From Turing patterns to chimera states in the 2D Brusselator model.

The Brusselator has been used as a prototype model for autocatalytic reactions and, in particular, for the Belousov-Zhabotinsky reaction. When coupled at the diffusive limit, the Brusselator undergoes a Turing bifurcation resulting in the formation of classical Turing patterns, such as spots, stripes, and spirals in two spatial dimensions. In the present study, we use generic nonlocally coupled Brusselators and show that in the limit of the coupling range R→1 (diffusive limit), the classical Turing patterns are recovered, while for intermediate coupling ranges and appropriate parameter values, chimera states are produced. This study demonstrates how the parameters of a typical nonlinear oscillator can be tuned so that the coupled system passes from spatially stable Turing structures to dynamical spatiotemporal chimera states.

Synchronization in Multiplex Leaky Integrate-and-Fire Networks With Nonlocal Interactions.

We study synchronization phenomena in a multiplex network composed of two rings with identical Leaky Integrate-and-Fire (LIF) oscillators located on the nodes of the rings. Within each ring the LIF oscillators interact nonlocally, while between rings there are one-to-one inter-ring interactions. This structure is motivated by the observed connectivity between the two hemispheres of the brain: within each hemisphere the various brain regions interact with neighboring regions, while across hemispheres each region interacts, primarily, with the functionally homologous region. We consider both positive (excitatory) and negative (inhibitory) linking. We identify numerically various parameter regimes where the multiplex network develops coexistence of active and subthreshold domains, chimera states, solitary states, full coherence or incoherence. In particular, for weak inter-ring coupling (weak multiplexing) different synchronization patterns on the two rings are supported. These are stable and are obtained when the intra-ring coupling values are near the critical points separating qualitatively distinct synchronization regimes, e.g., between the travelling fronts regime and the chimera state one.

Shooting solitaries due to small-world connectivity in leaky integrate-and-fire networks.

We study the synchronization properties in a network of leaky integrate-and-fire oscillators with nonlocal connectivity under probabilistic small-world rewiring. We demonstrate that the random links lead to the emergence of chimera-like states where the coherent regions are interrupted by scattered, short-lived solitaries; these are termed "shooting solitaries." Moreover, we provide evidence that random links enhance the appearance of chimera-like states for values of the parameter space that otherwise support synchronization. This last effect is counter-intuitive because by adding random links to the synchronous state, the system locally organizes into coherent and incoherent domains.

Controlling the Chimera Form in the Leaky Integrate-and-Fire Model.

We study the influence of broken connectivity and frequency disorder in systems of coupled neuronal oscillators. Under nonlocal coupling, systems of nonlinear oscillators, such as Kuramoto, FitzHugh-Nagumo, or integrate-and-fire oscillators, demonstrate nontrivial synchronization patterns. One of these patterns is the "chimera state," which consists of coexisting coherent and incoherent domains. In networks of biological neurons, the connectivity is not always perfect, but might be locally broken or interrupted due to pathologies, neuron degenerative disorders, or accidents. Our simulations show that destructed connectivity drastically affects synchronization, driving the coherent parts of the chimera state to cover symmetrically the region where the anomaly is located. The network synchronization decreases with the size of the destructed region as evidenced by the Kuramoto synchronization index. To the contrary, when keeping the connectivity of all nodes intact, altering the frequency in a block of oscillators drives the incoherent part of the chimera state toward the anomaly. This work is in line with recent dynamical approaches aiming to locate anomalies in the structure of brain networks, in particular when the anomalies have small, difficult-to-detect sizes.

Structural anomalies in brain networks induce dynamical pacemaker effects.

Dynamical effects on healthy brains and brains affected by tumor are investigated via numerical simulations. The brains are modeled as multilayer networks consisting of neuronal oscillators whose connectivities are extracted from Magnetic Resonance Imaging (MRI) data. The numerical results demonstrate that the healthy brain presents chimera-like states where regions with high white matter concentrations in the direction connecting the two hemispheres act as the coherent domain, while the rest of the brain presents incoherent oscillations. To the contrary, in brains with destructed structures, traveling waves are produced initiated at the region where the tumor is located. These areas act as the pacemaker of the waves sweeping across the brain. The numerical simulations are performed using two neuronal models: (a) the FitzHugh-Nagumo model and (b) the leaky integrate-and-fire model. Both models give consistent results regarding the chimera-like oscillations in healthy brains and the pacemaker effect in the tumorous brains. These results are considered a starting point for further investigation in the detection of tumors with small sizes before becoming discernible on MRI recordings as well as in tumor development and evolution.

Chimera patterns and subthreshold oscillations in two-dimensional networks of fractally coupled leaky integrate-and-fire neurons.

We discuss the effects that fractal coupling induces on chimera states in a network of leaky integrate-and-fire (LIF) oscillators arranged in a two-dimensional toroidal geometry. We provide evidence that the introduction of a hierarchical coupling topology in the form of a Sierpinski carpet gives rise to complex spatial structures such as multiple spots, stripe-and-grid chimeras, as well as traveling waves and subthreshold oscillations. Unlike in the case of typical nonlocal connectivity, when tuning the coupling strength to small positive values a spot chimera is formed with internal structure reminiscent of the fractal connectivity scheme. This is in line with previous results for one-dimensional networks, where hierarchical connectivity also induces chimeras with stratified spatial arrangements. In the case of negative coupling, cooperative effects produce subthreshold oscillating regions with traveling active islands crossing through them. Subthreshold oscillations and traveling waves are frequently reported in biological neural network experiments.

Three-dimensional chimera patterns in networks of spiking neuron oscillators.

We study the stable spatiotemporal patterns that arise in a three-dimensional (3D) network of neuron oscillators, whose dynamics is described by the leaky integrate-and-fire (LIF) model. More specifically, we investigate the form of the chimera states induced by a 3D coupling matrix with nonlocal topology. The observed patterns are in many cases direct generalizations of the corresponding two-dimensional (2D) patterns, e.g., spheres, layers, and cylinder grids. We also find cylindrical and "cross-layered" chimeras that do not have an equivalent in 2D systems. Quantitative measures are calculated, such as the ratio of synchronized and unsynchronized neurons as a function of the coupling range, the mean phase velocities, and the distribution of neurons in mean phase velocities. Based on these measures, the chimeras are categorized in two families. The first family of patterns is observed for weaker coupling and exhibits higher mean phase velocities for the unsynchronized areas of the network. The opposite holds for the second family, where the unsynchronized areas have lower mean phase velocities. The various measures demonstrate discontinuities, indicating criticality as the parameters cross from the first family of patterns to the second.

DNA viewed as an out-of-equilibrium structure.

The complexity of the primary structure of human DNA is explored using methods from nonequilibrium statistical mechanics, dynamical systems theory, and information theory. A collection of statistical analyses is performed on the DNA data and the results are compared with sequences derived from different stochastic processes. The use of χ^{2} tests shows that DNA can not be described as a low order Markov chain of order up to r=6. Although detailed balance seems to hold at the level of a binary alphabet, it fails when all four base pairs are considered, suggesting spatial asymmetry and irreversibility. Furthermore, the block entropy does not increase linearly with the block size, reflecting the long-range nature of the correlations in the human genomic sequences. To probe locally the spatial structure of the chain, we study the exit distances from a specific symbol, the distribution of recurrence distances, and the Hurst exponent, all of which show power law tails and long-range characteristics. These results suggest that human DNA can be viewed as a nonequilibrium structure maintained in its state through interactions with a constantly changing environment. Based solely on the exit distance distribution accounting for the nonequilibrium statistics and using the Monte Carlo rejection sampling method, we construct a model DNA sequence. This method allows us to keep both long- and short-range statistical characteristics of the native DNA data. The model sequence presents the same characteristic exponents as the natural DNA but fails to capture spatial correlations and point-to-point details.

Complexity measures for the evolutionary categorization of organisms.

Complexity measures are used to compare the genomic characteristics of five organisms belonging to distinct classes spanning the evolutionary tree: higher eukaryotes, amoebae, unicellular eukaryotes and bacteria. The comparisons are undertaken using the full four-letter alphabet and the coarse grained two-letter alphabets AG-CT and AT-CG. We show that the conditional probability matrix for the four-letter and AT-CG alphabet is markedly asymmetric in eukaryotes while it is nearly symmetric in bacterial genomes. Spatial asymmetry is revealed in the four-letter alphabet, signifying that the probability fluxes are nonvanishing and thus the reading sense of a sequence is irreversible for all organisms. Calculations of the block entropy and excess entropy demonstrate that the human genome accommodates better all possible block configurations, especially for long blocks. With respect to point-to-point details and to spatial arrangement of blocks the exit distance distributions from a particular letter demonstrate long distance characteristics in the eukaryotic sequences for all three alphabets, while the bacterial (prokaryotic) genomes deviate indicating short range characteristics. Overall, the conditional probability, the fluxes, the block entropy content and the exit distance distributions can be used as markers, discriminating between eukaryotic and prokaryotic DNA, allowing in many cases to discern details related to finer classes. In all cases the reduction from four letters to two masks some important statistical and spatial properties, with the AT-CG alphabet having higher ability of discrimination than the AG-CT one. In particular, the AT-CG alphabet reduction accentuates the CpG related properties (conditional probabilities w32, long ranged exit distance distribution for A and T nucleotides), but masks sequence asymmetry and irreversibility in all examined organisms.

Species mobility induces synchronization in chaotic population dynamics.

A prototype population dynamics model with cyclic domination of four species and empty sites is proposed for studying transition to synchronization. At the mean-field level the dynamics shows quasiperiodicity and chaos depending on the parameter values. The realization of the model on a square lattice shows that spatial restrictions and intrinsic stochasticity change the whole picture. The mean-field dynamics qualitatively remains only under global reactions, while local reactions drive the lattice to poisoning, where only some of the species survive. Nontrivial oscillatory steady states are developed if long-distance exchange is introduced due to gradual mixing with a certain probability. The mixing probability is shown to control the transition to synchronization which emerges abruptly following a phase slip scenario. Near the transition a typical intermittency crisis takes place, with phase slips becoming more infrequent as the transition is approached.

Multifractal analysis of nonhyperbolic coupled map lattices: application to genomic sequences.

Symbolic sequences generated by coupled map lattices (CMLs) can be used to model the chaotic-like structure of genomic sequences. In this study it is shown that diffusively coupled Chebyshev maps of order 4 (corresponding to a shift of four symbols) very closely reproduce the multifractal spectrum D(q) of human genomic sequences for coupling constant α = 0.35 ± 0.01 if q > 0. The presence of rare configurations causes deviations for q < 0, which disappear if the rare event statistics of the CML is modified. Such rare configurations are known to play specific functional roles in genomic sequences serving as promoters or regulatory elements.

The "reversed halo" sign in pneumonococcal pneumonia: a review with a case report.

The "reversed halo" sign (RHS) is a distinct radiological sign representing a focal rounded area of ground-glass opacity surrounded by a more or less complete ring of consolidation. Initially, it was reported in two cases of cryptogenic organizing pneumonia and was considered to be relatively specific of the disease. Since then, it has been reported in a wide variety of clinical entities, thus reducing its specificity. We describe the reversed halo sign in a case of pneumonococcal pneumonia. To the best of our knowledge, this is the first report in English literature. The presence of the "reversed halo" sign during the resolution phase of pneumonococcal pneumonia has serious implications. First, it further reduces its specificity. Second, it opens new areas of research regarding its significance in cases of cryptogenic organizing pneumonia.

Liposomal cisplatin combined with paclitaxel versus cisplatin and paclitaxel in non-small-cell lung cancer: a randomized phase III multicenter trial.

BACKGROUND: Liposomal cisplatin is a new formulation developed to reduce the systemic toxicity of cisplatin while simultaneously improving the targeting of the drug to the primary tumor and to metastases by increasing circulation time in the body fluids and tissues. The primary objectives were to determine nephrotoxicity, gastrointestinal side-effects, peripheral neuropathy and hematological toxicity and secondary objectives were to determine the response rate, time to tumor progression (TTP) and survival. PATIENTS AND METHODS: Two hundred and thirty-six chemotherapy-naive patients with inoperable non-small-cell lung cancer were randomly allocated to receive either 200 mg/m² of liposomal cisplatin and 135 mg/m² paclitaxel (arm A) or 75 mg/m² cisplatin and 135 mg/m² paclitaxel (arm B), once every 2 weeks on an outpatient basis. Two hundred and twenty-nine patients were assessable for toxicity, response rate and survival. Nine treatment cycles were planned. RESULTS: Arm A patients showed statistically significant lower nephrotoxicity, grade 3 and 4 leucopenia, grade 2 and 3 neuropathy, nausea, vomiting and fatigue. There was no significant difference in median and overall survival and TTP between the two arms; median survival was 9 and 10 months in arms A and B, respectively, and TTP was 6.5 and 6 months in arms A and B, respectively. CONCLUSIONS: Liposomal cisplatin in combination with paclitaxel has been shown to be much less toxic than the original cisplatin combined with paclitaxel. Nephrotoxicity in particular was negligible after liposomal cisplatin administration. TTP and survival were similar in both treatment arms.

Hierarchical multifractal representation of symbolic sequences and application to human chromosomes.

The two-dimensional density correlation matrix is constructed for symbolic sequences using contiguous segments of arbitrary size. The multifractal spectrum obtained from this matrix motif is shown to characterize the correlations in the symbolic sequences. This method is applied to entire human chromosomes, shuffled human chromosomes, reconstructed human genomic sequences and to artificial random sequences. It is shown that all human chromosomes have common characteristics in their multifractal spectrum and deviate substantially from random and uncorrelated sequences of the same size. Small deviations are observed between the longer and the shorter chromosomes, especially for the higher (in absolute values) statistical moments. The correlations are crucial for the form of the multifractal spectrum; surrogate shuffled chromosomes present randomlike spectrum, distinctly different from the actual chromosomes. Analytical approaches based on hierarchical superposition of tensor products show that retaining pair correlations in the sequences leads to a closer representation of the genomic multifractal spectra, especially in the region of negative exponents, due to the underrepresentation of various functional units (such as the cytosine-guanine CG combination and its complementary GC complex). Retaining higher-order correlations in the construction of the tensor products is a way to approach closer the structure of the multifractal spectra of the actual genomic sequences. This hierarchical approach is generic and is applicable to other correlated symbolic sequences.

Long range clustering of oligonucleotides containing the CG signal.

The distance distributions between successive occurrences of the same oligonucleotides in chromosomal DNA are studied, in different classes of higher eucaryotic organisms. A two-parameter modeling is undertaken and applied on the distance distribution of quintuplets (sequences of size five bps) and hexaplets (sequences of size six bps); the first parameter k refers to the short range exponential decay of the distributions, whereas the second parameter m refers to the power law behavior. A two-dimensional scatter plot representing the model equation demonstrates that the points corresponding to the distance distribution of oligonucleotides containing the CG consensus sequence (promoter of the RNA polymerase II) cluster together (group alpha), apart from all other oligonucleotides (group beta). This is shown for the available chordata Homo sapiens, Pan troglodytes, Mus musculus, Rattus norvegicus, Gallus gallus and Danio rerio. This clustering is less evident in lower Animalia and plants, such as Drosophila melanogaster, Caenorhabditis elegans and Arabidopsis thaliana. Moreover, in all organisms the oligonucleotides which contain any consensus sequence are found to be described by long range distributions, whereas all others have a stronger influence of short range decay. Various measures are introduced and evaluated, to numerically characterize the clustering of the two groups. The one which most clearly discriminates the two classes is shown to be the proximity factor.

Synchronization of stochastic oscillations due to long-range diffusion.

We investigate the effect of long-range diffusive mixing on stochastic processes taking place on low-dimensional catalytic supports. As a working example, the cyclic lattice Lotka-Volterra (LLV) model is used which is conservative at the mean-field level and demonstrates fractal patterns and local oscillations when realized on low-dimensional lattice supports. We show that the local oscillations are synchronized when a weak, long-range, diffusive process is added to LLV and global oscillations of limit cycle type emerge. This phenomenon is demonstrated as a nonequilibrium phase transition and takes place when the mixing-to-reaction rate p (order parameter) is above a critical point p_{c} . The value of the critical point is shown to depend on the kinetic parameters. The global oscillations in this case emerge as a result of phase synchronization between local oscillations on sublattices.

Power law exponents characterizing human DNA.

The size distributions of all known coding and noncoding DNA sequences are studied in all human chromosomes. In a unified approach, both introns and intergenic regions are treated as noncoding regions. The distributions of noncoding segments Pnc(S) of size S present long tails Pnc(S) approximately S(-1-mu nc) , with exponents mu nc ranging between 0.71 (for chromosome 13) and 1.2 (for chromosome 19). On the contrary, the exponential, short-range decay terms dominate in the distributions of coding (exon) segments Pc(S) in all chromosomes. Aiming to address the emergence of these statistical features, minimal, stochastic, mean-field models are proposed, based on randomly aggregating DNA strings with duplication, influx and outflux of genomic segments. These minimal models produce both the short-range statistics in the coding and the observed power law and fractal statistics in the noncoding DNA. The minimal models also demonstrate that although the two systems (coding and noncoding) coexist, alternating on the same linear chain, they act independently: the coding as a closed, equilibrium system and the noncoding as an open, out-of-equilibrium one.

Spatiotemporal oscillations and clustering in the Ziff-Gulari-Barshad model with surface reconstruction.

We study the dynamics of the Ziff-Gulari-Barshad (ZGB) model on square (sq) and hexagonal-honeycomb (hex) lattices and when surface restructuring is introduced. We show that the ZGB model exhibits nonequilibrium phase transitions on the hex lattice similar to the ones already observed on the sq lattice, but the critical values of the kinetic parameters depend crucially on the substrate type. If surface reconstruction (sq<-->hex) is assumed for high lattice coverage of one of the reactive species then persistent spatiotemporal oscillations and clustering of homologous species are observed for kinetic parameter values 0.348

Propagating waves in one-dimensional discrete networks of coupled units.

We investigate the behavior of discrete systems on a one-dimensional lattice composed of localized units interacting with each other through nonlocal, nonlinear reactive dynamics. In the presence of second-order and third-order steps coupling two or three neighboring sites, respectively, we observe, for appropriate initial conditions, the propagation of waves which subsist in the absence of mass transfer by diffusion. For the case of the third-order (bistable) model, a counterintuitive effect is also observed, whereby the homogeneously less stable state invades the more stable one under certain conditions. In the limit of a continuous space the dynamics of these networks is described by a generic evolution equation, from which some analytical predictions can be extracted. The relevance of this mode of information transmission in spatially extended systems of interest in physical chemistry and biology is discussed.

Nonextensivity of the cyclic lattice Lotka-Volterra model.

We numerically show that the lattice Lotka-Volterra model, when realized on a square lattice support, gives rise to a finite production, per unit time, of the nonextensive entropy S(q)=(1- summation operator (i)p(q)(i))/(q-1) (S(1)=- summation operator (i)p(i) ln p(i)). This finiteness only occurs for q=0.5 for the d=2 growth mode (growing droplet), and for q=0 for the d=1 one (growing stripe). This strong evidence of nonextensivity is consistent with the spontaneous emergence of local domains of identical particles with fractal boundaries and competing interactions. Such direct evidence is, to our knowledge, exhibited for the first time for a many-body system which, at the mean field level, is conservative.