Entropy inference and the James-Stein estimator, with application to nonlinear gene association networks

We present a procedure for effective estimation of entropy and mutual information from small-sample data, and apply it to the problem of inferring high-dimensional gene association networks. Specifically, we develop a James-Stein-type shrinkage estimator, resulting in a procedure that is highly efficient statistically as well as computationally. Despite its simplicity, we show that it outperforms eight other entropy estimation procedures across a diverse range of sampling scenarios and data-generating models, even in cases of severe undersampling. We illustrate the approach by analyzing E. coli gene expression data and computing an entropy-based gene-association network from gene expression data. A computer program is available that implements the proposed shrinkage estimator.Comment: 18 pages, 3 figures, 1 tabl

Review article

In eukaryotic cells, the trans-Golgi network (TGN) serves as a platform for secretory cargo sorting and trafficking. In recent years, it has become evident that a complex network of lipid-lipid and lipid-protein interactions contributes to these key functions. This review addresses the role of lipids at the TGN with a particular emphasis on sphingolipids and diacylglycerol. We further highlight how these lipids couple secretory cargo sorting and trafficking for spatiotemporal coordination of protein transport to the plasma membrane

Central Invariants and Frobenius-Schur Indicators for Semisimple Quasi-Hopf Algebras

In this paper, we obtain a canonical central element $\nu_H$ for each semi-simple quasi-Hopf algebra $H$ over any field $k$ and prove that $\nu_H$ is invariant under gauge transformations. We show that if $k$ is algebraically closed of characteristic zero then for any irreducible representation of $H$ which affords the character $\chi$, $\chi(\nu_H)$ takes only the values 0, 1 or -1, moreover if $H$ is a Hopf algebra or a twisted quantum double of a finite group then $\chi(\nu_H)$ is the corresponding Frobenius-Schur Indicator. We also prove an analog of a Theorem of Larson-Radford for split semi-simple quasi-Hopf algebra over any field $k$. Using this result, we establish the relationship between the antipode $S$, the values of $\chi(\nu_H)$, and certain associated bilinear forms when the underlying field $k$ is algebraically closed of characteristic zero.Comment: 32 pages (version 3

Database Semantics

For long-term upscaling, the computational reconstruction of a complex natural mechanism must be input-output equivalent with the prototype, i.e. the reconstruction must take the same input and produce the same output in the same processing order as the original. Accordingly, the modeling of natural language communication in Database Semantics (DBS) uses a time-linear derivation order for the speaker’s output and the hearer’s input. The language-dependent surfaces serving as the vehicle of content transfer from speaker to hearer are raw data without meaning or any grammatical properties whatsoever, but measurable by natural science