arXiv subjects

Stefan Hammer

Publications and source records attributed to Stefan Hammer.

4 recordsLinked to original sources

arXiv2026

Topological indices on self-similar graphs generated by groups

In this paper, we determine precise formulas for the diameters, the number of perfect matchings, and the Tutte polynomials for an infinite family of finite graphs, namely the Schreier graphs of tree automaton groups, also called tree graph automata. This enables us to easily find the number of spanning trees, spanning forests, and an explicit form for the chromatic polynomials. In the second part of the paper, we provide the precise values for the Wiener and Szeged index of any tree graph automaton.

math.CO↗

arXiv2022

Comparing Wiener, Szeged and revised Szeged index on cactus graphs

We show that on cactus graphs the Szeged index is bounded above by twice the Wiener index. For the revised Szeged index the situation is reversed if the graph class is further restricted. Namely, if all blocks of a cactus graph are cycles, then its revised Szeged index is bounded below by twice its Wiener index. Additionally, we show that these bounds are sharp and examine the cases of equality. Along the way, we provide a formulation of the revised Szeged index as a sum over vertices, which proves very helpful, and may be interesting in other contexts.

math.CO↗

arXiv2019

Evolving methods for rational de novo design of functional RNA molecules

Artificial RNA molecules with novel functionality have many applications in synthetic biology, pharmacy and white biotechnology. The de novo design of such devices using computational methods and prediction tools is a resource-efficient alternative to experimental screening and selection pipelines. In this review, we describe methods common to many such computational approaches, thoroughly dissect these methods and highlight open questions for the individual steps. Initially, it is essential to investigate the biological target system, the regulatory mechanism that will be exploited, as well as the desired components in order to define design objectives. Subsequent computational design is needed to combine the selected components and to obtain novel functionality. This process can usually be split into constrained sequence sampling, the formulation of an optimization problem and an in silico analysis to narrow down the number of candidates with respect to secondary goals. Finally, experimental analysis is important to check whether the defined design objectives are indeed met in the target environment and detailed characterization experiments should be performed to improve the mechanistic models and detect missing design requirements.

q-bio.BM↗

arXiv2018

Fixed-Parameter Tractable Sampling for RNA Design with Multiple Target Structures

The design of multi-stable RNA molecules has important applications in biology, medicine, and biotechnology. Synthetic design approaches profit strongly from effective in-silico methods, which can tremendously impact their cost and feasibility. We revisit a central ingredient of most in-silico design methods: the sampling of sequences for the design of multi-target structures, possibly including pseudoknots. For this task, we present the efficient, tree decomposition-based algorithm. Our fixed parameter tractable approach is underpinned by establishing the P-hardness of uniform sampling. Modeling the problem as a constraint network, our program supports generic Boltzmann-weighted sampling for arbitrary additive RNA energy models; this enables the generation of RNA sequences meeting specific goals like expected free energies or \GCb-content. Finally, we empirically study general properties of the approach and generate biologically relevant multi-target Boltzmann-weighted designs for a common design benchmark. Generating seed sequences with our program, we demonstrate significant improvements over the previously best multi-target sampling strategy (uniform sampling).Our software is freely available at: https://github.com/yannponty/RNARedPrint .

q-bio.QM↗