Relational Composition in Neural Networks: A Survey and Call to Action

Many neural nets appear to represent data as linear combinations of "feature vectors." Algorithms for discovering these vectors have seen impressive recent success. However, we argue that this success is incomplete without an understanding of relational composition: how (or whether) neural nets combine feature vectors to represent more complicated relationships. To facilitate research in this area, this paper offers a guided tour of various relational mechanisms that have been proposed, along with preliminary analysis of how such mechanisms might affect the search for interpretable features. We end with a series of promising areas for empirical research, which may help determine how neural networks represent structured data

Exotic trees

We discuss the scaling properties of free branched polymers. The scaling behaviour of the model is classified by the Hausdorff dimensions for the internal geometry: d_L and d_H, and for the external one: D_L and D_H. The dimensions d_H and D_H characterize the behaviour for long distances while d_L and D_L for short distances. We show that the internal Hausdorff dimension is d_L=2 for generic and scale-free trees, contrary to d_H which is known be equal two for generic trees and to vary between two and infinity for scale-free trees. We show that the external Hausdorff dimension D_H is directly related to the internal one as D_H = \alpha d_H, where \alpha is the stability index of the embedding weights for the nearest-vertex interactions. The index is \alpha=2 for weights from the gaussian domain of attraction and 0<\alpha <2 for those from the L\'evy domain of attraction. If the dimension D of the target space is larger than D_H one finds D_L=D_H, or otherwise D_L=D. The latter result means that the fractal structure cannot develop in a target space which has too low dimension.Comment: 33 pages, 6 eps figure

Allele-specific miRNA-binding analysis identifies candidate target genes for breast cancer risk

Most breast cancer (BC) risk-associated single-nucleotide polymorphisms (raSNPs) identified in genome-wide association studies (GWAS) are believed to cis-regulate the expression of genes. We hypothesise that cis-regulatory variants contributing to disease risk may be affecting microRNA (miRNA) genes and/or miRNA binding. To test this, we adapted two miRNA-binding prediction algorithms-TargetScan and miRanda-to perform allele-specific queries, and integrated differential allelic expression (DAE) and expression quantitative trait loci (eQTL) data, to query 150 genome-wide significant ( P≤5×10-8 ) raSNPs, plus proxies. We found that no raSNP mapped to a miRNA gene, suggesting that altered miRNA targeting is an unlikely mechanism involved in BC risk. Also, 11.5% (6 out of 52) raSNPs located in 3'-untranslated regions of putative miRNA target genes were predicted to alter miRNA::mRNA (messenger RNA) pair binding stability in five candidate target genes. Of these, we propose RNF115, at locus 1q21.1, as a strong novel target gene associated with BC risk, and reinforce the role of miRNA-mediated cis-regulation at locus 19p13.11. We believe that integrating allele-specific querying in miRNA-binding prediction, and data supporting cis-regulation of expression, improves the identification of candidate target genes in BC risk, as well as in other common cancers and complex diseases.Funding Agency Portuguese Foundation for Science and Technology CRESC ALGARVE 2020 European Union (EU) 303745 Maratona da Saude Award DL 57/2016/CP1361/CT0042 SFRH/BPD/99502/2014 CBMR-UID/BIM/04773/2013 POCI-01-0145-FEDER-022184info:eu-repo/semantics/publishedVersio

The puzzle of non-party actors in party democracy: Independents in Ireland

It is an accepted truth that parties are the central political actors in all liberal democracies. This dominance of parties is often considered the logical outcome of rational politicians’ attempts to maximize their utility in terms of votes and policy influence. However, the last twenty years have seen a number of significant Independent (i.e. non-party) actors emerge in more than a few political systems. From an actor-centred point of view, party affiliation can, depending on the particular environment, be rather a liability than an advantage, which has significant implications for the role of non-party actors in face of weakening party democracies. To demonstrate this point, we deliver an account of the rise of Independents in the Irish political system, opposed to the dominant scholarly perspective that tends to consider Independents as an idiosyncrasy. We show that the choice of organizational independence over party affiliation represents a reaction to incentives inherent in the electoral, parliamentary and governmental stages that can disfavour party as the most efficient vehicle for individual goal attainment. This becomes evident when avoiding the misleading comparison between parties as collective bodies with that of Independents as individuals, instead focussing on the respective strategic positions of the individual MPs

Ordered and Quantum Treemaps: Making Effective Use of 2D Space to Display Hierarchies (2001)

Treemaps, a space- filling method of visualizing large hierarchical data sets, are receiving increasing attention. Several algorithms have been proposed to create more useful displays by controlling the aspect ratios of the rectangles that make up a treemap. While these algorithms do improve visibility of small items in a single layout, they introduce instability over time in the display of dynamically changing data, fail to preserve order of the underlying data, and create layouts that are difficult to visually search. In addition, continuous treemap algorithms are not suitable for displaying quantum-sized objects within them, such as images. This paper introduces several new treemap algorithms, which address these shortcomings. In addition, we show a new application of these treemaps, using them to present groups of images. The ordered treemap algorithms ensure that items near each other in the given order will be near each other in the treemap layout. Using experimental evidence from Monte Carlo trials, we show that compared to other layout algorithms ordered treemaps are more stable while maintaining relatively favorable aspect ratios of the constituent rectangles. A second test set uses stock market data. The quantum treemap algorithms modify the layout of the continuous treemap algorithms to generate rectangles that are integral multiples of an input object size. The quantum treemap algorithm has been applied to PhotoMesa, an application that supports browsing of large numbers of images