Describing the complexity of systems: multi-variable "set complexity" and the information basis of systems biology

Context dependence is central to the description of complexity. Keying on the pairwise definition of "set complexity" we use an information theory approach to formulate general measures of systems complexity. We examine the properties of multi-variable dependency starting with the concept of interaction information. We then present a new measure for unbiased detection of multi-variable dependency, "differential interaction information." This quantity for two variables reduces to the pairwise "set complexity" previously proposed as a context-dependent measure of information in biological systems. We generalize it here to an arbitrary number of variables. Critical limiting properties of the "differential interaction information" are key to the generalization. This measure extends previous ideas about biological information and provides a more sophisticated basis for study of complexity. The properties of "differential interaction information" also suggest new approaches to data analysis. Given a data set of system measurements differential interaction information can provide a measure of collective dependence, which can be represented in hypergraphs describing complex system interaction patterns. We investigate this kind of analysis using simulated data sets. The conjoining of a generalized set complexity measure, multi-variable dependency analysis, and hypergraphs is our central result. While our focus is on complex biological systems, our results are applicable to any complex system.Comment: 44 pages, 12 figures; made revisions after peer revie

Visualising the structure of document search results: A comparison of graph theoretic approaches

This is the post-print of the article - Copyright @ 2010 Sage PublicationsPrevious work has shown that distance-similarity visualisation or ‘spatialisation’ can provide a potentially useful context in which to browse the results of a query search, enabling the user to adopt a simple local foraging or ‘cluster growing’ strategy to navigate through the retrieved document set. However, faithfully mapping feature-space models to visual space can be problematic owing to their inherent high dimensionality and non-linearity. Conventional linear approaches to dimension reduction tend to fail at this kind of task, sacrificing local structural in order to preserve a globally optimal mapping. In this paper the clustering performance of a recently proposed algorithm called isometric feature mapping (Isomap), which deals with non-linearity by transforming dissimilarities into geodesic distances, is compared to that of non-metric multidimensional scaling (MDS). Various graph pruning methods, for geodesic distance estimation, are also compared. Results show that Isomap is significantly better at preserving local structural detail than MDS, suggesting it is better suited to cluster growing and other semantic navigation tasks. Moreover, it is shown that applying a minimum-cost graph pruning criterion can provide a parameter-free alternative to the traditional K-neighbour method, resulting in spatial clustering that is equivalent to or better than that achieved using an optimal-K criterion

On the phase space structure of IP3 induced Ca2+ signalling and concepts for predictive modeling

The correspondence between mathematical structures and experimental systems is the basis of the generalizability of results found with specific systems, and is the basis of the predictive power of theoretical physics. While physicists have confidence in this correspondence, it is less recognized in cellular biophysics. On the one hand, the complex organization of cellular dynamics involving a plethora of interacting molecules and the basic observation of cell variability seem to question its possibility. The practical difficulties of deriving the equations describing cellular behaviour from first principles support these doubts. On the other hand, ignoring such a correspondence would severely limit the possibility of predictive quantitative theory in biophysics. Additionally, the existence of functional modules (like pathways) across cell types suggests also the existence of mathematical structures with comparable universality. Only a few cellular systems have been sufficiently investigated in a variety of cell types to follow up these basic questions. IP3 induced Ca2+ signalling is one of them, and the mathematical structure corresponding to it is subject of ongoing discussion. We review the system’s general properties observed in a variety of cell types. They are captured by a reaction diffusion system. We discuss the phase space structure of its local dynamics. The spiking regime corresponds to noisy excitability. Models focussing on different aspects can be derived starting from this phase space structure. We discuss how the initial assumptions on the set of stochastic variables and phase space structure shape the predictions of parameter dependencies of the mathematical models resulting from the derivation

Nonlocal stabilization of nonlinear beams in a self-focusing atomic vapor

We show that ballistic transport of optically excited atoms in an atomic vapor provides a nonlocal nonlinearity which stabilizes the propagation of vortex beams and higher order modes in the presence of a self-focusing nonlinearity. Numerical experiments demonstrate stable propagation of lowest and higher order vortices over a hundred diffraction lengths, before dissipation leads to decay of these structures.Comment: 3 figure

The spectral aerosol extinction monitoring system (SÇMS): Setup, observational products, and comparisons

The Spectral Aerosol Extinction Monitoring System (SÇMS) is presented that allows us to continuously measure the spectral extinction coefficient of atmospheric aerosol particles along an approximately 2.7 km long optical path at 30–50 m height above ground in Leipzig (51.3° N, 12.4° E), Germany. The fully automated instrument measures the ambient aerosol extinction coefficients from 300 to 1000 nm. The main goal of (SÇMS) observations are long-term studies of the relationship between particle extinction and relative humidity from below 40% to almost 100%. The setup is presented and observations (a case study and statistical results for 2009) are discussed in terms of time series of 550 nm particle optical depth, Ångström exponent, and particle size distribution retrieved from the spectrally resolved extinction. The SǼMS measurements are compared with simultaneously performed EARLINET (European Aerosol Research Lidar Network) lidar, AERONET (Aerosol Robotic Network) sun photometer, and in situ aerosol observations of particle size distribution and related extinction coefficients on the roof of our institute. Consistency between the different measurements is found, which corroborates the quality of the SǼMS observations. Statistical results of a period of 1 yr (2009) show mode extinction values of 0.09 km−1 (SÇMS), 0.075 km−1 (AERONET), and 0.03 km−1 (in situ). Ångström exponents for this period are 0.19 (390–880 nm,(SÇMS) and 1.55 (440–870 nm, AERONET)

Tracking azimuthons in nonlocal nonlinear media

We study the formation of azimuthons, i.e., rotating spatial solitons, in media with nonlocal focusing nonlinearity. We show that whole families of these solutions can be found by considering internal modes of classical non-rotating stationary solutions, namely vortex solitons. This offers an exhaustive method to identify azimuthons in a given nonlocal medium. We demonstrate formation of azimuthons of different vorticities and explain their properties by considering the strongly nonlocal limit of accessible solitons.Comment: 11 pages, 7 figure

High-quality ion beams by irradiating a nano-structured target with a petawatt laser pulse

We present a novel laser based ion acceleration scheme, where a petawatt circularly polarized laser pulse is shot on an ultra-thin (nano-scale) double-layer target. Our scheme allows the production of high-quality light ion beams with both energy and angular dispersion controllable by the target properties. We show that extraction of all electrons from the target by radiation pressure can lead to a very effective two step acceleration process for light ions if the target is designed correctly. Relativistic protons should be obtainable with pulse powers of a few petawatt. Careful analytical modeling yields estimates for characteristic beam parameters and requirements on the laser pulse quality, in excellent agreement with one and two-dimensional Particle-in Cell simulations.Comment: 18 pages, 7 figures, accepted in New. J. Phy

Cascaded self-compression of femtosecond pulses in filaments

Highly nonlinear wave propagation scenarios hold the potential to serve for energy concentration or pulse duration reduction of the input wave form, provided that a small range of input parameters be maintained. In particular when phenomena like rogue-wave formation or few-cycle optical pulses generation come into play, it becomes increasingly difficult to maintain control of the waveforms. Here we suggest an alternative approach towards the control of waveforms in a highly nonlinear system. Cascading pulse self-compression cycles at reduced nonlinearity limits the increase of input parameter sensitivity while still enabling an enhanced compression effect. This cascaded method is illustrated by experiments and in numerical simulations of the Nonlinear Schrödinger Equation, simulating the propagation of short optical pulses in a self-generated plasma

Profiling of Saharan dust from the Caribbean to western Africa - Part 1: Layering structures and optical properties from shipborne polarization/Raman lidar observations

We present final and quality-assured results of multiwavelength polarization/Raman lidar observations of the Saharan air layer (SAL) over the tropical Atlantic. Observations were performed aboard the German research vessel R/V Meteor during the 1-month transatlantic cruise from Guadeloupe to Cabo Verde over 4500 km from 61.5 to 20 degrees W at 14-15 degrees N in April-May 2013. First results of the ship-borne lidar measurements, conducted in the framework of SALTRACE (Saharan Aerosol Long-range Transport and Aerosol-Cloud Interaction Experiment), were reported by Kanitz et al. (2014). Here, we present four observational cases representing key stages of the SAL evolution between Africa and the Caribbean in detail in terms of layering structures and optical properties of the mixture of predominantly dust and aged smoke in the SAL. We discuss to what extent the lidar results confirm the validity of the SAL conceptual model which describes the dust long-range transport and removal processes over the tropical Atlantic. Our observations of a clean marine aerosol layer (MAL, layer from the surface to the SAL base) confirm the conceptual model and suggest that the removal of dust from the MAL, below the SAL, is very efficient. However, the removal of dust from the SAL assumed in the conceptual model to be caused by gravitational settling in combination with large-scale subsidence is weaker than expected. To explain the observed homogenous (height-independent) dust optical properties from the SAL base to the SAL top, from the African coast to the Caribbean, we have to assume that the particle sedimentation strength is reduced and dust vertical mixing and upward transport mechanisms must be active in the SAL. Based on lidar observations on 20 nights at different longitudes in May 2013, we found, on average, MAL and SAL layer mean values (at 532 nm) of the extinction-to-backscatter ratio (lidar ratio) of 17 +/- 5 sr (MAL) and 43 +/- 8 sr (SAL), of the particle linear depolarization ratio of 0.025 +/- 0 : 015 (MAL) and 0.19 +/- 0.09 (SAL), and of the particle extinction coefficient of 67 +/- 45Mm(-1) (MAL) and 68 +/- 37Mm(-1) (SAL). The 532 nm optical depth of the lofted SAL was found to be, on average, 0.15 +/- 0.13 during the ship cruise. The comparably low values of the SAL mean lidar ratio and depolarization ratio (compared to typical pure dust values of 50-60 sr and 0.3, respectively) in combination with backward trajectories indicate a smoke contribution to light extinction of the order of 20% during May 2013, at the end of the burning season in central-western Africa

Stability of two-dimensional spatial solitons in nonlocal nonlinear media

We discuss existence and stability of two-dimensional solitons in media with spatially nonlocal nonlinear response. We show that such systems, which include thermal nonlinearity and dipolar Bose Einstein condensates, may support a variety of stationary localized structures - including rotating spatial solitons. We also demonstrate that the stability of these structures critically depends on the spatial profile of the nonlocal response function.Comment: 8 pages, 9 figure