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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

The differential effect of pentoxifylline on cytokine production by alveolar macrophages and its clinical implications.

The aim of this study was to investigate the effects of pentoxifylline (PTX) on the production of TNF-alpha, IL-1 beta, IL-6 and GM-CSF by lipopolysaccharide (LPS)-stimulated alveolar macrophages (AM). AM and peripheral blood monocytes (PBM) from 10 patients were cultured for 24 h in the presence of LPS (10 micrograms ml-1) and PTX at concentrations of 2.0 mM, 1.0 mM, 0.5 mM, 0.1 mM and 0.01 mM. TNF-alpha and GM-CSF were measured from the culture supernatants of both the AM and PBM from all 10 patients and IL-1 beta and IL-6 from the culture supernatants of the AM from five patients. The TNF-alpha production by AM was significantly suppressed in the presence of PTX at concentrations of 2.0 and 1.0 mM, while production of IL-1 beta, IL-6 and GM-CSF remained unaffected. In PBM cultures, PTX significantly suppressed the production of TNF-alpha and GM-CSF, at all tested concentrations. The present study provides evidence that PTX selectively suppresses the production of TNF-alpha by LPS-stimulated AM and may have a role in the treatment of lung diseases where TNF-alpha is involved. The mode of administration of PTX should take into account the suppressive effect of this drug on GM-CSF production by PBM.

Reactive dynamics on two-dimensional supports: Monte Carlo simulations and mean-field theory.

Monte Carlo simulations and mean-field models are used for the study of nonequilibrium reactions taking place on the surface of a catalyst. The model represents the catalytic reduction of NO with H2 on a Pt surface. Both Monte Carlo simulations and mean-field results predict the existence of a critical surface in the parameter space where the catalyst remains active for long times. Outside this critical region the catalyst remains active for finite times only. A discrete version of the mean-field model is proposed that takes into account the discrete, two-dimensional nature of the catalyst. For homogeneous initial conditions this improved model provides better quantitative agreement with the Monte Carlo results.

Spontaneous formation of dynamical patterns with fractal fronts in the cyclic lattice Lotka-Volterra model.

Dynamical patterns, in the form of consecutive moving stripes or rings, are shown to develop spontaneously in the cyclic lattice Lotka-Volterra model, when realized on square lattice, at the reaction limited regime. Each stripe consists of different particles (species) and the borderlines between consecutive stripes are fractal. The interface width w between the different species scales as w(L,t) approximately L(alpha)f(t/L(z)), where L is the linear size of the interface, t is the time, and alpha and z are the static and dynamical critical exponents, respectively. The critical exponents were computed as alpha=0.49+/-0.03 and z=1.53+/-0.13 and the propagating fronts show dynamical characteristics similar to those of the Eden growth models.

Fractal properties of the lattice Lotka-Volterra model.

The lattice Lotka-Volterra (LLV) model is studied using mean-field analysis and Monte Carlo simulations. While the mean-field phase portrait consists of a center surrounded by an infinity of closed trajectories, when the process is restricted to a two-dimensional (2D) square lattice, local inhomogeneities/fluctuations appear. Spontaneous local clustering is observed on lattice and homogeneous initial distributions turn into clustered structures. Reactions take place only at the interfaces between different species and the borders adopt locally fractal structure. Intercluster surface reactions are responsible for the formation of local fluctuations of the species concentrations. The box-counting fractal dimension of the LLV dynamics on a 2D support is found to depend on the reaction constants while the upper bound of fractality determines the size of the local oscillators. Lacunarity analysis is used to determine the degree of clustering of homologous species. Besides the spontaneous clustering that takes place on a regular 2D lattice, the effects of fractal supports on the dynamics of the LLV are studied. For supports of dimensionality D(s)<2 the lattice can, for certain domains of the reaction constants, adopt a poisoned state where only one of the species survives. By appropriately selecting the fractal dimension of the substrate, it is possible to direct the system into a poisoned or oscillatory steady state at will.

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.

Oscillatory reactive dynamics on surfaces: a lattice limit cycle model.

Complex reactive dynamics on low-dimensional lattices is studied using mean-field models and Monte Carlo simulations. A lattice-compatible reactive scheme that gives rise to limit cycle behavior is constructed, involving a quadrimolecular reaction step and bimolecular adsorption and desorption steps. The resulting lattice limit cycle model is dissipative and, in the mean-field limit, exhibits sustained oscillations of the species concentrations for a wide range of parameter values. Lattice Monte Carlo simulations of the lattice limit cycle model show locally the emergence of sustained oscillations of the species concentrations. Random fluctuations of the concentrations, clustering between homologous species, and competition between the various clusters/species cause the in-phase oscillations of neighboring sites. Distant regions oscillate out of phase and spatial correlations decay exponentially with the distance. The amplitude and period of the local oscillations depend on the system parameters.

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.