Hierarchical Crossover and Probability Landscapes of Genetic Operators

The time evolution of a simple model for crossover is discussed. A variant of this model with an improved exploration behavior in phase space is derived as a subset of standard one- and multi-point crossover operations. This model is solved analytically in the flat fitness case. Numerical simulations compare the way of phase space exploration of different genetic operators. In the case of a non-flat fitness landscape, numerical solutions of the evolution equations point out ways to estimate premature convergence.Comment: 11 pages, uuencoded postcript fil

Eigendecompositions of Transfer Operators in Reproducing Kernel Hilbert Spaces

Transfer operators such as the Perron--Frobenius or Koopman operator play an important role in the global analysis of complex dynamical systems. The eigenfunctions of these operators can be used to detect metastable sets, to project the dynamics onto the dominant slow processes, or to separate superimposed signals. We extend transfer operator theory to reproducing kernel Hilbert spaces and show that these operators are related to Hilbert space representations of conditional distributions, known as conditional mean embeddings in the machine learning community. Moreover, numerical methods to compute empirical estimates of these embeddings are akin to data-driven methods for the approximation of transfer operators such as extended dynamic mode decomposition and its variants. One main benefit of the presented kernel-based approaches is that these methods can be applied to any domain where a similarity measure given by a kernel is available. We illustrate the results with the aid of guiding examples and highlight potential applications in molecular dynamics as well as video and text data analysis

Enumeration of saturated and unsaturated substituted N-heterocycles

Mathematical and computational approaches in chemistry and biochemistry fill a gap in respect to the analysis of the physicochemical features of compounds and their functionality and provide an overview of known as well as yet unknown, but hypothetically possible structures. Nitrogen containing heterocycles such as aziridine, azetidine and pyrrolidine bear a high potential in pharmacology, biotechnology and synthetic biology. Here, we present a mathematical enumeration procedure for all possible azaheterocycles with at least one substituent depending on the number of atoms in the ring, in the sense of saturated and unsaturated congeners. One subgroup belonging to that substance class is constituted by ring-shaped amino acids with a secondary amino group such as proline. A recursion formula is derived, which results in a modified Lucas number series. Moreover, an explicit formula for determining the number of such substances based on the Golden Ratio is given and a second one, based on binomial coefficients, is newly derived. This enumeration is a helpful tool for construction or complementation of virtual compound databases and for computer-assisted chemical synthesis route planning.Comment: 11 pages, 4 figure

Connexins evolved after early chordates lost innexin diversity

Gap junction channels are formed by two unrelated protein families. Non-chordates use the primordial innexins, while chordates use connexins that superseded the gap junction function of innexins. Chordates retained innexin-homologs, but N-glycosylation prevents them from forming gap junctions. It is puzzling why chordates seem to exclusively use the new gap junction protein and why no chordates should exist that use non-glycosylated innexins to form gap junctions. Here, we identified glycosylation sites of 2388 innexins from 174 non-chordate and 276 chordate species. Among all chordates, we found not a single innexin without glycosylation sites. Surprisingly, the glycosylation motif is also widespread among non-chordate innexins indicating that glycosylated innexins are not a novelty of chordates. In addition, we discovered a loss of innexin diversity during early chordate evolution. Most importantly, lancelets, which lack connexins, exclusively possess only one highly conserved innexin with one glycosylation site. A bottleneck effect might thus explain why connexins have become the only protein used to form chordate gap junctions

Recording from an Identified Neuron Efficiently Reveals Hazard for Brain Function in Risk Assessment

Modern societies use a continuously growing number of chemicals. Because these are released into the environment and are taken up by humans, rigorous (but practicable) risk assessment must precede the approval of new substances for commerce. A number of tests is applicable, but it has been very difficult to efficiently assay the effect of chemicals on communication and information processing in vivo in the adult vertebrate brain. Here, we suggest a straightforward way to rapidly and accurately detect effects of chemical exposure on action potential generation, synaptic transmission, central information processing, and even processing in sensory systems in vivo by recording from a single neuron. The approach is possible in an identified neuron in the hindbrain of fish that integrates various sources of information and whose properties are ideal for rapid analysis of the various effects chemicals can have on the nervous system. The analysis uses fish but, as we discuss here, key neuronal functions are conserved and differences can only be due to differences in metabolism or passage into the brain, factors that can easily be determined. Speed and efficiency of the method, therefore, make it suitable to provide information in risk assessment, as we illustrate here with the effects of bisphenols on adult brain function

Identification of Electrochemically Adsorbed Species via Electrochemical Microcalorimetry: Sulfate Adsorption on Au(111)

We investigate compositional changes of an electrochemical interface upon polarization with electrochemical microcalorimetry. From the heat exchanged at a Au(111) electrode upon sulfate adsorption, we determine the reaction entropy of the adsorption process for both neutral and acidic solutions, where the dominant species in solution changes from SO$_4$$^{2−}$ to HSO$_4$$^{−}$. In neutral solution, the reaction entropy is about 40 J mol$^{−1}$ K$^{−1}$ more positive than that in acidic solution over the complete sulfate adsorption region. This entropy offset is explicable by a deprotonation step of HSO$_4$$^{−}$ preceding sulfate adsorption in acidic solution, which shows that the adsorbing species is SO$_4$* in both solutions. The observed overall variation of the reaction entropy in the sulfate adsorption region of ca. 80 J mol$^{−1}$ K$^{−1}$ indicates significant sulfate-coverage dependent entropic contributions to the Free Enthalpy of the surface system