Phase behavior of grafted chain molecules: Influence of head size and chain length

Constant pressure Monte Carlo simulations of a coarse grained off-lattice model for monolayers of amphiphilic molecules at the air/water interface are presented. Our study focusses on phase transitions within a monolayer rather than on self aggregation. We thus model the molecules as stiff chains of Lennard-Jones spheres with one slightly larger repulsive end bead (head) grafted to a planar surface. Depending on the size of the head, the temperature and the pressure, we find a variety of phases, which differ in tilt order (including tilt direction), and in positional order. In particular, we observe a modulated phase with a striped superstructure. The modulation results from the competition between two length scales, the head size and the tail diameter. As this mechanism is fairly general, it may conceivably also be relevant in experimental monolayers. We argue that the superstructure would be very difficult to detect in a scattering experiment, which perhaps accounts for the fact that it has not been reported so far. Finally the effect of varying the chain length on the phase diagram is discussed. Except at high pressures and temperatures, the phase boundaries in systems with longer chains are shifted to higher temperatures.Comment: To appear in J. Chem. Phy

Discrete Nodal Domain Theorems

We give a detailed proof for two discrete analogues of Courant's Nodal Domain Theorem

High-precision covariant one-boson-exchange potentials for np scattering below 350 MeV

All realistic potential models for the two-nucleon interaction are to some extent based on boson exchange. However, in order to achieve an essentially perfect fit to the scattering data, characterized by a chi2/Ndata ~ 1, previous potentials have abandoned a pure one boson-exchange mechanism (OBE). Using a covariant theory, we have found a OBE potential that fits the 2006 world np data below 350 MeV with a chi2/Ndata = 1.06 for 3788 data. Our potential has fewer adjustable parameters than previous high-precision potentials, and also reproduces the experimental triton binding energy without introducing additional irreducible three-nucleon forces.Comment: 4 pages; revised version with augmented data sets; agrees with published versio

Metastable States in High Order Short-Range Spin Glasses

The mean number of metastable states in higher order short-range spin glasses is estimated analytically using a variational method introduced by Tanaka and Edwards for very large coordination numbers. For lattices with small connectivities, numerical simulations do not show any significant dependence on the relative positions of the interacting spins on the lattice, indicating thus that these systems can be described by a few macroscopic parameters. As an extremely anisotropic model we consider the low autocorrelated binary spin model and we show through numerical simulations that its landscape has an exceptionally large number of local optima

A Simple Data-Adaptive Probabilistic Variant Calling Model

Background: Several sources of noise obfuscate the identification of single nucleotide variation (SNV) in next generation sequencing data. For instance, errors may be introduced during library construction and sequencing steps. In addition, the reference genome and the algorithms used for the alignment of the reads are further critical factors determining the efficacy of variant calling methods. It is crucial to account for these factors in individual sequencing experiments. Results: We introduce a simple data-adaptive model for variant calling. This model automatically adjusts to specific factors such as alignment errors. To achieve this, several characteristics are sampled from sites with low mismatch rates, and these are used to estimate empirical log-likelihoods. These likelihoods are then combined to a score that typically gives rise to a mixture distribution. From these we determine a decision threshold to separate potentially variant sites from the noisy background. Conclusions: In simulations we show that our simple proposed model is competitive with frequently used much more complex SNV calling algorithms in terms of sensitivity and specificity. It performs specifically well in cases with low allele frequencies. The application to next-generation sequencing data reveals stark differences of the score distributions indicating a strong influence of data specific sources of noise. The proposed model is specifically designed to adjust to these differences.Comment: 19 pages, 6 figure

Cover-Encodings of Fitness Landscapes

The traditional way of tackling discrete optimization problems is by using local search on suitably defined cost or fitness landscapes. Such approaches are however limited by the slowing down that occurs when the local minima that are a feature of the typically rugged landscapes encountered arrest the progress of the search process. Another way of tackling optimization problems is by the use of heuristic approximations to estimate a global cost minimum. Here we present a combination of these two approaches by using cover-encoding maps which map processes from a larger search space to subsets of the original search space. The key idea is to construct cover-encoding maps with the help of suitable heuristics that single out near-optimal solutions and result in landscapes on the larger search space that no longer exhibit trapping local minima. We present cover-encoding maps for the problems of the traveling salesman, number partitioning, maximum matching and maximum clique; the practical feasibility of our method is demonstrated by simulations of adaptive walks on the corresponding encoded landscapes which find the global minima for these problems.Comment: 15 pages, 4 figure

Convex Cycle Bases

Convex cycles play a role e.g. in the context of product graphs. We introduce convex cycle bases and describe a polynomial-time algorithm that recognizes whether a given graph has a convex cycle basis and provides an explicit construction in the positive case. Relations between convex cycles bases and other types of cycles bases are discussed. In particular we show that if G has a unique minimal cycle bases, this basis is convex. Furthermore, we characterize a class of graphs with convex cycles bases that includes partial cubes and hence median graphs. (authors' abstract)Series: Research Report Series / Department of Statistics and Mathematic