General, PDB-based collective variables for protein folding

New, automated forms of data-analysis are required in order to understand the high-dimensional trajectories that are obtained from molecular dynamics simulations on proteins. Dimensionality reduction algorithms are particularly appealing in this regard as they allow one to construct unbiased, low-dimensional representations of the trajectory using only the information encoded in the trajectory. The downside of this approach is that different sets of coordinates are required for each different chemical systems under study precisely because the coordinates are constructed using information from the trajectory. In this paper we show how one can resolve this problem by using the sketch-map algorithm that we recently proposed to construct a low-dimensional representation of the structures contained in the protein data bank (PDB). We show that the resulting coordinates are as useful for analysing trajectory data as coordinates constructed using landmark configurations taken from the trajectory and that these coordinates can thus be used for understanding protein folding across a range of systems.

Finite domination and Novikov rings. Laurent polynomial rings in several variables

We present a homological characterisation of those chain complexes of modules over a Laurent polynomial ring in several indeterminates which are finitely dominated over the ground ring (that is, are a retract up to homotopy of a bounded complex of finitely generated free modules). The main tools, which we develop in the paper, are a non-standard totalisation construction for multi-complexes based on truncated products, and a high-dimensional mapping torus construction employing a theory of cubical diagrams that commute up to specified coherent homotopies.

Learning Bayesian Networks with Thousands of Variables

We present a method for learning Bayesian networks from data sets containing thousands of variables without the need for structure constraints. Our approach is made of two parts. The first is a novel algorithm that effectively explores the space of possible parent sets of a node. It guides the exploration towards the most promising parent sets on the basis of an approximated score function that is computed in constant time. The second part is an improvement of an existing ordering-based algorithm for structure optimization. The new algorithm provably achieves a higher score compared to its original formulation. Our novel approach consistently outperforms the state of the art on very large data sets.

Latent vs. Observed Variables: Analysis of Irrigation Water Efficiency Using SEM and SUR

In this paper we compare conceptualising single factor technical and allocative efficiency as indicators of a single latent variable, or as separate observed variables. In the former case, the impacts on both efficiency types are analysed by means of structural equation modeling (SEM), in the latter by seemingly unrelated regression (SUR). We compare estimation results of the two approaches based on a dataset on single factor irrigation water use efficiency obtained from a survey of 360 farmers in the Guanzhong Plain, China. The main methodological findings are that SEM allows identification of the most important dimension of irrigation water efficiency (technical efficiency) via comparison of their factor scores and reliability. Moreover, it reduces multicollinearity and attenuation bias. It thus is preferable to SUR. The SEM estimates show that perception of water scarcity is the most important positive determinant of both types of efficiency, followed by irrigation infrastructure, income and water price. Furthermore, there is a strong negative reverse effect from efficiency on perception.