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Jie Sun

Publications and source records attributed to Jie Sun.

At least 163 records · Page 9Linked to original sources
arXiv2013

On models of nonlinear evolution paths in adiabatic quantum algorithms

In this paper, we study two different nonlinear interpolating paths in adiabatic evolution algorithms for solving a particular class of quantum search problems where both the initial and final Hamiltonian are one-dimensional projector Hamiltonians on the corresponding ground state. If the overlap between the initial state and final state of the quantum system is not equal to zero, both of these models can provide a constant time speedup over the usual adiabatic algorithms by increasing some another corresponding "complexity". But when the initial state has a zero overlap with the solution state in the problem, the second model leads to an infinite time complexity of the algorithm for whatever interpolating functions being applied while the first one can still provide a constant running time. However, inspired by a related reference, a variant of the first model can be constructed which also fails for the problem when the overlap is exactly equal to zero if we want to make up the "intrinsic" fault of the second model-an increase in energy. Two concrete theorems are given to serve as explanations why neither of these two models can improve the usual adiabatic evolution algorithms for the phenomenon above. These just tell us what should be noted when using certain nonlinear evolution paths in adiabatic quantum algorithms for some special kind of problems.

quant-ph↗
arXiv2012

Effects of degree-frequency correlations on network synchronization: universality and full phase-locking

We introduce a model to study the effect of degree-frequency correlations on synchronization in networks of coupled oscillators. Analyzing this model, we find several remarkable characteristics. We find a stationary synchronized state that is (i) universal, i.e., the degree of synchrony, as measured by a global order parameter, is independent of network topology, and (ii) fully phase-locked, i.e., all oscillators become simultaneously phase-locked despite having different natural frequencies. This state separates qualitatively different behaviors for two other classes of correlations where, respectively, slow and fast oscillators can remain unsynchronized. We close by presenting analysis of the dynamics under arbitrary degree-frequency correlations.

nlin.AO↗
arXiv2011

Comment on "Controllability of Complex Networks with Nonlinear Dynamics"

The recent paper by W.-X. Wang, Y.-C. Lai, J. Ren, B. Li & C. Grebogi [arXiv:1107.2177v1] proposed a method for the control of complex networks with nonlinear dynamics based on linearizing the system around a finite number of local desired states. The authors purport that any bidirectional network with one-dimensional intrinsic node dynamics can be fully controlled by a single driver node, which can be any node in the network, regardless of the network topology. According to this result, a network with an arbitrarily large number of nodes (a million, a billion, or even more) could be controlled by a single node. Here we show, however, that this result is specious and that it does not hold true even for networks with only two nodes. We demonstrate that the erroneous results are a consequence of a fundamental flaw in the proposed method, namely, that reaching a local desired state using the proposed linearization procedure generally requires a nonlocal trajectory, which grossly violates the linear approximation. Their further conclusion that network systems with nonlinear dynamics are more controllable than those with linear dynamics is a known fact presented as novel based on a flawed argument. A central problem underlying the authors' argument is that their formulation is entirely based on the number of driver nodes required to reach a desired state---even when this number is one, keeping the system at that desired state generally requires directly controlling all nodes in the network. When this is taken into account, the conclusion that nonlinear dynamics can facilitate network control was already anticipated in S.P. Cornelius, W.L. Kath & A.E. Motter [arXiv:1105.3726v1], which is not referenced in their paper. If one insists on using the authors' formulation, then, in contradiction to their claim, nonlinear systems would never be more controllable than linear ones because...

cond-mat.dis-nn↗
arXiv2011

Robustness of Optimal Synchronization in Real Networks

Experimental studies of synchronization properties on networks with controlled connection topology can provide powerful insights into the physics of complex networks. Here, we report experimental results on the influence of connection topology on synchronization in fiber-optic networks of chaotic optoelectronic oscillators. We find that the recently predicted non-monotonic, cusp-like synchronization landscape manifests itself in the rate of convergence to the synchronous state. We also observe that networks with the same number of nodes, same number of links, and identical eigenvalues of the coupling matrix can exhibit fundamentally different approaches to synchronization. This previously unnoticed difference is determined by the degeneracy of associated eigenvectors in the presence of noise and mismatches encountered in real-world conditions.

nlin.CD↗
arXiv2011

A Mathematical Model for the Dynamics and Synchronization of Cows

We formulate a mathematical model for daily activities of a cow (eating, lying down, and standing) in terms of a piecewise affine dynamical system. We analyze the properties of this bovine dynamical system representing the single animal and develop an exact integrative form as a discrete-time mapping. We then couple multiple cow "oscillators" together to study synchrony and cooperation in cattle herds. We comment on the relevant biology and discuss extensions of our model. With this abstract approach, we not only investigate equations with interesting dynamics but also develop interesting biological predictions. In particular, our model illustrates that it is possible for cows to synchronize \emph{less} when the coupling is increased.

nlin.AO↗
arXiv2011

Optimal atomic-resolution structures of prion AGAAAAGA amyloid fibrils

X-ray crystallography is a powerful tool to determine the protein 3D structure. However, it is time-consuming and expensive, and not all proteins can be successfully crystallized, particularly for membrane proteins. Although nuclear magnetic resonance (NMR) spectroscopy is indeed a very powerful tool in determining the 3D structures of membrane proteins, it is also time-consuming and costly. To the best of the authors' knowledge, there is little structural data available on the AGAAAAGA palindrome in the hydrophobic region (113-120) of prion proteins due to the noncrystalline and insoluble nature of the amyloid fibril, although many experimental studies have shown that this region has amyloid fibril forming properties and plays an important role in prion diseases. In view of this, the present study is devoted to address this problem from computational approaches such as global energy optimization, simulated annealing, and structural bioinformatics. The optimal atomic-resolution structures of prion AGAAAAGA amyloid fibils reported in this paper have a value to the scientific community in its drive to find treatments for prion diseases.

q-bio.BM↗
arXiv2011

Universal central extensions of direct limits of Lie superalgebras

We show that the universal central extension of a direct limit of perfect Lie superalgebras L_i is (isomorphic to) the direct limit of the universal central extensions of L_i. As an application we describe the universal central extensions of some infinite rank Lie superalgebras.

math.RA↗
arXiv2010

Cyclotomic Temperley-Lieb algebra of type D and its representation theory

We define a new class of algebras, cyclotomic Temperley-Lieb algebras of type D, in a diagrammatic way, which is a generalization of Temperley-Lieb algebras of type D. We prove that the cyclotomic Temperley-Lieb algebras of type D are cellular. In fact, an explicit cellular basis is given by means of combinatorial methods. After determining all the irreducible representations of these algebras, we give a necessary and sufficient condition for a cyclotomic Temperley-Lieb algebra of type D to be quasi-hereditary.

math.RA↗
arXiv2010

Approximating Spectral Impact of Structural Perturbations in Large Networks

Determining the effect of structural perturbations on the eigenvalue spectra of networks is an important problem because the spectra characterize not only their topological structures, but also their dynamical behavior, such as synchronization and cascading processes on networks. Here we develop a theory for estimating the change of the largest eigenvalue of the adjacency matrix or the extreme eigenvalues of the graph Laplacian when small but arbitrary set of links are added or removed from the network. We demonstrate the effectiveness of our approximation schemes using both real and artificial networks, showing in particular that we can accurately obtain the spectral ranking of small subgraphs. We also propose a local iterative scheme which computes the relative ranking of a subgraph using only the connectivity information of its neighbors within a few links. Our results may not only contribute to our theoretical understanding of dynamical processes on networks, but also lead to practical applications in ranking subgraphs of real complex networks.

cond-mat.dis-nn↗
arXiv2010

Judging Model Reduction of Chaotic Systems via Optimal Shadowing Criteria

A common goal in the study of high dimensional and complex system is to model the system by a low order representation. In this letter we propose a general approach for assessing the quality of a reduced order model for high dimensional chaotic systems. The key of this approach is the use of optimal shadowing, combined with dimensionality reduction techniques. Rather than quantify the quality of a model based on the quality of predictions, which can be irrelevant for chaotic systems since even excellent models can do poorly, we suggest that a good model should allow shadowing by modeled data for long times; this principle leads directly to an optimal shadowing criterion of model reduction. This approach overcomes the usual difficulties encountered by traditional methods which either compare systems of the same size by normed-distance in the functional space, or measure how close an orbit generated by a model is to the observed data. Examples include interval arithmetic computations to validate the optimal shadowing.

nlin.CD↗
arXiv2010

Greedy Connectivity of Geographically Embedded Graphs

We introduce a measure of {\em greedy connectivity} for geographical networks (graphs embedded in space) and where the search for connecting paths relies only on local information, such as a node's location and that of its neighbors. Constraints of this type are common in everyday life applications. Greedy connectivity accounts also for imperfect transmission across established links and is larger the higher the proportion of nodes that can be reached from other nodes with a high probability. Greedy connectivity can be used as a criterion for optimal network design.

cond-mat.stat-mech↗
arXiv2009

Constructing Generalized Synchronization Manifolds by Manifold Equation

Full understanding of synchronous behavior in coupled dynamical systems beyond the identical case requires an explicit construction of the generalized synchronization manifold, whether we wish to compare the systems, or to understand their stability. Nonetheless, while synchronization has become an extremely popular topic, the bulk of the research in this area has been focused on the identical case, specifically because its invariant manifold is simply the identity function, and there have yet to be any generally workable methods to compute the generalized synchronization manifolds for non-identical systems. Here, we derive time dependent PDEs whose stationary solution mirrors exactly the generalized synchronization manifold, respecting its stability. We introduce a novel method for dealing with subtle issues with boundary conditions in the numerical scheme to solve the PDE, and we develop first order expansions close to the identical case. We give several examples of increasing sophistication, including coupled non-identical Van der Pol oscillators. By using the manifold equation, we also discuss the design of coupling to achieve desired synchronization.

nlin.CD↗
arXiv2009

Asymptotic behavior of the Kleinberg model

We study Kleinberg navigation (the search of a target in a d-dimensional lattice, where each site is connected to one other random site at distance r, with probability proportional to r^{-a}) by means of an exact master equation for the process. We show that the asymptotic scaling behavior for the delivery time T to a target at distance L scales as (ln L)^2 when a=d, and otherwise as L^x, with x=(d-a)/(d+1-a) for a d+1. These values of x exceed the rigorous lower-bounds established by Kleinberg. We also address the situation where there is a finite probability for the message to get lost along its way and find short delivery times (conditioned upon arrival) for a wide range of a's.

cond-mat.stat-mech↗
arXiv2008

Master Stability Functions for Coupled Near-Identical Dynamical Systems

We derive a master stability function (MSF) for synchronization in networks of coupled dynamical systems with small but arbitrary parametric variations. Analogous to the MSF for identical systems, our generalized MSF simultaneously solves the linear stability problem for near-synchronous states (NSS) for all possible connectivity structures. We also derive a general sufficient condition for stable near-synchronization and show that the synchronization error scales linearly with the magnitude of parameter variations.Our analysis underlines significant roles played by the Laplacian eigenvectors in the study of network synchronization of near-identical systems.

nlin.CD↗
arXiv2008

Synchronization Stability of Coupled Near-Identical Oscillator Network

We derive variational equations to analyze the stability of synchronization for coupled near-identical oscillators. To study the effect of parameter mismatch on the stability in a general fashion, we define master stability equations and associated master stability functions, which are independent of the network structure. In particular, we present several examples of coupled near-identical Lorenz systems configured in small networks (a ring graph and sequence networks) with a fixed parameter mismatch and a large Barabasi-Albert scale-free network with random parameter mismatch. We find that several different network architectures permit similar results despite various mismatch patterns.

nlin.CD↗
arXiv2008

Dynamic Computation of Network Statistics via Updating Schema

In this paper we derive an updating scheme for calculating some important network statistics such as degree, clustering coefficient, etc., aiming at reduce the amount of computation needed to track the evolving behavior of large networks; and more importantly, to provide efficient methods for potential use of modeling the evolution of networks. Using the updating scheme, the network statistics can be computed and updated easily and much faster than re-calculating each time for large evolving networks. The update formula can also be used to determine which edge/node will lead to the extremal change of network statistics, providing a way of predicting or designing evolution rule of networks.

physics.data-an↗
arXiv2008

Phase transition in the rich-get-richer mechanism due to finite-size effects

The rich-get-richer mechanism (agents increase their ``wealth'' randomly at a rate proportional to their holdings) is often invoked to explain the Pareto power-law distribution observed in many physical situations, such as the degree distribution of growing scale free nets. We use two different analytical approaches, as well as numerical simulations, to study the case where the number of agents is fixed and finite (but large), and the rich-get-richer mechanism is invoked a fraction r of the time (the remainder of the time wealth is disbursed by a homogeneous process). At short times, we recover the Pareto law observed for an unbounded number of agents. In later times, the (moving) distribution can be scaled to reveal a phase transition with a Gaussian asymptotic form for r < 1/2 and a Pareto-like tail (on the positive side) and a novel stretched exponential decay (on the negative side) for r > 1/2.

q-fin.GN↗