Probing the Unfolded Configurations of a β-Hairpin Using Sketch-Map

This work examines the conformational ensemble involved in β-hairpin folding by means of advanced molecular dynamics simulations and dimensionality reduction. A fully atomistic description of the protein and the surrounding solvent molecules is used, and this complex energy landscape is sampled by means of parallel tempering metadynamics simulations. The ensemble of configurations explored is analyzed using the recently proposed sketch-map algorithm. Further simulations allow us to probe how mutations affect the structures adopted by this protein. We find that many of the configurations adopted by a mutant are the same as those adopted by the wild-type protein. Furthermore, certain mutations destabilize secondary-structure-containing configurations by preventing the formation of hydrogen bonds or by promoting the formation of new intramolecular contacts. Our analysis demonstrates that machine-learning techniques can be used to study the energy landscapes of complex molecules and that the visualizations that are generated in this way provide a natural basis for examining how the stabilities of particular configurations of the molecule are affected by factors such as temperature or structural mutations.

Global Sensitivity Analysis for MAP Inference in Graphical Models

We study the sensitivity of a MAP configuration of a discrete probabilistic graphical model with respect to perturbations of its parameters. These perturbations are global, in the sense that simultaneous perturbations of all the parameters (or any chosen subset of them) are allowed. Our main contribution is an exact algorithm that can check whether the MAP configuration is robust with respect to given perturbations. Its complexity is essentially the same as that of obtaining the MAP configuration itself, so it can be promptly used with minimal effort. We use our algorithm to identify the largest global perturbation that does not induce a change in the MAP configuration, and we successfully apply this robustness measure in two practical scenarios: the prediction of facial action units with posed images and the classification of multiple real public data sets. A strong correlation between the proposed robustness measure and accuracy is verified in both scenarios.

New Complexity Results for MAP in Bayesian Networks

This paper presents new results for the (partial) maximum a posteriori (MAP) problem in Bayesian networks, which is the problem of querying the most probable state configuration of some of the network variables given evidence. It is demonstrated that the problem remains hard even in networks with very simple topology, such as binary polytrees and simple trees (including the Naive Bayes structure), which extends previous complexity results. Furthermore, a Fully Polynomial Time Approximation Scheme for MAP in networks with bounded treewidth and bounded number of states per variable is developed. Approximation schemes were thought to be impossible, but here it is shown otherwise under the assumptions just mentioned, which are adopted in most applications.

New Results for the MAP Problem in Bayesian Networks

This paper presents new results for the (partial) maximum a posteriori (MAP) problem in Bayesian networks, which is the problem of querying the most probable state configuration of some of the network variables given evidence. First, it is demonstrated that the problem remains hard even in networks with very simple topology, such as binary polytrees and simple trees (including the Naive Bayes structure). Such proofs extend previous complexity results for the problem. Inapproximability results are also derived in the case of trees if the number of states per variable is not bounded. Although the problem is shown to be hard and inapproximable even in very simple scenarios, a new exact algorithm is described that is empirically fast in networks of bounded treewidth and bounded number of states per variable. The same algorithm is used as basis of a Fully Polynomial Time Approximation Scheme for MAP under such assumptions. Approximation schemes were generally thought to be impossible for this problem, but we show otherwise for classes of networks that are important in practice. The algorithms are extensively tested using some well-known networks as well as random generated cases to show their effectiveness.

NP-hardness of MAP in Ternary Tree Bayesian Networks

This paper strengthens the NP-hardness result for the (partial) maximum a posteriori (MAP) problem in Bayesian networks with topology of trees (every variable has at most one parent) and variable cardinality at most three. MAP is the problem of querying the most probable state configuration of some (not necessarily all) of the network variables given evidence. It is demonstrated that the problem remains hard even in such simplistic networks.

Anytime Marginal MAP Inference

This paper presents a new anytime algorithm for the marginal MAP problem in graphical models of bounded treewidth. We show asymptotic convergence and theoretical error bounds for any fixed step. Experiments show that it compares well to a state-of-the-art systematic search algorithm.

Physical map and cosmid contig encompassing a new interstitial deletion of the X-linked lymphoproliferative syndrome region

The X-linked lymphoproliferative syndrome (XLP) is an inherited immuno-deficiency to Epstein-Barr virus infection that has been mapped to chromosome Xq25. Molecular analysis of XLP patients from ten different families identified a small interstitial constitutional deletion in 1 patient (XLP-D). This deletion, initially defined by a single marker, DF83, known to map to interval Xq24-q26.1, is nested within a previously reported and much larger deletion in another XLP patient (XLP-739). A cosmid minilibrary was constructed from a single mega-YAC and used to establish a contig encompassing the whole XLP-D deletion and a portion of the XLP-739 deletion. Based on this contig, the size of the XLP-D deletion can be estimated at 130 kb. The identification of this minimal deletion, within which at least a portion of the XLP gene is likely to reside, should greatly facilitate efforts in isolating the gene.