There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

High-throughput mRNA sequencing (RNA-Seq) promises simultaneous transcript discovery and abundance estimation. However, this would require algorithms that are not restricted by prior gene annotations and that account for alternative transcription and splicing. Here we introduce such algorithms in an open-source software program called Cufflinks. To test Cufflinks, we sequenced and analyzed >430 million paired 75-bp RNA-Seq reads from a mouse myoblast cell line over a differentiation time series. We detected 13,692 known transcripts and 3,724 previously unannotated ones, 62% of which are supported by independent expression data or by homologous genes in other species. Over the time series, 330 genes showed complete switches in the dominant transcription start site (TSS) or splice isoform, and we observed more subtle shifts in 1,304 other genes. These results suggest that Cufflinks can illuminate the substantial regulatory flexibility and complexity in even this well-studied model of muscle development and that it can improve transcriptome-based genome annotation.

/pdf/transcript-assembly-and-quantification-by-rna-seq-reveals-3e2dpnsxxg.pdf

Transcript assembly and quantification by RNA-Seq reveals unannotated transcripts and isoform switching during cell differentiation

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

Accurate modeling of geographic distributions of species is crucial to various applications in ecology and conservation. The best performing techniques often require some parameter tuning, which may be prohibitively time-consuming to do separately for each species, or unreliable for small or biased datasets. Additionally, even with the abundance of good quality data, users interested in the application of species models need not have the statistical knowledge required for detailed tuning. In such cases, it is desirable to use "default settings", tuned and validated on diverse datasets. Maxent is a recently introduced modeling technique, achieving high predictive accuracy and enjoying several additional attractive properties. The performance of Maxent is influenced by a moderate number of parameters. The first contribution of this paper is the empirical tuning of these parameters. Since many datasets lack information about species absence, we present a tuning method that uses presence-only data. We evaluate our method on independently collected high-quality presence-absence data. In addition to tuning, we introduce several concepts that improve the predictive accuracy and running time of Maxent. We introduce "hinge features" that model more complex relationships in the training data; we describe a new logistic output format that gives an estimate of probability of presence; finally we explore "background sampling" strategies that cope with sample selection bias and decrease model-building time. Our evaluation, based on a diverse dataset of 226 species from 6 regions, shows: 1) default settings tuned on presence-only data achieve performance which is almost as good as if they had been tuned on the evaluation data itself; 2) hinge features substantially improve model performance; 3) logistic output improves model calibration, so that large differences in output values correspond better to large differences in suitability; 4) "target-group" background sampling can give much better predictive performance than random background sampling; 5) random background sampling results in a dramatic decrease in running time, with no decrease in model performance.

https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.0906-7590.2008.5203.x

Modeling of species distributions with Maxent: new extensions and a comprehensive evaluation

Large intergenic noncoding RNAs (lincRNAs) are emerging as key regulators of diverse cellular processes. Determining the function of individual lincRNAs remains a challenge. Recent advances in RNA sequencing (RNA-seq) and computational methods allow for an unprecedented analysis of such transcripts. Here, we present an integrative approach to define a reference catalog of >8000 human lincRNAs. Our catalog unifies previously existing annotation sources with transcripts we assembled from RNA-seq data collected from ~4 billion RNA-seq reads across 24 tissues and cell types. We characterize each lincRNA by a panorama of >30 properties, including sequence, structural, transcriptional, and orthology features. We found that lincRNA expression is strikingly tissue-specific compared with coding genes, and that lincRNAs are typically coexpressed with their neighboring genes, albeit to an extent similar to that of pairs of neighboring protein-coding genes. We distinguish an additional subset of transcripts that have high evolutionary conservation but may include short ORFs and may serve as either lincRNAs or small peptides. Our integrated, comprehensive, yet conservative reference catalog of human lincRNAs reveals the global properties of lincRNAs and will facilitate experimental studies and further functional classification of these genes.

/pdf/integrative-annotation-of-human-large-intergenic-noncoding-42fhlcbilq.pdf

Integrative annotation of human large intergenic noncoding RNAs reveals global properties and specific subclasses

This paper describes the Jensen-Shannon divergence (JSD) and Hilbert space embedding. With natural definitions making these considerations precise, one finds that the general Jensen-Shannon divergence related to the mixture is the minimum redundancy, which can be achieved by the observer. The set of distributions with the metric /spl radic/JSD can even be embedded isometrically into Hilbert space and the embedding can be identified.

Jensen-Shannon divergence and Hilbert space embedding

Inequalities which connect information divergence with other measures of discrimination or distance between probability distributions are used in information theory and its applications to mathematical statistics, ergodic theory, and other scientific fields. We suggest new inequalities of this type, often based on underlying identities. As a consequence, we obtain certain improvements of the well-known Pinsker inequality. Our study depends on two measures of discrimination, called capacitory discrimination and triangular discrimination. The discussion contains references to related research and comparison with other measures of discrimination, e.g., Ali-Silvey-Csiszar (1996, 1966) divergences and, in particular, the Hellinger distance.

Some inequalities for information divergence and related measures of discrimination

Let V and D denote, respectively, total variation and divergence. We study lower bounds of D with V fixed. The theoretically best (i.e., largest) lower bound determines a function L=L(V), Vajda's (1970) tight lower bound. The main result is an exact parametrization of L. This leads to Taylor polynomials which are lower bounds for L, and thereby to extensions of the classical Pinsker (1960) inequality which has numerous applications, cf. Pinsker and followers.

Refinements of Pinsker's inequality

Measure and integral, definitions.- Basic result on construction of a measure.- Basic result on construction of an integral.- Finitely additive theory.- From "Baire" measures to "Borel" measures, an abstract approach.- Construction of measures by approximation from outside and by approximation from inside.- On the possibility of providing a space of measures with a vague topology.- Definition and basic properties of the weak topology.- Compactness in the weak topology.- Criteria for weak convergence.- On the structure of M +(X).- A problem related to questions of uniformity.- First solution of the ?-problem.- Second solution of the ?-problem.- Uniformity classes.- Joint continuity.- Preservation of weak convergence.

Topology and Measure

Let (I, </) be a measurable space, referred to as the state space. The state space is discrete if I is countable and J consists of all subsets of I. By 77 we denote the set of countable decompositions of I in measurable sets, directed in the usual way by refinement. 770 denotes the subset of 17 consisting of finite decompositions. By a distribution we mean a probability measure on (/, J). The set of all distributions is denoted by M. For p.e M and n e II, \\x | n denotes the restriction of \\x to the ff-algebra generated by %. For a point function <p on I, <<p, /i> denotes the expectation of q> w.r.t. /.i. For a set function (p on «/, <<p, /*>„ denotes expectation of (p w.r.t. H | n, i.e. (<p,H->K = Z<l>(A)n(A).

Flemming Topsøe

Papers

Jensen-Shannon divergence and Hilbert space embedding

Some inequalities for information divergence and related measures of discrimination

Refinements of Pinsker's inequality

Topology and Measure

Information-theoretical optimization techniques