Spatial Chaos Research Articles

Spatial chaos and complexity in the intracellular space of cancer and normal cells

BackgroundOne of the most challenging problems in biological image analysis is the quantification of the dynamical mechanism and complexity of the intracellular space. This paper investigates potential spatial chaos and complex behavior of the intracellular space of typical cancer and normal cell images whose structural details are revealed by the combination of scanning electron microscopy and focused ion beam systems. Such numerical quantifications have important implications for computer modeling and simulation of diseases.MethodsCancer cell lines derived from a human head and neck squamous cell carcinoma (SCC-61) and normal mouse embryonic fibroblast (MEF) cells produced by focused ion beam scanning electron microscopes were used in this study. Spatial distributions of the organelles of cancer and normal cells can be analyzed at both short range and long range of the bounded dynamical system of the image space, depending on the orientations of the spatial cell. A procedure was designed for calculating the largest Lyapunov exponent, which is an indicator of the potential chaotic behavior in intracellular images. Furthermore, the sample entropy and regularity dimension were applied to measure the complexity of the intracellular images.ResultsPositive values of the largest Lyapunov exponents (LLEs) of the intracellular space of the SCC-61 were obtained in different spatial orientations for both long-range and short-range models, suggesting the chaotic behavior of the cell. The MEF has smaller positive values of LLEs in the long range than those of the SCC-61, and zero vales of the LLEs in the short range analysis, suggesting a non-chaotic behavior. The intracellular space of the SCC-61 is found to be more complex than that of the MEF. The degree of complexity measured in the spatial distribution of the intracellular space in the diagonal direction was found to be approximately twice larger than the complexity measured in the horizontal and vertical directions.ConclusionInitial findings are promising for characterizing different types of cells and therefore useful for studying cancer cells in the spatial domain using state-of-the-art imaging technology. The measures of the chaotic behavior and complexity of the spatial cell will help computational biologists gain insights into identifying associations between the oscillation patterns and spatial parameters of cells, and appropriate model for simulating cancer cell signaling networks for cancer treatment and new drug discovery.

Testing for presence of known and unknown molecules in imaging mass spectrometry

Imaging mass spectrometry has emerged in the past decade as a label-free, spatially resolved and multi-purpose bioanalytical technique for direct analysis of biological samples. However, solving two everyday data analysis problems still requires expert judgment: (i) the detection of unknown molecules and (ii) the testing for presence of known molecules. We developed a measure of spatial chaos of a molecular image corresponding to a mass-to-charge value, which is a proxy for the molecular presence, and developed methods solving considered problems. The statistical evaluation was performed on a dataset from a rat brain section with test sets of molecular images selected by an expert. The measure of spatial chaos has shown high agreement with expert judges. The method for detection of unknown molecules allowed us to find structured molecular images corresponding to spectral peaks of any low intensity. The test for presence applied to a list of endogenous peptides ranked them according to the proposed measure of their presence in the sample. The source code and test sets of mass-to-charge images are available at http://www.math.uni-bremen.de/∼theodore. Supplementary materials are available at Bioinformatics online. theodore@uni-bremen.de.

Pattern dynamics and filamentation of femtosecond terawatt laser pulses in air including the higher-order Kerr effects

Plasma defocusing and higher-order Kerr effects on multiple filamentation and pattern formation of ultrashort laser pulse propagation in air are investigated. Linear analyses and numerical results show that these two saturable nonlinear effects can destroy the coherent evolution of the laser field, and small-scale spatial turbulent structures rapidly appear. For the two-dimensional case, numerical simulations show that blow-up-like solutions, spatial chaos, and pseudorecurrence can appear at higher laser intensities if only plasma defocusing is included. These complex patterns result from the stochastic evolution of the higher- or shorter-wavelength modes of the laser light spectrum. From the viewpoint of nonlinear dynamics, filamentation can be attributed to the modulational instability of these spatial incoherent localized structures. Furthermore, filament patterns associated with multiphoton ionization of the air molecules with and without higher-order Kerr effects are compared.

A Self-Adaptive Parallel Encryption Algorithm Based on Discrete 2D-Logistic Map

A self-adaptive parallel encryption algorithm based on discrete 2D-Logistic map is developed according to the position scrambling and diffusion of multi-direction in variable space of spatial chaos. The binary sequences b1b2b3···bn are obtained according to the user key, in which the binary sequence 0 and 1 denote distribution mode of processors and the number of binary sequence n denotes cycle number. Then the pseudorandom 2D matrix is generated by 2D-Logistic map, and adaptive segmentation is applied in image matrix and pseudorandom matrix according to the value and the number of binary sequence. The parallel operation is used among blocks to improve efficiency and meet real-time demand in transmission processes. However, the pixel permutation is applied in partitioned matrix through ergodic matrix generated by pseudo-random matrix-block to decrease the correlation of adjacent pixels. Then the pixel substitution is used for fully diffusing through cipher block chaining mode until n cycles. The proposed algorithm can meet the three requirements of parallel operation in image encryption and the real-time requirement in transmission processes. The security is proved by theoretical analysis and simulation results.

Chaotic movement of vortices in superconductors of high-Tc superconducting maglev system at a high speed

Vortex motion in superconductors of high-Tc superconducting maglev system is studied by a computational simulation. The vortex system is treated in a similar fashion, as a system where defects are arranged in periodic arrays and driven by an alternating current (AC) field. Computational simulation reveals that due to the high nonlinearity of the vortex-defect interaction, the system shows typical chaotic characters. Effects of the vortex-vortex coupling, the driving frequency, and the vortex viscosity on the vortex motion have been studied to reveal the interaction between the spatial and temporal chaos. It is found that the mean-field approach is a good approximation to describe the vortex motion in one dimensional vortex system under an AC driving field. The vortex motion under the damping mode is a kind of self-organized motion. Lastly, the spatial chaos can dominate the chaotic behavior of the system.

Transition from spatial coherence to incoherence in coupled chaotic systems

We investigate the spatio-temporal dynamics of coupled chaotic systems with nonlocal interactions, where each element is coupled to its nearest neighbors within a finite range. Depending upon the coupling strength and coupling radius, we find characteristic spatial patterns such as wavelike profiles and study the transition from coherence to incoherence leading to spatial chaos. We analyze the origin of this transition based on numerical simulations and support the results by theoretical derivations, identifying a critical coupling strength and a scaling relation of the coherent profiles. To demonstrate the universality of our findings, we consider time-discrete as well as time-continuous chaotic models realized as a logistic map and a Rössler or Lorenz system, respectively. Thereby, we establish the coherence-incoherence transition in networks of coupled identical oscillators.

Multistability of twisted states in non-locally coupled Kuramoto-type models

A ring of N identical phase oscillators with interactions between L-nearest neighbors is considered, where L ranges from 1 (local coupling) to N/2 (global coupling). The coupling function is a simple sinusoid, as in the Kuramoto model, but with a minus sign which has a profound influence on its behavior. Without the limitation of the generality, the frequency of the free-running oscillators can be set to zero. The resulting system is of gradient type, and therefore, all its solutions converge to an equilibrium point. All so-called q-twisted states, where the phase difference between neighboring oscillators on the ring is 2πq/N, are equilibrium points, where q is an integer. Their stability in the limit N → ∞ is discussed along the line of Wiley et al. [Chaos 16, 015103 (2006)] In addition, we prove that when a twisted state is asymptotically stable for the infinite system, it is also asymptotically stable for sufficiently large N. Note that for smaller N, the same q-twisted states may become unstable and other q-twisted states may become stable. Finally, the existence of additional equilibrium states, called here multi-twisted states, is shown by numerical simulation. The phase difference between neighboring oscillators is approximately 2πq/N in one sector of the ring, -2πq/N in another sector, and it has intermediate values between the two sectors. Our numerical investigation suggests that the number of different stable multi-twisted states grows exponentially as N → ∞. It is possible to interpret the equilibrium points of the coupled phase oscillator network as trajectories of a discrete-time translational dynamical system where the space-variable (position on the ring) plays the role of time. The q-twisted states are then fixed points, and the multi-twisted states are periodic solutions of period N that are close to a heteroclinic cycle. Due to the apparently exponentially fast growing number of such stable periodic solutions, the system shows spatial chaos as N → ∞.

Effects of nonlocal coupling on the dynamics of neural systems

Event Abstract Back to Event Effects of nonlocal coupling on the dynamics of neural systems Philipp Hövel1, 2* and Iryna Omelchenko1, 2 1 Technische Universität Berlin, Physics, Germany 2 Bernstein Center for Computational Neuroscience Berlin, Germany Understanding the dynamics on networks is at the heart of modern nonlinear science and has a wide applicability to neuroscience. The interplay of network topology and local dynamics opens a variety of dynamical phenomena such as synchronization, clustering, waves, kinks, complex patterns, and chaos. Here we study the spatio-temporal dynamics of coupled neural oscillators with nonlocal interactions. In the considered configuration each element is coupled to its nearest neighbors within a finite range. Depending upon the control parameters chosen as coupling strength and coupling radius, we investigate the cooperative dynamics in a generic model for type-II excitability given by FitzHugh-Nagumo equations. The individual systems are considered to operate above a Hopf bifurcation, that is, they operate in the oscillatory regime. On the basis of previous results on nonlocally coupled discrete maps and chaotic systems, we demonstrate the universality of a transition from coherence to incoherence in such systems, giving rise to spatial chaos and so-called chimera states. The latter arise as hybrid spatial patterns in regular networks of identical oscillators and consist of parts with high spatial coherence and regions where spatial coherence is lost. We analyze the regions of stability of various types of solutions in the parameter space of coupling strength and coupling radius: completely synchronous oscillations, wave-like profiles, cluster states as well as partially incoherent states. Furthermore, we study the robustness of the observed patterns in the presence of inhomogeneities of the local elements that are introduced via different threshold parameters in the FitzHugh-Nagumo system. Acknowledgements Supported by the BMBF under the grant no. 01GQ1001B (Förderkennzeichen). Keywords: dynamics, incoherence, nonlocal coupling, oscillations, synchronization Conference: Bernstein Conference 2012, Munich, Germany, 12 Sep - 14 Sep, 2012. Presentation Type: Poster Topic: Abstracts Citation: Hövel P and Omelchenko I (2012). Effects of nonlocal coupling on the dynamics of neural systems. Front. Comput. Neurosci. Conference Abstract: Bernstein Conference 2012. doi: 10.3389/conf.fncom.2012.55.00221 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 10 May 2012; Published Online: 12 Sep 2012. * Correspondence: Dr. Philipp Hövel, Technische Universität Berlin, Physics, Berlin, 10623, Germany, phoevel@physik.tu-berlin.de Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Philipp Hövel Iryna Omelchenko Google Philipp Hövel Iryna Omelchenko Google Scholar Philipp Hövel Iryna Omelchenko PubMed Philipp Hövel Iryna Omelchenko Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Loss of Coherence in Dynamical Networks: Spatial Chaos and Chimera States

We discuss the breakdown of spatial coherence in networks of coupled oscillators with nonlocal interaction. By systematically analyzing the dependence of the spatiotemporal dynamics on the range and strength of coupling, we uncover a dynamical bifurcation scenario for the coherence-incoherence transition which starts with the appearance of narrow layers of incoherence occupying eventually the whole space. Our findings for coupled chaotic and periodic maps as well as for time-continuous Rössler systems reveal that intermediate, partially coherent states represent characteristic spatiotemporal patterns at the transition from coherence to incoherence.

Coupling between temporal and spatial chaos of vortex state in superconductors with periodical pinning arrays

Vortex motion in the background of many vortices is investigated by a mean field approach. Effects of the vortex–vortex coupling, the driving frequency, and the vortex viscosity on the vortex motion have been studied to reveal the interaction between the spatial and temporal chaos. It is found that the mean-field approach is a good approximation to describe the vortex motion in one dimensional vortex system. The vortex motion under the damping mode is a kind of self-organized motion. The spatial chaos can dominate the chaotic behavior of the system.

Prediction method for risks of coal and gas outbursts based on spatial chaos theory using gas desorption index of drill cuttings

Based on the evolution of geological dynamics and spatial chaos theory, we proposed the advanced prediction an advanced prediction method of a gas desorption index of drill cuttings to predict coal and gas outbursts. We investigated and verified the prediction method by a spatial series data of a gas desorption index of drill cuttings obtained from the II3112 coal roadway at the Shitai Mine. Our experimental results show that the spatial distribution of the gas desorption index of drill cuttings has some chaotic characteristics, which implies that the risk of coal and gas outbursts can be predicted by spatial chaos theory. We also found that a proper amount of sample data needs to be chosen in order to ensure the accuracy and practical maneuverability of prediction. The relative prediction error is small when the prediction pace is chosen carefully. In our experiments, it turned out that the optimum number of sample points is 80 and the optimum prediction pace 30. The corresponding advanced prediction pace basically meets the requirements of engineering applications.

Erratum: Spatial chaos of traveling waves has a given velocity [Phys. Rev. E80, 025203(R) (2009)

Erratum: Spatial chaos of traveling waves has a given velocity [Phys. Rev. E<b>80</b>, 025203(R) (2009)

Cryptographic spatial chaos sequence

In this paper, a novel pseudo-random sequence generator (PRSG) based on spatial chaos system is proposed. The statistical tests and correlation analysis on the proposed PRSG are performed by the well-known Federal Information Processing Standards FIPS140-1, and the experimental results show that the image encryption based on spatial chaos ergodic matrix has good random statistical characteristics, large key space and great sensitivity of the sequence.

SPATIALLY CHAOTIC BIFURCATIONS OF AN ELASTIC WEB OF LINKS

Spatially chaotic bifurcations of an elastic web of links are investigated. We numerically construct the global bifurcation diagrams uniquely describing the buckled states, and show that the exponential growth of the number of equilibrium branches with the size of the web indicates spatial chaos. The types of bifurcations from the trivial equilibrium branch are also determined, and we show that cusp catastrophes of any order can appear. This observation relates the buckling of the elastic web of links to the buckling of rods with finite shear and infinite bending and normal stiffness.

325 Food does not affect the pharmacokinetics of CS-7017 in healthy subjects: results from an open label, phase I, two-treatment, three-period, crossover study

We present an analytical study of chaos in a charged black hole in the extended phase space in the context of the Poincare–Melnikov theory. Along with some background on dynamical systems, we compute the relevant Melnikov function and find its zeros. Then we analyse these zeros either to identify the temporal chaos in the spinodal region, or to observe spatial chaos in the small/large black hole equilibrium configuration. As a byproduct, we derive a constraint on the Black hole' charge required to produce chaotic behaviour. To the best of our knowledge, this is the first endeavour to understand the correlation between chaos and phase picture in black holes.

Comparison of recurrence quantification methods for the analysis of temporal and spatial chaos

A comparative study of the recurrence properties of time series and two-dimensional spatial data is performed by means of Recurrence Quantification Analysis. The recent extension to distributed data of methods based on recurrences reveals new insights improving the performances of the approach for the analysis of complex spatial patterns. Indeed, the measures determinism and entropy provide significant information about the small and large scale characterization of the patterns allowing for a better connection to the physical properties of the spatial system under investigation.

Self-organised spatial patterns and chaos in a ratio-dependent predator–prey system

Mechanisms and scenarios of pattern formation in predator–prey systems have been a focus of many studies recently as they are thought to mimic the processes of ecological patterning in real-world ecosystems. Considerable work has been done with regards to both Turing and non-Turing patterns where the latter often appears to be chaotic. In particular, spatiotemporal chaos remains a controversial issue as it can have important implications for population dynamics. Most of the results, however, were obtained in terms of ‘traditional’ predator–prey models where the per capita predation rate depends on the prey density only. A relatively new family of ratio-dependent predator–prey models remains less studied and still poorly understood, especially when space is taken into account explicitly, in spite of their apparent ecological relevance. In this paper, we consider spatiotemporal pattern formation in a ratio-dependent predator–prey system. We show that the system can develop patterns both inside and outside of the Turing parameter domain. Contrary to widespread opinion, we show that the interaction between two different type of instability, such as the Turing–Hopf bifurcation, does not necessarily lead to the onset of chaos; on the contrary, the emerging patterns remain stationary and almost regular. Spatiotemporal chaos can only be observed for parameters well inside the Turing–Hopf domain. We then investigate the relative importance of these two instability types on the onset of chaos and show that, in a ratio-dependent predator–prey system, the Hopf bifurcation is indeed essential for the onset of chaos whilst the Turing instability is not.

A new cryptosystem based on spatial chaotic system

Encryption of images is different from that of texts due to some intrinsic features of images such as bulk data capacity and high redundancy, which is generally difficult to handle by traditional methods. This paper proposes a new spatial chaos system (SCS), which is investigated by conducting FIPS 140-1 statistic test, and is especially useful for encryption of digital images. It is shown how to adapt a two dimensional (2D) ergodic matrix obtained from SCS to permute the positions of image pixels and confuse the relationship between the cipher image and plain image simultaneously. Experimental results show that the performance and security of the proposed cryptographic system are better than those of existing lower dimensional chaotic cryptographic systems.

GEO-MATHEMATICAL MODELLING OF SPATIAL-ECOLOGICAL COMPLEX SYSTEMS: AN EVALUATION

Assessing the complexity of landscapes is one of the top research priorities for Physical Geography and Ecology. This paper aims at a methodological evaluation of the discrete and analytical mathematical models hitherto available for quantitative assessments of spatial ecological complex systems. These models are derived from cellular automata and nonlinear dynamics. They describe complex features and processes in landscapes, such as spatial ecological nonlinear interactions, unpredictability and chaos, self-organization and pattern formation. Beginning with a distinction between two basic types of spatial ecological complexity (structural, functional), and after reviewing the quantitative methods so far available to assess it, the areas where the major challenges (and hence, difficulties) for future research arise are identified. These are: a) to develop measures of structural spatial-ecological complexity, b) to find Lyapunov functions for dynamical systems describing spatial interactions on the landscape (and related attractors), and c) to combine discrete time and continuous spatial data and models.

Realitas dan Tatanan Urban Kota-Kota di Jepang

Despite the highly praised for technology achievements and prosperities, the morphology and appearance of Cities in Japan are often criticized as dull, uninteresting, brutal, and chaos. The question is, how do cities in Japan gain stability while the reality of the urban condition is in a chaos? Is there something behind the chaos that makes urban dwellers of Japanese cities able to relatively live comfortably and safely? This paper analyses some aspects which shaped Japan urbanism, from disorderly addressing system to the speed of building transformations that considerably high. Findings on the hidden orders behind the chaos of Japanese cities reveal an understanding that the spatial and physical chaos of a dense city are not always identified as a social chaos.