Identifying the community structure of the international-trade multi-network

We study the community structure of the multi-network of commodity-specific trade relations among world countries over the 1992-2003 period. We compare structures across commodities and time by means of the normalized mutual information index (NMI). We also compare them with exogenous community structures induced by geography and regional trade agreements. We find that commodity-specific community structures are very heterogeneous and much more fragmented than that characterizing the aggregate ITN. This shows that the aggregate properties of the ITN may result (and be very different) from the aggregation of very diverse commodity-specific layers of the multi-network. We also show that commodity-specific community structures, especially those related to the chemical sector, are becoming more and more similar to the aggregate one. Finally, our findings suggest that geography-induced partitions of our set of countries are much more correlated with observed community structures than partitions induced by regional-trade agreements. This result strengthens previous findings from the empirical literature on trade.     

Statistical properties and universality in earthquake and solar flare occurrence

Earthquakes are phenomena of great complexity, however some simple general laws govern the statistics of their occurrence. Some of these most important laws exhibit scale invariance, as the Gutenberg-Richter law and the Omori law. The origin of these scaling behaviours is not yet fully understood and a natural fondamental question concerns the existence of these features also in other complex phenomena. A direct inspection of experimental catalogues has shown that the stochastic processes underlying solar flare and earthquake occurrence have universal properties. Another intensively debated question is the existence of correlations between magnitudes of subsequent earthquakes. Our recent analysis of the Southern California Catalogue has shown that non-zero magnitude correlations exist. A branching model based on a dynamical scaling hypothesis, relating magnitude to time, reproduces the hierarchical organization in time and magnitude of events and the observed magnitude correlations.     

The Local Structure of Globalization

We study the evolution of the network of foreign direct investment (FDI) in the international electricity industry during the period 1994–2003. We assume that the ties in the network of investment relations between countries are created and deleted in continuous time, according to a conditional Gibbs distribution. This assumption allows us to take simultaneously into account the aggregate predictions of the well-established gravity model of international trade as well as local dependencies between network ties connecting the countries in our sample. According to the modified version of the gravity model that we specify, the probability of observing an investment tie between two countries depends on the mass of the economies involved, their physical distance, and the tendency of the network to self-organize into local configurations of network ties. While the limiting distribution of the data generating process is an exponential random graph model, we do not assume the system to be in equilibrium. We find evidence of the effects of the standard gravity model of international trade on evolution of the global FDI network. However, we also provide evidence of significant dyadic and extra-dyadic dependencies between investment ties that are typically ignored in available research. We show that local dependencies between national electricity industries are sufficient for explaining global properties of the network of foreign direct investments. We also show, however, that network dependencies vary significantly over time giving rise to a time-heterogeneous localized process of network evolution.     

Is “relative quantum phase” transitive?

I discuss the question: Is it possible to prepare, by purely thermodynamic means, an ensemble described by a quantum state having a definite phase relation between two component states which have never been in direct contact? Resolution of this question requires us to take explicit account of the nature of the correlations between the system and its thermal environment.     

Inequality relations for the hierarchy of quantum correlations in two-qubit systems

Entanglement, quantum steering and Bell nonlocality can be used to describe the distinct quantum correlations of quantum systems. Because of their different characteristics and application fields, how to divide them quantitatively and accurately becomes particularly important. Based on the sufficient and necessary criterion for quantum steering of an arbitrary two-qubit T-state, we derive the inequality relations between quantum steering and entanglement as well as between quantum steering and Bell nonlocality for the T-state. Additionally, we have verified those relations experimentally.     

Quantum States as Objective Informational Bridges

A quantum state represents neither properties of a physical system nor anyone’s knowledge of its properties. The important question is not what quantum states represent but how they are used—as informational bridges. Knowing about some physical situations (its backing conditions), an agent may assign a quantum state to form expectations about other possible physical situations (its advice conditions). Quantum states are objective: only expectations based on correct state assignments are generally reliable. If a quantum state represents anything, it is the objective probabilistic relations between its backing conditions and its advice conditions. This paper offers an account of quantum states and their function as informational bridges, in quantum teleportation and elsewhere.     

Dynamical correlations in the Dual Parton Model

The effect of multiple ‘chain’ contributions to particle production, which appears in the Dual Parton Model at collider energies, is investigated in an exploratory model, in which other sources of correlations are largely neglected. Attention is given to the question of KNO scaling for the multiplicities observed in restricted or unrestricted rapidity ranges. The rapidity distribution associated with a fixed number of particles within a suitably chosen interval, is found to be sensitive to details of the mechanism of multiple chain production.     

Power-law regularities in human language

Complex structure of human language enables us to exchange very complicated information. This communication system obeys some common nonlinear statistical regularities. We investigate four important long-range features of human language. We perform our calculations for adopted works of seven famous litterateurs. Zipf’s law and Heaps’ law, which imply well-known power-law behaviors, are established in human language, showing a qualitative inverse relation with each other. Furthermore, the informational content associated with the words ordering, is measured by using an entropic metric. We also calculate fractal dimension of words in the text by using box counting method. The fractal dimension of each word, that is a positive value less than or equal to one, exhibits its spatial distribution in the text. Generally, we can claim that the Human language follows the mentioned power-law regularities. Power-law relations imply the existence of long-range correlations between the word types, to convey an especial idea.     

Equivalent Forms of Dirac Equations in Curved Space-times and Generalized de Broglie Relations

One may ask whether the relations between energy and frequency and between momentum and wave vector, introduced for matter waves by de Broglie, are rigorously valid in the presence of gravity. In this paper, we show this to be true for Dirac equations in a background of gravitational and electromagnetic fields. We first transform any Dirac equation into an equivalent canonical form, sometimes used in particular cases to solve Dirac equations in a curved space-time. This canonical form is needed to apply Whitham’s Lagrangian method. The latter method, unlike the Wentzel–Kramers–Brillouin method, places no restriction on the magnitude of Planck’s constant to obtain wave packets and furthermore preserves the symmetries of the Dirac Lagrangian. We show by using canonical Dirac fields in a curved space-time that the probability current has a Gordon decomposition into a convection current and a spin current and that the spin current vanishes in the Whitham approximation, which explains the negligible effect of spin on wave packet solutions, independent of the size of Planck’s constant. We further discuss the classical-quantum correspondence in a curved space-time based on both Lagrangian and Hamiltonian formulations of the Whitham equations. We show that the generalized de Broglie relations in a curved space-time are a direct consequence of Whitham’s Lagrangian method and not just a physical hypothesis as introduced by Einstein and de Broglie and by many quantum mechanics textbooks.     

Statistics in the landscape of intersecting brane models

An approach towards a statistical survey of four-dimensional supersymmetric vacua in the string theory landscape is described and illustrated with three examples of ensembles of intersecting D-brane models. The question whether it is conceivable to make predictions based on statistical distributions is discussed. Especially interesting in this context are possible correlations between low energy observables. As an example we look at correlations between properties of the gauge sector of intersecting D-brane models and Gepner model constructions. Based on a talk presented at “The 15th International Conference on Supersymmetry and the Unification of Fundamental Interactions”, July 26–August 1, 2007, Karlsruhe, Germany.     

Quantum and classical correlations in a classical dephasing environment

We calculate the non-Markovian dynamics of quantum correlations, including entanglement and discord, and classical correlation in a two-qubit system with Ornstein-Uhlenbeck noise and discuss the relations in these correlations. It?s found that the initial-state parameters and the non-Markovian properties play an important role in these dynamics behaviors.     

Formality for Lie Algebroids

Using Dolgushev’s generalization of Fedosov’s method for deformation quantization, we give a positive answer to a question of P. Xu: can one prove a formality theorem for Lie algebroids ? As a direct application of this result, we obtain that any triangular Lie bialgebroid is quantizable.     

Entanglement Between Demand and Supply in Markets with Bandwagon Goods

Whenever customers’ choices (e.g. to buy or not a given good) depend on others choices (cases coined ‘positive externalities’ or ‘bandwagon effect’ in the economic literature), the demand may be multiply valued: for a same posted price, there is either a small number of buyers, or a large one—in which case one says that the customers coordinate. This leads to a dilemma for the seller: should he sell at a high price, targeting a small number of buyers, or at low price targeting a large number of buyers? In this paper we show that the interaction between demand and supply is even more complex than expected, leading to what we call the curse of coordination: the pricing strategy for the seller which aimed at maximizing his profit corresponds to posting a price which, not only assumes that the customers will coordinate, but also lies very near the critical price value at which such high demand no more exists. This is obtained by the detailed mathematical analysis of a particular model formally related to the Random Field Ising Model and to a model introduced in social sciences by T.C. Schelling in the 70’s.     

Additivity Relations of Quantum Correlations for Three-qubit Entangled State in Atom-cavity System

Taking advantage of quantum discord and negativity respectively, four additivity relations of quantum correlations are studied in the atom-cavity system, for three identical two-level atoms resonantly interact with a single-mode high-Q cavity simultaneously. Through numerical analysis, we find that in this model of atom-cavity system, four additivity relations of negativity are always satisfied well, no matter tripartite are in the pure states or the mixed states, while the results of quantum discord are not always satisfied. What’s more, if and only if the mixed three-atom states evolve into the pure states again, four additivity inequality relations of quantum discord and negativity become equalities simultaneously.     

Microstructural Characteristics of the Weighted and Directed International Crop Trade Networks

With increasing global demand for food, international food trade is playing a critical role in balancing the food supply and demand across different regions. Here, using trade datasets of four crops that provide more than 50% of the calories consumed globally, we constructed four international crop trade networks (iCTNs). We observed the increasing globalization in the international crop trade and different trade patterns in different iCTNs. The distributions of node degrees deviate from power laws, and the distributions of link weights follow power laws. We also found that the in-degree is positively correlated with the out-degree, but negatively correlated with the clustering coefficient. This indicates that the numbers of trade partners affect the tendency of economies to form clusters. In addition, each iCTN exhibits a unique topology which is different from the whole food network studied by many researchers. Our analysis on the microstructural characteristics of different iCTNs provides highly valuable insights into distinctive features of specific crop trades and has potential implications for model construction and food security.     

Electron correlations and many-body techniques in magnetism

Recent progress in the theory of magnetism and electron correlations is reviewed to clarify the theories developed in the last decade and their mutual relations. A historical development of the theory of magnetism is outlined, and the dynamical coherent potential approximation (CPA) which completely takes account of the dynamical spin and charge fluctuations within the single-site approximation is introduced. Both the dynamical effects on various magnetic properties and the many-body band structure are shown to be explained on the same footing. It is shown that the dynamical CPA is equivalent to the other single-site theories of strongly correlated electrons: the many-body CPA, the dynamical mean-field theory (DMFT), and the projection operator method CPA (PM-CPA). These theories are elucidated with use of a common concept of effective medium or coherent potential. The effects of orbital degeneracy and the realistic calculation scheme are discussed with an emphasis on Hund’s rule coupling. Non-local theories of magnetism and electron correlations which go beyond the single-site approximation are presented. They include the molecular dynamics approach to the magnetic short range order, the dynamical cluster methods as a direct extension of the DMFT, and the self-consistent projection operator approach as an extension of the PM-CPA with use of the incremental cluster expansion. The current problems of their approaches and their future perspective are discussed.     

Nestedness-Based Measurement of Evolutionarily Stable Equilibrium of Global Production System

A nested structure is a structural feature that is conducive to system stability formed by the coevolution of biological species in mutualistic ecosystems The coopetition relationship and value flow between industrial sectors in the global value chain are similar to the mutualistic ecosystem in nature. That is, the global economic system is always changing to form one dynamic equilibrium after another. In this paper, a nestedness-based analytical framework is used to define the generalist and specialist sectors for the purpose of analyzing the changes in the global supply pattern. We study why the global economic system can reach a stable equilibrium, what the role of different sectors play in the steady status, and how to enhance the stability of the global economic system. In detail, the domestic trade network, export trade network and import trade network of each country are extracted. Then, an econometric model is designed to analyze how the microstructure of the production system affects a country’s macroeconomic performance.     

Applications of progenitor sum rules in nuclear theory

The energy-weighted sum rules, obtained by taking matrix elements of double commutators with the nuclear Hamiltonian of appropriately defined densities, are didactically reviewed.Following a catalogue of applications such sum rules have found in theoretical nuclear physics, the progenitor sum rules (PSR's) are derived using standard commutator relations for second-quantized nucleon field operators. This leads to the extension of PSR's to coupled Fermi-Bose systems, and in particular, to a simple model of interacting mesons and nucleons. The effects of interactions are also discussed from the point of view of (static) exchange potentials. The relation of the dipole sum rule to nuclear photoabsorption is reviewed briefly.The application of PSR's to the calculation of longitudinal inelastic form factors, and the use of the “doorway hypothesis” is discussed in detail, together with the semiclassical collective-oscillation interpretation of these results proposed by Bertsch. Suzuki's very interesting applications of PSR to the evaluation of collective mass parameters, coupling constants, and polarization functions of the Bohr-Mottelson self-consistent mean-field theory are also given a detailed treatment. Certain miscellaneous applications of PSR to calculation of Coulombic isospin mixing, to energy shifts in isospin multiplets, and to induced moments and effective charges are collected and discussed in a unified manner. The review concludes with a discussion of the qualitative character of the nuclear photoabsorption strength below the meson production threshold, especially with regard to the question of to what extent the (γ, NN) reaction is sensitive to pair correlations in the nuclear ground state.