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Pan Zhang

Publications and source records attributed to Pan Zhang.

At least 181 records · Page 10Linked to original sources
arXiv2016

Inference of the sparse kinetic Ising model using the decimation method

In this paper we study the inference of the kinetic Ising model on sparse graphs by the decimation method. The decimation method, which was first proposed in [Phys. Rev. Lett. 112, 070603] for the static inverse Ising problem, tries to recover the topology of the inferred system by setting the weakest couplings to zero iteratively. During the decimation process the likelihood function is maximized over the remaining couplings. Unlike the $\ell_1$-optimization based methods, the decimation method does not use the Laplace distribution as a heuristic choice of prior to select a sparse solution. In our case, the whole process can be done automatically without fixing any parameters by hand. We show that in the dynamical inference problem, where the task is to reconstruct the couplings of an Ising model given the data, the decimation process can be applied naturally into a maximum-likelihood optimization algorithm, as opposed to the static case where pseudo-likelihood method needs to be adopted. We also use extensive numerical studies to validate the accuracy of our methods in dynamical inference problems. Our results illustrate that on various topologies and with different distribution of couplings, the decimation method outperforms the widely-used $\ell _1$-optimization based methods.

cond-mat.dis-nn↗
arXiv2016

A New ZrCuSiAs-Type Superconductor: ThFeAsN

We report the first nitrogen-containing iron-pnictide superconductor ThFeAsN, which is synthesized by a solid-state reaction in an evacuated container. The compound crystallizes in a ZrCuSiAs-type structure with the space group P4/nmm and lattice parameters a=4.0367(1) Å and c=8.5262(2) Å at 300 K. The electrical resistivity and dc magnetic susceptibility measurements indicate superconductivity at 30 K for the nominally undoped ThFeAsN.

cond-mat.supr-con↗
arXiv2015

On CR Submanifolds of Maximal CR Dimension with Flat Normal Connection of a Complex Projective Space

In this paper, we study the CR submanifolds of maximal CR dimension with flat normal connection of a complex projective space. We first investigate the position of the umbilical normal vector in the normal bundle, especially for the submanifolds of dimension 3. Then as the application, we prove the non-existence of a class of CR submanifolds of maximal CR dimension with flat normal connection.

math.DG↗
arXiv2015

Evaluating accuracy of community detection using the relative normalized mutual information

The Normalized Mutual Information (NMI) has been widely used to evaluate the accuracy of community detection algorithms. However in this article we show that the NMI is seriously affected by systematic errors due to finite size of networks, and may give a wrong estimate of performance of algorithms in some cases. We give a simple theory to the finite-size effect of NMI and test our theory numerically. Then we propose a new metric for the accuracy of community detection, namely the relative Normalized Mutual Information (rNMI), which considers statistical significance of the NMI by comparing it with the expected NMI of random partitions. Our numerical experiments show that the rNMI overcomes the finite-size effect of the NMI.

physics.soc-ph↗
arXiv2015

Community detection in networks with unequal groups

Recently, a phase transition has been discovered in the network community detection problem below which no algorithm can tell which nodes belong to which communities with success any better than a random guess. This result has, however, so far been limited to the case where the communities have the same size or the same average degree. Here we consider the case where the sizes or average degrees are different. This asymmetry allows us to assign nodes to communities with better-than- random success by examining their local neighborhoods. Using the cavity method, we show that this removes the detectability transition completely for networks with four groups or fewer, while for more than four groups the transition persists up to a critical amount of asymmetry but not beyond. The critical point in the latter case coincides with the point at which local information percolates, causing a global transition from a less-accurate solution to a more-accurate one.

cs.SI↗
arXiv2015

Solution space structure of random constraint satisfaction problems with growing domains

In this paper we study the solution space structure of model RB, a standard prototype of Constraint Satisfaction Problem (CSPs) with growing domains. Using rigorous the first and the second moment method, we show that in the solvable phase close to the satisfiability transition, solutions are clustered into exponential number of well-separated clusters, with each cluster contains sub-exponential number of solutions. As a consequence, the system has a clustering (dynamical) transition but no condensation transition. This picture of phase diagram is different from other classic random CSPs with fixed domain size, such as random K-Satisfiability (K-SAT) and graph coloring problems, where condensation transition exists and is distinct from satisfiability transition. Our result verifies the non-rigorous results obtained using cavity method from spin glass theory, and sheds light on the structures of solution spaces of problems with a large number of states.

cond-mat.dis-nn↗
arXiv2015

Detectability thresholds and optimal algorithms for community structure in dynamic networks

We study the fundamental limits on learning latent community structure in dynamic networks. Specifically, we study dynamic stochastic block models where nodes change their community membership over time, but where edges are generated independently at each time step. In this setting (which is a special case of several existing models), we are able to derive the detectability threshold exactly, as a function of the rate of change and the strength of the communities. Below this threshold, we claim that no algorithm can identify the communities better than chance. We then give two algorithms that are optimal in the sense that they succeed all the way down to this limit. The first uses belief propagation (BP), which gives asymptotically optimal accuracy, and the second is a fast spectral clustering algorithm, based on linearizing the BP equations. We verify our analytic and algorithmic results via numerical simulation, and close with a brief discussion of extensions and open questions.

stat.ML↗
arXiv2015

Coexistence of superconductivity and complex 4$f$ magnetism in Eu$_{0.5}$Ce$_{0.5}$BiS$_{2}$F

EuBiS$_{2}$F is a self-doped superconductor due to the mixed valence of Eu. Here we report that, with the Ce substitution for Eu by 50 at.\%, the material exhibits ferromagnetic ordering at 8 K for the Ce-4$f$ moment, superconductivity at 2.2 K in the BiS$_2$ layers, and possibly antiferromagnetic ordering at 2.1 K for the Eu-4$f$ spins. The Eu valence is essentially divalent with the Ce incorporation. We tentatively interpret the coexistence of ferromagnetism and superconductivity by considering different Bi-6$p$ orbitals that are responsible for superconductivity itself and for mediating the ferromagnetic interaction, respectively. We argue that the antiferromagnetic ordering of the Eu-4$f$ spins is most likely due to a magnetic dipole-dipole interaction.

cond-mat.supr-con↗
arXiv2014

Scalable detection of statistically significant communities and hierarchies, using message-passing for modularity

Modularity is a popular measure of community structure. However, maximizing the modularity can lead to many competing partitions, with almost the same modularity, that are poorly correlated with each other. It can also produce illusory "communities" in random graphs where none exist. We address this problem by using the modularity as a Hamiltonian at finite temperature, and using an efficient Belief Propagation algorithm to obtain the consensus of many partitions with high modularity, rather than looking for a single partition that maximizes it. We show analytically and numerically that the proposed algorithm works all the way down to the detectability transition in networks generated by the stochastic block model. It also performs well on real-world networks, revealing large communities in some networks where previous work has claimed no communities exist. Finally we show that by applying our algorithm recursively, subdividing communities until no statistically-significant subcommunities can be found, we can detect hierarchical structure in real-world networks more efficiently than previous methods.

physics.soc-ph↗
arXiv2014

Pressure-enhanced superconductivity in Eu$_3$Bi$_2$S$_4$F$_4$

The pressure effect on the newly discovered charge-transferred BiS$_2$-based superconductor, Eu$_3$Bi$_2$S$_4$F$_4$, with a $T_c$ of 1.5 K at ambient pressure, is investigated by transport and magnetic measurements. Accompanied with the enhancement of metallicity under pressures, the onset superconducting transition temperature increases abruptly around 1.0 GPa, reaching $\sim$10.0 K at 2.26 GPa. AC magnetic susceptibility measurements indicate that a new superconducting phase with a higher $T_c$ emerges and dominates at high pressures. In the broad pressure window of 0.68 GPa$\leq$$p$$\leq$2.00 GPa, the high-$T_c$ phase coexists with the low-$T_c$ phase. Hall effect measurements reveal a significant difference in electronic structures between the two superconducting phases. Our work devotes the effort to establish the commonality of pressure effect on the BiS$_2$-based superconductors, and also uncovers the importance of electron carrier density in the high-$T_c$ phase.

cond-mat.supr-con↗
arXiv2014

Anomalous Eu Valence State and Superconductivity in Undoped Eu3Bi2S4F4

We have synthesized a novel europium bismuth sulfofluoride, Eu3Bi2S4F4, by solid-state reactions in sealed evacuated quartz ampoules. The compound crystallizes in a tetragonal lattice (space group I4/mmm, a = 4.0771(1) A, c = 32.4330(6) A, and Z = 2), in which CaF2-type Eu3F4 layers and NaCl-like BiS2 bilayers stack alternately along the crystallographic c axis. There are two crystallographically distinct Eu sites, Eu(1) and Eu(2) at the Wyckoff positions 4e and 2a, respectively. Our bond-valence-sum calculation, based on the refined structural data, indicates that Eu(1) is essentially divalent, whilst Eu(2) has an average valence of +2.64(5). This anomalous Eu valence state is further confirmed and supported, respectively, by Mossbauer and magnetization measurements. The Eu3+ components donate electrons into the conduction bands that are mainly composed of Bi- 6px and 6py states. Consequently, the material itself shows metallic conduction, and superconducts at 1.5 K without extrinsic chemical doping.

cond-mat.supr-con↗
arXiv2014

Non-backtracking operator for Ising model and its application in attractor neural networks

The non-backtracking operator was recently shown to give a redemption for spectral clustering in sparse graphs. In this paper we consider non-backtracking operator for Ising model on a general graph with a general coupling distribution by linearizing Belief Propagation algorithm at paramagnetic fixed-point. The spectrum of the operator is studied, the sharp edge of bulk and possible real eigenvalues outside the bulk are computed analytically as a function of couplings and temperature. We show the applications of the operator in attractor neural networks. At thermodynamic limit, our result recovers the phase boundaries of Hopfield model obtained by replica method. On single instances of Hopfield model, its eigenvectors can be used to retrieve all patterns simultaneously. We also give an example on how to control the neural networks, i.e. making network more sparse while keeping patterns stable, using the non-backtracking operator and matrix perturbation theory.

cond-mat.dis-nn↗
arXiv2014

Charge-density wave, superconductivity and $f$-electron valence instability in EuBiS$_2$F

Superconductivity (SC) and charge-density wave (CDW) are two contrasting yet relevant collective electronic states which have received sustained interest for decades. Here we report that, in a layered europium bismuth sulfofluoride, EuBiS$_2$F, a CDW-like transition occurs at 280 K, below which SC emerges at 0.3 K, without any extrinsic doping. The Eu ions were found to exhibit an anomalously temperature-independent mixed valence of about +2.2, associated with the formation of CDW. The mixed valence of Eu gives rise to self electron doping into the conduction bands mainly consisting of the in-plane Bi-6$p$ states, which in turn brings about the CDW and SC. In particular, the electronic specific-heat coefficient is enhanced by ~ 50 times, owing to the significant hybridizations between Eu-4$f$ and Bi-6$p$ electrons, as verified by band-structure calculations. Thus, EuBiS$_2$F manifests itself as an unprecedented material that simultaneously accommodates SC, CDW and $f$-electron valence instability.

cond-mat.supr-con↗
arXiv2014

Phase transitions in semisupervised clustering of sparse networks

Predicting labels of nodes in a network, such as community memberships or demographic variables, is an important problem with applications in social and biological networks. A recently-discovered phase transition puts fundamental limits on the accuracy of these predictions if we have access only to the network topology. However, if we know the correct labels of some fraction $α$ of the nodes, we can do better. We study the phase diagram of this "semisupervised" learning problem for networks generated by the stochastic block model. We use the cavity method and the associated belief propagation algorithm to study what accuracy can be achieved as a function of $α$. For $k = 2$ groups, we find that the detectability transition disappears for any $α> 0$, in agreement with previous work. For larger $k$ where a hard but detectable regime exists, we find that the easy/hard transition (the point at which efficient algorithms can do better than chance) becomes a line of transitions where the accuracy jumps discontinuously at a critical value of $α$. This line ends in a critical point with a second-order transition, beyond which the accuracy is a continuous function of $α$. We demonstrate qualitatively similar transitions in two real-world networks.

cs.SI↗
arXiv2013

K and Mn co-doped BaCd2As2: a hexagonal structured bulk diluted magnetic semiconductor with large magnetoresistance

A bulk diluted magnetic semiconductor was found in the K and Mn co-doped BaCd2As2 system. Different from recently reported tetragonal ThCr2Si2-structured II-II-V based(Ba,K)(Zn,Mn)2As2, the Ba1-yKyCd2-xMnxAs2 system has a hexagonal CaAl2Si2-type structure with the Cd2As2 layer forming a honeycomb-like network. The Mn concentration reaches up to its x ? 0.4. Magnetization measurements show that the samples undergo ferromagnetic transitions with Curie temperature up to 16 K. With low coercive field less than 10 Oe and large magnetoresistence of about -70%, the hexagonal structured Ba1-yKyCd2-xMnxAs2 can be served as a promising candidate for spin manipulations.

cond-mat.str-el↗
arXiv2013

The hard-core model on random graphs revisited

We revisit the classical hard-core model, also known as independent set and dual to vertex cover problem, where one puts particles with a first-neighbor hard-core repulsion on the vertices of a random graph. Although the case of random graphs with small and very large average degrees respectively are quite well understood, they yield qualitatively different results and our aim here is to reconciliate these two cases. We revisit results that can be obtained using the (heuristic) cavity method and show that it provides a closed-form conjecture for the exact density of the densest packing on random regular graphs with degree K>=20, and that for K>16 the nature of the phase transition is the same as for large K. This also shows that the hard-code model is the simplest mean-field lattice model for structural glasses and jamming.

cond-mat.dis-nn↗
arXiv2013

Spectral redemption: clustering sparse networks

Spectral algorithms are classic approaches to clustering and community detection in networks. However, for sparse networks the standard versions of these algorithms are suboptimal, in some cases completely failing to detect communities even when other algorithms such as belief propagation can do so. Here we introduce a new class of spectral algorithms based on a non-backtracking walk on the directed edges of the graph. The spectrum of this operator is much better-behaved than that of the adjacency matrix or other commonly used matrices, maintaining a strong separation between the bulk eigenvalues and the eigenvalues relevant to community structure even in the sparse case. We show that our algorithm is optimal for graphs generated by the stochastic block model, detecting communities all the way down to the theoretical limit. We also show the spectrum of the non-backtracking operator for some real-world networks, illustrating its advantages over traditional spectral clustering.

cs.SI↗