Abstract:
The present-day proliferation in epigenomics, in the exploration of the dynamic regulatory layers that insulate the genome's static DNA sequence, has been enabled by novel high-throughput techniques for interrogating the positioning of DNA (hydroxy)methylation, histone marks and open chromatin. The ready availability of genomic data, without which we could not map the location of these features, has provided the essential context needed to make biological sense of the high-throughput data, and so propel epigenomics to the forefront of mainstream biology.In this special issue, Genome Biology presents a collection of articles that describe a diverse range of novel insights into epigenomes, from human disease to ciliate reproduction to the containment of endogenous retroviruses. We also include a number of methods that will improve and simplify the study of epigenomics, in particular the computational steps that follow data generation. Finally, a selection of review and comment articles give an overview of current and future directions in epigenomics research.The availability of new high-throughput methods creates a demand for software tools to process and analyze the overwhelming flow of unintelligible raw data that will inevitably be produced. Genome Biology has a proud history of publishing the most popular examples of such tools, with high profile examples including Bowtie [1] (next-generation sequencing data), MACS [2] (ChIP-seq data) and DEseq [3] (RNA-seq data). The challenge of designing bioinformatics tools for the ever expanding number of DNA methylation genome-wide profiling methods has been taken up by many bioinformatics labs [4]. In the past few months, for example, Genome Biology has published SWAN [5], a method for reducing technical variation in data from the cutting-edge Illumina HumanMethylation450 BeadChip platform, and Bis-SNP [6], a method for calling SNPs in bisulfite sequencing data, which also has the advantage of improving the accuracy of meth

Abstract:
We derive a new estimate of the size of finite sets of points in metric spaces with few distances. The following applications are considered: (1) we improve the Ray-Chaudhuri--Wilson bound of the size of uniform intersecting families of subsets; (2) we refine the bound of Delsarte-Goethals-Seidel on the maximum size of spherical sets with few distances; (3) we prove a new bound on codes with few distances in the Hamming space, improving an earlier result of Delsarte. We also find the size of maximal binary codes and maximal constant-weight codes of small length with 2 and 3 distances.

Abstract:
Few-body hadronic observables play an essential role in a wide number of processes relevant for both particle and nuclear physics. In order for Lattice QCD to offer insight into the interpretation of few-body states, a theoretical infrastructure must be developed to map Euclidean-time correlation functions to the desired Minkowski-time few-body observables. In this talk, I review the formal challenges associated with the studies of such systems via Lattice QCD, as first introduced by Maiani and Testa, and I also review the methodology to circumvent said limitations. The first main example of the latter is the formalism by Luscher to analyze elastic scattering and a second is the method by Lellouch and Luscher to analyze weak decays. I discus recent theoretical generalizations of these frameworks that allow for the determination of scattering amplitudes, resonances, nonlocal contribution to matrix elements, and form factors below and above inelastic thresholds. Finally, I outline outstanding problems, including those that are now beginning to be addressed.

Abstract:
We present a comprehensive framework for treating the nonlinear interaction of few-cycle pulses using an envelope description that goes beyond the traditional SVEA method. This is applied to a range of simulations that demonstrate how the effect of a $\chi^{(2)}$ nonlinearity differs between the many-cycle and few-cycle cases. Our approach, which includes diffraction, dispersion, multiple fields, and a wide range of nonlinearities, builds upon the work of Brabec and Krausz[1] and Porras[2]. No approximations are made until the final stage when a particular problem is considered. The original version (v1) of this arXiv paper is close to the published Phys.Rev.A. version, and much smaller in size.

Abstract:
We study the problem of counting the number of varieties in families which have a rational point. We give conditions on the singular fibres that force very few of the varieties in the family to contain a rational point, in a precise quantitative sense. This generalises and unifies existing results in the literature by Serre, Browning-Dietmann, Bright-Browning-Loughran, Graber-Harris-Mazur-Starr, et al.

Abstract:
I discuss the role of relativistic quantum mechanics in few-body physics, various formulations of relativistic few-body quantum mechanics and how they are related.

Abstract:
These lectures contain a theoretical introduction to the few-body problem with short-range resonant binary interactions. In the first part we discuss the effective range expansion for the two-body scattering amplitude emphasizing the role of the resonance width. In the second part we review the Efimov effect for three atoms, describe the difference in between the Efimovian and non-Efimovian regimes, and discuss the dependence of three-body observables on quantum symmetry, mass imbalance, and resonance width. In the third part we derive the Skorniakov and Ter-Martirosian equation and give several illustrative examples of its solution.

Abstract:
The "slope-number" of a graph $G$ is the minimum number of distinct edge slopes in a straight-line drawing of $G$ in the plane. We prove that for $\Delta\geq5$ and all large $n$, there is a $\Delta$-regular $n$-vertex graph with slope-number at least $n^{1-\frac{8+\epsilon}{\Delta+4}}$. This is the best known lower bound on the slope-number of a graph with bounded degree. We prove upper and lower bounds on the slope-number of complete bipartite graphs. We prove a general upper bound on the slope-number of an arbitrary graph in terms of its bandwidth. It follows that the slope-number of interval graphs, cocomparability graphs, and AT-free graphs is at most a function of the maximum degree. We prove that graphs of bounded degree and bounded treewidth have slope-number at most $O(\log n)$. Finally we prove that every graph has a drawing with one bend per edge, in which the number of slopes is at most one more than the maximum degree. In a companion paper (http://arxiv.org/abs/math/0606450), planar drawings of graphs with few slopes are also considered.

Abstract:
We show two results related to the Hamiltonicity and $k$-Path algorithms in undirected graphs by Bj\"orklund [FOCS'10], and Bj\"orklund et al., [arXiv'10]. First, we demonstrate that the technique used can be generalized to finding some $k$-vertex tree with $l$ leaves in an $n$-vertex undirected graph in $O^*(1.657^k2^{l/2})$ time. It can be applied as a subroutine to solve the $k$-Internal Spanning Tree ($k$-IST) problem in $O^*(\min(3.455^k, 1.946^n))$ time using polynomial space, improving upon previous algorithms for this problem. In particular, for the first time we break the natural barrier of $O^*(2^n)$. Second, we show that the iterated random bipartition employed by the algorithm can be improved whenever the host graph admits a vertex coloring with few colors; it can be an ordinary proper vertex coloring, a fractional vertex coloring, or a vector coloring. In effect, we show improved bounds for $k$-Path and Hamiltonicity in any graph of maximum degree $\Delta=4,\ldots,12$ or with vector chromatic number at most 8.