New approach for solving master equation of open atomic system

We describe a new approach called Ket-Bra Entangled State (KBES) Method which enables one convert master equations into Schr\"odinger-like equation. In sharply contrast to the super-operator method, the KBES method is applicable for any master equation of finite-level system in theory, and the calculation can be completed by computer. With this method, we obtain the exact dynamic evolution of a radioactivity damped 2-level atom in time-dependent external field, and a 3-level atom coupled with bath; Moreover, the master equation of N-qubits Heisenberg chain each qubit coupled with a reservoir is also resolved in Sec.III; Besides, the paper briefly discuss the physical implications of the solution.Comment: 7 pages, 5figure

Fully distributed cooperation for networked uncertain mobile manipulators

This paper investigates a fully distributed cooperation scheme for networked mobile manipulators. To achieve cooperative task allocation in a distributed way, an adaptation-based estimation law is established for each robotic agent to estimate the desired local trajectory. In addition, wrench synthesis is analyzed in detail to lay a solid foundation for tight cooperation tasks. Together with the estimated task, a set of distributed adaptive controllers is proposed to achieve motion synchronization of the mobile manipulator ensemble over a directed graph with a spanning tree irrespective of the kinematic and dynamic uncertainties in both the mobile manipulators and the tightly grasped object. The controlled synchronization alleviates the performance degradation caused by the estimation/tracking discrepancy during the transient phase. The proposed scheme requires no persistent excitation condition and avoids the use of noisy Cartesian-space velocities. Furthermore, it is independent from the object's center of mass by employing formation-based task allocation and a task-oriented strategy. These attractive attributes facilitate the practical application of the scheme. It is theoretically proven that convergence of the cooperative task tracking error is guaranteed. Simulation results validate the efficacy and demonstrate the expected performance of the proposed scheme.Comment: 18 pages with 13 figures. Final version with experiment to appear in IEEE Transactions on Robotic

The Alexander and Jones Polynomials Through Representations of Rook Algebras

In the 1920's Artin defined the braid group in an attempt to understand knots in a more algebraic setting. A braid is a certain arrangement of strings in three-dimensional space. It is a celebrated theorem of Alexander that every knot is obtainable from a braid by identifying the endpoints of each string. Because of this correspondence, the Jones and Alexander polynomials, two of the most important knot invariants, can be described completely using the braid group. There has been a recent growth of interest in other diagrammatic algebras, whose elements have a similar topological flavor to the braid group. These have wide ranging applications in areas including representation theory and quantum computation. We consider representations of the braid group when passed through another diagrammatic algebra, the planar rook algebra. By studying traces of these matrices, we recover both the Jones and Alexander polynomials

3D-A-Nets: 3D Deep Dense Descriptor for Volumetric Shapes with Adversarial Networks

Recently researchers have been shifting their focus towards learned 3D shape descriptors from hand-craft ones to better address challenging issues of the deformation and structural variation inherently present in 3D objects. 3D geometric data are often transformed to 3D Voxel grids with regular format in order to be better fed to a deep neural net architecture. However, the computational intractability of direct application of 3D convolutional nets to 3D volumetric data severely limits the efficiency (i.e. slow processing) and effectiveness (i.e. unsatisfied accuracy) in processing 3D geometric data. In this paper, powered with a novel design of adversarial networks (3D-A-Nets), we have developed a novel 3D deep dense shape descriptor (3D-DDSD) to address the challenging issues of efficient and effective 3D volumetric data processing. We developed new definition of 2D multilayer dense representation (MDR) of 3D volumetric data to extract concise but geometrically informative shape description and a novel design of adversarial networks that jointly train a set of convolution neural network (CNN), recurrent neural network (RNN) and an adversarial discriminator. More specifically, the generator network produces 3D shape features that encourages the clustering of samples from the same category with correct class label, whereas the discriminator network discourages the clustering by assigning them misleading adversarial class labels. By addressing the challenges posed by the computational inefficiency of direct application of CNN to 3D volumetric data, 3D-A-Nets can learn high-quality 3D-DSDD which demonstrates superior performance on 3D shape classification and retrieval over other state-of-the-art techniques by a great margin.Comment: 8 pages, 8 figure

Global Convergence of Analytic Neural Networks with Event-triggered Synaptic Feedbacks

In this paper, we investigate convergence of a class of analytic neural networks with event-triggered rule. This model is general and include Hopfield neural network as a special case. The event-trigger rule efficiently reduces the frequency of information transmission between synapses of the neurons. The synaptic feedback of each neuron keeps a constant value based on the outputs of its neighbours at its latest triggering time but changes until the next triggering time of this neuron that is determined by certain criterion via its neighborhood information. It is proved that the analytic neural network is completely stable under this event-triggered rule. The main technique of proof is the {\L}ojasiewicz inequality to prove the finiteness of trajectory length. The realization of this event-triggered rule is verified by the exclusion of Zeno behaviors. Numerical examples are provided to illustrate the theoretical results and present the optimisation capability of the network dynamics

A New Route to the Interpretation of Hopf Invariant

We discuss an object from algebraic topology, Hopf invariant, and reinterpret it in terms of the $\phi$-mapping topological current theory. The main purpose in this paper is to present a new theoretical framework which can directly give the relationship between Hopf invariant and the linking numbers of the higher dimensional submanifolds of Euclidean space $R^{2n-1}$. For the sake of this purpose we introduce a topological tensor current which can naturally deduce the $(n-1)$ dimensional topological defect in $R^{2n-1}$ space. If these $(n-1)$ dimensional topological defects are closed oriented submanifolds of $R^{2n-1}$, they are just the $(n-1)$ dimensional knots. The linking number of these knots is well defined. Using the inner structure of the topological tensor current, the relationship between Hopf invariant and the linking numbers of the higher dimensional knots can be constructed.Comment: 13 pages, no figures, Accepted by Commun. Theor. Phys. (Beijing, China

Design and Analysis of Dynamic Auto Scaling Algorithm (DASA) for 5G Mobile Networks

Network Function Virtualization (NFV) enables mobile operators to virtualize their network entities as Virtualized Network Functions (VNFs), offering fine-grained on-demand network capabilities. VNFs can be dynamically scale-in/out to meet the performance requirements for future 5G networks. However, designing an auto-scaling algorithm with low operation cost and low latency while considering the capacity of legacy network equipment is a challenge. In this paper, we propose a VNF Dynamic Auto Scaling Algorithm (DASA) considering the tradeoff between performance and operation cost. We also develop an analytical model to quantify the tradeoff and validate the analysis through extensive simulations. The system is modeled as a queueing model while legacy network equipment is considered as a reserved block of servers. The VNF instances are powered on and off according to the number of job requests. The results show that the proposed DASA can significantly reduce operation cost given the latency upper-bound. Moreover, the models provide a quick way to evaluate the cost-performance tradeoff without wide deployment, which can save cost and time.Comment: 18 pages, 13 figure

Topological Properties of Phase Singularities in Wave Fields

Phase singularities as topological objects of wave fields appear in a variety of physical, chemical, and biological scenarios. In this paper, by making use of the $\phi$-mapping topological current theory, we study the topological properties of the phase singularities in two and three dimensional space in details. The topological inner structure of the phase singularities are obtained, and the topological charge of the phase singularities are expressed by the topological numbers: Hopf indices and Brouwer degrees. Furthermore, the topological invariant of the closed and knotted phase singularities in three dimensional space are also discussed in details.Comment: 6 page

Stability of Analytic Neural Networks with Event-triggered Synaptic Feedbacks

In this paper, we investigate stability of a class of analytic neural networks with the synaptic feedback via event-triggered rules. This model is general and include Hopfield neural network as a special case. These event-trigger rules can efficiently reduces loads of computation and information transmission at synapses of the neurons. The synaptic feedback of each neuron keeps a constant value based on the outputs of the other neurons at its latest triggering time but changes at its next triggering time, which is determined by certain criterion. It is proved that every trajectory of the analytic neural network converges to certain equilibrium under this event-triggered rule for all initial values except a set of zero measure. The main technique of the proof is the Lojasiewicz inequality to prove the finiteness of trajectory length. The realization of this event-triggered rule is verified by the exclusion of Zeno behaviors. Numerical examples are provided to illustrate the efficiency of the theoretical results.Comment: 12 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:1504.0808

Statistical Delay Control and QoS-Driven Power Allocation Over Two-Hop Wireless Relay Links

The time-varying feature of wireless channels usually makes the hard delay bound for data transmissions unrealistic to guarantee. In contrast, the statistically-bounded delay with a small violation probability has been widely used for delay quality-of-service (QoS) characterization and evaluation. While existing research mainly focused on the statistical-delay control in single-hop links, in this paper we propose the QoS-driven power-allocation scheme over two-hop wireless relay links to statistically upper-bound the end-to-end delay under the decodeand- forward (DF) relay transmissions. Specifically, by applying the effective capacity and effective bandwidth theories, we first analyze the delay-bound violation probability over two tops each with independent service processes. Then, we show that an efficient approach for statistical-delay guarantees is to make the delay distributions of both hops identical, which, however, needs to be obtained through asymmetric resource allocations over the two hops. Motivated by this fact, we formulate and solve an optimization problem aiming at minimizing the average power consumptions to satisfy the specified end-to-end delay-bound violation probability over two-hop relay links. Also conducted is a set of simulations results to show the impact of the QoS requirements, traffic load, and position of the relay node on the power allocation under our proposed optimal scheme