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We study spatiotemporal patterns produced by small-world networks of biologically motivated nonlinear oscillators from a data-analysis perspective. It is shown that the connectivity levels of such systems can be reconstructed by analyzing heterogeneity and fluctuation content of the patterns. These properties are determined by applying spatiotemporal filters described in [Physica A 289 (2001) 498] to pairs of oscillators in a network. Possible applications of our method to biological data (e.g., time-resolved cDNA microarray data), in order to distinguish densely connected systems from sparsely connected systems, are commented on.

We present a direct way to model short- and medium-range correlations in DNA sequences and to separate them from long-range correlations. To do so, we discuss symbol sequences generated by a discrete autoregressive process of order p, DAR(p). These sequences display higher-order Markov properties but are based on very few parameters. The aim of our investigation is (1) to introduce with such DAR(p) processes a parameter-efficient tool for generating higher-order Markov processes on a discrete alphabet, (2) to study, how the parameters of the process determine the statistical properties of the sequence and (3) to provide the mathematical tools for estimating the parameters from a given experimental sequence. The statistical properties of the generated sequences, expressed in terms of parameters in the DAR(p) process, are monitored with methods from information theory. The implications of our findings for DNA sequences are discussed and some application is given. In particular, it is shown, how short-range correlations in DNA sequences can be parameterised by such a process.

Crassulacean acid metabolism (CAM) serves as a botanical model system for the investigation of circadian rhythmicity. In a new set of experiments with the obligatory CAM plant Kalanchoe daigremontiana the response to periodic stimulations with temperature pulses has been studied. On the basis of an experimental phase–response curve of net CO 2 -gas exchange the effect of periodic stimulation has been simulated using a finite-difference equation. These simulations revealed the locations of two period-2 cycles in the CO 2 uptake of the CAM plant. In subsequent experiments based upon the simulated bifurcation diagram the position and amplitude of one of these cycles were confirmed, while experimental evidence for the second cycle could be found. Possible roles of such dynamics for the functioning of the biological clock are discussed.

We show that recent methods from nonlinear dynamics and complexity theory developed in theoretical physics can and should be applied to the description and analysis of systems in plant physiology, in particular to interpret data series in time and space, i.e., rhythms and pattern formation processes. We start with a brief introduction into the key ideas of nonlinear dynamics, including a short outline of topics which are currently the focus of theoretical interest, in particular the concept, origin and possible function of noise in biological systems. The theoretical concepts are applied to a model system of circadian rhythmicity in plant physiology, crassulacean acid metabolism. With this application, we illustrate the main idea of our article: nonlinear dynamics serves as a remarkable tool for unveiling the internal mechanisms at work in a system's process of self-organization.

Quantification methods for spatiotemporal patterns are introduced, which are based on nearest-neighbor considerations inspired by cellular automata as well as by more complex spatiotemporal dynamics. In particular, spatial and temporal structures, which can be found in aggregation and clustering phenomena, are quantified by introducing the concept of cellular automata (CA) measures for homogeneity and for the amount of fluctuations contributing to the observed dynamics. The aim of this paper is to define such measures and then test their performance on theoretically generated data sets. These tests with exemplary spatiotemporal patterns show the applicability of these methods for data analysis. For example, with the help of the CA fluctuation number we are able to extract the amount of noise present in spatiotemporal data. The observables constructed with the help of such CA techniques have straightforward applications in life sciences, where the quantitative analysis of spatiotemporal patterns still suffers from the lack of a standardized set of analysis techniques.

Using linearly polarized tagged photons from coherent bremsstrahlung, differential cross sections and beam asymmetries for Compton scattering by 4 He have been measured at MAMI in the energy interval between 150 MeV and 500 MeV for scattering angles of θ γ lab =37°, 93° and 137°, thus largely increasing the available data base. Improved calculations in terms of the Δ -hole model completely fail to describe the data at large scattering angles. The same proved to be true for a schematic model, even after taking into account properties of nuclear photo-absorption in very detail.

The universal curve σ A of nuclear photoabsorption is investigated within a Fermi gas model of nuclear matter. An energy range from pion threshold up to 400 MeV is considered. The interactions between nucleon, pion, Δ-isobar and photon are considered in the non-relativistic approximation with corrections of the order 1 M taken into account with respect to proton mass. Analytical expressions are obtained, in which the influence of nuclear correlations and two-nucleon contributions is studied explicitly. The contributions of real and virtual pions are found to be sufficient to obtain agreement with experimental data in this energy range. An extension of the model calculation to nucleon knock-out reactions is discussed.

Biorhythm research is currently dominated by the quest for the biological clock or circadian oscillator on a genetic basis. One of us has reviewed the plant biological literature in a contribution to last year’s volume of this series (Luttge 2002). However, while spontaneous ultradian frequency rhythms remain a central topic in neurobiology with the electrical firing of neurons, and oscillations of cyclic adenosine-monophosphate (cAMP) secretion, attraction and pattern formation of amoebae of the slime mold Dictyostelium (e.g. Berridge and Rapp 1979) and the oscillatory behaviour of glycolysis (e.g., Berridge and Rapp 1979; Olsen and Degn 1985; Rapp 1986; see also below Sect. 2.2) are much studied, astonishingly little research effort is currently devoted to ultradian high frequency oscillations in plant biology. This is regrettable because much can be learnt from the study of high frequency rhythms. This is so not only because it is often much easier to keep systems studied under strict experimental control and obtain more readily sufficiently extended time series of measurements for theoretical analysis than with the much longer circadian oscillations. Although we must remember that in Drosophila both the circadian rhythm of eclosion and locomotor activity and the very short ultradian rhythm of the male courtship song seem to be governed by the same PER gene (Dunlap 1993), studying high frequency oscillations mostly implies that we set ourselves free from being paralyzed by the evolutionary and genetic biological clock enigma.

Differential cross sections for elastic scattering of photons have been measured for $^{40}$Ca at energies of 58 and 74 MeV and for $^{16}$O and $^4$He at 61 MeV, in the angular range from 45$^o$ to 150$^o$. Evidence is obtained that there are no significant in-medium modifications of the electromagnetic polarizabilities except for those originating from meson exchange currents., 20 pages including 5 Figures