Social learning with bounded confidence and heterogeneous agents

This paper investigates an opinion formation model in social networks with bounded confidence and heterogeneous agents. The network topologies are shaped by the homophily of beliefs, which means any pair of agents are neighbors only if their belief difference is not larger than a positive constant called the bound of confidence. We consider a model with both informed agents and uninformed agents, the essential difference between which is the informed agents have access to outside signals which are function of the underlying true state of the social event concerned. More precisely, the informed agents update their beliefs by combining the Bayesian posterior beliefs based on their private observations and weighted averages of the beliefs of their neighbors. The uninformed agents update their beliefs simply by linearly combining the beliefs of their neighbors. We find that the whole group can learn the true state only if the bound of confidence is larger than a positive threshold which is related to the population density. Furthermore, simulations show that the proportion of informed agents required for collective learning decreases as the population density increases. By tuning the learning speed of informed agents, we find the following: the higher the speed, the shorter the time needed for the whole group to achieve a steady state, and on the other hand, the higher the speed, the lower the proportion of agents with successful learning — there is a trade-off.     

Universality class of nonequilibrium phase transitions with infinitely many absorbing states

We consider systems whose steady states exhibit a nonequilibrium phase transition from an active state to one-among an infinite number-absorbing state, as some control parameter is varied across a threshold value. The pair contact process, stochastic fixed-energy sandpiles, activated random walks, and many other cellular automata or reaction-diffusion processes are covered by our analysis. We argue that the upper-critical dimension below which anomalous fluctuation driven scaling appears is d(c)=6, in contrast to a widespread belief. We provide the exponents governing the critical behavior close to or at the transition point to first order in an epsilon =6-d expansion.     

Probability of inconsistencies in theory revision

We present a model for studying communities of epistemically interacting agents who update their belief states by averaging (in a specified way) the belief states of other agents in the community. The agents in our model have a rich belief state, involving multiple independent issues which are interrelated in such a way that they form a theory of the world. Our main goal is to calculate the probability for an agent to end up in an inconsistent belief state due to updating (in the given way). To that end, an analytical expression is given and evaluated numerically, both exactly and using statistical sampling. It is shown that, under the assumptions of our model, an agent always has a probability of less than 2% of ending up in an inconsistent belief state. Moreover, this probability can be made arbitrarily small by increasing the number of independent issues the agents have to judge or by increasing the group size. A real-world situation to which this model applies is a group of experts participating in a Delphi-study.     

Particle-hole symmetry and the Pfaffian state

We show that the particle-hole conjugate of the Pfaffian state-or "anti-Pfaffian" state-is in a different universality class from the Pfaffian state, with different topological order. The two states can be distinguished easily by their edge physics: their edges differ in both their thermal Hall conductance and their tunneling exponents. At the same time, the two states are exactly degenerate in energy for a nu=5/2 quantum Hall system in the idealized limit of zero Landau level mixing. Thus, both are good candidates for the observed sigma_{xy}=5/2(e;{2}/h) quantum Hall plateau.     

Comment on “Convergence towards asymptotic state in 1-D mappings: A scaling investigation” [Phys. Lett. A 379 (18–19) (2015) 1246–1250]

Nonequilibrium phase transitions are characterized by the so-called critical exponents, each of which is related to a different observable. Systems that share the same set of values for these exponents also share the same universality class. Thus, it is important that the exponents are named and treated in a standardized framework. In this comment, we reinterpret the exponents obtained by Teixeira et al. [1] for the logistic and cubic maps in order to correctly state the universality class of their bifurcations, since these maps may describe the mean-field solution of stochastic spreading processes.     

Spectroscopy of nanoscopic semiconductor rings

Making use of self-assembly techniques, we realize nanoscopic semiconductor quantum rings in which the electronic states are in the true quantum limit. We employ two complementary spectroscopic techniques to investigate both the ground states and the excitations of these rings. Applying a magnetic field perpendicular to the plane of the rings, we find that, when approximately one flux quantum threads the interior of each ring, a change in the ground state from angular momentum l = 0 to l = -1 takes place. This ground state transition is revealed both by a drastic modification of the excitation spectrum and by a change in the magnetic-field dispersion of the single-electron charging energy.     

Dynamic critical properties of a one-dimensional probabilistic cellular automaton

Dynamic properties of a one-dimensional probabilistic cellular automaton are studied by Monte Carlo simulation near a critical point which marks a second-order phase transition from an active state to an effectively unique absorbing state. Values obtained for the dynamic critical exponents indicate that the transition belongs to the universality class of directed percolation. Finally the model is compared with a previously studied one to show that a difference in the nature of the absorbing states places them in different universality classes. Received: 6 February 1998 / Revised and Accepted: 17 February 1998     

Robust entanglement

It is common belief among physicists that entangled states of quantum systems lose their coherence rather quickly. The reason is that any interaction with the environment which distinguishes between the entangled sub-systems collapses the quantum state. Here we investigate entangled states of two trapped Ca⁺ ions and observe robust entanglement lasting for more than 20 s.     

Ordering in Heisenberg spin glasses

For five different Heisenberg spin glass systems, torque experiments were performed in applied magnetic fields up to 4 T. The Dzyaloshinski-Moriya random anisotropy strengths, the in-field torque onset temperatures, and the torque relaxation were measured. Critical exponents were estimated independently using a standard protocol. The data are strong evidence for a true spin glass ordered state which survives under high applied magnetic fields; they can be interpreted consistently in terms of a chiral ordering model with replica symmetry breaking as proposed by Kawamura and co-workers.     

Electron self-trapping at quantum and classical critical points

Using Feynman path integral technique estimations of the ground state energy have been found for a conduction electron interacting with order parameter fluctuations near quantum critical points. In some cases only singular perturbation theory in the coupling constant emerges for the electron ground state energy. It is shown that an autolocalized state (quantum fluctuon) can be formed and its characteristics have been calculated depending on critical exponents for both weak and strong coupling regimes. The concept of fluctuon is considered also for the classical critical point (at finite temperatures) and the difference between quantum and classical cases has been investigated. It is shown that, whereas the quantum fluctuon energy is connected with a true boundary of the energy spectrum, for classical fluctuon it is just a saddle-point solution for the chemical potential in the exponential density of states fluctuation tail.     

Topology of trajectories of the 2D Navier-Stokes equations

In spectral form the 2D incompressible Navier-Stokes equations in a square periodic region will be represented by 430 complex Fourier amplitudes which correspond to isotropic truncation of the upper wave number 16. For small viscosity, we have found five equilibrium states I-V in the entire range of forcing; I-fixed point, II-circle, III-closed orbit, IV-torus, and V-chaos. The fixed-point equilibrium state is the laminar flow. As the forcing passes through a critical value, the fixed point evolves directly to equilibrium state III under a typical multimode forcing. The chaotic transition takes place on a 2-torus-like manifold (equilibrium state IV) which is the product space of a circle and the closed orbit of equilibrium state III, similar to the quasiperiodic 2-torus of Ruelle and Takens. For sufficiently large forcing, the evolution of equilibrium state V is nothing but a simulation of quasistationary 2D turbulence. From the Lyapunov exponents of turbulent flows, we have evaluated the constants in the theoretical results of Foias and his colleagues, which relate the determining mode and fractal dimension with the enstrophy dissipation wave number of 2D turbulence.     

Digraph states and their neural network representations

With the rapid development of machine learning, artificial neural networks provide a powerful tool to represent or approximate many-body quantum states. It was proved that every graph state can be generated by a neural network. Here, we introduce digraph states and explore their neural network representations (NNRs). Based on some discussions about digraph states and neural network quantum states (NNQSs), we construct explicitly an NNR for any digraph state, implying every digraph state is an NNQS. The obtained results will provide a theoretical foundation for solving the quantum many-body problem with machine learning method whenever the wave-function is known as an unknown digraph state or it can be approximated by digraph states.     

Electronic properties of quasiperiodic Fibonacci chain including second-neighbor hopping in the tight-binding model

We present an exact real-space renormalization group (RSRG) scheme for the electronic Green's functions of one-dimensional tight-binding systems having both nearest-neighbor and next-nearest-neighbor hopping integrals, and determine the electronic density of states for the quasiperiodic Fibonacci chain. This RSRG method also gives the Lyapunov exponents for the eigenstates. The Lyapunov exponents and the analysis of the flow pattern of hopping integrals under renormalization provide information about the nature of the eigenstates. Next we develop a transfer matrix formalism for this generalized tight-binding system, which enables us to determine the wave function amplitudes. Interestingly, we observe that like the nearest-neighbor tight-binding Fibonacci chain, the present generalized tight-binding system also have critical eigenstates, Cantor-set energy spectrum and highly fragmented density of states. It indicates that these exotic physical properties are really the characteristics of the underlying quasiperiodic structure. Received 5 April 1999     

Transitions to synchrony in coupled bursting neurons

Certain cells in the brain, for example, thalamic neurons during sleep, show spike-burst activity. We study such spike-burst neural activity and the transitions to a synchronized state using a model of coupled bursting neurons. In an electrically coupled network, we show that the increase of coupling strength increases incoherence first and then induces two different transitions to synchronized states, one associated with bursts and the other with spikes. These sequential transitions to synchronized states are determined by the zero crossings of the maximum transverse Lyapunov exponents. These results suggest that synchronization of spike-burst activity is a multi-time-scale phenomenon and burst synchrony is a precursor to spike synchrony.     

Reduction of quantum phase fluctuations in intermediate states

Recently we have shown that the reduction of the Carruthers-Nieto symmetric quantum phase fluctuation parameter (U) with respect to its coherent state value corresponds to an antibunched state, but the converse is not true. Consequently reduction of U is a stronger criterion of nonclassicality than the lowest order antibunching. Here we have studied the possibilities of reduction of U in intermediate states by using the Barnett-Pegg formalism. We have shown that the reduction of phase fluctuation parameter U can be seen in different intermediate states, such as binomial state, generalized binomial state, hypergeometric state, negative binomial state, and photon added coherent state. It is also shown that the depth of nonclassicality can be controlled by various parameters related to intermediate states. Further, we have provided specific examples of antibunched states, for which U is greater than its Poissonian state value.     

Code Optimization,Frozen Glassy Phase and Improved Decoding Algorithms for Low-Density Parity-Check Codes

The statistical physics properties of low-density parity-check codes for the binary symmetric channel are investigated as a spin glass problem with multi-spin interactions and quenched random fields by the cavity method. By evaluating the entropy function at the Nishimori temperature, we find that irregular constructions with heterogeneous degree distribution of check(bit) nodes have higher decoding thresholds compared to regular counterparts with homogeneous degree distribution. We also show that the instability of the mean-field calculation takes place only after the entropy crisis, suggesting the presence of a frozen glassy phase at low temperatures. When no prior knowledge of channel noise is assumed(searching for the ground state), we find that a reinforced strategy on normal belief propagation will boost the decoding threshold to a higher value than the normal belief propagation. This value is close to the dynamical transition where all local search heuristics fail to identify the true message(codeword or the ferromagnetic state). After the dynamical transition, the number of metastable states with larger energy density(than the ferromagnetic state)becomes exponentially numerous. When the noise level of the transmission channel approaches the static transition point, there starts to exist exponentially numerous codewords sharing the identical ferromagnetic energy.     

Experimental bifurcation analysis of an impact oscillator—Determining stability

We propose and investigate three different methods for assessing stability of dynamical equilibrium states during experimental bifurcation analysis, using a control-based continuation method. The idea is to modify or turn off the control at an equilibrium state and study the resulting behavior. As a proof of concept the three methods are successfully implemented and tested for a harmonically forced impact oscillator with a hardening spring nonlinearity, and controlled by electromagnetic actuators. We show that under certain conditions it is possible to quantify the instability in terms of finite-time Lyapunov exponents. As a special case we study an isolated branch in the bifurcation diagram brought into existence by a 1:3 subharmonic resonance. On this isola it is only possible to determine stability using one of the three methods, which is due to the fact that only this method guarantees that the equilibrium state can be restored after measuring stability.     

利用广义Bell态信道联合远程制备一个任意三量子比特态

研究了一个联合远程制备任意三量子比特态的方案。该方案利用广义的Bell态作为量子信道,两个发送者分别选择合适的测量基进行测量,然后利用经典信道把测量结果传送出去,接收者根据测量结果对自己手中的粒子采取适当的幺正操作,然后引入辅助粒子并进行选择性测量,就能概率性的得到想要制备的量子态。研究结果表明:利用不同形式的广义Bell态信道成功实现联合远程制备一个任意三量子比特态的概率是一样的,当量子信道处于最大纠缠态时,可以得到最大的成功概率。     

A Matrix-Valued Point Interactions Model

We study a matrix-valued Schrödinger operator with random point interactions. We prove the absence of absolutely continuous spectrum for this operator by proving that, away from a discrete set, its Lyapunov exponents do not vanish. For this we use a criterion by Gol’dsheid and Margulis and we prove the Zariski denseness, in the symplectic group, of the group generated by the transfer matrices. Then we prove estimates on the transfer matrices which lead to the Hölder continuity of the Lyapunov exponents. After proving the existence of the integrated density of states of the operator, we also prove its Hölder continuity by proving a Thouless formula which links the integrated density of states to the sum of the positive Lyapunov exponents.