Repetition Based Pattern (RBP)
In this paper, we show that standard feed-forward and recurrent neural networks fail to learn abstract patterns based on identity rules. We propose Repetition Based Pattern (RBP) extensions to neural network structures that solve this problem and answer, as well as raise, questions about integrating structures for inductive bias into neural networks. Examples of abstract patterns are the sequence patterns ABA and ABB where A or B can be any object. These were introduced by Marcus et al (1999) who also found that 7 month old infants recognise these patterns in sequences that use an unfamiliar vocabulary while simple recurrent neural networks do not.This result has been contested in the literature but it is confirmed by our experiments. We also show that the inability to generalise extends to different, previously untested, settings. We propose a new approach to modify standard neural network architectures, called Repetition Based Patterns (RBP) with different variants for classification and prediction. Our experiments show that neural networks with the appropriate RBP structure achieve perfect classification and prediction performance on synthetic data, including mixed concrete and abstract patterns. RBP also improves neural network performance in experiments with real-world sequence prediction tasks. We discuss these finding in terms of challenges for neural network models and identify consequences from this result in terms of developing inductive biases for neural network learning. …

Apache Hive
The Apache Hive (TM) data warehouse software facilitates querying and managing large datasets residing in distributed storage. Built on top of Apache Hadoop (TM), it provides * tools to enable easy data extract/transform/load (ETL) * a mechanism to impose structure on a variety of data formats * access to files stored either directly in Apache HDFS (TM) or in other data storage systems such as Apache HBase (TM) * query execution via MapReduce Hive defines a simple SQL-like query language, called HiveQL, that enables users familiar with SQL to query the data. At the same time, this language also allows programmers who are familiar with the MapReduce framework to be able to plug in their custom mappers and reducers to perform more sophisticated analysis that may not be supported by the built-in capabilities of the language. HiveQL can also be extended with custom scalar functions (UDF’s), aggregations (UDAF’s), and table functions (UDTF’s). …

Burning Number
We introduce a new graph parameter called the burning number, inspired by contact processes on graphs such as graph bootstrap percolation, and graph searching paradigms such as Firefighter. The burning number measures the speed of the spread of contagion in a graph; the lower the burning number, the faster the contagion spreads. We provide a number of properties of the burning number, including characterizations and bounds. The burning number is computed for several graph classes, and is derived for the graphs generated by the Iterated Local Transitivity model for social networks. …

Auer-Gervini Graphical Bayesian Approach
This article approaches the problem of selecting significant principal components from a Bayesian model selection perspective. The resulting Bayes rule provides a simple graphical technique that can be used instead of (or together with) the popular scree plot to determine the number of significant components to retain. We study the theoretical properties of the new method and show, by examples and simulation, that it provides more clear-cut answers than the scree plot in many interesting situations. …