Induction equations for fundamental fields and dark matter

The paper outlines some aspects of the theory of gravity and electromagnetism based on a topology-geometric interpretation of matter and its properties as manifestations of a non-Euclidean geometry of the physical hypersurface of dimension 3 embedded in a Euclidean space of dimension 4. We derive the basic equations of the theory, leading to equations similar to those of the classical theory of gravity and electromagnetism as well as those of quantum theory. It is shown that in this theory the observed effect of a hidden mass, or dark matter, is explained in a natural way by effects of the geometry of the physical hypersurface.     

Dynamical Solution to the Quantum Measurement Problem, Causality, and Paradoxes of the Quantum Century

A history and drama of the development of quantum theory is outlined starting from the discovery of the Plank's constant exactly 100 years ago. It is shown that before the rise of quantum mechanics 75 years ago, the quantum theory had appeared first in the form of the statistics of quantum thermal noise and quantum spontaneous jumps which have never been explained by quantum mechanics. Moreover, the only reasonable probabilistic interpretation of quantum theory put forward by Max Born was in fact in irreconcilable contradiction with traditional mechanical reality and causality. This led to numerous quantum paradoxes; some of them, related to the great inventors of quantum theory such as Einstein and Schrödinger, are reconsidered in the paper. The development of quantum measurement theory, initiated by von Neumann, indicated a possibility for the resolution of this interpretational crisis by a divorce of the algebra of dynamical generators and a subalgebra of the actual observables. It is shown that within this approach quantum causality can be rehabilitated in the form of a superselection rule for compatibility of past observables with the potential future. This rule together with self-compatibility of measurements ensuring the consitency of histories is called the nondemolition principle. The application of these rules in the form of dynamical commutation relations leads to the derivation of the von Neumann projection postulate, as well as to more general reductions, instantaneous, spontaneous, and even continuous in time. This gives a quantum probabilistic solution in the form of dynamical filtering equations to the notorious measurement problem which was tackled unsuccessfully by many famous physicists starting from Schrödinger and Bohr. The simplest Markovian quantum stochastic model for time-continuous measurements involves a boundary-value problem in second quantization for input "offer" waves in one extra dimension, and a reduction of the algebra of "actual" observables to an Abelian subalgebra for the output waves.     

A Quantum Theory of Consciousness

The relationship between quantum collapse and consciousness is reconsidered under the assumption that quantum collapse is an objective dynamical process. We argue that the conscious observer can have a distinct role from the physical measuring device during the process of quantum collapse owing to the intrinsic nature of consciousness; the conscious observer can know whether he is in a definite state or a quantum superposition of definite states, while the physical measuring device cannot “know”. As a result, the consciousness observer can distinguish the definite states and their quantum superposition, while the physical measuring device without consciousness cannot do. This provides a possible quantum physical method to distinguish man and machine. The new result also implies that consciousness has causal efficacies in the physical world when considering the existence of quantum collapse. Accordingly consciousness is not reducible or emergent, but a new fundamental property of matter. This may establish a quantum basis for panpsychism, and make it be a promising solution to the hard problem of consciousness. Furthermore, it is suggested that a unified theory of matter and consciousness includes two parts: one is the psychophysical principle or corresponding principle between conscious content and matter state, and the other is the complete quantum evolution of matter state, which includes the definite nonlinear evolution element introduced by consciousness and relating to conscious content. Lastly, some experimental schemes are presented to test the proposed quantum theory of consciousness.

Improving transient performance of adaptive control architectures using frequency-limited system error dynamics

Although adaptive control theory offers mathematical tools to achieve system performance without excessive reliance on dynamical system models, its applications to safety-critical systems can be limited due to poor transient performance and robustness. In this paper, we develop an adaptive control architecture to achieve stabilisation and command following of uncertain dynamical systems with improved transient performance. Our framework consists of a new reference system and an adaptive controller. The proposed reference system captures a desired closed-loop dynamical system behaviour modified by a mismatch term representing the high-frequency content between the uncertain dynamical system and this reference system, i.e., the system error. In particular, this mismatch term allows the frequency content of the system error dynamics to be limited, which is used to drive the adaptive controller. It is shown that this key feature of our framework yields fast adaptation without incurring high-frequency oscillations in the transient performance. We further show the effects of design parameters on the system performance, analyse closeness of the uncertain dynamical system to the unmodified (ideal) reference system, discuss robustness of the proposed approach with respect to time-varying uncertainties and disturbances, and make connections to gradient minimisation and classical control theory. A numerical example is provided to demonstrate the efficacy of the proposed architecture.     

State-Space Reconstruction and Spatio-Temporal Prediction of Lattice Dynamical Systems

This paper addresses the problems of state space reconstruction and spatio-temporal prediction for lattice dynamical systems. It is shown that the state space of any finite lattice dynamical system can be embedded into a reconstruction space for almost every, in the sense of prevalence, smooth measurement mapping as long as the dimension of the reconstruction space is larger than twice the size of the lattice. Based on this result, an input-output spatio-temporal dynamical relation for each site within the lattice is derived and used for spatio-temporal prediction of the system. In the case of infinite lattice dynamical systems, an approach based on constructing local lattice dynamical systems is proposed. It is shown that the finite dimensional results can be directly applied to the local modelling and spatio-temporal prediction for infinite lattice dynamical systems. Two numerical examples are provided to demonstrate the proposed theory and approach     

Constraining bouncing cosmology caused by the Casimir effect

We constrain the Friedmann-Robertson-Walker (FRW) model with a “radiation-like” contribution to the Friedmann equation against the astronomical data. We analyze the observational bounds on a (1 + z)⁴ term from type Ia supernovae (SNIa) data, Fanaroff-Riley type IIb (FRIIb) radio galaxy (RG) data, baryon oscillation peak and cosmic microwave background radiation (CMBR) observations. We argue that it is not possible to determine the energy densities of individual components scaling like radiation from a kinematic astronomical test. The bounds for the density parameter of the total radiation-like term can be obtained. We find different interpretations of the presence of a scaling-like radiation term: the FRW universe filled with a massless scalar field in a quantum regime (the Casimir effect), the FRW model in a semiclassical approximation of loop quantum gravity, the FRW model in the Randall-Sundrum scenario with dark radiation or a cosmological model with global rotation. In this paper, we mainly concentrate on the Casimir effect arising from quantum effects of a scalar field. This contribution can describe a decaying part of the cosmological constant. We discuss the back-reaction of gravity on the Casimir-type force which is a manifestation of the vacuum fluctuations of the quantum scalar field at low temperature. It is shown that, while the Casimir energy gives rise to the accelerating Universe, the cosmological constant term is still required. We argue that a small negative contribution of a radiation-like term can reconcile the tension between the observed primordial ⁴ He and D abundances. Moreover, the presence of such a contribution can also remove the disagreement between the Hubble parameter H ₀ values obtained from the SNIa and Wilkinson Microwave Anisotropy Probe (WMAP) satellite data.     

Stochastic Schrödinger Equations as Limit of Discrete Filtering

We consider an open model possessing a Markovian quantum stochastic limit and derive the limit stochastic Schrödinger equations for the wave function conditioned on indirect observations using only the von Neumann projection postulate. We show that the diffusion (Gaussian) situation is universal as a result of the central limit theorem with the quantum jump (Poissonian) situation being an exceptional case. It is shown that, starting from the correponding limiting open systems dynamics, the theory of quantum filtering leads to the same equations, therefore establishing consistency of the quantum stochastic approach for limiting Markovian models.     

量子多目标进化算法研究

本文首次将量子计算的理论用于多目标优化,提出量子多目标进化算法（QMOEA）,其采用量子位染色体表示法,利用量子门旋转策略和量子变异实现群体的进化,使用ε支配关系构造外部种群以此保持算法的较好分布性,提出基于快速排序的非劣最优解构造方法加快算法运行效率,实验表明,这种方法与经典的多目标进化算法SPEA2相比,其收敛性更好且分布更均匀     

The CGMV method for quantum walks

We review the main aspects of a recent approach to quantum walks, the CGMV method. This method proceeds by reducing the unitary evolution to canonical form, given by the so-called CMV matrices, which act as a link to the theory of orthogonal polynomials on the unit circle. This connection allows one to obtain results for quantum walks which are hard to tackle with other methods. Behind the above connections lies the discovery of a new quantum dynamical interpretation for well known mathematical tools in complex analysis. Among the standard examples which will illustrate the CGMV method are the famous Hadamard and Grover models, but we will go further showing that CGMV can deal even with non-translation invariant quantum walks. CGMV is not only a useful technique to study quantum walks, but also a method to construct quantum walks à la carte. Following this idea, a few more examples illustrate the versatility of the method. In particular, a quantum walk based on a construction of a measure on the unit circle due to F. Riesz will point out possible non-standard behaviours in quantum walks.     

Dark energy and inflation in a gravitational wave dominated universe

The empty space (with no matter fields) is not really empty because of natural metric fluctuations, quantum (gravitons) and classical (gravitational waves). We show that gravitons as well as classical gravitational waves of super-horizon wavelengths are able to form a de Sitter state of the empty homogeneous isotropic Universe. This state is an exact solution to the self-consistent equations of finite one-loop quantum gravity for gravitons in the empty FLRW space. It is also an exact solution to the selfconsistent equations of back-reaction for classical gravitational waves in the same space. Technically, to get this de Sitter solution in both quantum and classical cases, it is necessary to carry out a transition to imaginary time and then to return to real time, which is possible because this de Sitter state is invariant with respect to Wick rotation. Such a procedure means that time was used as a complex variable, and this fact has a deep but still not understood significance. The de Sitter accelerated expansion of the empty Universe naturally explains the origin of dark energy and inflation because the Universe is empty at the start (inflation) and by the end (dark energy) of its evolution. This theory is consistent with the existing observational data. The CMB anisotropy of the order of 10^?5 is produced by fluctuations in the number of gravitons. The existence of a threshold and a unique coincidence of topologically impenetrable barriers for tunneling takes place for the matter-dominated epoch and de Sitter State only. These facts provide a solution to the coincidence problem. The theoretical prediction that the equation-of-state parameter should be w > ?1 for inflation and w < ?1 for dark energy is consistentwith the observational data. To provide the reader with a complete picture, this paper gather together new and some published results of the graviton theory of the origin of inflation and dark energy.     

Quantum Ergodic Theory and Communication Channels

The recently developed theory of the noncommutative dynamical entropy is applied to the theory of quantum communication channels. It is argued that the speed of information transmission is bounded by the dynamical entropy of the information carrier treated as a quantum dynamical system. The proof is given for two classes of communication channels. For the first one the input and output are classical devices which produce strings of bits, while for the second one the input and output messages are quantum states.     

Spatially flat FRW models with torsion

We study flat Friedmann universes filled with a perfect fluid and a nonminimally coupled ghost scalar field with polynomial potentials of the fourth degree V(Φ) in the framework of the Einstein-Cartan theory. Exact general solutions are obtained and analyzed for an arbitrary coupling constant ξ. A comparative analysis of cosmological models with and without a perfect fluid is carried out. Some effects of V(Φ) and the perfect fluid are elucidated. It is shown that some models admit a unified scenario for dark matter and dark energy.     

Real-time computing without stable states: a new framework for neural computation based on perturbations

A key challenge for neural modeling is to explain how a continuous stream of multimodal input from a rapidly changing environment can be processed by stereotypical recurrent circuits of integrate-and-fire neurons in real time. We propose a new computational model for real-time computing on time-varying input that provides an alternative to paradigms based on Turing machines or attractor neural networks. It does not require a task-dependent construction of neural circuits. Instead, it is based on principles of high-dimensional dynamical systems in combination with statistical learning theory and can be implemented on generic evolved or found recurrent circuitry. It is shown that the inherent transient dynamics of the high-dimensional dynamical system formed by a sufficiently large and heterogeneous neural circuit may serve as universal analog fading memory. Readout neurons can learn to extract in real time from the current state of such recurrent neural circuit information about current and past inputs that may be needed for diverse tasks. Stable internal states are not required for giving a stable output, since transient internal states can be transformed by readout neurons into stable target outputs due to the high dimensionality of the dynamical system. Our approach is based on a rigorous computational model, the liquid state machine, that, unlike Turing machines, does not require sequential transitions between well-defined discrete internal states. It is supported, as the Turing machine is, by rigorous mathematical results that predict universal computational power under idealized conditions, but for the biologically more realistic scenario of real-time processing of time-varying inputs. Our approach provides new perspectives for the interpretation of neural coding, the design of experiments and data analysis in neurophysiology, and the solution of problems in robotics and neurotechnology.     

Mathematical Theory of Duality Quantum Computers

We present a mathematical theory for a new type of quantum computer called a duality quantum computer that has recently been proposed. We discuss the nonunitarity of certain circuits of a duality quantum computer and point out a paradoxical situation that occurs when mixed states are considered. It is shown that a duality quantum computer can measure itself without needing a separate measurement apparatus to determine its final state.      

Advances in automation and control research in China

Automation is the utilization of control techniques together with other information technology to control industrial processes, reducing the need for human intervention. It plays a highly important role in social and economy as well as in daily life. Control theory is the theory of automation, and is an interdisciplinary branch of engineering and mathematics, examining the behavior of dynamical systems. China has a long history of manufacturing automatic devices. In recent years, some rapid progresses in control theory have been made in China. Many new theories and new methodologies have been developed to meet the increasing demands in industry, agriculture, defense, and other social sectors. Contemporary sciences such as complexity, systems biology, quantum technologies, have also found their close links to control theories and technologies. On the other hand, control theory itself has many unsolved fundamental problems requiring further studies and investigation. This paper is to review the development and progress that have been made in all these aspects in China. Some remarks on the future development of control theory are also presented.     

Density evolution in the new modified Chaplygin gas model

In this paper, we have considered a new modified Chaplygin gas (NMCG) model which interpolates between radiation at an early stage and ΛCDM at a late stage. This model is regarded a unification of dark energy and dark matter (with a general form of matter). We have derived the density parameters from the equation of motion for interaction between dark energy and dark matter. Also, we have studied the evolution of various components of the density parameters.     

A new integral inequality and its applications to robust control problems of uncertain nonlinear systems

In this paper, a new integral inequality is presented. By combining this integral inequality with adaptive approach, new design methods can be developed to synthesize some adaptive robust control schemes for a large class of uncertain nonlinear systems and to deal with well the unknown nonlinearities appearing in uncertain nonlinear control dynamical systems. As an application of the presented integral inequality to control theory, the robust stabilization problem is considered for a class of uncertain strict‐feedback nonlinear systems with both time‐delay and unknown dead‐zone input nonlinearities. It is shown that there are two main merits in the design method based on the integral inequality presented in this paper. The first one is that one need not estimate and know the unknown nonlinearities to synthesize some stabilizing control schemes. The second one is that the resulting feedback control schemes have rather simple structure.