Biomedical subjects

Alexander K Hartmann

Publications and source records attributed to Alexander K Hartmann.

5 recordsLinked to original sources

PubMed2005

Dependence of RNA secondary structure on the energy model.

We analyze a microscopic RNA model, which includes two widely used models as limiting cases; namely, it contains terms for bond as well as for stacking energies. We numerically investigate possible changes in the qualitative and quantitative behavior while going from one model to the other; in particular, we test whether a transition occurs when continuously moving from one model to the other. For this we calculate various thermodynamic quantities, at both zero temperature and finite temperatures. All calculations can be done efficiently in polynomial time by a dynamic programming algorithm. We do not find a sign for the transition between the models, but the critical exponent nu of the correlation length, describing the phase transition in all models to an ordered low-temperature phase, seems to depend continuously on the model. Finally, we apply the epsilon -coupling method to study low-energy excitations. The exponent theta describing the energy scaling of the excitations seems to depend not much on the energy model.

Algorithms↗

PubMed2004

Clustering analysis of the ground-state structure of the vertex-cover problem.

Vertex cover is one of the classical NP-complete problems in theoretical computer science. A vertex cover of a graph is a subset of vertices such that for each edge at least one of the two endpoints is contained in the subset. When studied on Erdo s-Re nyi random graphs (with connectivity c) one observes a threshold behavior: In the thermodynamic limit the size of the minimal vertex cover is independent of the specific graph. Recent analytical studies show that on the phase boundary, for small connectivities c<e , the system is replica symmetric, while for larger connectivities replica symmetry breaking occurs. This change coincides with a change of the typical running time of algorithms from polynomial to exponential. To understand the reasons for this behavior and to compare with the analytical results, we numerically analyze the structure of the solution landscape. For this purpose, we have also developed an algorithm, which allows the calculation of the backbone, without the need to enumerate all solutions. We study exact solutions found with a branch-and-bound algorithm as well as configurations obtained via a Monte Carlo simulation. We analyze the cluster structure of the solution landscape by direct clustering of the states, by analyzing the eigenvalue spectrum of correlation matrices and by using a hierarchical clustering method. All results are compatible with a change at c=e . For small connectivities, the solutions are collected in a finite small number of clusters, while the number of clusters diverges slowly with system size for larger connectivities and replica symmetry breaking, but not one-step replica symmetry breaking (1-RSB) occurs.

Journal Article↗

PubMed2003

Solving satisfiability problems by fluctuations: the dynamics of stochastic local search algorithms.

Stochastic local search algorithms are frequently used to numerically solve hard combinatorial optimization or decision problems. We give numerical and approximate analytical descriptions of the dynamics of such algorithms applied to random satisfiability problems. We find two different dynamical regimes, depending on the number of constraints per variable: For low constraintness, the problems are solved efficiently, i.e., in linear time. For higher constraintness, the solution times become exponential. We observe that the dynamical behavior is characterized by a fast equilibration and fluctuations around this equilibrium. If the algorithm runs long enough, an exponentially rare fluctuation towards a solution appears.

Journal Article↗

PubMed2003

Depinning of elastic manifolds.

We compute roughness exponents of elastic d-dimensional manifolds in (d+1)-dimensional embedding spaces at the depinning transition for d=1, em leader,4. Our numerical method is rigorously based on a Hamiltonian formulation; it allows us to determine the critical manifold in finite samples for an arbitrary convex elastic energy. For a harmonic elastic energy (Delta(2) model), we find values of the roughness exponent between the one-loop and two-loop functional renormalization group results, in good agreement with earlier cellular automaton simulations. We find that the Delta(2) model is unstable with respect both to slight stiffening and to weakening of the elastic potential. Anharmonic corrections to the elastic energy allow us to obtain the critical exponents of the quenched Kardar, Parisi, Zhang class.

Journal Article↗

PubMed2002

Sampling rare events: statistics of local sequence alignments.

A method to calculate probability distributions in regions where the events are very unlikely (e.g., p approximately 10(-40)) is presented. The basic idea is to map the underlying model on a physical system. The system is simulated at a low temperature, such that preferably configurations with originally low probabilities are generated. Since the distribution of such a physical system is known, the original unbiased distribution can be obtained. As an application, local alignment of protein sequences is studied. The deviation of the distribution p(S) of optimum scores from the extreme-value distribution is quantified. This deviation decreases with growing sequence length.

Journal Article↗