Covering Pairs in Directed Acyclic Graphs

The Minimum Path Cover problem on directed acyclic graphs (DAGs) is a classical problem that provides a clear and simple mathematical formulation for several applications in different areas and that has an efficient algorithmic solution. In this paper, we study the computational complexity of two constrained variants of Minimum Path Cover motivated by the recent introduction of next-generation sequencing technologies in bioinformatics. The first problem (MinPCRP), given a DAG and a set of pairs of vertices, asks for a minimum cardinality set of paths "covering" all the vertices such that both vertices of each pair belong to the same path. For this problem, we show that, while it is NP-hard to compute if there exists a solution consisting of at most three paths, it is possible to decide in polynomial time whether a solution consisting of at most two paths exists. The second problem (MaxRPSP), given a DAG and a set of pairs of vertices, asks for a path containing the maximum number of the given pairs of vertices. We show its NP-hardness and also its W[1]-hardness when parametrized by the number of covered pairs. On the positive side, we give a fixed-parameter algorithm when the parameter is the maximum overlapping degree, a natural parameter in the bioinformatics applications of the problem

Cerulean: A hybrid assembly using high throughput short and long reads

Genome assembly using high throughput data with short reads, arguably, remains an unresolvable task in repetitive genomes, since when the length of a repeat exceeds the read length, it becomes difficult to unambiguously connect the flanking regions. The emergence of third generation sequencing (Pacific Biosciences) with long reads enables the opportunity to resolve complicated repeats that could not be resolved by the short read data. However, these long reads have high error rate and it is an uphill task to assemble the genome without using additional high quality short reads. Recently, Koren et al. 2012 proposed an approach to use high quality short reads data to correct these long reads and, thus, make the assembly from long reads possible. However, due to the large size of both dataset (short and long reads), error-correction of these long reads requires excessively high computational resources, even on small bacterial genomes. In this work, instead of error correction of long reads, we first assemble the short reads and later map these long reads on the assembly graph to resolve repeats. Contribution: We present a hybrid assembly approach that is both computationally effective and produces high quality assemblies. Our algorithm first operates with a simplified version of the assembly graph consisting only of long contigs and gradually improves the assembly by adding smaller contigs in each iteration. In contrast to the state-of-the-art long reads error correction technique, which requires high computational resources and long running time on a supercomputer even for bacterial genome datasets, our software can produce comparable assembly using only a standard desktop in a short running time.Comment: Peer-reviewed and presented as part of the 13th Workshop on Algorithms in Bioinformatics (WABI2013

Abnormal phenomena in a one-dimensional periodic structure containing left-handed materials

The explicit dispersion equation for a one-dimensional periodic structure with alternative layers of left-handed material (LHM) and right-handed material (RHM) is given and analyzed. Some abnormal phenomena such as spurious modes with complex frequencies, discrete modes and photon tunnelling modes are observed in the band structure. The existence of spurious modes with complex frequencies is a common problem in the calculation of the band structure for such a photonic crystal. Physical explanation and significance are given for the discrete modes (with real values of wave number) and photon tunnelling propagation modes (with imaginary wave numbers in a limited region).Comment: 10 pages, 4 figure

Quasi-local Energy for Spherically Symmetric Spacetimes

We present two complementary approaches for determining the reference for the covariant Hamiltonian boundary term quasi-local energy and test them on spherically symmetric spacetimes. On the one hand, we isometrically match the 2-surface and extremize the energy. This can be done in two ways, which we call programs I (without constraint) and II (with additional constraints). On the other hand, we match the orthonormal 4-frames of the dynamic and the reference spacetimes. Then, if we further specify the observer by requiring the reference displacement to be the timelike Killing vector of the reference, the result is the same as program I, and the energy can be positive, zero, or even negative. If, instead, we require that the Lie derivatives of the two-area along the displacement vector in both the dynamic and reference spacetimes to be the same, the result is the same as program II, and it satisfies the usual criteria: the energies are non-negative and vanish only for Minkowski (or anti-de Sitter) spacetime.Comment: 16 pages, no figure

Reproductive Tract Disorders among Afghan Refugee Women Attending Health Clinics in Haripur, Pakistan

Afghans comprise one of the largest groups of refugees in the world, with the majority living in Pakistan. The objective of this study was to identify commonly-occurring reproductive tract infections (RTIs), describe knowledge of women about RTIs, and assess physical and behavioural factors contributing to the development of RTIs. Afghan women presenting at Basic Health Units in refugee camps in Haripur, Pakistan, with reproductive health-related complaints, were included in the study (n=634). Data collection included implementation of an interviewer-administered questionnaire, along with a physical examination and laboratory tests. A descriptive analysis was conducted first. Qualitative data were coded and analyzed using predetermined themes. Chi-square test was used for determining the possible relationships between a binary outcome and categorical risk factors. Over three-fourths (76.7%) of those who reported to the health clinics with reproductive complaints had an RTI. Nearly half (49.5%) of these women were diagnosed with some form of vaginitis, and 14.7% were diagnosed with clinical suspicion of pelvic inflammatory disease (PID). Women with cervical prolapse (p=0.033) or who cleansed after intercourse (p=0.002) were more likely to have vaginitis. There was a significant difference (p=0.017) in the prevalence of suspected PID among women who used mud only (11.1%), any water (18.8%), and an old cloth or toilet paper (9.8%) for cleansing after defaecation. Specific physical and behavioural contributors to the high prevalence of RTIs in this population were identified, and recommendations to ameliorate these factors are offered

A first principles study of sub-monolayer Ge on Si(001)

Experimental observations of heteroepitaxial growth of Ge on Si(001) show a (2xn) reconstruction for sub-monolayer coverages, with dimer rows crossed by missing-dimer trenches. We present first-principles density-functional calculations designed to elucidate the energetics and relaxed geometries associated with this reconstruction. We also address the problem of how the formation energies of reconstructions having different stoichiometries should be compared. The calculations reveal a strong dependence of the formation energy of the missing-dimer trenches on spacing n, and demonstrate that this dependence stems almost entirely from elastic relaxation. The results provide a natural explanation for the experimentally observed spacings in the region of n \~ 8.Comment: 13 pages, 4 figures, submitted to Surface Scienc

Out-of-equilibrium singlet-triplet Kondo effect in a single C_60 quantum dot

We have used an electromigration technique to fabricate a $\rm{C_{{60}}}$ single-molecule transistor (SMT). Besides describing our electromigration procedure, we focus and present an experimental study of a single molecule quantum dot containing an even number of electrons, revealing, for two different samples, a clear out-of-equilibrium Kondo effect. Low temperature magneto-transport studies are provided, which demonstrates a Zeeman splitting of the finite bias anomaly.Comment: 6 pages, 4 figure

Influence of uniaxial tensile stress on the mechanical and piezoelectric properties of short-period ferroelectric superlattice

Tetragonal ferroelectric/ferroelectric BaTiO3/PbTiO3 superlattice under uniaxial tensile stress along the c axis is investigated from first principles. We show that the calculated ideal tensile strength is 6.85 GPa and that the superlattice under the loading of uniaxial tensile stress becomes soft along the nonpolar axes. We also find that the appropriately applied uniaxial tensile stress can significantly enhance the piezoelectricity for the superlattice, with piezoelectric coefficient d33 increasing from the ground state value by a factor of about 8, reaching 678.42 pC/N. The underlying mechanism for the enhancement of piezoelectricity is discussed