Transcriptional enhancers play critical roles in regulation of gene expression, but their identification in the eukaryotic genome has been challenging. Recently, it was shown that enhancers in the mammalian genome are associated with characteristic histone modification patterns, which have been increasingly exploited for enhancer identification. However, only a limited number of cell types or chromatin marks have previously been investigated for this purpose, leaving the question unanswered whether there exists an optimal set of histone modifications for enhancer prediction in different cell types. Here, we address this issue by exploring genome-wide profiles of 24 histone modifications in two distinct human cell types, embryonic stem cells and lung fibroblasts. We developed a Random-Forest based algorithm, RFECS (Random Forest based Enhancer identification from Chromatin States) to integrate histone modification profiles for identification of enhancers, and used it to identify enhancers in a number of cell-types. We show that RFECS not only leads to more accurate and precise prediction of enhancers than previous methods, but also helps identify the most informative and robust set of three chromatin marks for enhancer prediction.

For several computational problems in homotopy theory, we obtain algorithms with running time polynomial in the input size. In particular, for every fixed k ≥ 2, there is a polynomial-time algorithm that, for a 1-connected topological space X given as a finite simplicial complex, or more generally, as a simplicial set with polynomial-time homology, computes the kth homotopy group π k (X), as well as the first k stages of a Postnikov system of X. Combined with results of an earlier paper, this yields a polynomial-time computation of [X, Y ], i.e., all homotopy classes of continuous mappings X → Y , under the assumption that Y is (k−1)-connected and dim X ≤ 2k − 2. We also obtain a polynomial-time solution of the extension problem, where the input consists of finite simplicial complexes X, Y , where Y is (k−1)-connected and dim X ≤ 2k − 1, plus a subspace A ⊆ X and a (simplicial) map f : A → Y , and the question is the extendability of f to all of X.The algorithms are based on the notion of a simplicial set with polynomial-time homology, which is an enhancement of the notion of a simplicial set with effective homology developed earlier by Sergeraert and his co-workers. Our polynomial-time algorithms are obtained by showing that simplicial sets with polynomial-time homology are closed under various operations, most notably, Cartesian products, twisted Cartesian products, and classifying space. One of the key components is also polynomial-time homology for the Eilenberg-MacLane space K(Z, 1), provided in another recent paper by Krčál, Matoušek, and Sergeraert.

Prions induce lethal neurodegeneration and consist of PrPSc, an aggregated conformer of the cellular prion protein PrPC. Antibody-derived ligands to the globular domain of PrPC (collectively termed GDL) are also neurotoxic. Here we show that GDL and prion infections activate the same pathways. Firstly, both GDL and prion infection of cerebellar organotypic cultured slices (COCS) induced the production of reactive oxygen species (ROS). Accordingly, ROS scavenging, which counteracts GDL toxicity in vitro and in vivo, prolonged the lifespan of prion-infected mice and protected prion-infected COCS from neurodegeneration. Instead, neither glutamate receptor antagonists nor inhibitors of endoplasmic reticulum calcium channels abolished neurotoxicity in either model. Secondly, antibodies against the flexible tail (FT) of PrPC reduced neurotoxicity in both GDL-exposed and prion-infected COCS, suggesting that the FT executes toxicity in both paradigms. Thirdly, the PERK pathway of the unfolded protein response was activated in both models. Finally, 80% of transcriptionally downregulated genes overlapped between prion-infected and GDL-treated COCS. We conclude that GDL mimic the interaction of PrPSc with PrPC, thereby triggering the downstream events characteristic of prion infection.

We consider an online version of the conflict-free coloring of a set of points on the line, where each newly inserted point must be assigned a color upon insertion, and at all times the coloring has to be conflict-free, in the sense that in every interval I there is a color that appears exactly once in I. We present several deterministic and randomized algorithms for achieving this goal, and analyze their performance, that is, the maximum number of colors that they need to use, as a function of the number n of inserted points. We first show that a natural and simple (deterministic) approach may perform rather poorly, requiring Ω(√ n) colors in the worst case. We then derive several efficient algorithms. The first algorithm is randomized and simple to analyze; it requires an expected number of at most O(log 2 n) colors, and produces a coloring which is valid with high probability. The second algorithm is deterministic, and is a variant of the initial simple algorithm; it uses a maximum of Θ(log 2 n) colors. The third algorithm is a randomized variant of the second algorithm; it requires an expected number of at most O(log n log log n) colors and always produces a valid coloring. We also analyze the performance of the simplest proposed algorithm when the points are inserted in a random order, and present an incomplete analysis that indicates that, with high probability, it uses only O(log n) colors. Finally, we show that in the extension of this problem to two dimensions, where the relevant ranges are disks, n colors may be required in the worst case.

Abstract. Let EMBED k→d be the following algorithmic problem: Given a finite simplicial complex K of dimension at most k, does there exist a (piecewise linear) embedding of K into R d ?Known results easily imply the polynomiality of EMBED k→2 (k = 1, 2; the case k = 1, d = 2 is graph planarity) and of EMBED k→2k for all k ≥ 3.We show that the celebrated result of Novikov on the algorithmic unsolvability of recognizing the 5-sphere implies that EMBED d→d and EMBED (d−1)→d are undecidable for each d ≥ 5. Our main result is the NP-hardness of EMBED 2→4 and, more generally, of EMBED k→d for all k, d with d ≥ 4 and d ≥ k ≥ (2d − 2)/3. These dimensions fall outside the metastable range of a theorem of Haefliger and Weber, which characterizes embeddability using the deleted product obstruction. Our reductions are based on examples, due to Segal, Spież, Freedman, Krushkal, Teichner, and Skopenkov, showing that outside the metastable range the deleted product obstruction is not sufficient to characterize embeddability.