Symmetry in Critical Random Boolean Network Dynamics

Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be used both to greatly simplify analysis and to characterize different types of dynamics. Symmetry in Boolean networks is found by determining the frequency at which the various Boolean output functions occur. There are classes of functions that consist of Boolean functions that behave similarly. These classes are orbits of the controlling symmetry group. We find that the symmetry that controls the critical random Boolean networks is expressed through the frequency by which output functions are utilized by nodes that remain active on dynamical attractors. This symmetry preserves canalization, a form of network robustness. We compare it to a different symmetry known to control the dynamics of an evolutionary process that allows Boolean networks to organize into a critical state. Our results demonstrate the usefulness and power of using the symmetry of the behavior of the nodes to characterize complex network dynamics, and introduce a novel approach to the analysis of heterogeneous complex systems

Recent results in Euclidean dynamical triangulations

We study a formulation of lattice gravity defined via Euclidean dynamical triangulations (EDT). After fine-tuning a non-trivial local measure term we find evidence that four-dimensional, semi-classical geometries are recovered at long distance scales in the continuum limit. Furthermore, we find that the spectral dimension at short distance scales is consistent with 3/2, a value that is also observed in the causal dynamical triangulation (CDT) approach to quantum gravity.Comment: 7 pages, 3 figures. Proceedings for the 3rd conference of the Polish society on relativit

Lattice Quantum Gravity and Asymptotic Safety

We study the nonperturbative formulation of quantum gravity defined via Euclidean dynamical triangulations (EDT) in an attempt to make contact with Weinberg's asymptotic safety scenario. We find that a fine-tuning is necessary in order to recover semiclassical behavior. Such a fine-tuning is generally associated with the breaking of a target symmetry by the lattice regulator; in this case we argue that the target symmetry is the general coordinate invariance of the theory. After introducing and fine-tuning a nontrivial local measure term, we find no barrier to taking a continuum limit, and we find evidence that four-dimensional, semiclassical geometries are recovered at long distance scales in the continuum limit. We also find that the spectral dimension at short distance scales is consistent with 3/2, a value that could resolve the tension between asymptotic safety and the holographic entropy scaling of black holes. We argue that the number of relevant couplings in the continuum theory is one, once symmetry breaking by the lattice regulator is accounted for. Such a theory is maximally predictive, with no adjustable parameters. The cosmological constant in Planck units is the only relevant parameter, which serves to set the lattice scale. The cosmological constant in Planck units is of order 1 in the ultraviolet and undergoes renormalization group running to small values in the infrared. If these findings hold up under further scrutiny, the lattice may provide a nonperturbative definition of a renormalizable quantum field theory of general relativity with no adjustable parameters and a cosmological constant that is naturally small in the infrared.Comment: 69 pages, 25 figures. Revised discussion of target symmetry throughout paper. Numerical results unchanged and main conclusions largely unchanged. Added references and corrected typos. Conforms with version published in Phys. Rev.

Phase Diagram for a 2-D Two-Temperature Diffusive XY Model

Using Monte Carlo simulations, we determine the phase diagram of a diffusive two-temperature XY model. When the two temperatures are equal the system becomes the equilibrium XY model with the continuous Kosterlitz-Thouless (KT) vortex-antivortex unbinding phase transition. When the two temperatures are unequal the system is driven by an energy flow through the system from the higher temperature heat-bath to the lower temperature one and reaches a far-from-equilibrium steady state. We show that the nonequilibrium phase diagram contains three phases: A homogenous disordered phase and two phases with long range, spin-wave order. Two critical lines, representing continuous phase transitions from a homogenous disordered phase to two phases of long range order, meet at the equilibrium the KT point. The shape of the nonequilibrium critical lines as they approach the KT point is described by a crossover exponent of phi = 2.52 \pm 0.05. Finally, we suggest that the transition between the two phases with long-range order is first-order, making the KT-point where all three phases meet a bicritical point.Comment: 5 pages, 4 figure

All scale-free networks are sparse

We study the realizability of scale free-networks with a given degree sequence, showing that the fraction of realizable sequences undergoes two first-order transitions at the values 0 and 2 of the power-law exponent. We substantiate this finding by analytical reasoning and by a numerical method, proposed here, based on extreme value arguments, which can be applied to any given degree distribution. Our results reveal a fundamental reason why large scale-free networks without constraints on minimum and maximum degree must be sparse.Comment: 4 pages, 2 figure

Information processing and signal integration in bacterial quorum sensing

Bacteria communicate using secreted chemical signaling molecules called autoinducers in a process known as quorum sensing. The quorum-sensing network of the marine bacterium {\it Vibrio harveyi} employs three autoinducers, each known to encode distinct ecological information. Yet how cells integrate and interpret the information contained within the three autoinducer signals remains a mystery. Here, we develop a new framework for analyzing signal integration based on Information Theory and use it to analyze quorum sensing in {\it V. harveyi}. We quantify how much the cells can learn about individual autoinducers and explain the experimentally observed input-output relation of the {\it V. harveyi} quorum-sensing circuit. Our results suggest that the need to limit interference between input signals places strong constraints on the architecture of bacterial signal-integration networks, and that bacteria likely have evolved active strategies for minimizing this interference. Here we analyze two such strategies: manipulation of autoinducer production and feedback on receptor number ratios.Comment: Supporting information is in appendi

Eigenvalue Separation in Some Random Matrix Models

The eigenvalue density for members of the Gaussian orthogonal and unitary ensembles follows the Wigner semi-circle law. If the Gaussian entries are all shifted by a constant amount c/Sqrt(2N), where N is the size of the matrix, in the large N limit a single eigenvalue will separate from the support of the Wigner semi-circle provided c > 1. In this study, using an asymptotic analysis of the secular equation for the eigenvalue condition, we compare this effect to analogous effects occurring in general variance Wishart matrices and matrices from the shifted mean chiral ensemble. We undertake an analogous comparative study of eigenvalue separation properties when the size of the matrices are fixed and c goes to infinity, and higher rank analogues of this setting. This is done using exact expressions for eigenvalue probability densities in terms of generalized hypergeometric functions, and using the interpretation of the latter as a Green function in the Dyson Brownian motion model. For the shifted mean Gaussian unitary ensemble and its analogues an alternative approach is to use exact expressions for the correlation functions in terms of classical orthogonal polynomials and associated multiple generalizations. By using these exact expressions to compute and plot the eigenvalue density, illustrations of the various eigenvalue separation effects are obtained.Comment: 25 pages, 9 figures include

Competition in Social Networks: Emergence of a Scale-free Leadership Structure and Collective Efficiency

Using the minority game as a model for competition dynamics, we investigate the effects of inter-agent communications on the global evolution of the dynamics of a society characterized by competition for limited resources. The agents communicate across a social network with small-world character that forms the static substrate of a second network, the influence network, which is dynamically coupled to the evolution of the game. The influence network is a directed network, defined by the inter-agent communication links on the substrate along which communicated information is acted upon. We show that the influence network spontaneously develops hubs with a broad distribution of in-degrees, defining a robust leadership structure that is scale-free. Furthermore, in realistic parameter ranges, facilitated by information exchange on the network, agents can generate a high degree of cooperation making the collective almost maximally efficient.Comment: 4 pages, 2 postscript figures include

Rescue nasopharyngeal tube for preterm infants non-responsive to initial ventilation after birth

BACKGROUND Physiological changes during the insertion of a rescue nasopharyngeal tube (NPT) after birth are unclear. METHODS Observational study of very preterm infants in the delivery room. Data were extracted at predefined timepoints starting with first facemask placement after birth until 5 min after insertion of NPT. End-expiratory lung impedance (EELI), heart rate (HR) and SpO$_{2}$/FiO$_{2}$-ratio were analysed over time. Changes during the same time span of NIPPV via facemask and NIPPV via NPT were compared. RESULTS Overall, 1154 inflations in 15 infants were analysed. After NPT insertion, EELI increased significantly [0.33 AU/kg (0.19-0.57), p < 0.001]. Compared with the mask period, changes in EELI were not significantly larger during the NPT period [median difference (IQR) = 0.14 AU/kg (-0.14-0.53); p = 0.12]. Insertion of the NPT was associated with significant improvement in HR [52 (33-96); p = 0.001] and SpO$_{2}$/FiO$_{2}$-ratio [161 (69-169); p < 0.001] not observed during the mask period. CONCLUSIONS In very preterm infants non-responsive to initial facemask ventilation after birth, insertion of an NPT resulted in a considerable increase in EELI. This additional gain in lung volume was associated with an immediate improvement in clinical parameters. The use of a NPT may prevent intubation in selected non-responsive infants. IMPACT After birth, a nasopharyngeal tube may be considered as a rescue airway in newborn infants non-responsive to initial positive pressure ventilation via facemask. Although it is widely used among clinicians, its effect on lung volumes and physiological parameters remains unclear. Insertion of a rescue NPT resulted in a considerable increase in lung volume but this was not significantly larger than during facemask ventilation. However, insertion of a rescue NPT was associated with a significant and clinically important improvement in heart rate and oxygenation. This study highlights the importance of individual strategies in preterm resuscitation and introduces the NPT as a valid option