Abstract:
We investigate a phase-field-crystal model for homogeneous nucleation. Instead of solving the time evolution of a density field towards equilibrium we use a String Method to identify saddle points in phase space. The saddle points allow to obtain the nucleation barrier and the critical nucleus. The advantage of using the phase-field-crystal model for this task is its ability to resolve atomistic effects. The obtained results indicate different properties of the critical nucleus compared with bulk crystals and show a detailed description of the nucleation process.

Abstract:
We present a dynamic model to study ordering of particles on arbitrary curved surfaces. Thereby the particles are represented as maxima in a density field and a surface partial differential equation for the density field is solved to the minimal energy configuration. We study annihilation of dislocations within the ordered sytem and premelting along grain boundary scars. The obtained minimal energy configurations on a sphere are compared with existing results and scaling laws are computed for the number of excess dislocations as a function of system size.

Abstract:
The phase-field crystal model is by now widely used in order to predict crystal nucleation and growth. For colloidal solidification with completely overdamped individual particle motion, we show that the phase-field crystal dynamics can be derived from the microscopic Smoluchowski equation via dynamical density functional theory. The different underlying approximations are discussed. In particular, a variant of the phase-field crystal model is proposed which involves less approximations than the standard phase-field crystal model. We finally test the validity of these phase-field crystal models against dynamical density functional theory. In particular, the velocities of a linear crystal front from the undercooled melt are compared as a function of the undercooling for a two-dimensional colloidal suspension of parallel dipoles. Good agreement is only obtained by a drastic scaling of the free energies in the phase-field crystal model in order to match the bulk freezing transition point.

Abstract:
Grain growth experiments on thin metallic films have shown the geometric and topological characteristics of the grain structure to be universal and independent of many experimental conditions. The universal size distribution, however, is found to differ both qualitatively and quantitatively from the standard Mullins curvature driven model of grain growth; with the experiments exhibiting an excess of small grains (termed an "ear") and an excess of very large grains (termed a "tail") compared with the model. While a plethora of extensions of the Mullins model have been proposed to explain these characteristics, none have been successful. In this work, large scale simulations of a model that resolves the atomic scale on diffusive time scales, the phase field crystal model, is used to examine the complex phenomena of grain growth. The results are in remarkable agreement with the experimental results, recovering the characteristic "ear" and "tail" features of the experimental grain size distribution. The simulations also indicate that while the geometric and topological characteristics are universal, the dynamic growth exponent is not.

Abstract:
Here, we show that the use of Bayesian networks (BNs) allows accurate prediction of evolutionary conserved exon skipping events. At a stringent false positive rate of 0.5%, our BN achieves an improved true positive rate of 61%, compared to a previously reported 50% on the same dataset using support vector machines (SVMs). Incorporating several novel discriminative features such as intronic splicing regulatory elements leads to the improvement. Features related to mRNA secondary structure increase the prediction performance, corroborating previous findings that secondary structures are important for exon recognition. Random labelling tests rule out overfitting. Cross-validation on another dataset confirms the increased performance. When using the same dataset and the same set of features, the BN matches the performance of an SVM in earlier literature. Remarkably, we could show that about half of the exons which are labelled constitutive but receive a high probability of being alternative by the BN, are in fact alternative exons according to the latest EST data. Finally, we predict exon skipping without using conservation-based features, and achieve a true positive rate of 29% at a false positive rate of 0.5%.BNs can be used to achieve accurate identification of alternative exons and provide clues about possible dependencies between relevant features. The near-identical performance of the BN and SVM when using the same features shows that good classification depends more on features than on the choice of classifier. Conservation based features continue to be the most informative, and hence distinguishing alternative exons from constitutive ones without using conservation based features remains a challenging problem.Eukaryotic primary mRNAs consist of exons and introns. The mature transcript as the substrate for translation is produced by removing introns in a process called splicing. Splicing can be either constitutive, always producing the same mRNA, or alternative,

Abstract:
By using a phase-field crystal (PFC) model, the liquid-crystal growth of the plastic triangular phase is simulated with emphasis on crystal shape and topological defect formation. The equilibrium shape of a plastic triangular crystal (PTC) grown from a isotropic phase is compared with that grown from a columnar/smectic A (CSA) phase. While the shape of a PTC nucleus in the isotropic phase is almost identical to that of a classical PFC model, the shape of a PTC nucleus in CSA is affected by the orientation of stripes in the CSA phase, and irregular hexagonal, elliptical, octagonal, and rectangular shapes are obtained. Concerning the dynamics of the growth process we analyse the topological structure of the nematic-order, which starts from nucleation of $+\frac{1}{2}$ and $-\frac{1}{2}$ disclination pairs at the PTC growth front and evolves into hexagonal cells consisting of $+1$ vortices surrounded by six satellite $-\frac{1}{2}$ disclinations. It is found that the orientational and the positional order do not evolve simultaneously, the orientational order evolves behind the positional order, leading to a large transition zone, which can span over several lattice spacings.

Abstract:
There have been two different methods for checking the satisfiability of feature descriptions that use the functional uncertainty device, namely~\cite{Kaplan:88CO} and \cite{Backofen:94JSC}. Although only the one in \cite{Backofen:94JSC} solves the satisfiability problem completely, both methods have their merits. But it may happen that in one single description, there are parts where the first method is more appropriate, and other parts where the second should be applied. In this paper, we present a common framework that allows one to combine both methods. This is done by presenting a set of rules for simplifying feature descriptions. The different methods are described as different controls on this rule set, where a control specifies in which order the different rules must be applied.

Abstract:
Various feature descriptions are being employed in logic programming languages and constrained-based grammar formalisms. The common notational primitive of these descriptions are functional attributes called features. The descriptions considered in this paper are the possibly quantified first-order formulae obtained from a signature of binary and unary predicates called features and sorts, respectively. We establish a first-order theory FT by means of three axiom schemes, show its completeness, and construct three elementarily equivalent models. One of the models consists of so-called feature graphs, a data structure common in computational linguistics. The other two models consist of so-called feature trees, a record-like data structure generalizing the trees corresponding to first-order terms. Our completeness proof exhibits a terminating simplification system deciding validity and satisfiability of possibly quantified feature descriptions.

Abstract:
In contrast to stochastic approaches, which are not capable of answering many fundamental questions, our methods are based on fast, non-heuristic techniques. The resulting tools are designed for high-throughput studies of 3D-lattice proteins utilising the Hydrophobic-Polar (HP) model. The source bundle is freely available [1].The CPSP-tools package is the first set of exact and complete methods for extensive, high-throughput studies of non-restricted 3D-lattice protein models. In particular, our package deals with cubic and face centered cubic (FCC) lattices.The organisation of bio-molecules, in particular proteins, in the sequence and structure space has recently been attracting increased attention. Particularly questions concerning finding the native structure or investigating the kinetics and evolution of proteins have been widely studied. These problems are often tackled using simplified models such as the Hydrophobic-Polar (HP) model (e.g. Jacob et al. [2]). Though abstract, these models are computationally feasible and do allow for deeper insights into fundamental and general principles [2-4].Several recurring tasks can be identified in such studies using simplified models. Namely, predicting the native structure, classifying whether a sequence is protein-like, calculating its degeneracy and stability, or the design of sequences that optimally fold to a given structure. The problems associated with these tasks are computationally very hard (NP-complete) [5-7]. Nevertheless, these tasks demand for exact and complete (i.e. non-heuristic) methods. It is important to note that stochastic methods cannot be used for proving optimality and in particular proving that a sequence has a unique lowest energy (protein-like) fold [8].Consequently, with the exception of Yue and Dill [9], all studies requiring complete and exact answers to optimal structure prediction were based on exhaustive enumeration. These studies were, hence, confined to small sequence lengths. In other

Abstract:
Lattice protein models, as the Hydrophobic-Polar (HP) model, are a common abstraction to enable exhaustive studies on structure, function, or evolution of proteins. A main issue is the high number of optimal structures, resulting from the hydrophobicity-based energy function applied. We introduce an equivalence relation on protein structures that correlates to the energy function. We discuss the efficient enumeration of optimal representatives of the corresponding equivalence classes and the application of the results.