Emergence of information transmission in a prebiotic RNA reactor

A poorly understood step in the transition from a chemical to a biological world is the emergence of self-replicating molecular systems. We study how a precursor for such a replicator might arise in a hydrothermal RNA reactor, which accumulates longer sequences from unbiased monomer influx and random ligation. In the reactor, intra- and intermolecular base pairing locally protects from random cleavage. By analyzing stochastic simulations, we find temporal sequence correlations that constitute a signature of information transmission, weaker but of the same form as in a true replicator.     

Hörmander Class of Pseudo-Differential Operators on Compact Lie Groups and Global Hypoellipticity

In this paper we give several global characterisations of the Hörmander class \(\Psi ^m(G)\) of pseudo-differential operators on compact Lie groups in terms of the representation theory of the group. The result is applied to give criteria for the ellipticity and the global hypoellipticity of pseudo-differential operators in terms of their matrix-valued full symbols. Several examples of the first and second order globally hypoelliptic differential operators are given, in particular of operators that are locally not invertible nor hypoelliptic but globally are. Where the global hypoelliptiticy fails, one can construct explicit examples based on the analysis of the global symbols.     

Optimizing cost flows by edge cost and capacity upgrade

We examine a network upgrade problem for cost flows. A budget can be distributed among the arcs of the network. An investment on each single arc can be used either to decrease the arc flow cost, or to increase the arc capacity, or both. The goal is to maximize the flow through the network while not exceeding bounds on the budget and on the total flow cost.

The problems are NP-hard even on series-parallel graphs. We provide an approximation algorithm on series-parallel graphs which, for arbitrary δ,>0, produces a solution which exceeds the bounds on the budget and the flow cost by factors of at most 1+δ and 1+, respectively, while the amount of flow is at least that of an optimum solution. The running time of the algorithm is polynomial in the input size and 1/(δ). In addition we give an approximation algorithm on general graphs applicable to problem instances with small arc capacities.     

Über eine quantitative Reaction des Lignins

Ohne Zusammenfassung     

Novel cyclization cascades to functionalized indanes and tetrahydronaphthalenes

Cyclization cascades involving C-C bond formations followed by lactonization reactions provide fast access to structurally complex tricyclic indane and tetrahydronaphthalene derivatives.     

Asymptotic Behavior of the Value Functions of Discrete-Time Discounted Optimal Control

We study deterministic discounted optimal control problems associated with discrete-time systems. It is shown that, for small discount rates, the controllability properties of the underlying system can guarantee the convergence of the discounted value function to the value function of the average yield. An application in the theory of exponential growth rates of discrete inclusions is presented. This application motivates the analysis of infinite-horizon optimal control problems with running yields that are unbounded from below.