Lorentzian and Euclidean Quantum Gravity - Analytical and Numerical Results

We review some recent attempts to extract information about the nature of quantum gravity, with and without matter, by quantum field theoretical methods. More specifically, we work within a covariant lattice approach where the individual space-time geometries are constructed from fundamental simplicial building blocks, and the path integral over geometries is approximated by summing over a class of piece-wise linear geometries. This method of ``dynamical triangulations'' is very powerful in 2d, where the regularized theory can be solved explicitly, and gives us more insights into the quantum nature of 2d space-time than continuum methods are presently able to provide. It also allows us to establish an explicit relation between the Lorentzian- and Euclidean-signature quantum theories. Analogous regularized gravitational models can be set up in higher dimensions. Some analytic tools exist to study their state sums, but, unlike in 2d, no complete analytic solutions have yet been constructed. However, a great advantage of our approach is the fact that it is well-suited for numerical simulations. In the second part of this review we describe the relevant Monte Carlo techniques, as well as some of the physical results that have been obtained from the simulations of Euclidean gravity. We also explain why the Lorentzian version of dynamical triangulations is a promising candidate for a non-perturbative theory of quantum gravity.Comment: 69 pages, 16 figures, references adde

Detecting Community Structure in Dynamic Social Networks Using the Concept of Leadership

Detecting community structure in social networks is a fundamental problem empowering us to identify groups of actors with similar interests. There have been extensive works focusing on finding communities in static networks, however, in reality, due to dynamic nature of social networks, they are evolving continuously. Ignoring the dynamic aspect of social networks, neither allows us to capture evolutionary behavior of the network nor to predict the future status of individuals. Aside from being dynamic, another significant characteristic of real-world social networks is the presence of leaders, i.e. nodes with high degree centrality having a high attraction to absorb other members and hence to form a local community. In this paper, we devised an efficient method to incrementally detect communities in highly dynamic social networks using the intuitive idea of importance and persistence of community leaders over time. Our proposed method is able to find new communities based on the previous structure of the network without recomputing them from scratch. This unique feature, enables us to efficiently detect and track communities over time rapidly. Experimental results on the synthetic and real-world social networks demonstrate that our method is both effective and efficient in discovering communities in dynamic social networks

Growing Scale-Free Networks with Tunable Clustering

We extend the standard scale-free network model to include a ``triad formation step''. We analyze the geometric properties of networks generated by this algorithm both analytically and by numerical calculations, and find that our model possesses the same characteristics as the standard scale-free networks like the power-law degree distribution and the small average geodesic length, but with the high-clustering at the same time. In our model, the clustering coefficient is also shown to be tunable simply by changing a control parameter - the average number of triad formation trials per time step.Comment: Accepted for publication in Phys. Rev.

Making a Universe

For understanding the origin of anisotropies in the cosmic microwave background, rules to construct a quantized universe is proposed based on the dynamical triangulation method of the simplicial quantum gravity. A $d$-dimensional universe having the topology $D^d$ is created numerically in terms of a simplicial manifold with $d$-simplices as the building blocks. The space coordinates of a universe are identified on the boundary surface $S^{d-1}$, and the time coordinate is defined along the direction perpendicular to $S^{d-1}$. Numerical simulations are made mainly for 2-dimensional universes, and analyzed to examine appropriateness of the construction rules by comparing to analytic results of the matrix model and the Liouville theory. Furthermore, a simulation in 4-dimension is made, and the result suggests an ability to analyze the observations on anisotropies by comparing to the scalar curvature correlation of a $S^2$-surface formed as the last scattering surface in the $S^3$ universe.Comment: 27pages,18figures,using jpsj.st

Discrete approaches to quantum gravity in four dimensions

The construction of a consistent theory of quantum gravity is a problem in theoretical physics that has so far defied all attempts at resolution. One ansatz to try to obtain a non-trivial quantum theory proceeds via a discretization of space-time and the Einstein action. I review here three major areas of research: gauge-theoretic approaches, both in a path-integral and a Hamiltonian formulation, quantum Regge calculus, and the method of dynamical triangulations, confining attention to work that is strictly four-dimensional, strictly discrete, and strictly quantum in nature.Comment: 33 pages, invited contribution to Living Reviews in Relativity; the author welcomes any comments and suggestion

Statistical mechanics of complex networks

Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network's robustness against failures and attacks.Comment: 54 pages, submitted to Reviews of Modern Physic

Does Banque de France control inflation and unemployment?

We re-estimate statistical properties and predictive power of a set of Phillips curves, which are expressed as linear and lagged relationships between the rates of inflation, unemployment, and change in labour force. For France, several relationships were estimated eight years ago. The change rate of labour force was used as a driving force of inflation and unemployment within the Phillips curve framework. The set of nested models starts with a simplistic version without autoregressive terms and one lagged term of explanatory variable. The lag is determined empirically together with all coefficients. The model is estimated using the Boundary Element Method (BEM) with the least squares method applied to the integral solutions of the differential equations. All models include one structural break might be associated with revisions to definitions and measurement procedures in the 1980s and 1990s as well as with the change in monetary policy in 1994-1995. For the GDP deflator, our original model provided a root mean squared forecast error (RMSFE) of 1.0% per year at a four-year horizon for the period between 1971 and 2004. The rate of CPI inflation is predicted with RMSFE=1.5% per year. For the naive (no change) forecast, RMSFE at the same time horizon is 2.95% and 3.3% per year, respectively. Our model outperforms the naive one by a factor of 2 to 3. The relationships for inflation were successfully tested for cointegration. We have formally estimated several vector error correction (VEC) models for two measures of inflation. At a four year horizon, the estimated VECMs provide significant statistical improvements on the results obtained by the BEM: RMSFE=0.8% per year for the GDP deflator and ~1.2% per year for CPI. For a two year horizon, the VECMs improve RMSFEs by a factor of 2, with the smallest RMSFE=0.5% per year for the GDP deflator.Comment: 25 pages, 12 figure

Black Holes at Future Colliders and Beyond: a Topical Review

One of the most dramatic consequences of low-scale (~1 TeV) quantum gravity in models with large or warped extra dimension(s) is copious production of mini black holes at future colliders and in ultra-high-energy cosmic ray collisions. Hawking radiation of these black holes is expected to be constrained mainly to our three-dimensional world and results in rich phenomenology. In this topical review we discuss the current status of astrophysical observations of black holes and selected aspects of mini black hole phenomenology, such as production at colliders and in cosmic rays, black hole decay properties, Hawking radiation as a sensitive probe of the dimensionality of extra space, as well as an exciting possibility of finding new physics in the decays of black holes.Comment: 31 pages, 10 figures To appear in the Journal of Physics

Boolean Dynamics with Random Couplings

This paper reviews a class of generic dissipative dynamical systems called N-K models. In these models, the dynamics of N elements, defined as Boolean variables, develop step by step, clocked by a discrete time variable. Each of the N Boolean elements at a given time is given a value which depends upon K elements in the previous time step. We review the work of many authors on the behavior of the models, looking particularly at the structure and lengths of their cycles, the sizes of their basins of attraction, and the flow of information through the systems. In the limit of infinite N, there is a phase transition between a chaotic and an ordered phase, with a critical phase in between. We argue that the behavior of this system depends significantly on the topology of the network connections. If the elements are placed upon a lattice with dimension d, the system shows correlations related to the standard percolation or directed percolation phase transition on such a lattice. On the other hand, a very different behavior is seen in the Kauffman net in which all spins are equally likely to be coupled to a given spin. In this situation, coupling loops are mostly suppressed, and the behavior of the system is much more like that of a mean field theory. We also describe possible applications of the models to, for example, genetic networks, cell differentiation, evolution, democracy in social systems and neural networks.Comment: 69 pages, 16 figures, Submitted to Springer Applied Mathematical Sciences Serie