arXiv subjects
Publications and source records attributed to Bo Zhou.
We study the effect of three types of graft transformations to increase or decrease the distance spectral radius of uniform hypergraphs, and we determined the unique $k$-uniform hypertrees with maximum, second maximum, minimum and second minimum distance spectral radius, respectively.
Caching and multicasting at base stations are two promising approaches to support massive content delivery over wireless networks. However, existing scheduling designs do not make full use of the advantages of the two approaches. In this paper, we consider the optimal dynamic multicast scheduling to jointly minimize the average delay, power, and fetching costs for cache-enabled content-centric wireless networks. We formulate this stochastic optimization problem as an infinite horizon average cost Markov decision process (MDP). It is well-known to be a difficult problem due to the curse of dimensionality, and there generally only exist numerical solutions. By using relative value iteration algorithm and the special structures of the request queue dynamics, we analyze the properties of the value function and the state-action cost function of the MDP for both the uniform and nonuniform channel cases. Based on these properties, we show that the optimal policy, which is adaptive to the request queue state, has a switch structure in the uniform case and a partial switch structure in the nonuniform case. Moreover, in the uniform case with two contents, we show that the switch curve is monotonically non-decreasing. Then, by exploiting these structural properties of the optimal policy, we propose two low-complexity optimal algorithms. Motivated by the switch structures of the optimal policy, to further reduce the complexity, we also propose a low-complexity suboptimal policy, which possesses similar structural properties to the optimal policy, and develop a low-complexity algorithm to compute this policy.
We extend the new concept of nonlocalized clustering to the nucleus 10Be with proton number Z=4 and neutron number N=6 (N=Z+2). The Tohsaki-Horiuchi-Schuck-Röpke (THSR) wave function is formulated for the description of different structures of 10Be. Physical properties such as energy spectrum and root-mean-square radii are calculated for the first two 0+ states and corresponding rotational bands. With only one single THSR wave function, the calculated results show good agreement with other models and experimental values. We apply, for the first time, the THSR wave function on the chain orbit (σ-orbit) structure in the 0^+_2 state of 10Be. The ring orbit (π-orbit) and σ-orbit structures are further illustrated by calculating the density distribution of the valence neutrons. We also investigate the dynamics of ff-clusters and the correlations of two valence neutrons in 10Be.
A microscopic calculation of $α$-cluster preformation probability and $α$ decay width in the typical $α$ emitter $^{212}$Po is presented. Results are obtained by improving a recent approach to describe $α$ preformation in $^{212}$Po [Phys. Rev. C 90, 034304 (2014)] implementing four-nucleon correlations (quartetting). Using the actually measured density distribution of the $^{208}$ Pb core, the calculated alpha decay width of $^{212}$Po agrees fairly well with the measured one.
Optimal queueing control of multi-hop networks remains a challenging problem even in the simplest scenarios. In this paper, we consider a two-hop half-duplex relaying system with random channel connectivity. The relay is equipped with a finite buffer. We focus on stochastic link selection and transmission rate control to maximize the average system throughput subject to a half-duplex constraint. We formulate this stochastic optimization problem as an infinite horizon average cost Markov decision process (MDP), which is well-known to be a difficult problem. By using sample-path analysis and exploiting the specific problem structure, we first obtain an \emph{equivalent Bellman equation} with reduced state and action spaces. By using \emph{relative value iteration algorithm}, we analyze the properties of the value function of the MDP. Then, we show that the optimal policy has a threshold-based structure by characterizing the \emph{supermodularity} in the optimal control. Based on the threshold-based structure and Markov chain theory, we further simplify the original complex stochastic optimization problem to a static optimization problem over a small discrete feasible set and propose a low-complexity algorithm to solve the simplified static optimization problem by making use of its special structure. Furthermore, we obtain the closed-form optimal threshold for the symmetric case. The analytical results obtained in this paper also provide design insights for two-hop relaying systems with multiple relays equipped with finite relay buffers.
Three-dimensional (3D) topological Weyl semimetals (TWSs) represent a novel state of quantum matter with unusual electronic structures that resemble both a "3D graphene" and a topological insulator by possessing pairs of Weyl points (through which the electronic bands disperse linearly along all three momentum directions) connected by topological surface states, forming the unique "Fermi-arc" type Fermi-surface (FS). Each Weyl point is chiral and contains half of the degrees of freedom of a Dirac point, and can be viewed as a magnetic monopole in the momentum space. Here, by performing angle-resolved photoemission spectroscopy on non-centrosymmetric compound TaAs, we observed its complete band structures including the unique "Fermi-arc" FS and linear bulk band dispersion across the Weyl points, in excellent agreement with the theoretical calculations. This discovery not only confirms TaAs as the first 3D TWS, but also provides an ideal platform for realizing exotic physical phenomena (e.g. negative magnetoresistance, chiral magnetic effects and quantum anomalous Hall effect) which may also lead to novel future applications.
In this paper, we study the existence of random periodic solutions for semilinear stochastic differential equations. We identify these as the solutions of coupled forward-backward infinite horizon stochastic integral equations in general cases. We then use the argument of the relative compactness of Wiener-Sobolev spaces in $C^0([0, T], L^2(Ω))$ and generalized Schauder's fixed point theorem to prove the existence of a solution of the coupled stochastic forward-backward infinite horizon integral equations. The condition on $F$ is then further weakened by applying the coupling method of forward and backward Gronwall inequalities. The results are also valid for stationary solutions as a special case when the period $τ$ can be an arbitrary number.\
The nonlocalized aspect of clustering, which is a new concept for self-conjugate nuclei, is extended for the investigation of the N{\not=}Z nucleus ${}^9$Be. A modified version of the THSR (Tohsaki-Horiuchi-Schuck-Röpke) wave function is introduced based on the container picture. It is found that the constructed negative-parity THSR wave function is very suitable for describing the cluster states of ${}^9$Be. Namely the nonlocalized clustering is shown to prevail in ${}^9$Be. The calculated binding energy and radius of ${}^9$Be are consistent with calculations in other models and with experimental values. The squared overlaps between the THSR wave function and the Brink+GCM wave function for the $3/2^-$ rotational band of ${}^9$Be are found to be near 96%. Furthermore, by showing the density distribution of the ground state of ${}^9$Be, the π-orbit structure is naturally reproduced by using this THSR wave function.
It is shown that the single $0^+$ THSR (Tohsaki-Horiuchi-Schuck-Röpke) wave function which is extended to include 2$α$ correlation is almost completely equivalent to the 3$α$ wave function obtained as the full solution of 3$α$ cluster model. Their squared overlap is as high as 98\% while it is 93\% if the 2$α$ correlation is not included. This result implies that, by incorporating the 2$α$ correlation in the 3$α$ model, the ground state of $^{12}$C is describable in the container picture which is valid for the Hoyle state for which the 2$α$ correlation is weak and a single $0^+$ THSR wave function without 2$α$ correlation is almost completely equivalent to the full solution of 3$α$ cluster model.
An effective $α$ particle equation is derived for cases where an $α$ particle is formed on top of a doubly magic nucleus. As an example, we consider $^{212}$Po with the $α$ on top of the $^{208}$ Pb core. We will consider the core nucleus infinitely heavy, so that the $α$ particle moves with respect to a fixed center, i.e., recoil effects are neglected. The fully quantal solution of the problem is discussed. The approach is inspired by the THSR (Tohsaki-Horiuchi-Schuck-Röpke) wave function concept that has been successfully applied to light nuclei. Shell model calculations are improved by including four-particle ($α$-like) correlations that are of relevance when the matter density becomes low. In the region where the $α$-like cluster penetrates the core nucleus, the intrinsic bound state wave function transforms at a critical density into an unbound four-nucleon shell model state. Exploratory calculations for $^{212}$Po are presented. Such preformed cluster states are only hardly described by shell model calculations. Reasons for different physics behavior of an $α$-like cluster with respect to a deuteron-like cluster are discussed.
We characterize all connected graphs with second distance eigenvalue less than $-0.5858$.
We propose a scalable semiparametric Bayesian model to capture dependencies among multiple neurons by detecting their co-firing (possibly with some lag time) patterns over time. After discretizing time so there is at most one spike at each interval, the resulting sequence of 1's (spike) and 0's (silence) for each neuron is modeled using the logistic function of a continuous latent variable with a Gaussian process prior. For multiple neurons, the corresponding marginal distributions are coupled to their joint probability distribution using a parametric copula model. The advantages of our approach are as follows: the nonparametric component (i.e., the Gaussian process model) provides a flexible framework for modeling the underlying firing rates; the parametric component (i.e., the copula model) allows us to make inference regarding both contemporaneous and lagged relationships among neurons; using the copula model, we construct multivariate probabilistic models by separating the modeling of univariate marginal distributions from the modeling of dependence structure among variables; our method is easy to implement using a computationally efficient sampling algorithm that can be easily extended to high dimensional problems. Using simulated data, we show that our approach could correctly capture temporal dependencies in firing rates and identify synchronous neurons. We also apply our model to spike train data obtained from prefrontal cortical areas in rat's brain.
Strong spin-orbit coupling in topological insulators results in the ubiquitously observed weak antilocalization feature in their magnetoresistance. Here we present magnetoresistance measurements in ultra thin films of the topological insulator Bi_2Se_3, and show that in the 2D quantum limit, in which the topological insulator bulk becomes quantized, an additional negative magnetoresistance feature appears. Detailed analysis associates this feature with weak localization of the quantized bulk channels, providing thus evidence for this quantization. Examination of the dephasing fields at different temperatures indicates different scattering mechanism in the bulk vs the surface states.
Quantum systems in confined geometries are host to novel physical phenomena. Examples include quantum Hall systems in semiconductors and Dirac electrons in graphene. Interest in such systems has also been intensified by the recent discovery of a large enhancement in photoluminescence quantum efficiency and a potential route to valleytronics in atomically thin layers of transition metal dichalcogenides, MX2 (M = Mo, W; X = S, Se, Te), which are closely related to the indirect to direct bandgap transition in monolayers. Here, we report the first direct observation of the transition from indirect to direct bandgap in monolayer samples by using angle resolved photoemission spectroscopy on high-quality thin films of MoSe2 with variable thickness, grown by molecular beam epitaxy. The band structure measured experimentally indicates a stronger tendency of monolayer MoSe2 towards a direct bandgap, as well as a larger gap size, than theoretically predicted. Moreover, our finding of a significant spin-splitting of 180 meV at the valence band maximum of a monolayer MoSe2 film could expand its possible application to spintronic devices.
A container picture is proposed for understanding cluster dynamics where the clusters make nonlocalized motion occupying the lowest orbit of the cluster mean-field potential characterized by the size parameter $``B"$ in the THSR (Tohsaki-Horiuchi-Schuck-Röpke) wave function. The nonlocalized cluster aspects of the inversion-doublet bands in $^{20}$Ne which have been considered as a typical manifestation of localized clustering are discussed. So far unexplained puzzling features of the THSR wave function, namely that after angular-momentum projection for two cluster systems the prolate THSR wave function is almost 100$\%$ equivalent to an oblate THSR wave function is clarified. It is shown that the true intrinsic two-cluster THSR configuration is nonetheless prolate. The proposal of the container picture is based on the fact that typical cluster systems, 2$α$, 3$α$, and $α$+$^{16}$O, are all well described by a single THSR wave function. It will be shown for the case of linear-chain states with two and three $α$-clusters as well as for the $α$+$^{16}$O system that localization is entirely of kinematical origin, that is, due to the inter-cluster Pauli repulsion. It is concluded that this feature is general for nuclear cluster states.
In this paper, we determine the maximal Laplacian and signless Laplacian spectral radii for graphs with fixed number of vertices and domination number, and characterize the extremal graphs respectively.
We give some properties of skew spectrum of a graph, especially, we answer negatively a problem concerning the skew characteristic polynomial and matching polynomial in [M. Cavers et al., Skew-adjacency matrices of graphs, Linear Algebra Appl. 436 (2012) 4512--4529].
We give upper and lower bounds for the spectral radius of a nonnegative matrix by using its average 2-row sums, and characterize the equality cases if the matrix is irreducible. We also apply these bounds to various nonnegative matrices associated with a graph, including the adjacency matrix, the signless Laplacian matrix, the distance matrix, the distance signless Laplacian matrix, and the reciprocal distance matrix.