[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

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Convex Analysisの二,三の進展について

Fractional Differential Equations

The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

Many ``real-world'' networks are clearly defined while most ``social'' networks are to some extent subjective. Indeed, the accuracy of empirically-determined social networks is a question of some concern because individuals may have distinct perceptions of what constitutes a social link. One unambiguous type of connection is sexual contact. Here we analyze data on the sexual behavior of a random sample of individuals, and find that the cumulative distributions of the number of sexual partners during the twelve months prior to the survey decays as a power law with similar exponents $\alpha \approx 2.4$ for females and males. The scale-free nature of the web of human sexual contacts suggests that strategic interventions aimed at preventing the spread of sexually-transmitted diseases may be the most efficient approach.

The Web of Human Sexual Contacts

The study of rumor spreading has become an important issue on complex social networks. On the basis of prior studies, we propose a modified ​susceptible–exposed–infected–removed (SEIR) model with hesitating mechanism by considering the attractiveness and fuzziness of the content of rumors. We derive mean-field equations to characterize the dynamics of SEIR model on both homogeneous and heterogeneous networks. Then a steady-state analysis is conducted to investigate the spreading threshold and the final rumor size. Simulations on both artificial and real networks show that a decrease of fuzziness can effectively increase the spreading threshold of the SEIR model and reduce the maximum rumor influence. In addition, the spreading threshold is independent of the attractiveness of rumor. Simulation results also show that the speed of rumor spreading obeys the relation “BA network > WS network”, whereas the final scale of spreading obeys the opposite relation.

Rumor spreading model considering hesitating mechanism in complex social networks

In this brief, a new noncoherent chaos-based communication scheme, named high-efficiency differential chaos shift keying (DCSK) (HE-DCSK), is proposed. By recycling each reference sample in DCSK, 2 bits of data can be carried in one data-modulated sample sequence, which offers our scheme double bandwidth efficiency and nonrepeated transmitted signal less prone to interception in comparison to DCSK. The bit-error performance of the proposed scheme is studied analytically based on Gaussian approximation for discrete-time implementations. Simulations in additive-white-Gaussian-noise channel are performed and compared with DCSK and correlation delay shift keying (CDSK) schemes. Results show that the bit-error rate performance of HE-DCSK can always outperform CDSK and be even better than DCSK with typical spreading factors and at reasonable Eb/No levels.

High-Efficiency Differential-Chaos-Shift-Keying Scheme for Chaos-Based Noncoherent Communication

In this paper, a new approach for synchronization of complex dynamical networks is proposed based on state observer design. Unlike the common diagonally coupling networks, where full state coupling is typically needed between two nodes, here it is suggested that only a scalar coupling signal is required to achieve network synchronization. Some conditions for synchronization, in the form of an inequality, are established based on the Lyapunov stability theory, which can be transformed to a linear matrix inequality and easily solved by a numerical toolbox. Two typical dynamical network configurations, i.e., global coupling and nearest-neighbor coupling, with each node being a modified Chua's circuit, are simulated. It is demonstrated that the proposed scheme is effective in achieving the expected chaos synchronization in the complex network

A State-Observer-Based Approach for Synchronization in Complex Dynamical Networks

Based on the Lyapunov stabilization theory and Gerschgorin theorem, a simple generic criterion is derived for global synchronization of two coupled chaotic systems with a unidirectional linear error feedback coupling. This simple criterion is applicable to a large class of chaotic systems, where only a few algebraic inequalities are involved. To demonstrate the efficiency of design, the suggested approach is applied to some typical chaotic systems with different types of nonlinearities, such as the original Chua’s circuit, the modified Chua’s circuit with a sine function, and the R€ o chaotic system. It is proved that these synchronizations are ensured by suitably designing the coupling parameters.

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A simple global synchronization criterion for coupled chaotic systems

In this paper, a fractional-order recurrent neural network is proposed and several topics related to the dynamics of such a network are investigated, such as the stability, Hopf bifurcations, and undamped oscillations. The stability domain of the trivial steady state is completely characterized with respect to network parameters and orders of the commensurate-order neural network. Based on the stability analysis, the critical values of the fractional order are identified, where Hopf bifurcations occur and a family of oscillations bifurcate from the trivial steady state. Then, the parametric range of undamped oscillations is also estimated and the frequency and amplitude of oscillations are determined analytically and numerically for such commensurate-order networks. Meanwhile, it is shown that the incommensurate-order neural network can also exhibit a Hopf bifurcation as the network parameter passes through a critical value which can be determined exactly. The frequency and amplitude of bifurcated oscillations are determined.

Guo-Ping Jiang

Papers

Rumor spreading model considering hesitating mechanism in complex social networks

High-Efficiency Differential-Chaos-Shift-Keying Scheme for Chaos-Based Noncoherent Communication

A State-Observer-Based Approach for Synchronization in Complex Dynamical Networks

A simple global synchronization criterion for coupled chaotic systems

Undamped Oscillations Generated by Hopf Bifurcations in Fractional-Order Recurrent Neural Networks With Caputo Derivative