Topological causality analysis of horizontal gas-liquid flows based on cross map of phase spaces

Nonlinear systems are always characterized by the interactions between constituents which yield data in the form of time series. Exploration of the causality between the times series is beneficial for understanding the dynamics of the system. We introduce a topological causality method to explore the dynamics of horizontal gas-liquid flows. First, the principle of the topological causality algorithm is illustrated and validated using the Lorenz system and transfer entropy. Then, we conducted an experiment of gas-liquid flows in a horizontal pipe, during which a wire-mesh sensor (WMS) was used to capture the flow structures. The WMS data at different time frames are embedded in high-dimension phase spaces. Through building a cross map between coupled phase spaces, a cross map smoothness was employed to derive the topological causality index. The causality index enables us to understand the mechanism of the flow pattern transition and the intrinsic dynamics of the transient gas-liquid flows.     

Radiation Reaction of a Nonrelativistic Quantum Charged Particle

An alternative approach to analyze the nonrelativistic quantum dynamics of a rigid and extended charged particle taking into account the radiation reaction is discussed with detail. Interpretation of the field operators as annihilation and creation ones, theory of perturbations and renormalization are not used. The analysis is carried out in the Heisenberg picture with the electromagnetic field expanded in a complete orthogonal basis set of functions which allows the electromagnetic field to satisfy arbitrary boundary conditions. The corresponding coefficients are the field operators which satisfy the usual commutation relations. A nonlinear equation of motion for the charged particle is obtained. A careful consideration of the quantum effects allows the derivation of a linear equation of motion which is free of both runaway solutions and preacceleration, even for a point charge. Also, the electromagnetic mass, which is defined as the coefficient of the acceleration operator, vanishes for a point particle. However, this does not mean that the results are free of ambiguities which are exhibited and discussed.     

The Gravitational Field of an Electrically Charged Mass Point and the Causality Principle in the RTG

We find the effective Riemannian space–time corresponding to the gravitational field generated by a charged mass point in the framework of the relativistic theory of gravity. The causality principle plays an important role in solving this problem. The analytic form and the domain of definition, i.e., the gravitational radius, of the obtained solution differ from the corresponding results in Einstein's general relativity theory.     

When Can Statistical Theories Be Causally Closed?

The notion of common cause closedness of a classical, Kolmogorovian probability space with respect to a causal independence relation between the random events is defined, and propositions are presented that characterize common cause closedness for specific probability spaces. It is proved in particular that no probability space with a finite number of random events can contain common causes of all the correlations it predicts; however, it is demonstrated that probability spaces even with a finite number of random events can be common cause closed with respect to a causal independence relation that is stronger than logical independence. Furthermore it is shown that infinite, atomless probability spaces are always common cause closed in the strongest possible sense. Open problems concerning common cause closedness are formulated and the results are interpreted from the perspective of Reichenbach's Common Cause Principle (RCCP).     

Causality Implies Formal State Collapse

A physical theory of experiments carried out in a space-time region can accommodate a detector localized in another space-like separated region, in three, not necessarily exclusive, ways: (1) the detector formally collapses physical states across space-like separations, (2) the detector enables superluminal signals, and (3) the theory becomes logically inconsistent. If such a theory admits autonomous evolving states, the space-like collapse must be instantaneous. Time-like separation does not allow such conclusions. We also prove some simple results on structural stability: within the set of all possible theories, under a weak empirical topology, the set of all theories with superluminal signals and the set of all theories with retrograde signals are both open and dense.     

Entanglement, Joint Measurement, and State Reduction

Entanglement is perhaps the most important new feature of the quantum world. It is expressed in quantum theory by the joint measurement formula. We prove the formula for projection valued observables from a plausible assumption, which for spacelike separated measurements is a consequence of causality. State reduction is simply a way to express the joint measurement formula after one measurement has been made, and its result known.     

On integro‐differential inclusions with operator‐valued kernels

We study integro‐differential inclusions in Hilbert spaces with operator‐valued kernels and give sufficient conditions for the well‐posedness. We show that several types of integro‐differential equations and inclusions are covered by the class of evolutionary inclusions, and we therefore give criteria for the well‐posedness within this framework. As an example, we apply our results to the equations of visco‐elasticity and to a class of nonlinear integro‐differential inclusions describing phase transition phenomena in materials with memory. Copyright © 2014 John Wiley & Sons, Ltd.     

On non-stationary solutions to MSDDEs: Representations and the cointegration space

In this paper we study solutions to multivariate stochastic delay differential equations (MSDDEs) and their relation to the discrete-time cointegrated VAR model. In particular, we observe that an MSDDE can always be written in an error correction form and, under suitable conditions, we argue that a process with stationary increments is a solution to the MSDDE if and only if it admits a certain Granger type representation. A direct implication of these results is a complete characterization of the cointegration space. Finally, the relation between MSDDEs and invertible multivariate CARMA equations is used to introduce the cointegrated MCARMA processes.     

沪深300股指期货日内绝对收益率与成交量之间动态关系研究

均值为零的观测样本绝对收益率可以看作波动率的无偏估计量,因此本文选取连续20个交易日的日内高频数据来研究沪深300股指期货日内绝对收益率和成交量之间的动态关系。在检验了样本稳定性后,文章采用格兰杰检验方法检验了股指期货日内绝对收益率和成交量之间的因果关系,检验结果表明:所有样本的成交量均不是绝对收益率的格兰杰原因,而20个样本中的15个样本的绝对收益率是成交量的格兰杰原因。随后我们使用向量自回归模型分别对15个模型的系数做估计,并对模型估计结果做了脉冲响应分析。研究发现,在此高频抽样条件下,与以往研究不同,沪深300股指期货绝对收益率的变化会明显降低其观测期的成交量。因此,在股指期货日内成交量与绝对收益率的研究中,历史成交量与收益率都对当前成交量有着重要影响;而绝对收益率只受历史绝对收益率的影响。     

股票回报率与汇率的关系——基于中国的实证

考察了上海股票市场A股的回报率与人民币汇率的关系．首先,经过单位根检验发现：股票回报率与人民币名义汇率是一阶单整。接着,利用Engle—Granger协整检验得到：在5％的显著性水平下,股票回报率与人民汇率没有长期均衡关系,但不能够拒绝短期单方向的Granger因果关系,即人民币名义汇率是股票回报率的Granger原因．