Punctuated evolution due to delayed carrying capacity

A new delay equation is introduced to describe the punctuated evolution of complex nonlinear systems. A detailed analytical and numerical investigation provides the classification of all possible types of solutions for the dynamics of a population in the four main regimes dominated respectively by: (i) gain and competition, (ii) gain and cooperation, (iii) loss and competition and (iv) loss and cooperation. Our delay equation may exhibit bistability in some parameter range, as well as a rich set of regimes, including monotonic decay to zero, smooth exponential growth, punctuated unlimited growth, punctuated growth or alternation to a stationary level, oscillatory approach to a stationary level, sustainable oscillations, finite-time singularities as well as finite-time death.     

The spin symmetry for deformed generalized Pöschl-Teller potential

In the case of spin symmetry we solve the Dirac equation with scalar and vector deformed generalized Pöschl-Teller (DGPT) potential and obtain exact energy equation and spinor wave functions for s-wave bound states. We find that there are only positive energy states for bound states in the case of spin symmetry based on the strong regularity restriction condition λ<−η for the wave functions. The energy eigenvalue approaches a constant when the potential parameter α goes to zero. Two special cases such as generalized PT potential and standard PT potential are also briefly discussed.     

Comparison of immunization strategies in geographical networks

The epidemic spread and immunizations in geographically embedded scale-free (SF) and Watts-Strogatz (WS) networks are numerically investigated. We make a realistic assumption that it takes time which we call the detection time, for a vertex to be identified as infected, and implement two different immunization strategies: one is based on connection neighbors (CN) of the infected vertex with the exact information of the network structure utilized and the other is based on spatial neighbors (SN) with only geographical distances taken into account. We find that the decrease of the detection time is crucial for a successful immunization in general. Simulation results show that for both SF networks and WS networks, the SN strategy always performs better than the CN strategy, especially for more heterogeneous SF networks at long detection time. The observation is verified by checking the number of the infected nodes being immunized. We found that in geographical space, the distance preferences in the network construction process and the geographically decaying infection rate are key factors that make the SN immunization strategy outperforms the CN strategy. It indicates that even in the absence of the full knowledge of network connectivity we can still stop the epidemic spread efficiently only by using geographical information as in the SN strategy, which may have potential applications for preventing the real epidemic spread.     

Detect overlapping and hierarchical community structure in networks

Clustering and community structure is crucial for many network systems and the related dynamic processes. It has been shown that communities are usually overlapping and hierarchical. However, previous methods investigate these two properties of community structure separately. This paper proposes an algorithm (EAGLE) to detect both the overlapping and hierarchical properties of complex community structure together. This algorithm deals with the set of maximal cliques and adopts an agglomerative framework. The quality function of modularity is extended to evaluate the goodness of a cover. The examples of application to real world networks give excellent results.     

Majority-vote model with different agents

We consider the majority-vote model with noise in a network of social interactions for a system with two classes of individuals, class σ and class τ. For the two-agent model each class has its own dynamics, with individuals of σ class being influenced by neighbors of both classes, while the individuals of type τ are influenced only by neighbors of that class. We use Monte Carlo simulations and finite-size scaling techniques to estimate the critical properties of the system in the stationary state. The calculated values of the critical noise parameters, and , allow us to identify five distinct regions in the phase diagram on the q_τ-q_σ plane. The critical exponents for each class are the same and we conclude that the present model belongs to the same universality class as the two-dimensional Ising model.     

High-spin excitations of 81, 82, 83, 85Se : Competing single-particle and collective structures around N = 50

The ^{81, 82, 83, 85}Se nuclei have been produced as fission fragments in the fusion reaction ¹⁸O + ²⁰⁸Pb at 85MeV bombarding energy and studied with the Euroball IV array. Their high-spin level schemes have been built from the triple -ray coincidence data and - angular correlations have been analyzed in order to assign spin and parity values to many observed states. The lowest-spin states of the two-neutron and three-neutron configurations are strongly mixed with two-proton excitations among the fp orbits. On the other hand, the highest-spin states of these neutron configurations are found to remain almost pure. Neutron excitation across the N = 50 gap is observed both in ⁸³Se₄₉ and in ⁸⁵Se₅₁ .     

Socio-economical dynamics as a solvable spin system on co-evolving networks

We consider social systems in which agents are not only characterized by their states but also have the freedom to choose their interaction partners to maximize their utility. We map such systems onto an Ising model in which spins are dynamically coupled by links in a dynamical network. In this model there are two dynamical quantitieswhich arrange towards a minimum energy state in the canonical framework:the spins, s_i, and the adjacency matrix elements, c_ij.The model is exactly solvable because microcanonical partition functions reduce to productsof binomial factors as a direct consequence of the c_ij minimizing energy. We solve the system for finite sizes and for the two possible thermodynamic limits and discussthe phase diagrams.     

Sexually Transmitted Diseases on Bipartite Graph

We study the susceptible infected-susceptible （SIS） epidemic model on bipartite graph. According to the difference of sex conception in western and oriental nations, we construct the Barabasi Albert Barabasi Albert （BA-BA） model and Barabasi-Albert Homogeneity （BA-HO） model for sexually transmitted diseases （STDs）. Applying the rate equation approach, the positive equilibria of both models are given analytically. We find that the ratio between infected females and infected males is distinctly different in both models and the infected density in the BA-HO model is much less than that in the BA-BA model. These results explain that the countries with small ratio have less infected density than those with large ratio. Our numerical simulations verify these theoretical results.     

An Alternative Method for Calculating Bound-State of Energy Eigenvalues of Klein-Gordon for Quasi-exactly Solvable Potentials

We obtain the bound-state energy of the Klein-Gordon equation for some examples of quasi-exactly solvable potentials within the framework of asymptotic iteration method （AIM）. The eigenvalues are calculated for type- 1 solutions. The whole quasi-exactly solvable potentials are generated from the defined relation between the vector and scalar potentials.     

SQUID sensor application for small metallic particle detection

High-Tc superconducting quantum interference device (SQUID) is an ultra-sensitive magnetic sensor. Since the performance of the SQUID is improved and stabilized, now it is ready for application. One strong candidate for application is a detection system of magnetic foreign matters in industrial products or beverages. There is a possibility that ultra-small metallic foreign matter has been accidentally mixed with industrial products such as lithium ion batteries. If this happens, the manufacturer of the product suffers a great loss recalling products. The outer dimension of metallic particles less than 100 μm cannot be detected by an X-ray imaging, which is commonly used for the inspection. Ionization of the material is also a big issue for beverages in the case of the X-ray imaging. Therefore a highly sensitive and safety detection system for small foreign matters is required. We developed detection systems based on high-Tc SQUID with a high-performance magnetic shield. We could successfully measure small iron particles of 100 μm on a belt conveyer and stainless steel balls of 300 μm in water. These detection levels were hard to be achieved by a conventional X-ray detection or other methods.