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

Heavy-tailed kernels reveal a finer cluster structure in t-SNE visualisations

T-distributed stochastic neighbour embedding (t-SNE) is a widely used data visualisation technique. It differs from its predecessor SNE by the low-dimensional similarity kernel: the Gaussian kernel was replaced by the heavy-tailed Cauchy kernel, solving the "crowding problem" of SNE. Here, we develop an efficient implementation of t-SNE for a $t$-distribution kernel with an arbitrary degree of freedom $\nu$, with $\nu\to\infty$ corresponding to SNE and $\nu=1$ corresponding to the standard t-SNE. Using theoretical analysis and toy examples, we show that $\nu<1$ can further reduce the crowding problem and reveal finer cluster structure that is invisible in standard t-SNE. We further demonstrate the striking effect of heavier-tailed kernels on large real-life data sets such as MNIST, single-cell RNA-sequencing data, and the HathiTrust library. We use domain knowledge to confirm that the revealed clusters are meaningful. Overall, we argue that modifying the tail heaviness of the t-SNE kernel can yield additional insight into the cluster structure of the data

Targeting and Function of the Mitochondrial Fission Factor GDAP1 Are Dependent on Its Tail-Anchor

Proteins controlling mitochondrial dynamics are often targeted to and anchored into the mitochondrial outer membrane (MOM) by their carboxyl-terminal tail-anchor domain (TA). However, it is not known whether the TA modulates protein function. GDAP1 is a mitochondrial fission factor with two neighboring hydrophobic domains each flanked by basic amino acids (aa). Here we define GDAP1 as TA MOM protein. GDAP1 carries a single transmembrane domain (TMD) that is, together with the adjacent basic aa, critical for MOM targeting. The flanking N-terminal region containing the other hydrophobic domain is located in the cytoplasm. TMD sequence, length, and high hydrophobicity do not influence GDAP1 fission function if MOM targeting is maintained. The basic aa bordering the TMD in the cytoplasm, however, are required for both targeting of GDAP1 as part of the TA and GDAP1-mediated fission. Thus, this GDAP1 region contains critical overlapping motifs defining intracellular targeting by the TA concomitant with functional aspects

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