Network Geometry and Complexity

Higher order networks are able to characterize data as different as functional brain networks, protein interaction networks and social networks beyond the framework of pairwise interactions. Most notably higher order networks include simplicial complexes formed not only by nodes and links but also by triangles, tetrahedra, etc. More in general, higher-order networks can be cell-complexes formed by gluing convex polytopes along their faces. Interestingly, higher order networks have a natural geometric interpretation and therefore constitute a natural way to explore the discrete network geometry of complex networks. Here we investigate the rich interplay between emergent network geometry of higher order networks and their complexity in the framework of a non-equilibrium model called Network Geometry with Flavor. This model, originally proposed for capturing the evolution of simplicial complexes, is here extended to cell-complexes formed by subsequently gluing different copies of an arbitrary regular polytope. We reveal the interplay between complexity and geometry of the higher order networks generated by the model by studying the emergent community structure and the degree distribution as a function of the regular polytope forming its building blocks. Additionally, we discuss the underlying hyperbolic nature of the emergent geometry and we relate the spectral dimension of the higher-order network to the dimension and nature of its building blocks.     

Combinatorial Laplacian and entropy of simplicial complexes associated with complex networks

Simplicial complexes represent useful and accurate models of complex networks and complex systems in general. We explore the properties of spectra of combinatorial Laplacian operator of simplicial complexes and show its relationship with connectivity properties of the Q-vector and with connectivities of cliques in the simplicial clique complex. We demonstrate the need for higher order analysis in complex networks and compare the results with ordinary graph spectra. Methods and results are obtained using social network of the Zachary karate club.     

三量子比特Dicke模型中的两体和三体纠缠动力学

本文利用绝热近似方法和精确对角化方法研究三量子比特Dicke模型中的纠缠动力学.处于两种典型的纠缠态GHZ态和W态上的量子比特在时间演化过程中与辐射光场发生强耦合作用,在各种子系统间产生纠缠,通过分析这些纠缠的演化特性发现初始GHZ态的三体纠缠鲁棒性比W态强,这与旋波近似结论一致.与旋波近似下结果不同的是,两种态中任意...     

Remarks on the entropy of 3-manifolds

We give a simple combinatoric proof of an exponential upper bound on the number of distinct 3-manifolds that can be constructed by successively identifying nearest neighbour pairs of triangles in the boundary of a simplicial 3-ball and show that all closed simplicial manifolds that can be constructed in this manner are homeomorphic to S3. We discuss the problem of proving that all 3-dimensional simplicial spheres can be obtained by this construction and give an example of a simplicial 3-ball whose boundary triangles can be identified pairwise such that no triangle is identified with any of its neighbours and the resulting 3-dimensional simplicial complex is a simply connected 3-manifold.     

Spin-entanglement in a three electron system produced in double Auger decay

The simultaneous emission of two electrons in photoionization, or in the non-radiative spontaneous decay of an inner-shell vacancy, are two of the best known examples of the failure of the independent-particle model of atoms and molecules. The later of these provides also one of the two competitive processes, following inner-shell photoionization, for producing three flying electrons which can, for example, be used in implementing many protocols hitherto developed in quantum information. The correlation properties of the three-particle system consisting of these two electrons plus the photoelectron are analyzed using methods from quantum information theory. The entanglement of the consequent tripartite spin-state is shown to be completely independent of the mechanism(s) which may be responsible for the emission of these three electronic qubits in two different steps in the absence of spin-orbit interaction. Our analysis shows that the tripartite state formed in the present case is more like a  |W〉  class of states possessing pairwise entanglement. The experimental characterization of these states is fully achieved merely by the measurements of the energies of three flying electrons, without requiring any entanglement witness or other similar protocols hitherto developed in quantum information. Changes in these entanglement properties of a tripartite state of electronic qubits on the inclusion of the spin-orbit interaction have also been discussed.     

Quantum game theory and open access publishing

The digital revolution of the information age and in particular the sweeping changes of scientific communication brought about by computing and novel communication technology, potentiate global, high grade scientific information for free. The arXiv, for example, is the leading scientific communication platform, mainly for mathematics and physics, where everyone in the world has free access on. While in some scientific disciplines the open access way is successfully realized, other disciplines (e.g. humanities and social sciences) dwell on the traditional path, even though many scientists belonging to these communities approve the open access principle. In this paper we try to explain these different publication patterns by using a game theoretical approach. Based on the assumption, that the main goal of scientists is the maximization of their reputation, we model different possible game settings, namely a zero sum game, the prisoners’ dilemma case and a version of the stag hunt game, that show the dilemma of scientists belonging to “non-open access communities”. From an individual perspective, they have no incentive to deviate from the Nash equilibrium of traditional publishing. By extending the model using the quantum game theory approach it can be shown, that if the strength of entanglement exceeds a certain value, the scientists will overcome the dilemma and terminate to publish only traditionally in all three settings.     

Continuous-variable quantum information processing with squeezed states of light

We investigate experiments of continuous-variable quantum information processing based on the teleportation scheme. Quantum teleportation, which is realized by a two-mode squeezed vacuum state and measurement-and-feedforward, is considered as an elementary quantum circuit as well as quantum communication. By modifying ancilla states or measurement-and-feedforwards, we can realize various quantum circuits which suffice for universal quantum computation. In order to realize the teleportation-based computation we improve the level of squeezing, and fidelity of teleportation. With a high-fidelity teleporter we demonstrate some advanced teleportation experiments, i.e., teleportation of a squeezed state and sequential teleportation of a coherent state. Moreover, as an example of the teleportation-based computation, we build a QND interaction gate which is a continuous-variable analog of a CNOT gate. A QND interaction gate is constructed only with ancillary squeezed vacuum states and measurement-and-feedforwards. We also create continuous-variable four mode cluster type entanglement for further application, namely, one-way quantum computation.     

A network approach based on cliques

The characterization of complex networks is a procedure that is currently found in several research studies. Nevertheless, few studies present a discussion on networks in which the basic element is a clique. In this paper, we propose an approach based on a network of cliques. This approach consists not only of a set of new indices to capture the properties of a network of cliques but also of a method to characterize complex networks of cliques (i.e., some of the parameters are proposed to characterize the small-world phenomenon in networks of cliques). The results obtained are consistent with results from classical methods used to characterize complex networks.     

Factorization of topology changing amplitudes in the Regge calculus approach to quantum cosmology

We study the form of topology changing amplitudes within the Regge calculus approach to four-dimensional gravity. The four-dimensional simplicial complex is chosen to be a cone over the disjoint union of a number of topologically distinct lens spaces. By restricting attention to a simplicial minisuperspace, the analytic properties of the Regge action can be identified explicitly. The classical extrema and convergent steepest descent contours defining these amplitudes are determined, and a factorization property is established. In the cases studied, we find ground state wave functions which predict Lorentzian oscillatory behaviour in the late universe.     

基于发布订阅的分布式监控主动消息交互研究

针对分布式调度监控系统的客户服务器处理效率不高的问题,利用发布订阅消息通信技术,结合公共信息模型,提出了一种分布式监控主动消息交互的新方法。对量测类信息流和控制类信息流进行了实时交互接口设计,融入JMS消息服务器消息主题和发布订阅传输交互模式。该方法在工程中进行了应用,以石德线为算例,进行模拟量和状态量信息的交互实验,完成了单点和多点信息的交互传输,实现了实时变位信息向监控画面的主动即时传输,为分布式调度监控处理提供了一种新的高效实现方法。     

The Linear Relationship Model with LASSO for Studying Stock Networks

The correlation-based network is a powerful tool to reveal the influential mechanisms and relations in stock markets. However, current methods for developing network models are dominantly based on the pairwise relationship of positive correlations. This work proposes a new approach for developing stock relationship networks by using the linear relationship model with LASSO to explore negative correlations under a systemic framework. The developed model not only preserves positive links with statistical significance but also includes link directions and negative correlations. We also introduce blends cliques with the balance theory to investigate the consistency properties of the developed networks. The ASX 200 stock data with 194 stocks are applied to evaluate the effectiveness of our proposed method. Results suggest that the developed networks not only are highly consistent with the correlation coefficient in terms of positive or negative correlations but also provide influence directions in stock markets.     

Chaos in social learning with multiple true states

Most existing social learning models assume that there is only one underlying true state. In this work, we consider a social learning model with multiple true states, in which agents in different groups receive different signal sequences generated by their corresponding underlying true states. Each agent updates his belief by combining his rational self-adjustment based on the external signals he received and the influence of his neighbors according to their communication. We observe chaotic oscillation in the belief evolution, which implies that neither true state could be learnt correctly by calculating the largest Lyapunov exponents and Hurst exponents.     

High-Dimensional Bell State Analysis for Photon-Atoms Hybrid System

High-dimensional Bell state analysis (HDBSA) has great application potential in the high-capacity quantum communication and quantum information processing. In this paper, we propose a scheme to completely distinguish the 2^N-dimensional Bell states of a hybrid system with the help of the nonlinear interaction between the Λ-type atoms and a photon system. We use the unit-probability quantum teleportation with non-maximum entanglement as an example to show the application of HDBSA. Finally, we discuss its possible realization with current experimental techniques. Our HDBSA protocol may pave a new way for high-capacity long-distance quantum communication.

     

Time evolution of pairwise entanglement between two atoms

We investigate dynamics of pairwise entanglement between two atoms for various entangled initial states. The initial entanglement shows an interesting time evolution, including entanglement sudden death. The initial portion of the excited state is responsible for the sudden death of the entanglement. The initial portion of excited–ground–ground state or the initial photons in the system can induce pairwise entanglement. Meanwhile, we find that our model gives a concrete example to support the two theorems in [F. Verstraete, K. Audenaert, J. Dehaene and B. De Moor, J. Phys. A: Math. Gen. 34 (2001) 10327].     

Influence of a network structure on the network effect in the communication service market

In this study, we analyze the network effect in a model of a personal communication market, by using a multi-agent based simulation approach. We introduce into the simulation model complex network structures as the interaction patterns of agents. With complex network models, we investigate the dynamics of a market in which two providers are competing. We also examine the structure of networks that affect the complex behavior of the market. By a series of simulations, we show that the structural properties of complex networks, such as the clustering coefficient and degree correlation, have a major influence on the dynamics of the market. We find that the network effect is increased if the interaction pattern of agents is characterized by a high clustering coefficient, or a positive degree correlation. We also discuss a suitable model of the interaction pattern for reproducing market dynamics in the real world, by performing simulations using real data of a social network.     

Extended entanglement to quantum networks

Connecting individual quantum systems through quantum channels leads to develop quantum networks crucial to perform multipartite communication or quantum cryptography. We present two techniques to generate entanglement among different parties at larger scale. In the first approach cavity QED technique is used to produce extended entanglement in atomic internal and external degrees of freedom. In this scheme we entangle two tagged atoms in their momentum state with cavity fields. Later, interaction of two auxiliary atoms with the two cavity fields in non-dispersive and dispersive fashion transforms the atoms–fields entanglement to atoms–atoms entanglement. Quantum measurement on auxiliary atoms generates extended entangled state in atomic degrees of freedom. In the second approach we take three cavities in which the two cavities have separate entangled state with third cavity in two modes which are distinguishable. Applying quantum measurement process on third cavity, we develop extended entangled state among the three cavities. We provide experimental parameters to realize the work in laboratory experiment.     

具有Dzyaloshinskii-Moriya相互作用的三量子比特海森伯模型中的对纠缠

研究了一维三量子比特海森伯模型中的对纠缠的提高和控制问题,在该系统中引入了Dzyaloshinskii-Moriya（DM)相互作用,通过求解共生来计算两量子比特之间的热纠缠,结果表明：对于XXX模型,引入DM相互作用D,可以诱导铁磁和反铁磁自旋链产生热纠缠,尽管它们产生热纠缠所需的D值大小不同.对于XXZ模型,引入DM相互作用后,可以使原本不存在热纠缠的反铁磁自旋链产生纠缠,而且对于铁磁和反铁磁这两种XXZ自旋链,DM相互作用和各向异 关键词： 纠缠 XXX模型')" href="#">XXX模型 XXZ模型')" href="#">XXZ模型 Dzyaloshinskii-Moriya相互作用     

A complex network model for seismicity based on mutual information

Seismicity is the product of the interaction between the different parts of the lithosphere. Here, we model each part of the Earth as a cell that is constantly communicating its state to its environment. As a neuron is stimulated and produces an output, the different parts of the lithosphere are constantly stimulated by both other cells and the ductile part of the lithosphere, and produce an output in the form of a stress transfer or an earthquake. This output depends on the properties of each part of the Earth’s crust and the magnitude of the inputs. In this study, we propose an approach to the quantification of this communication, with the aid of the Information Theory, and model seismicity as a Complex Network. We have used data from California, and this new approach gives a better understanding of the processes involved in the formation of seismic patterns in that region.     

On the coherent behavior of pancreatic beta cell clusters

Beta cells in pancreas represent an example of coupled biological oscillators which via communication pathways, are able to synchronize their electrical activity, giving rise to pulsatile insulin release. In this work we numerically analyze scale free self-similarity features of membrane voltage signal power density spectrum, through a stochastic dynamical model for beta cells in the islets of Langerhans fine tuned on mouse experimental data. Adopting the algebraic approach of coherent state formalism, we show how coherent molecular domains can arise from proper functional conditions leading to a parallelism with “phase transition” phenomena of field theory.