The classical and quantum synchronization between two scattering modes in Bose–Einstein condensates

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We study the time evolution of holographic mutual and tripartite information for a zero temperature CFT, derives to a non-relativistic thermal Lifshitz field theory by a quantum quench. We observe that the symmetry breaking does not play any role in the phase space, phase of parameters of sub-systems, and the length of disentangling transition. Nevertheless, mutual and tripartite information indeed depend on the rate of symmetry breaking. We also find that for large enough values of δt the quantity teqδt−1, where δt and teq are injection time and equilibration time respectively, behaves adiabatically, i.e. its value is independent of length of separation between sub-systems. We also show that tripartite information is always non-positive during the process indicates that mutual information is monogamous.

Summary form only given. The capacity of the message-passing decoder for LDPC codes can be computed by the density evolution algorithm by iteratively computing message densities. The infinite-dimensional problem of iteratively calculating the message densities in the case of the binary input AWGN channel and the belief propagation decoder can be simplified to a one-dimensional problem by using a Gaussian approximation. By assuming Gaussian densities the density evolution simplifies to updating means of Gaussian densities. An improved Gaussian approximation algorithm is suggested for computing the capacity of the BP decoder based on the mutual information measure. An analytical method for computing the mutual information of a transmitted bit with the message corresponding to it is proposed. Using this method we can approximate the non-Gaussian message by a Gaussian message that has the same mutual information with the transmitted bit. Computationally, the algorithm is similar to the Gaussian approximation algorithm proposed in Chung (2001). For various regular LDPC codes that were examined, the algorithm computed threshold values within 0.01dB or less from the exact threshold which is an improvement over the Gaussian approximation. Furthermore, additional insight on the convergence process can be gained from EXIT charts that can be derived from the algorithm. This can assist in designing better irregular LDPC codes.

Measures of relevance between features play an important role in classification and regression analysis. Mutual information has been proved to be an effective measure for categorical features. However, there is a limitation in computing relevance between numerical features with mutual information. In this work, we generalize Shannon's information entropy to neighborhood information entropy and propose a measure of neighborhood mutual information. It is shown that the new measure is a natural extension of classical mutual information which reduces to the classical one if features are discrete; thus the new measure can also be used to compute the relevance between discrete variables. In experiment, we show that neighborhood mutual information produces the nearly same outputs as mutual information. However, unlike mutual information, no discretization is required in computing relevance when used the proposed algorithm.

1. Introduction Non linear dynamics (Medio, 1992) in combination with neural networks had applied in a wide variety of fields, e.g. physics, engineering, ecology and economics. The economist interest is focused on the ability of forecasting an economic time series using time series analysis (Thalassinos and Pociovalisteanu, 2007). In this work we have applied non linear time series analysis in monthly values of Greece Total Industry index. We cover time period from 01.01.1962 until 01.04.2011. We have applied the method of Grassberger and Procaccia (Grassberge and Procaccia, 1983a and 1983b) to evaluate the minimum embedding dimension of each the system. In a second stage using the neural network (Hanias, Curtis, Thalassinos, 2007; Thalassinos et al., 2008 and 2009) we achieved an out of sample multi step time series prediction. 2. Time Series The data for the Production of Total Industry in Greece are collected from Organization for Economic Co-operation and Development and presented as a signal x=x(t) as it shown at Figure 1 (01.01.1962 - 01.04.2011). The sampling rate is At=1 month and the number of data are N=592. 3 [FIGURE 1 OMITTED] 3. State Space Reconstruction For a scalar time series, in our case the time series is the Production of Total Industry index, the phase space can be reconstructed using the methods of delays. The basic idea in the method of delays is that the evolution of any single variable of a system is determined by the other variables, with which it interacts. Information about the relevant variables is thus implicitly contained in the history of any single variable. On the basis of this an equivalent phase space can be reconstructed. From our data we construct a vector [[bar.X].sub.i], i=1 to N, in the m dimensional phase space given by the following relation (Kantz and Schreiber, 1997; Takens, 1981). [[bar.X].sub.i] = {xi,xi-[tau],xi-2[tau], .... xi+(m-1)x}[tau] (1) This vector represents a point to the m dimensional phase space in which the attractor is embedded each time, where [tau] is the time delay [tau]=i[DELTA]t. The element xi represents a value of the examined scalar time series in time corresponding to the ith component of the time series. Use of this method, reduces phase space reconstruction to the problem of proper determining suitable values of m and t. The choice of these values is not always simple, especially when we do not have any additional information about the original system and the only source of data is a simple sequence of scalar values, acquired from the original system. The dimension, where a time delay reconstruction of the phase space provides a necessary number of coordinates to unfold the dynamics from overlaps on itself caused by projection, is called embedding dimension m. a. Time delay [tau] Using the average mutual information we can obtain x less associated with linear point of view, and thus more suitable for dealing with nonlinear problems. The average mutual information may be expressed by the following formula (Kantz and Schreiber, 1997; Takens, 1981). [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2) where P(xi) represents probability of value xi and P(xi, xi+[tau]) is joint probability. In general, I([tau]) expresses the amount of information (in bits), which may be extracted from the value in time xi about the value in time xi+[tau]. As [tau], suitable for the phase space reconstruction, is the first minimum of I(t). [FIGURE 2 OMITTED] As shown in Figure 2, in our case the mutual information function I(t) exhibits a local minimum at 4 time steps and, thus, we shall consider [tau] = 4 to be the optimum delay time. b. Embedding dimension m One method to determine the presence of chaos is to calculate the fractal dimension, which will be non integer for chaotic systems. Even though there exists a number of definitions for the dimension of a fractal object (Box counting dimension, Information Dimension, etc. …

Emotion recognition has drawn a great deal of attention in brain computer interface field. Researches have come to the conclusion that nonlinear features are more successful in emotion classification because of non-stationary and chaotic behavior of biological signals, especially electroencephalogram (EEG). In this study, a new method based on phase space dynamics and Poincare sections is introduced to classify emotions. This transformation quantifies the phase space and represents its characteristics in a new state space which can simply reflect the signal behavior. Not only are the proposed state space and quantifiers effective to appropriately describe nonlinear signal dynamics, but also this method successfully works in real-world applications like EEG-based emotion recognition. In this work, EEGs are transformed into the new state space and Poincare intersections are considered as features with the aim of classifying EEGs into four emotional groups based on arousal and valence values. A reliable dataset is used, and classification accuracy is about 82%. As results suggest, the proposed method and features are efficient in this task in comparison with previous studies employing the same dataset.

Stock correlation networks use stock price data to explore the relationship between different stocks listed in the stock market. Currently this relationship is dominantly measured by the Pearson correlation coefficient. However, financial data suggest that nonlinear relationships may exist in the stock prices of different shares. To address this issue, this work uses mutual information to characterize the nonlinear relationship between stocks. Using 280 stocks traded at the Shanghai Stocks Exchange in China during the period of 2014-2016, we first compare the effectiveness of the correlation coefficient and mutual information for measuring stock relationships. Based on these two measures, we then develop two stock networks using the Minimum Spanning Tree method and study the topological properties of these networks, including degree, path length and the power-law distribution. The relationship network based on mutual information has a better distribution of the degree and larger value of the power-law distribution than those using the correlation coefficient. Numerical results show that mutual information is a more effective approach than the correlation coefficient to measure the stock relationship in a stock market that may undergo large fluctuations of stock prices.

In this work we apply the network physiology paradigm to retrieve information from central and autonomic nervous systems before focal epileptic seizure, represented respectively by electroencephalogram (EEG) signals and R-R intervals (RRI), and investigate on the presence and strength of brain-heart interactions by computing mutual information (MI) measures. Statistical significance of MI values was tested through surrogate time series generated with the random shuffle approach. Our results suggest that the proposed method for aligning signals representing brain and heart activity measured with different sampling rates, is capable of revealing coupling between RRI representing heart system, and aligned averaged power spectrum of brain processes, measured with EEG, resulting in significant MI. For electrodes C3, Fp2, Cz, and T4 in correspondingly α, β, γ, and total frequency bands, we obtain significantly smaller values of MI in the pre-ictal period in comparison with baseline period, as well as general decrease of significant and all estimated MI values before the focal seizure can be observed.

The Correlation Power Analysis (CPA) is probably the most used side-channel attack because it seems to fit the power model of most standard CMOS devices and is very efficiently computed. However, the Pearson correlation coefficient used in the CPA measures only linear statistical dependences where the Mutual Information (MI) takes into account both linear and nonlinear dependences. Even if there can be simultaneously large correlation coefficients quantified by the correlation coefficient and weak dependences quantified by the MI, we can expect to get a more profound understanding about interactions from an MI Analysis (MIA). We study methods that improve the non-parametric Probability Density Functions (PDF) in the estimation of the entropies and, in particular, the use of B-spline basis functions as pdf estimators. Our results indicate an improvement of two fold in the number of required samples compared to a classic MI estimation. The B-spline smoothing technique can also be applied to the rencently introduced Cramer-von-Mises test.

The dynamics of passage and capture into resonance of a distribution of particles driven by a chirped frequency perturbation is discussed. The resonant capture in this case involves crossing of the separatrix by individual particles and, therefore, the adiabatic theorem cannot be used in studying this problem no matter how slow the variation of the driving frequency is. It is shown that, if instead of analysing complicated single particle dynamics in passage through resonance, one considers the slow evolution of a whole distribution of initial conditions in phase space, the adiabaticity and phase space incompressibility arguments yield a solution to the resonant passage problem. This approach is illustrated in the case of an ensemble of electrons driven by a chirped frequency wave passing through Cherenkov resonances with the velocity distribution of electrons.

The phase-space dynamics of runaway electrons is studied, including the influence of loop voltage, radiation damping, and collisions. A theoretical model and a numerical algorithm for the runaway dynamics in phase space are developed. Instead of standard integrators, such as the Runge–Kutta method, a variational symplectic integrator is applied to simulate the long-term dynamics of a runaway electron. The variational symplectic integrator is able to globally bound the numerical error for arbitrary number of time-steps, and thus accurately track the runaway trajectory in phase space. Simulation results show that the circulating orbits of runaway electrons drift outward toward the wall, which is consistent with experimental observations. The physics of the outward drift is analyzed. It is found that the outward drift is caused by the imbalance between the increase of mechanical angular momentum and the input of toroidal angular momentum due to the parallel acceleration. An analytical expression of the outward drift velocity is derived. The knowledge of trajectory of runaway electrons in configuration space sheds light on how the electrons hit the first wall, and thus provides clues for possible remedies.

Rayleigh–Bénard convection, i.e. the flow of a fluid between two parallel plates that is driven by a temperature gradient, is an idealised set-up to study thermal convection. Of special interest are the statistics of the turbulent temperature field, which we are investigating and comparing for three different geometries, namely convection with periodic horizontal boundary conditions in three and two dimensions as well as convection in a cylindrical vessel, in order to determine the similarities and differences. To this end, we derive an exact evolution equation for the temperature probability density function. Unclosed terms are expressed as conditional averages of velocities and heat diffusion, which are estimated from direct numerical simulations. This framework lets us identify the average behaviour of a fluid particle by revealing the mean evolution of a fluid with different temperatures in different parts of the convection cell. We connect the statistics to the dynamics of Rayleigh–Bénard convection, giving deeper insights into the temperature statistics and transport mechanisms. We find that the average behaviour is described by closed cycles in phase space that reconstruct the typical Rayleigh–Bénard cycle of fluid heating up at the bottom, rising up to the top plate, cooling down and falling again. The detailed behaviour shows subtle differences between the three cases.

Information sharing among cryptocurrencies: Evidence from mutual information and approximate entropy during COVID-19

We use information theory to study the information transmission through a simple gene cascade where the product of an unregulated gene regulates the expression activity of a cooperative genetic switch. While the input signal is provided by the upstream gene with two states, we consider that the expression of downstream gene is controlled by a cis-regulatory system with three binding sites for the regulator product, which can bind cooperatively. By computing exactly the associated probability distributions, we estimate information transmission thought the mutual information measure. We found that the mutual information associated with unimodal input signal is lower than the associated with bimodal inputs. We also observe that mutual information presents a maximum in the cooperativity intensity, and the position of this maximum depends on the kinetic rates of the promoter. Furthermore, we found that the bursting dynamics of the input signal can enhance the information transmission capacity.

The security of border and transportation systems is a critical component of the national strategy for homeland security. The security concerns at the border are not independent of law enforcement in border-area jurisdictions because information known by local law enforcement agencies may provide valuable leads useful for securing the border and transportation infrastructure. The combined analysis of law enforcement information and data generated by vehicle license plate readers at the international borders can be used to identify suspicious vehicles at ports of entry. This not only generates better quality leads for border protection agents but may also serve to reduce wait times for commerce, vehicles, and people as they cross the border. In this paper we use the mutual information concept to identify vehicles that frequently cross the border with vehicles that are involved in criminal activity. We find that the mutual information measure can be used to identify vehicles that can be potentially targeted at the border.