Information flow between stock markets: A Koopman decomposition approach

Stock markets in the world are linked by complicated and dynamical relationships into a temporal network.Extensive works have provided us with rich findings from the topological properties and their evolutionary trajectories,but the underlying dynamical mechanism is still not in order.In the present work,we proposed a technical scheme to reveal the dynamical law from the temporal network.The index records for the global stock markets form a multivariate time series.One separates the series into segments and calculates the information flows between the markets,resulting in a temporal market network representing the state and its evolution.Then the technique of the Koopman decomposition operator is adopted to find the law stored in the information flows.The results show that the stock market system has a high flexibility,i.e.,it jumps easily between different states.The information flows mainly from high to low volatility stock markets.And the dynamical process of information flow is composed of many dynamic modes distribute homogenously in a wide range of periods from one month to several ten years,but there exist only nine modes dominating the macroscopic patterns.     

Crossover Phenomena in Detrended Fluctuation Analysis Used in Financial Markets

A systematic analysis of Shanghai and Japan stock indices for the period of Jan. 1984 to Dec. 2005 is performed. After stationarity is verified by ADF （Augmented Dickey-Fuller） test, the power spectrum of the data exhibits a power law decay as a whole characterized by 1/f^β processes with possible long range correlations. Subsequently, by using the method of detrended fluctuation analysis （DFA） of the general volatility in the stock markets, we find that the long-range correlations are occurred among the return series and the crossover phenomena exhibit in the results obviously.Further, Shanghai stock market shows long-range correlations in short time scale and shows short-range correlations in long time scale. Whereas, for Japan stock market, the data behaves oppositely absolutely. Last, we compare the varying of scale exponent in large volatility between two stock markets. All results obtained may indicate the possibility of characteristic of multifractal scaling behavior of the financial markets.     

Regular nonlinear response of the driven Duffing oscillator to chaotic time series

Nonlinear response of the driven Duffng oscillator to periodic or quasi-periodic signals has been well studied.In this paper,we investigate the nonlinear response of the driven Duffng oscillator to non-periodic,more specifically,chaotic time series.Through numerical simulations,we find that the driven Duffng oscillator can also show regular nonlinear response to the chaotic time series with different degree of chaos as generated by the same chaotic series generating model,and there exists a relationship between the state of the driven Duffng oscillator and the chaoticity of the input signal of the driven Duffng oscillator.One real-world and two artificial chaotic time series are used to verify the new feature of Duffng oscillator.A potential application of the new feature of Duffng oscillator is also indicated.     

Time series prediction using wavelet process neural network

In the real world, the inputs of many complicated systems are time-varying functions or processes. In order to predict the outputs of these systems with high speed and accuracy, this paper proposes a time series prediction model based on the wavelet process neural network, and develops the corresponding learning algorithm based on the expansion of the orthogonal basis functions. The effectiveness of the proposed time series prediction model and its learning algorithm is proved by the Macke-Glass time series prediction, and the comparative prediction results indicate that the proposed time series prediction model based on the wavelet process neural network seems to perform well and appears suitable for using as a good tool to predict the highly complex nonlinear time series.     

Chaos Identification Based on Component Reordering and Visibility Graph

The identification between chaotic systems and stochastic processes is not easy since they have numerous similarities. In this study, we propose a novel approach to distinguish between chaotic systems and stochastic processes based on the component reordering procedure and the visibility graph algorithm. It is found that time series and their reordered components will show diverse characteristics in the ‘visibility domain'. For chaotic series, there are huge differences between the degree distribution obtained from the original series and that obtained from the corresponding reordered component. For correlated stochastic series, there are only small differences between the two degree distributions. For uncorrelated stochastic series, there are slight differences between them. Based on this discovery, the well-known Kullback-Leible divergence is used to quantify the difference between the two degree distributions and to distinguish between chaotic systems, correlated and uncorrelated stochastic processes.Moreover,one chaotic map, three chaotic systems and three different stochastic processes are utilized to illustrate the feasibility and effectiveness of the proposed method. Numerical results show that the proposed method is not only effective to distinguish between chaotic systems, correlated and uncorrelated stochastic processes, but also easy to operate.     

Functional Time Series Prediction Using Process Neural Network

Time series prediction methods based on conventional neural networks do not take into account the functional relations between the discrete observed values in the time series. This usually causes a low prediction accuracy. To solve this problem, a functional time series prediction model based on a process neural network is proposed in this paper. A Levenberg-Marquardt learning algorithm based on the expansion of the orthonormal basis functions is developed to train the proposed functional time series prediction model. The efficiency of the proposed functional time series prediction model and the corresponding learning algorithm is verified by the prediction of the monthly mean sunspot numbers. The comparative test results indicate that process neural network is a promising tool for functional time series prediction.     

Co-evolution of the brand effect and competitiveness in evolving networks

The principle that ‘the brand effect is attractive’ underlies the preferential attachment. Here we show that the brand effect is just one dimension of attractiveness. Another dimension is competitiveness. We firstly introduce a general framework that allows us to investigate the competitive aspect of real networks, instead of simply preferring popular nodes. Our model accurately describes the evolution of social and technological networks. The phenomenon that more competitive nodes become richer can help us to understand the evolution of many competitive systems in nature and society. In general,the paper provides an explicit analytical expression of degree distributions of the network. In particular, the model yields a nontrivial time evolution of nodes’ properties and the scale-free behavior with exponents depending on the microscopic parameters characterizing the competition rules. Secondly, through theoretical analyses and numerical simulations, we reveal that our model has not only the universality for the homogeneous weighted network, but also the character for the heterogeneous weighted network. Thirdly, we also develop a model based on the profit-driven mechanism. It can better describe the observed phenomenon in enterprise cooperation networks. We show that the standard preferential attachment,the growing random graph, the initial attractiveness model, the fitness model, and weighted networks can all be seen as degenerate cases of our model.     

Control of sudden transition between classical and quantum correlations of two strongly driven atoms in dissipative cavities

We investigate analytically the dynamics of classical and quantum correlations between two strongly driven atoms, each of which is trapped inside a dissipative cavity. It is found that there exists a finite time interval during which the quantum discord initially prepared in the X-type states is not destroyed by the decay of the cavities. The sudden transition between classical correlation and quantum discord is sensitive to the initial-state parameter, the cavity decay rate, and the cavity mode-driving field detuning. Interestingly, we show that the transition time can be prolonged significantly by increasing the degree of the detuning.     

Prisoner's Dilemma on Co-Evolving Networks without Strategy Update

We investigate the game theory in a structured population with the assumption that the evolution of network structure is far faster than that of strategy update. We find that the degree distribution for the finM network consists of two distinct parts： the low degree part which is contributed to by defectors and a broadband in the regime with high degree which is formed by cooperators. The structure of the final network and the final strategy pattern have also been numerically proved to be independent of the game parameters.     

Determination of quantum toric error correction code threshold using convolutional neural network decoders

Quantum error correction technology is an important solution to solve the noise interference generated during the operation of quantum computers.In order to find the best syndrome of the stabilizer code in quantum error correction,we need to find a fast and close to the optimal threshold decoder.In this work,we build a convolutional neural network(CNN)decoder to correct errors in the toric code based on the system research of machine learning.We analyze and optimize various conditions that affect CNN,and use the RestNet network architecture to reduce the running time.It is shortened by 30%-40%,and we finally design an optimized algorithm for CNN decoder.In this way,the threshold accuracy of the neural network decoder is made to reach 10.8%,which is closer to the optimal threshold of about 11%.The previous threshold of 8.9%-10.3%has been slightly improved,and there is no need to verify the basic noise.     

Superconductivity-related insulating behavior

We present the results of an experimental study of superconducting, disordered, thin films of amorphous indium oxide. These films can be driven from the superconducting phase to a reentrant insulating state by the application of a perpendicular magnetic field (B). We find that the high-B insulator exhibits activated transport with a characteristic temperature, TI. TI has a maximum value (TpI) that is close to the superconducting transition temperature (Tc) at B=0, suggesting a possible relation between the conduction mechanisms in the superconducting and insulating phases. Tp(I) and Tc display opposite dependences on the disorder strength.     

Transition from Josephson behavior to depairing behavior in ion-implanted molybdenum weak links

We compare our results for the temperature and bridge-length dependence of the critical supercurrent in ion-implanted molybdenum weak links with a new theory by Likharev and Yakobson. This is the first such comparison to their theory, and quantitative agreement is found. Also, at temperatures for which Likharev and Yakobson predict a sinusoidal current-phase relation, the rf response of our weak links agrees well with shunted junction model computations based on a sinusoidal current-phase relation.     

Mixed-valence behavior of TmSe

Using the observation that the dominant interatomic coupling characteristic of mixed valence arises from the motion of f-electrons between strongly coupled Hund's rule atoms, the magnetic properties of TmSe are semi-quantitatively understood. For TmSe with Tm²⁺ concentration $\text{? 0.3}$, a transition to a state with a spontaneous net moment is predicted.     

Multicritical behavior in ferroelectrics

Solid state systems exhibit besides usual second order phase transitions a rich variety of multicritical phenomena like Lifshitz points (or lines), tricritical points (or lines) and even tricritical Lifshitz points. Realizations of such points are numerous and were also verified in the family of ferroelectrics of the type (Pb_ySn_1y)₂P₂(Se_xS_1-x)₆. A review of the critical behavior at such points is presented here. Because of the importance of the uniaxial dipolar interaction in ferroelectrics the critical behavior is different from systems with short range interaction only. Moreover the coupling to the elastic degrees of freedom may not be neglected, and leads under certain conditions to a critical temperature dependence in certain elastic constants. Crossover phenomena, which are expected in the experimental accessible region of experiments are also considered.     

Environmental behavior of actinides

Since the plutonium concentration in ocean waters is quite low, most of the plutonium deposited in marine waters has been sorbed onto plants and sediments. Actinides in natural waters usually are not in a state of thermodynamic equilibrium for long time periods as their solubility and migration behavior is strongly related to the form in which the nuclides are introduced initially into the aquatic system for long time periods. Their solubility depends on pH (hydrolysis), E _H (oxidation state), reaction with complexants (e.g., carbonate, phosphate, humic acid, etc.), sorption to surfaces of minerals and/or colloids, etc. The primary variable is the oxidation state of the actinide cation. Actinides can be present in more than one oxidation state which complicates modeling actinide environmental behavior.Np(V)O₂ ⁺ and Pu(V)O₂ ⁺ are weakly complexing and resistant to hydrolysis and subsequent precipitation, but both can undergo reduction to the IV oxidation state. The solubility of NpO₂ ⁺ can be as high as 10^?4M, while that of PuO₂ ⁺ is more limited as the very low solubility of Pu(OH)₄ promotes reduction to Pu(IV). The solubility of hexavalent UO₂ ²⁺ in sea water is limited by hydrolysis, but has a relatively high concentration due to carbonate complexation. Americium(III) hydroxocarbonate, Am(CO₃)(OH), is the limiting species for the solubility of Am(III) in sea water. Thorium has a very low solubility due to the formation of Th(OH)₄.     

Environmental behavior of actinides

Since the plutonium concentration in ocean waters is quite low, most of the plutonium deposited in marine waters has been sorbed onto plants and sediments. Actinides in natural waters usually are not in a state of thermodynamic equilibrium for long time periods as their solubility and migration behavior is strongly related to the form in which the nuclides are introduced initially into the aquatic system for long time periods. Their solubility depends on pH (hydrolysis), E _H (oxidation state), reaction with complexants (e.g., carbonate, phosphate, humic acid, etc.), sorption to surfaces of minerals and/or colloids, etc. The primary variable is the oxidation state of the actinide cation. Actinides can be present in more than one oxidation state which complicates modeling actinide environmental behavior. Np(V)O ₂ ⁺ and Pu(V)O ₂ ⁺ are weakly complexing and resistant to hydrolysis and subsequent precipitation, but both can undergo reduction to the IV oxidation state. The solubility of NpO ₂ ⁺ can be as high as 10⁻⁴M, while that of PuO ₂ ⁺ is more limited as the very low solubility of Pu(OH)₄ promotes reduction to Pu(IV). The solubility of hexavalent UO ₂ ²⁺ in sea water is limited by hydrolysis, but has a relatively high concentration due to carbonate complexation. Americium(III) hydroxocarbonate, Am(CO₃)(OH), is the limiting species for the solubility of Am(III) in sea water. Thorium has a very low solubility due to the formation of Th(OH)₄.     

Glassy behavior of light

We study the nonlinear dynamics of a multimode random laser using the methods of statistical physics of disordered systems. A replica-symmetry breaking phase transition is predicted as a function of the pump intensity. We thus show that light propagating in a random nonlinear medium displays glassy behavior; i.e., the photon gas has a multitude of metastable states and a nonvanishing complexity, corresponding to mode-locking processes in random lasers. The present work reveals the existence of new physical phenomena, and demonstrates how nonlinear optics and random lasers can be a benchmark for the modern theory of complex systems and glasses.