First-principles study of high conductance DNA sequencing with carbon nanotube electrodes

Rapid and cost-effective DNA sequencing at the single nucleotide level might be achieved by measuring a transverse electronic current as single-stranded DNA is pulled through a nano-sized pore. In order to enhance the electronic coupling between the nucleotides and the electrodes and hence the current signals, we employ a pair of single-walled close-ended (6,6) carbon nanotubes (CNTs) as electrodes. We then investigate the electron transport properties of nucleotides sandwiched between such electrodes by using first-principles quantum transport theory. In particular we consider the extreme case where the separation between the electrodes is the smallest possible that still allows the DNA translocation. The benzene-like ring at the end cap of the CNT can strongly couple with the nucleobases and therefore both reduce conformational fluctuations and significantly improve the conductance. The optimal molecular configurations, at which the nucleotides strongly couple to the CNTs, and which yield the largest transmission, are first identified. Then the electronic structures and the electron transport of these optimal configurations are analyzed. The typical tunneling currents are of the order of 50 nA for voltages up to 1 V. At higher bias, where resonant transport through the molecular states is possible, the current is of the order of several $\mu$A. Below 1 V the currents associated to the different nucleotides are consistently distinguishable, with adenine having the largest current, guanine the second-largest, cytosine the third and finally thymine the smallest. We further calculate the transmission coefficient profiles as the nucleotides are dragged along the DNA translocation path and investigate the effects of configurational variations. Based on these results we propose a DNA sequencing protocol combining three possible data analysis strategies.Comment: 12 pages, 17 figures, 3 table

New Results for the Minimum Weight Triangulation Problem

The current best polynomial time approximation algorithm produces a triangulation that can be O(log n) times the weight of the optimal triangulation. We propose an algorithm that triangulates a set P of n points in a plane in O(n3) time and that never does worse than the greedy triangulation. We investigate issues of local optimality pertaining to known triangulation algorithms and suggest an interesting new approach to studying triangulation algorithms. We restate the minimum weight triangulation problem as a graph problem and show the NP-hardness of a closely related graph problem. Finally, we show that the constrained problem of computing the minimum weight triangulation, given a set of points in a plane and enough edges to form a triangulation, is NP-hard. These results are an advance towards a proof that the minimum weight triangulation problem is NP-hard

Stack and Queue Layouts of Posets

The stacknumber (queuenumber) of a poset is defined as the stacknumber (queuenumber) of its Hasse diagram viewed as a directed acyclic graph. Upper bounds on the queuenumber of a poset are derived in terms of its jumpnumber, its length, its width, and the queuenumber of its covering graph. A lower bound of is shown for the queuenumber of the class of planar posets. The queuenumber of a planar poset is shown to be within a small constant factor of its width. The stacknumber of posets with planar covering graphs is shown to be . These results exhibit sharp differences between the stacknumber and queuenumber of posets as well as between the stacknumber (queuenumber) of a poset and the stacknumber (queuenumber) of its covering graph

New Results for the Minimum Weight Triangulation Problem

Given a finite set of points in a plane, a triangulation is a maximal set of non-intersecting line segments connecting the points. The weight of a triangulation is the sum of the Euclidean lengths of its line segments. Given a set of points in a plane, the minimum weight triangulation problem is to find a triangulation whose weight is minimal. No polynomial time algorithm is known to solve this problem, and it is unknown whether the problem is NP-hard. The current best polynomial time approximation algorithm produces a triangulation that can be 0(log n) times the weight of the optimal triangulation. We propose an algorithm that triangulates a set P, of n points in a plane in 0(n-cubed) time and that never does worse than the greedy triangulation. The algorithm produces an optimal triangulation if the points P are the vertices of a convex polygon. The algorithm has the flavor of a heuristic proposed by Lingas and analysis similar to his can be performed for our algorithm also, but experimental results indicate that our algorithm performs much better than the heuristic of Lingas. The results comparing the optimal triangulation with the performance of our algorithm, the heuristic of Lingas, and the greedy algorithm are within 0(1) of an optimal triangulation. We investigate issues of local optimality pertaining to known triangulation algorithms. We define the notion of k-optimality which suggests an interesting new approach to studying triangulation algorithms. We restate the minimum weight triangulation problem as a graph problem and show that NP-hardness of a closely related graph problem. Finally, we show that the constrained problem of computing the minimum weight of triangulation, given a set of points in a plane and enough edges to form a triangulation, is NP-hard. These results are an advance towards a proof that the minimum weight triangulation problem is NP-hard

An Improved Bound for First-Fit on Posets Without Two Long Incomparable Chains

It is known that the First-Fit algorithm for partitioning a poset P into chains uses relatively few chains when P does not have two incomparable chains each of size k. In particular, if P has width w then Bosek, Krawczyk, and Szczypka (SIAM J. Discrete Math., 23(4):1992--1999, 2010) proved an upper bound of ckw^{2} on the number of chains used by First-Fit for some constant c, while Joret and Milans (Order, 28(3):455--464, 2011) gave one of ck^{2}w. In this paper we prove an upper bound of the form ckw. This is best possible up to the value of c.Comment: v3: referees' comments incorporate

Exchange interactions and magnetic phases of transition metal oxides: benchmarking advanced ab initio methods

The magnetic properties of the transition metal monoxides MnO and NiO are investigated at equilibrium and under pressure via several advanced first-principles methods coupled with Heisenberg Hamiltonian MonteCarlo. The comparative first-principles analysis involves two promising beyond-local density functionals approaches, namely the hybrid density functional theory and the recently developed variational pseudo-self-interaction correction method, implemented with both plane-wave and atomic-orbital basis sets. The advanced functionals deliver a very satisfying rendition, curing the main drawbacks of the local functionals and improving over many other previous theoretical predictions. Furthermore, and most importantly, they convincingly demonstrate a degree of internal consistency, despite differences emerging due to methodological details (e.g. plane waves vs. atomic orbitals

Atomic self-interaction correction for molecules and solids

We present an atomic orbital based approximate scheme for self-interaction correction (SIC) to the local density approximation of density functional theory. The method, based on the idea of Filippetti and Spaldin [Phys. Rev. B 67, 125109 (2003)], is implemented in a code using localized numerical atomic orbital basis sets and is now suitable for both molecules and extended solids. After deriving the fundamental equations as a non-variational approximation of the self-consistent SIC theory, we present results for a wide range of molecules and insulators. In particular, we investigate the effect of re-scaling the self-interaction correction and we establish a link with the existing atomic-like corrective scheme LDA+U. We find that when no re-scaling is applied, i.e. when we consider the entire atomic correction, the Kohn-Sham HOMO eigenvalue is a rather good approximation to the experimental ionization potential for molecules. Similarly the HOMO eigenvalues of negatively charged molecules reproduce closely the molecular affinities. In contrast a re-scaling of about 50% is necessary to reproduce insulator bandgaps in solids, which otherwise are largely overestimated. The method therefore represents a Kohn-Sham based single-particle theory and offers good prospects for applications where the actual position of the Kohn-Sham eigenvalues is important, such as quantum transport.Comment: 16 pages, 7 figure

Defining disease modification in myelofibrosis in the era of targeted therapy

The development of targeted therapies for the treatment of myelofibrosis highlights a unique issue in a field that has historically relied on symptom relief, rather than survival benefit or modification of disease course, as key response criteria. There is, therefore, a need to understand what constitutes disease modification of myelofibrosis to advance appropriate drug development and therapeutic pathways. Here, the authors discuss recent clinical trial data of agents in development and dissect the potential for novel end points to act as disease modifying parameters. Using the rationale garnered from latest clinical and scientific evidence, the authors propose a definition of disease modification in myelofibrosis. With improved overall survival a critical outcome, alongside the normalization of hematopoiesis and improvement in bone marrow fibrosis, there will be an increasing need for surrogate measures of survival for use in the early stages of trials. As such, the design of future clinical trials will require re-evaluation and updating to incorporate informative parameters and end points with standardized definitions and methodologies

Counting Complex Disordered States by Efficient Pattern Matching: Chromatic Polynomials and Potts Partition Functions

Counting problems, determining the number of possible states of a large system under certain constraints, play an important role in many areas of science. They naturally arise for complex disordered systems in physics and chemistry, in mathematical graph theory, and in computer science. Counting problems, however, are among the hardest problems to access computationally. Here, we suggest a novel method to access a benchmark counting problem, finding chromatic polynomials of graphs. We develop a vertex-oriented symbolic pattern matching algorithm that exploits the equivalence between the chromatic polynomial and the zero-temperature partition function of the Potts antiferromagnet on the same graph. Implementing this bottom-up algorithm using appropriate computer algebra, the new method outperforms standard top-down methods by several orders of magnitude, already for moderately sized graphs. As a first application, we compute chromatic polynomials of samples of the simple cubic lattice, for the first time computationally accessing three-dimensional lattices of physical relevance. The method offers straightforward generalizations to several other counting problems.Comment: 7 pages, 4 figure

Impurity-Ion pair induced high-temperature ferromagnetism in Co-doped ZnO

Magnetic 3d-ions doped into wide-gap oxides show signatures of room temperature ferromagnetism, although their concentration is two orders of magnitude smaller than that in conventional magnets. The prototype of these exceptional materials is Co-doped ZnO, for which an explanation of the room temperature ferromagnetism is still elusive. Here we demonstrate that magnetism originates from Co2+ oxygen-vacancy pairs with a partially filled level close to the ZnO conduction band minimum. The magnetic interaction between these pairs is sufficiently long-ranged to cause percolation at moderate concentrations. However, magnetically correlated clusters large enough to show hysteresis at room temperature already form below the percolation threshold and explain the current experimental findings. Our work demonstrates that the magnetism in ZnO:Co is entirely governed by intrinsic defects and a phase diagram is presented. This suggests a recipe for tailoring the magnetic properties of spintronics materials by controlling their intrinsic defects