Chaotic-periodic transition in a two-sided minority game

Phase transitions are being used increasingly to probe the collective behaviors of social human systems. In this study, we propose a different way of investigating such transitions in a human system by establishing a two-sided minority game model. A new type of agents who can actively transfer resources are added to our artificial bipartite resource-allocation market. The degree of deviation from equilibria is characterized by the entropy-like quantity of market complexity. Under different threshold values, Q _th , two phases are found by calculating the exponents of the associated power spectra. For large values of Q _th , the general motion of strategies for the agents is relatively periodic whereas for low values of Q _th , the motion becomes chaotic. The transition occurs abruptly at a critical value of Q _th . Our simulation results were also tested based on human experiments. The results of this study suggest that a chaotic-periodic transition related to the quantity of market information should exist in most bipartite markets, thereby allowing better control of such a transition and providing a better understanding of the endogenous emergence of business cycles from the perspective of quantum mechanics.     

Adaptive cyclically dominating game on co-evolving networks: numerical and analytic results

A co-evolving and adaptive Rock (R)–Paper (P)–Scissors (S) game (ARPS) in which an agent uses one of three cyclically dominating strategies is proposed and studied numerically and analytically. An agent takes adaptive actions to achieve a neighborhood to his advantage by rewiring a dissatisfying link with a probability p or switching strategy with a probability 1 - p. Numerical results revealed two phases in the steady state. An active phase for p < p _c has one connected network of agents using different strategies who are continually interacting and taking adaptive actions. A frozen phase for p > p _c has three separate clusters of agents using only R, P, and S, respectively with terminated adaptive actions. A mean-field theory based on the link densities in co-evolving network is formulated and the trinomial closure scheme is applied to obtain analytical solutions. The analytic results agree with simulation results on ARPS well. In addition, the different probabilities of winning, losing, and drawing a game among the agents are identified as the origin of the small discrepancy between analytic and simulation results. As a result of the adaptive actions, agents of higher degrees are often those being taken advantage of. Agents with a smaller (larger) degree than the mean degree have a higher (smaller) probability of winning than losing. The results are informative for future attempts on formulating more accurate theories.     

<Emphasis Type="Italic">Ab initio</Emphasis> theory of the electronic structure and spectra of impurity <Emphasis Type="Italic">nl</Emphasis> ions

The fundamentals of the theory of the electronic structure of impurity clusters and the results of numerical calculations for the iron-, lanthanum-, and actinium-group ions in Me⁺ⁿ: [L]_k clusters are presented. The effects of the interionic distance and ligands in the Me⁺ⁿ: [L]_k clusters on the electronic structure of the nl ^N and nl^N?1n′l′ configurations of the 3d, 4f, and 5f ions are considered. The correspondence between the optical and x-ray spectra of different impurity crystals is also analyzed.     

A Monte Carlo study of the first-order transition in a Heisenberg FCC antiferromagnet

A nearest neighbor Heisenberg antiferromagnet on a face-centered cubic lattice is studied by extensive Monte Carlo simulations in zero magnetic field. The parallel tempering algorithm is utilized, which allows one to overcome a slow relaxation of the magnetic order parameter and to fully equilibrate moderately sized clusters with up to N ? 7 × 10³ spins. By collecting energy and order parameter histograms on clusters with up to N ? 2 × 10⁴ sites, we accurately locate the first-order transition point at T _c = 0.4459(1)J.     

Non-Fermi liquid theory of quantum Hall effects

Within the Grassmannian U(2N)/U(N) × U(N) nonlinear σ-model representation of localization, one can study the low-energy dynamics of both a free and interacting electron gas. We study the crossover between these two fundamentally different physical problems. We show how the topological arguments for the exact quantization of the Hall conductance are extended to include the Coulomb interaction problem. We discuss dynamical scaling and make contact with the theory of variable range hopping.     

Correlation of the molecular structure of discotic nematic liquid crystals with their orientational order and specific features of the nematic-isotropic phase transition

The orientational order parameter S of molecules in high-temperature discotic nematic liquid-crystal phases of triphenylene derivatives is investigated as a function of the length of side flexible molecular chains at different temperatures. It is established that the orientational order parameters S in the range of the transition from the nematic phase to the isotropic liquid phase (the N _D -I transition) are smaller than those predicted from the molecular-statistical theory and computer simulation. It is shown that the N _D -I transition is close to both the isolated Landau point and the tricritical point (regardless of the chemical structure of the molecules and the anisotropy of dispersion intermolecular interactions). Consistent explanations are offered for a number of experimental findings, such as the anomalously small changes in the enthalpy and entropy upon the N _D -I transition (as compared to those revealed upon the N-I transition in calamitic nematic liquid crystals), the anomalously strong response of the isotropic phase of discotic nematic liquid crystals to external fields (thermodynamically conjugate to the order parameter S) and the long relaxation times of this response, and the formation of cybotactic discotic molecular clusters in the isotropic phase in the vicinity of the N _D -I transition.     

Bad communities with high modularity

In this paper we discuss some problematic aspects of Newman and Girvan’s modularity function Q _N . Given a graph G, the modularity of G can be written as Q _N = Q _f ? Q ₀, where Q _f is the intracluster edge fraction of G and Q ₀ is the expected intracluster edge fraction of the null model, i.e., a randomly connected graph with same expected degree distribution as G. It follows that the maximization of Q _N must accomodate two factors pulling in opposite directions:Q _f favors a small number of clusters and Q ₀ favors many balanced (i.e., with approximately equal degrees) clusters. In certain cases the Q ₀ term can cause overestimation of the true cluster number; this is the opposite of the well-known underestimation effect caused by the “resolution limit” of modularity. We illustrate the overestimation effect by constructing families of graphs with a “natural” community structure which, however, does not maximize modularity. In fact, we show there exist graphs G with a “natural clustering” V of G and another, balanced clustering U of G such that (i) the pair (G, U) has higher modularity than (G, V) and (ii) V and U are arbitrarily different.     

Randall–Sundrum II model from small field inflation in light of planck data and reheating temperature

We focus on the behaviours of small field of an arctangent potential form, in Randall–Sundrum II braneworld. Within this framework, there is only one brane with positive tension while the second membrane is sent to infinity, and the configuration the model allows to localize the gravity on the curvature of the bulk. In that context, we found that inflationary observables (n _s, r, and dn _s/dlnk) depend only on the e-folding number N. From the power perturbation value P _R (k) given by the latest observational measurements, we evaluate the values of brane tension λ and the energy scale V ₀, and we have shown that the various inflationary perturbation parameters are widely consistent with the recent Planck data for a suitable choice of value of the number N. Concerning the reheating phase, we found a large value of the temperature T _re ～ 5 × 10¹⁴ GeV.     

Is the number of light flavors in QCD great?

At a qualitative level, it is well known that QCD featuring a large number of quark flavors must differ drastically from actual QCD. However, it is possible to consider the large-N_f limit (where N_f is the number of light flavors in QCD) such that the basic dynamics of the system remains unchanged. This is the region of chiral perturbation theory, where the limit N_f → ∞ is simultaneously the limit of a large number of colors, N_c. Features are indicated that make it possible, in such a situation, to compare analytically the same quantity in a simplified model of actual QCD and in the large-N_f limit, and methods are proposed for calculating these features. Calculations in the limit N_f → ∞ are of no use in assessing quantities of the theory at small N f.     

Dependence of the surface energy on the size and shape of a nanocrystal

An expression is derived for the surface energy σ as a function of the size and shape of a nanocrystal. It is shown that the wider the deviation of the shape parameter f from unity, the more pronounced the decrease in the surface energy σ with a decrease in the number N of atoms in the nanocrystal. The dependences of the average coordination number, the surface energy, and the melting temperature on the number N exhibit an oscillatory behavior with maxima at points corresponding to numbers of atoms forming a defect-free cube. The surface energy decreases with an increase in the temperature T. It is found that the smaller the nanocrystal size or the greater the deviation of the nanocrystal shape from the thermodynamically most stable shape (a cube), the larger the quantity-(dσ/dT). It is established that the nanocrystal undergoes melting when the surface energy decreases to a value at which it becomes independent of the nanocrystal size and shape. The conditions providing fragmentation and dendritization of the crystal are discussed. It is demonstrated that, at N>1000, the dependence σ(N) coincides, to a high accuracy, with the dependence of the surface tension of the nanocrystal on N. The inference is made that bimorphism is characteristic of nanocrystals. This implies that nanocrystals can have platelike and rodlike shapes with equal probability.     

Massive hyper-Kähler sigma models and BPS domain walls

With the non-Abelian hyper-Kähler quotient by U(M) and SU(M) gauge groups, we give the massive hyper-Kähler sigma models that are not toric in the N=1 superfield formalism. The U(M) quotient gives N!/[M!(N-M)!] (N is the number of flavors) discrete vacua that may allow various types of domain walls, whereas the SU(M) quotient gives no discrete vacua. We derive a BPS domain-wall solution in the case of N = 2 and M = 1 in the U(M) quotient model.     

Detection of SF<Subscript>6</Subscript> molecules sublimating from the surface of (CO<Subscript>2</Subscript>)<Subscript><Emphasis Type="Italic">N</Emphasis></Subscript> nanoparticles in a cluster beam by the infrared multiphoton excitation method

It has been found that SF₆ molecules captured by large van der Waals clusters (CO₂) _N (where N ≥ 10² is the number of monomers in a cluster) in intersecting molecular and cluster beams sublimate from the surface of clusters after a certain time and carry information on the velocity and temperature (internal energy) of clusters. Experiments have been carried out for detecting these molecules by means of a pyroelectric detector and the infrared multiphoton excitation method. The multiphoton absorption spectra of molecules sublimating from the surface of clusters have been obtained. The temperature of the (CO₂) _N nanoparticles in the cluster beam has been estimated using these spectra and comparing them with the infrared multiphoton absorption spectra of SF₆ in the initial molecular beam.     

Quantification of Quantum Entanglement in a Multiparticle System of Two-Level Atoms Interacting with a Squeezed Vacuum State of the Radiation Field

We quantify multiparticle quantum entanglement in a system of N two-level atoms interacting with a squeezed vacuum state of the electromagnetic field. We calculate the amount of quantum entanglement present among one hundred such two-level atoms and also show the variation of that entanglement with the radiation field parameter. We show the continuous variation of the amount of quantum entanglement as we continuously increase the number of atoms from N = 2 to N = 100. We also discuss that the multiparticle correlations among the N two-level atoms are made up of all possible bipartite correlations among the N atoms.     

Topologic distance in the Lucena network

The Lucena network (LN) is the dual of a multifractal partition of the square. We analyzethe relation between the typical topologic distance l and the number ofvertices Nof the LN. The multifractal partition has one parameter ρ which controls thegeometrical asymmetry of the multifractal. In the limit of ρ → 1 the blocks of thepartition are squared, the connections amont the blocks are short range, the LN is moreregular and the relation l ∝ √N is observed. For the limit ρ → 0 the blocks arestrongly asymmetric, long range connections appear, and the topologic distance followsl ∝(log?N)^α, a weak smallworld phenomenon. For any network size we calculate analytically the size of the minimumdistance l_min (ρ → 0) and the maximaldistance l_max (ρ → 1). The distance in theweak small world regime is calculated using the number of vertices inside a radius oflength land taking into account the network average connectivity and the exponent α.     

Dimension of mesogenic molecules as atomic clusters

The problem regarding the mass dimension D of mesogenic molecules as atomic clusters is formulated and solved using computer simulation and analytical calculations. For a large number of compounds belonging to different chemical classes, it is shown that the cores of discotic lacunar (rodlike, lathlike) molecules forming nematic or columnar discotic (calamitic) phases have a fractional dimension 1 < D _c < 2 (D _c ≈ 1). The dependences of the dimension D _c on the symmetry, the conformation, and the structural-chemical features of the molecular core are determined. It is demonstrated that, in the region of side flexible chains in molecules of both types, the dimension D _ch can be either smaller or larger than unity, depending on the chain conformation. An analytical expression accounting for the results of numerical experiments is obtained for the dimension D _ch .     

EXAFS study of copper complexes with azomethinic ligand environment

A series of copper metallochelates C₂₂H₁₈CuN₄O₂ X (X = Se, S, O) as models of active centers of natural metalloproteins have been synthesized on the basis of new azomethine ligand systems. The structure of the complexes has been studied by extended X-ray absorption fine-structure spectroscopy. It is shown that, in the metallochelates with X = Se or S, one azomethine chalcogen-containing ligand undergoes tridentate interaction with copper ions, while the other ligand is an acetate group. As a result, a complex with the N₂O₂ X environment is formed, where one of the oxygen atoms of the acetate group is at a large distance from the metal ion: R = 2.56–2.68 Å. For the metallochelate with X = O, coordination of the acetate group by a copper ion is found to be absent, and only interaction with azomethine ligands having average Cu-N/O distances R = 1.96–2.04 Å is observed.     

Treatment of pairing in small systems by Green functions

A finite system of fermions with pairing interaction is treated by the Green function method. It is shown that a finite number of “bound pairs” must be assumed to get the correct properties of the system in that region of the interaction strength where the BCS-solution is incorrect. Also the difference betweenE ₀(N+2)?E ₀(N) andE ₀(N)?E ₀(N?2),E ₀(N) being the ground state energy of theN-particle system, has to be considered. The formulae derived give an interpolation between the region where perturbation theory applies and the region of validity of the BCS-equations.     

Noisy Hegselmann-Krause Systems: Phase Transition and the 2<Emphasis Type="Italic">R</Emphasis>-Conjecture

The classic Hegselmann-Krause (HK) model for opinion dynamics consists of a set of agents on the real line, each one instructed to move, at every time step, to the mass center of the agents within a fixed distance R. In this work, we investigate the effects of noise in the continuous-time version of the model as described by its mean-field Fokker-Planck equation. In the presence of a finite number of agents, the system exhibits a phase transition from order to disorder as the noise increases. We introduce an order parameter to track the phase transition and resolve the corresponding phase diagram. The system undergoes a phase transition for small R but none for larger R. Based on the stability analysis of the mean-field equation, we derive the existence of a forbidden zone for the disordered phase to emerge. We also provide a theoretical explanation for the well-known 2R conjecture, which states that, for a random initial distribution in a fixed interval, the final configuration consists of clusters separated by a distance of roughly 2R. Our theoretical analysis confirms previous simulations and predicts properties of the noisy HK model in higher dimension.     

Quantum-Size Dependence of the Energy for Vacancy Formation in Charged Small Metal Clusters. Drop Model

Self-consistent computations of the monovacancy formation energy are performed for Na _N , Mg _N , and Al _N (12 < N ≤ 168) spherical clusters in the drop model for stable jelly. Scenarios of the Schottky vacancy formation and “bubble vacancy blowing” are considered. It is shown that the asymptotic behavior of the size dependences of the energy for the vacancy formation by these two mechanisms is different and the difference between the characteristics of a charged and neutral cluster is entirely determined by the difference between the ionization potentials of clusters and the energies of electron attachment to them.