approach to the clustering of microarray expression data, in particular, of tissue samples on a very large number of genes. The latter is a nonstandard problem in parametric cluster analysis because the dimension of the feature space (the number of genes) is typically much greater than the number of tissues. A feasible approach is provided by first selecting a subset of the genes relevant for the clustering of the tissue samples by fitting mixtures of tdistributions to rank the genes in order of increasing size of the likelihood ratio statistic for the test of one versus two components in the mixture model. The imposition of a threshold on the likelihood ratio statistic used in conjunction with a threshold on the size of a cluster allows the selection of a relevant set of genes. However, even this reduced set of genes will usually be too large for a normal mixture model to be fitted directly to the tissues, and so the use of mixtures of factor analyzers is exploited to reduce effectively the dimension of the feature space of genes. Results: The usefulness of the EMMIX-GENE approach for the clustering of tissue samples is demonstrated on two well-known data sets on colon and leukaemia tissues. For both data sets, relevant subsets of the genes are able to be selected that reveal interesting clusterings of the tissues that are either consistent with the external classification of the tissues or with background and biological knowledge of these sets. Availability: EMMIX-GENE is available at http://www.maths.uq.edu.au/~gjm/emmix-gene/ Contact: gjm@maths.uq.edu.au

This paper proposes a peer-to-peer (P2P) energy trading scheme that can help a centralized power system to reduce the total electricity demand of its customers at the peak hour. To do so, a cooperative Stackelberg game is formulated, in which the centralized power system acts as the leader that needs to decide on a price at the peak demand period to incentivize prosumers to not seek any energy from it. The prosumers, on the other hand, act as followers and respond to the leader’s decision by forming suitable coalitions with neighboring prosumers in order to participate in P2P energy trading to meet their energy demand. The properties of the proposed Stackelberg game are studied. It is shown that the game has a unique and stable Stackelberg equilibrium, as a result of the stability of prosumers’ coalitions. At the equilibrium, the leader chooses its strategy using a derived closed-form expression, while the prosumers choose their equilibrium coalition structure. An algorithm is proposed that enables the centralized power system and the prosumers to reach the equilibrium solution. Numerical case studies demonstrate the beneficial properties of the proposed scheme.

This paper explores the feasibility of social cooperation between prosumers within an energy network in establishing their sustainable participation in peer-to-peer (P2P) energy trading. In particular, a canonical coalition game (CCG) is utilized to propose a P2P energy trading scheme, in which a set of participating prosumers form a coalition group to trade their energy, if there is any, with one another. By exploring the concept of the core of the designed CCG framework, the mid-market rate is utilized as a pricing mechanism of the proposed P2P trading to confirm the stability of the coalition as well as to guarantee the benefit to the prosumers for forming the social coalition. The paper further introduces the motivational psychology models that are relevant to the proposed P2P scheme and it is shown that the outcomes of the proposed P2P energy trading scheme satisfy the discussed models. Consequently, it is proven that the proposed scheme is consumer-centric and has the potential to corroborate sustainable prosumer participation in P2P energy trading. Finally, some numerical examples are provided to demonstrate the beneficial properties of the proposed scheme.

Motivation: An important problem in microarray experiments is the detection of genes that are differentially expressed in a given number of classes. We provide a straightforward and easily implemented method for estimating the posterior probability that an individual gene is null. The problem can be expressed in a two-component mixture framework, using an empirical Bayes approach. Current methods of implementing this approach either have some limitations due to the minimal assumptions made or with more specific assumptions are computationally intensive. Results: By converting to a z-score the value of the test statistic used to test the significance of each gene, we propose a simple two-component normal mixture that models adequately the distribution of this score. The usefulness of our approach is demonstrated on three real datasets. Availability: An R-program for implementing the approach is freely available at Contact:gjm@maths.uq.edu.au Supplementary information: