Eigenvectors of Z-tensors associated with least H-eigenvalue with application to hypergraphs

Unlike an irreducible $Z$-matrices, a weakly irreducible $Z$-tensor $\mathcal{A}$ can have more than one eigenvector associated with the least H-eigenvalue. We show that there are finitely many eigenvectors of $\mathcal{A}$ associated with the least H-eigenvalue. If $\mathcal{A}$ is further combinatorial symmetric, the number of such eigenvectors can be obtained explicitly by the Smith normal form of the incidence matrix of $\mathcal{A}$. When applying to a connected uniform hypergraph $G$, we prove that the number of Laplacian eigenvectors of $G$ associated with the zero eigenvalue is equal to the the number of adjacency eigenvectors of $G$ associated with the spectral radius, which is also equal to the number of signless Laplacian eigenvectors of $G$ associated with the zero eigenvalue if zero is an signless Laplacian eigenvalue

A Combinatorial Method for Computing Characteristic Polynomials of Starlike Hypergraphs

By using the Poisson formula for resultants and the variants of chip-firing game on graphs, we provide a combinatorial method for computing a class of of resultants, i.e. the characteristic polynomials of the adjacency tensors of starlike hypergraphs including hyperpaths and hyperstars,which are given recursively and explicitly

Normal heat conduction in lattice models with asymmetry harmonic interparticle interactions

We study the thermal conduction behaviors of one-dimensional lattice models with asymmetry harmonic interparticle interactions in this paper. Normal thermal conductivity independent of the system size is observed when the lattice chains are long enough. Because only the harmonic interactions are involved, the result confirms without ambiguous interpretation that the asymmetry plays key role in resulting in the normal thermal conduction in one-dimensional momentum conserving lattices. Both equilibrium and nonequilibrium simulations are performed to support the conclusion.Comment: 4 pages,3 figure

Review of Smart Meter Data Analytics: Applications, Methodologies, and Challenges

The widespread popularity of smart meters enables an immense amount of fine-grained electricity consumption data to be collected. Meanwhile, the deregulation of the power industry, particularly on the delivery side, has continuously been moving forward worldwide. How to employ massive smart meter data to promote and enhance the efficiency and sustainability of the power grid is a pressing issue. To date, substantial works have been conducted on smart meter data analytics. To provide a comprehensive overview of the current research and to identify challenges for future research, this paper conducts an application-oriented review of smart meter data analytics. Following the three stages of analytics, namely, descriptive, predictive and prescriptive analytics, we identify the key application areas as load analysis, load forecasting, and load management. We also review the techniques and methodologies adopted or developed to address each application. In addition, we also discuss some research trends, such as big data issues, novel machine learning technologies, new business models, the transition of energy systems, and data privacy and security.Comment: IEEE Transactions on Smart Grid, 201

BBU effect in an ERL-FEL two-purpose test facility

Both the Energy Recovery Linac (ERL) and Free Electron laser (FEL) are considered to be candidates of the fourth generation light source. It is proposed to combine FEL into an ERL facility to integrate the advantages of both ERL and FEL, and to realize a compact two-purpose light source. A test facility to verify this principle is being designed at the Institute of High Energy Physics, Beijing. One main concern is the beam breakup (BBU) instability which limits the available beam current. To this end, we developed a numerical simulation code to calculate the BBU threshold, which is found to have only a small reduction even in a high-FEL-bunch-charge operation mode, compared with that in the case with ERL bunches only. However, even with ERL beam current far below BBU threshold, we observed a fluctuation of the central orbit of the ERL bunches in the presence of FEL beam. We then present a physical model of BBU and understand the mechanism of the orbit-fluctuation in an ERL-FEL two-purpose machine. We found that by choosing an appropriate FEL bunch repetition rate, the central orbit fluctuation amplitude can be well controlled.Comment: 10 pages, 9 figure

High speed error correction for continuous-variable quantum key distribution with multi-edge type LDPC code

Error correction is a significant step in postprocessing of continuous-variable quantum key distribution system, which is used to make two distant legitimate parties share identical corrected keys. We propose an experiment demonstration of high speed error correction with multi-edge type low-density parity check (MET-LDPC) codes based on graphic processing unit (GPU). GPU supports to calculate the messages of MET-LDPC codes simultaneously and decode multiple codewords in parallel. We optimize the memory structure of parity check matrix and the belief propagation decoding algorithm to reduce computational complexity. Our results show that GPU-based decoding algorithm greatly improves the error correction speed. For the three typical code rate, i.e., 0.1, 0.05 and 0.02, when the block length is $10^6$ and the iteration number are 100, 150 and 200, the average error correction speed can be respectively achieved to 30.39Mbits/s (over three times faster than previous demonstrations), 21.23Mbits/s and 16.41Mbits/s with 64 codewords decoding in parallel, which supports high-speed real-time continuous-variable quantum key distribution system.Comment: 8 pages, 2 figure

The Production of X(3940)X(3940) and X(4160)X(4160) in BcB_c decays

Considering $X(3940)$ and $X(4160)$ as $\eta_c(3S)$ and $\eta_c(4S)$, we study the productions of $X(3940)$ and $X(4160)$ in exclusive weak decays of $B_c$ meson by the improved Bethe-Salpeter(B-S) Method. Using the relativistic B-S equation and Mandelstam formalism, we calculate the corresponding decay form factors. The predictions of the corresponding branching ratios are: $Br(B_c^+\to X(3940)e^+\nu_e)$$=1.0\times10^{-4}$ and $Br(B_c^+\to X(4160)e^+\nu_e)=2.4\times10^{-5}$. That will provide us a new way to observe the $X(3940)$ and $X(4160)$ in the future, as well as to improve the knowledge of $B_c$ meson decay.Comment: 15 pages, 7 figure

The weak decay BcB_c to Z(3930)Z(3930) and X(4160)X(4160) by Bethe-Salpeter method

Considering $Z(3930)$ and $X(4160)$ as $\chi_{c2}(2P)$ and $\chi_{c2}(3P)$ states, the semileptonic and nonleptonic of $B_c$ decays to $Z(3930)$ and $X(4160)$ are studied by the improved Bethe-Salpeter(B-S) Method. The form factors of decay are calculated through the overlap integrals of the meson wave functions in the whole accessible kinematical range. The influence of relativistic corrections are considered in the exclusive decays. Branching ratios of $B_c$ weak decays to $Z(3930)$ and $X(4160)$ are predicted. Some of the branching ratios are: $Br(B_c^+\to Z(3930)e^+\nu_e)$$=(3.03^{+0.09}_{-0.16})\times 10^{-4}$ and $Br(B_c^+\to X(4160)e^+\nu_e)$$=(3.55^{+0.83}_{-0.35})\times 10^{-6}$. These results may provide useful information to discover $Z(3930)$ and $X(4160)$ and the necessary information for the phenomenological study of $B_c$ physics.Comment: arXiv admin note: substantial text overlap with arXiv:1605.0909

Full Large-Scale Diversity Space Codes for MIMO Optical Wireless Communications

In this paper, we consider a multiple-input-multiple-output optical wireless communication (MIMO-OWC) system suffering from log-normal fading. In this scenario, a general criterion for the design of full large-scale diversity space code (FLDSC) with the maximum likelihood (ML) detector is developed. Based on our criterion, FLDSC is attained if and only if all the entries of the space coding matrix are positive. Particularly for $2\times 2$ MIMO-OWC with unipolar pulse amplitude modulation (PAM), a closed-form linear FLDSC satisfying this criterion is attained by smartly taking advantage of some available properties as well as by developing some new interesting properties on Farey sequences in number theory to rigorously attack the continuous and discrete variables mixed max-min problem. In fact, this specific design not only proves that a repetition code (RC) is the best linear FLDSC, but also uncovers a significant difference between MIMO radio frequency (RF) communications and MIMO-OWC that space-only transmission is sufficient for a full diversity achievement. Computer simulations demonstrate that FLDSC substantially outperforms spatial multiplexing with the same total optical power and spectral efficiency and the latter obtains only the small-scale diversity gain.Comment: accepted by ISIT 201

Tur\'an's problem and Ramsey numbers for trees

Let $T_n^1=(V,E_1)$ and $T_n^2=(V,E_2)$ be the trees on $n$ vertices with $V=\{v_0,v_1,\ldots,v_{n-1}\}$, $E_1=\{v_0v_1,\ldots,v_0v_{n-3},v_{n-4}v_{n-2},v_{n-3}v_{n-1}\}$, and $E_2=\{v_0v_1,\ldots,$ $v_0v_{n-3},v_{n-3}v_{n-2}, v_{n-3}v_{n-1}\}$. In this paper, for $p\ge n\ge 5$ we obtain explicit formulas for \ex(p;T_n^1) and \ex(p;T_n^2), where \ex(p;L) denotes the maximal number of edges in a graph of order $p$ not containing $L$ as a subgraph. Let r(G\sb 1, G\sb 2) be the Ramsey number of the two graphs $G_1$ and $G_2$. In this paper we also obtain some explicit formulas for $r(T_m,T_n^i)$, where $i\in\{1,2\}$ and $T_m$ is a tree on $m$ vertices with $\Delta(T_m)\le m-3$.Comment: 21 page